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The EIRENE Code User Manual Version: 11/2009

1. 10E Data for algebraic function of surface crossing tallies DO 105 IALSI 1 NALSI ALSTRNG TXTTLS IALSI NTLSR TXTSPS IALSI NTLSR TXTUNS IALSI NTLSR 105 CONTINUE optional in versions Eirene 993 and younger 10F Data for energy spectra DO 106 IADSP 1 NADSPC ISPSRF IPTYP IPSP ISPTYP NSPS ISRFCLL IDIREC SPCMN SPCMX SPC_SHIFT SPCPLT_X SPCPLT_Y SPCPLT_SAME if idirec ne 0 SPCVX SPCVY SPCVZ 106 CONTINUE Meaning of the input variables for additional volume and surface averaged Tallies NADVI_ Total number of additional volume averaged track length estimated tallies NCLVI Total number of additional volume averaged collision estimated tallies NALVI Total number of tallies defined as algebraic expressions of other volume averaged tallies NADSI Total number of additional surface averaged tallies NALSI Total number of tallies defined as algebraic expressions of other surface averaged tallies NADSPC Total number of surface or cell averaged energy spectra 2 10 1 Additional volume averaged tallies tracklength estimator IADVE flag for scaling factor for this tally carried out in subroutine MCARLO 1 scale tally per unit volume 1 cm The tally is printed and plotted in the units 1 c
2. No Name Macroscopic quantity 1 Dim Units Estim 1 POTAT Particle Flux incident Atoms NATM amp T C 2 PRFAAT Particle Flux emitted Ats gt Atoms NATM amp T C 3 PRFMAT Particle Flux emitted Mls gt Atoms NATM amp T C 4 PRFIAT Particle Flux emitted T I gt Atoms NATM amp T C 5 PRFPAT Particle Flux emitted B I gt Atoms NATM amp T C 6 POTML Particle Flux incident Molecules NMOL amp T C 7 PRFAML Particle Flux emitted Ats gt Molecules NMOL amp T C 8 PRFMML Particle Flux emitted Mls Molecules NMOL amp T C 9 PRFIML Particle Flux emitted T I gt Molecules NMOL amp T C 10 PRFPML Particle Flux emitted B I Molecules NMOL amp T C 11 POTIO Particle Flux incident Test Ions NION amp T C 12 PRFAIO Particle Flux emitted Ats gt Test Ions NION amp T C 13 PRFMIO Particle Flux emitted Mls Test Ions NION amp T C 14 PRFIJO Particle Flux emitted T I gt Test Ions NION amp T C 15 PRFPIO Particle Flux emitted B I gt Test Ions NION amp T C 16 POTPL Particle Flux incident Bulk Ions NPLS amp T C 17 EOTAT Energy Flux incident Atoms NATM watt T C 18 ERFAAT Energy Flux emitted Ats gt Atoms NATM watt T C 19 ERFMAT Energy Flux emitted Mls Atoms NATM watt T C 20 ERFIAT Energy Flux emitted T I Atoms NATM watt T C 21 ERFPAT Ener
3. 195 Meaning of the Input Variables for this block NPRNLI Total number of test particles in time dependent arrays census arrays NPRNLI must be lt NPRNL see PARMUSR The runs stops at latest when NPRNLI scores are on the census array If NPRNLI gt 0 but the rest of the data in this block are not specified then a default time horizon is defined See default values specified below In case NLERG TRUE see input block 1 a time horizon is absolutely necessary in order to prevent infinite histories Therefore in case NUERG TRUE and NPRNLI 0 an automatic correction to NPRNLI 100 is carried out NINITL_READ new 2013 Same as NINITL in block 7 provides random number seed for time stratum sampling from census array default 0 no fresh initialization of random number generator for this stratum NPRMUL new 2013 Multiplicative factor for NPRNLI in order to increase size of census to more than 999 999 particles NPTST Same as NPTS in block 7 This is the number of histories which are continued from a previous time cycle Time dependence stratum ISTRA NSTRAI 1 The initial coordinates are randomly sampled with replacement from the census array data from an earlier time cycle The probability for sampling a particular particle from the census array is proportional to its weight stored on the census array as well Due to sampling with
4. 108 New option in 2006 In case ID1 4 i e four post collision particles not counting electrons DO K 1 NRCS IREACS IBULKS ISCD1S ISCD2S ISCD3S ISCD4 ISCDES ESTMS EELECS EBULKS ESCD1S EDUMMY FREACS FLDLMS ENDDO where stands for either A atoms M molecules I test ions PH photons or P bulk ions I e a species block consists of one species specification card ISPZ and NRC reaction decks of two cards each For some particle species in particular for hydrogenic atoms molecules and molecular ions and for helium atoms EIRENE has default A amp M data to which it resorts if no reaction cards are in the input deck i e if NRC 0 see below for a particular species These default models are described at the end of this section They are overruled by the reaction cards In order to de activate all possible reactions also the default reactions e g to simulate the collision less Knudsen flow for a particular test particle species one must set NRC 1 for this test particle species Usually a particular particle type and species in the species blocks is identified by an integer IPART LMN 3 digits Here N fixes the type of the particle M is the number of particles characterized by IPART and L is the species index within the specified group type of particles The following values of N are cu
5. Meaning of the Input Variables ILREF Flag for choice of local reflection model 1 TRIM database reflection model is used NLTRIM must be TRUE 2 modified Behrisch Matrix model is used 3 user supplied reflection model see section B 3 Subroutine REFUSR Default ILREF 2 ILSPT Flag for choice of local sputtering model Let ILSPT MN with M and N single digit integers each Then N controls the options for physical sputtering and M controls chemical sputtering See subroutine SPUTER N 0 no physical sputtering at this surface N 1 constant physical sputtering rate see parameter RECYCS below N 2 modified Roth Bogdansky formula for sputter yield Thompson energy distri bution and cosine angular distribution for emitted particles see references BJ and B8 N 9 was option N 3 in Eirene 2004 and older user supplied sputtering model see section B Entry SPTUSR to subroutine REFUSR M 0 no chemical sputtering at this surface M 1 constant chemical sputtering rate see parameter RECYCC below M 2 Roth formula for chemical sputter yield thermal distribution for emitted par ticles see reference B9 weak flux dependence option A6 M 3 Roth formula for chemical sputter yield thermal distribution for emitted par ticles see reference B9 strong flux dependence option A7 M 4 Roth formula for chemical sputter yield thermal distribution for emitted par ticle
6. IFEXMN FPARM J J 1 3 various extrapolation expressions 2j x at the low end x lt RMN x Fia or x T are available IFEXMN 1 CLiguntS 0 e g cross section with nonzero threshold at RMN TFEXMN 2 y x FPARM 1 CLlow FPARM 2 yP PARM log y recommended for cross section extrapolation at high energy end for reactions with nonzero threshold at FPARM 1 eV IFEXMN 3 y log x In eZiow z FPARM 1 y FPARM 2 IFEXMN 4 not in use IFEXMN 5 y log z In eajow a FPARM I y IFEXMN lt 0 linear extrapolation in log log scale Coefficients FPARM J J 1 2 are automati cally determined e g in function CROSS FPARM 3 0 D0 and then extrapo lation option IFEXMN 5 is used with these coefficients same as IFEXMN 3 in this case IFEXMX FPARM J J 4 6 same as above but for high parameter range extrapolation eX pign x 4A Atoms Species Cards NATMI Total number of atomic species blocks IATM irrelevant labelling index 4B Molecules Species Cards NMOLI Total number of molecule species blocks IMOL irrelevant labelling index 4C Test Ions Species Cards NIONI Total number of test ion species blocks 117 HON irrelevant labelling index 4D Photon Species Cards NPHOTI Total number of photon species blocks IPHOT irrelevant labelling index The meaning of the variables in a species block is as follows TEXT Name of the species on printout and plo
7. K 1 Increase the actual additional cell number NACELL for a particle striking the surface in the direction of the surface normal by ILACLL Decrease NA CELL by ILACLL if the particle is striking in the negative direction Speci fication of ILACLL is via the input variable ILCELL see below K 2 as K 1 but with the direction of the surface normal reversed for this option for particles inside the standard mesh i e not in the additional cell region K 1 Increase the standard mesh block number NBLOCK for a particle strik ing the surface in the direction of the surface normal by ILBLCK Decrease NBLOCK by ILBLCK if the particle is striking in the negative direction Specification of ILBLCK is via the input variable ILCELL see below K 2 as K 1 but with the direction of the surface normal reversed J for particles at the boundary between additional and standard mesh regions J 1 entrance into standard mesh block no NBLOCK ILBLCK or exit from standard mesh into additional cell NACELL ILACLL Specification of IEACLL and ILBLCK is via the input variable ILCELL see below If ILACLL 0 then no switch to additional cell is operated E g for surfaces which are reflecting from this side J 2 asJ 1 The direction of the surface normal does not matter here 100 I similar to J flag i e for transitions between standard and additional meshes but different cell number switching I 1 Entrance into
8. L M N 1 06 distribution at at b 2 L M N 2 Uniform distribution on the interval a b L M N 3 Truncated exponential decay with decay length on the interval a b Le the sampling distribution reads f x c exp a A if x a b and f x 0 elsewhere with normalizing constant c A exp a A exp b A L M N 4 Step function see below Function STEP subsection ZLI only one of either L or M or N should be 4 K 1 06 distribution at TIMEO for time of particle birth A delta function source in time for the kinetic equation in integral form corresponds to an initial condition for time dependent linear kinetic integro differential equation K 2 Uniform distribution in TIME0 TIME0 DTIMV for time of particle birth Default K 2 in time dependent mode NTIME gt 0 and K 1 TIMEO 0 in time independent mode NTIME 0 see section ZI SORIND Flag to choose one from the various step functions SORLIM option 4 which have been defined in the initialization phase Up to NSTEP PARMUSR see section ET step functions can be described there SORIND is the labelling index of the se lected step function Each step function STEP ISTEP can consist of step functions for fluxes of up to NSPZ species see ZLI NSPZ depends upon the initialization of this function By default the source species index NSPEZ is used when sampling from step functions New option Aug 2006 e g for testing isotope effects If SORIND g
9. N the responses R 2 13 with respect to detector function g are estimated as the arithmetic mean of functions statistics or estimators X w Le Re R Y _ X lw 3 16 The proper choice of the number of histories N depends on the variance o X of the esti mator X and is highly problem specific In EIRENE it can range from N 2 for conditional expectation estimators and point sources in phase space up to values of several millions for N 1 3 1 Unbiased estimators One possible choice for X w is the so called collision estimator X I 1 Xe wP Z sela JI E 3 17 This estimator is for example used in the DEGAS code L3 It can be shown B in a tedious but mathematically strict way that the statistical expectation E X produces j l R E X9 f d w X w h w 3 18 with h w being the probability density for finding a chain w from the Markoff process de fined above i e X is an unbiased estimator for R Other estimators track length type estimators are employed frequently These estimators are unbiased as well but have higher moments different from those of X Instead of evalu ating the detector function g x at the points of collisions x as X does they involve line integrals of g x along the trajectories e g Xi wp 3 l f E ds al Iry 6 19 with R E X E X It has been shown e g in BJ that the collision estimator derived not f
10. which store the test particle population at time t ti t At t iAt TIME0O ITIME NTMSTP DTIMV are filled and prepared for the next time cycle The census arrays from the previous time cycle if any i e at t t _1 are overwritten here After the last time cycle the census arrays are written on file fort 15 in order to permit continuation in time in a next run The background conditions and source distributions or any other input parameters for the next time cycle can be modified in subroutine TMSUSR which is called from subroutine TMSTEP If the population on the census array is not empty or known from a previous run NFILE J flag see above then this census population defines one additional stratum for the current cycle I e the census population then determines the initial condition for the distribution function f r v i t to The source strength FLUX is computed from that initial condition NOPTIM Default 1 NOPTM1 Default 1 NGEOM_USR for value 1 user defined external geometry package LEVGEO 10 then no grid storage is provided in EIRENE Default 0 NCOUP_INPUT 1 Storage for data transfer via coupling routines 0 no such storage Default 1 NSMSTRA_ Sum over strata disabled for value 0 enabled for value 1 Default 1 76 NSTORAM Storage vs speed in atomic data evaluation Maximum storage fastest com putation 9 Minimum storage maximum work slowest option 0 Default 9
11. 1 10 1 Line shape options Emission of photons from a particular line is simulated by sampling firstly the location of emission and secondly the frequency and direction of emission Spatial distribution of pho ton emission is treated in EIRENE in exactly the same way as for any other particle type neutrals ions and actually using the same modules of code for that Emission from the transition 2 gt k from an upper state i nl of an atom is treated by abuse of language as volume recombination source The position is sampled from the spatial distribution AiP F which because the Einstein emission coefficient A is constant is the same as the spatial distribution P F of upper state particle density Given the birth point 7 of the photon and hence all local parameters of the host medium at this point the frequency v in fact the energy hv is sampled from the normalized line shape function v The following line shape options are currently available 57 ISHAPE 0 6 profile mono energetic emission not yet available for absorption ISHAPE 1 pure Doppler profile ISHAPE 2 Lorentz profile truncated at zero ISHAPE 3 Doppler convoluted Lorentz profile i e Voight profile ISHAPE 4 LORVDW convoluted Lorentz and van der Waals pressure broadened pro file ISHAPE 5 Doppler broadened LORVDW profile ISHAPE 6 normal Zeeman triplet d profile in each component ISHAPE 7 Doppler broadened Zeeman 0 profile
12. NGSTAL Storage for spatial distribution of surface tallies on non default standard surfaces for value 1 For value 0 only total spatially integrated surfaces fluxes Default 0 NRTAL Condensing mesh cells into fewer larger cells for output volume tallies The under lying fine mesh has NRAD cells see input block 2 The coarser mesh obtained from condensing cells into one larger cell has NRTAL cells Default 0 Then internally NRTAL NRAD and no condensation is carried out NCLTAL URAD IRTAL grid cell IRAD is condensed into the larger cell IRTAL I e output is average over a larger cell IRTAL which is comprised of all cells IRAD such that NCLTALUIRAD IRTAL IRAD 1 NRAD The input data in input block 5 background medium are always given on the fine mesh size NRAD For output tallies cell averaging several cells IRAD1 IRAD2 can be condensed into one larger cell IRTAL Cell volumes scoring statistics are automatically done on the coarser grid size NRTAL The index array NCLTAL NRAD can be defined in the problem specific user rou tines see section B e g INIUSR GEOUSR etc Default NCLTAL IRAD IRAD for IRAD 1 NRAD NREAC_ ADD Storage for additional reaction decks read onto EIRENE arrays in USR routines post processing etc Default 0 NLSCL Some volume averaged tallies are re scaled in order to exactly preserve the total number of particles which otherwise would be the case only up to s
13. are surface averaged tallies in this terminology 196 Fluxes onto this surface are stored on the arrays for a surface no NLIM NSTSI 1 which is added automatically to the NLIM additional and NSTSI non default standard surfaces The time surface is transparent for NTMSTP 1 steps and absorbing afterwards i e absorbing at time t NTMSTP x DTIMV Snapshot tallies are averages over NTMSTP time steps Default NTMSTP 1 If NTMSTP lt 0 then each particle can score an unlimited number of times on census i e the time surface is always transparent This option can be used for initialization of census arrays for time dependent runs The census arrays then represent a stationary distribution corresponding to a certain constant in time influx of particles rather than an estimate at a fixed time Hence for any fixed detector function volume averaged tally the snapshot estimator should give the same results up to statistical precision as the track length estimator or the collision estimator Note that in order to obtain this stationary estimate from snapshot estimates an additional multiplicative factor DTIMV s see next is applied to snapshot tallies in case NTMSTP lt 0 DTIMV Length of each individual internal time step seconds Default DTIMV 1 D 02 TIMEO Initial time to of the first time step irrelevant only for printout and book keeping Default TIMEO 0 NSNVI Number of snapshot tallies computed from census arrays In
14. test particle for otherwise this process is not relevant for the transport problem solved by EIRENE e particles A are always bulk particles i e from the list of bulk ions input block 5 or electrons 107 particle B may be one test particle Then this process A B must be included in the list of reaction decks for this test particle B Hence b 1 then particle B may also be one bulk particle Then this process may be included in input block 7 as a volume source recombination of two bulk particles into at least one test particle M and or N particles M and or N can be either secondary test particles or secondary bulk parti cles non linear processes i e processes in which both A and B should in principle stand for test particles can be included by specifying particle A as bulk particle in input block 5 and simultaneously as test particle in input block 4 The 5 parameters density tem perature and drift velocity for the artificial bulk species A are iterated in a sequence of EIRENE runs option NITER input block 1 and code module MODUSR f In cases in which species M and or N are also available as real or artificial bulk species there is the choice to specify secondaries from a reaction either as test particles and to continue the history with those after a collision event or alternatively to spec ify them as bulk particles and stop the traje
15. Any test particle crossing a S amp R surface in the negative direction is split into SPLPAR identical but independent particles with properly reduced weight If a particle crosses a S amp R surface in the positive direction then it is either killed or continues it s flight with properly increased weight The surface orientation can be reversed by using a negative value for the the splitting parameter SPLPAR MAXLEV Maximum number of levels for splitting lt 15 MAXRAD Total number of radial splitting surfaces NRIST lt MAXRAD lt NRIST MAXRAD lt 0 MAXRAD is used the position of the radial splitting surfaces is automatically defined and a constant splitting parameter SPLPAR see below is used for radial splitting and RR MAXRAD gt 0 radial surfaces with numbers NSSPL IN IN 1 MAXRAD are S amp R surfaces The splitting parameter for surface NSSPL IN is PRMSPL IN 170 MAXPOL Total number of poloidal splitting surfaces 0 lt MAXPOL lt NP2ND The S amp R surfaces and splitting parameters are selected as in the case of radial surfaces see above MAXTOR Total number of toroidal splitting surfaces 0 lt MAXTOR lt NT3RD The S amp R surfaces and splitting parameters are selected as in the case of radial surfaces see above MAXADD Total number of additional splitting surfaces 0 lt MAXADD lt NLIMI The S amp R surfaces and splitting parameters are selected as in the case of radial surfaces see above
16. EGENPH dito Energy flux Photons NPHOT watt em 3 Tl 71 VGENA dito momentum flux Atoms NATM as MAPL Tl 72 VGENM dito momentum flux Molecules NMOL as MMPL Tl 73 VGENI dito momentum flux Test ions NION as MIPL Tl 74 VGENPH dito momentum flux Photons NPHOT as MPHPL Tl 75 PPAT primary particle sources rate Atoms from plasma NATM amp cm 3 Cl 76 PPML primary particle sources rate Molecules NMOL amp cm 3 Cl 77 PPIO primary particle sources rate Test ions NION amp cm 3 Cl 78 PPPHT primary particle sources rate Photons NPHOT amp cm 3 Cl 79 PPPL primary particle sources rate Bulk Ions NPLS amp cm 3 Cl 80 EPAT primary energy sources rate Atoms 1 watt cm 3 Cl 81 EPML primary energy sources rate Molecules 1 watt cm 3 Cl 82 EPIO primary energy sources rate Test ions 1 watt cm 3 Cl 83 EPPHT primary energy sources rate Photons 1 watt cm 3 Cl 84 EPPL primary energy sources rate Bulk Ions 1 watt cm 3 Cl 85 VXDENA momentum density x direction Atoms NATM g cm s cm 3 Tl 86 VXDENM momentum density x direction Molecules NMOL g cm s cm 3 Tl 87 VXDENI momentum density x direction Test Ions NION g cm s cm 3 Tl 88 VXDENPH momentum density x direction Photons NPHOT g cm s cm 3 Tl 89 VYDENA momentum density y direction Atoms NATM g cm s cm 3 Tl 90 VYDENM momentum density y direction Molecules NMOL g cm s cm 3 Tl 91 VYDENI momentum density y direction Test Ions NION g cm s cm
17. It also allows to make connection to the so called Green s functions Monte Carlo concept originally developed for quantum mechanical problems involving so lutions to the Schr dinger equation A corresponding discussion is postponed to section LZI A direct intuitive interpretation of the integral equation is already sufficient to under stand the Monte Carlo method of solution and shall be given first In CId x and x are the states at two successive collisions jumps The integral f dz in Id is to be understood as an integral over all initial coordinates i e over the entire physical space the full velocity space and a summation over all species indices The transition kernel K is usually decomposed in our context into a collision and a transport kernel i e C and T where Kir v i gt r v i C t v t gt v i T v i r gt r 2 8 The kernel C is excluding normalization the conditional distribution for new co ordinates v i given that a particle of species 7 and with velocity v has undergone a collision at position r This kernel can further be decomposed into Lk Clr v i v i Xp Clr v a gt V i gt Pk k with summation over the index k for the different types of collision processes under consid eration and p defined as the conditional probability for a collision to be of type k The normalizing factor 1 cplx Df Clr v i gt v i Ch C
18. e 1 65 73 Dhion Un T UT 2v7 Tri g Vr This non analog sampling of the source term introduces additional statistical fluctuations in the results since the initial test particle weights fluctuate with variance ow diy w x ninl 1 oV ag 5 74 where b 2 T T We use the ansatz b C V 1 and compute numerically that value of C which minimizes o in the range 0 lt V lt 1 We find C 0 6026 This means that the ratio of the real temperature T and the non analog temperature Tri should be chosen to be T Pe 1 0 6026 V This choice optimizes the statistical performance In principle of course any other T could have been used without introducing bias into the algorithm The mean energy of ions generated by this sampling procedure is note the distribution T is already normalized to flux one l dvi f d dur v7 F Us v2 oT Shiol V 5 75 oo oCo 0 YE with the half sided integration for the 7 component of v and ol Here we have decomposed the drift velocity V4 into a normal to the surface 7 component Va and a o component V4 parallel to the wall surface 2 Va Vaal Vao V2 vr V2 or Note that for V 0 this reduces to the expected formula yg 2 V Furthermore if V 0 normal incidence and V 1 i e for the Bohm sheath condition M 1 in case of Te T then yg for the forward sided fluxes approaches the valu
19. CONST Fit parameters are directly read from input file up to nine coefficients In EIRENE 200os or later Optional Further parameter FTFLAG length not more than 9 characters IR CONST H123 FTFLAG optional CRC MASSP MASST DP format 13 1X A6 1X A4 A9 xxxX A3 213 3E12 4 i e Reading of FTFLAG is optional Default for FTFLAG 0 Parameter REAC does not exist Extrapolation flags RMN and RMX are not in use in this case and may be omitted for photons database FILNAM PHOTON IR PHOTON H123 REAC format 13 1X A6 1X A4 Axxx IPRFTYPE PLSC3 MESS FREMD NRJPRT DO IFREMD KENN K6 format 16 1xX A2 3X 16 ENDDO ILe after the first line there is a special format for this set of input cards in case of photonic processes read from the spectral database PHOTON In case JFREMD gt 0 the additional cards specify options for foreign pressure line broadening Then the subroutine SLREAC is called which picks the atomic data fit coefficients for reaction IR from the file FILNAM It then stores this information on the arrays in Module COMAMEF with label JR x 4A atoms species cards NATMI DO 44 IATM 1 NATMI read NATMI species blocks with A 110 44 CONTINUE x 4B molecules species cards NMOLTI DO 46 IMOL 1 NMOLI read NMOLI species blocks with M 46 CONTINUE x 4C test ions
20. DO 121 CHORI 1 NCHORI TXTSIG NSPTAL NSPSCL NSPNEW NSPCHR NSPSTR NSPSPZ NSPINI NSPEND NSPBLC NSPADD EMIN1 EMAX1 ESHIFT PIVOT XPIVOT YPIVOT ZPIVOT ICHORD XCHORD YCHORD ZCHORD 121 CONTINUE PLCHOR PLSPEC ENDIF Meaning of the Input Variables for Diagnostic Module NCHORI Total number of different line of sights NCHENI ABS NCHENI is the total number of energies at which the spectrum is eval uated irrelevant e g for total signals such as Lyman and Balmer emissivity without line shape resolution The energy grid is equidistant on a linear scale if NCHENI gt 0 and equidistant on a logarithmic scale otherwise 190 TXTSIG Text in printout at the beginning of the data from this line of sight integral NSPTAL Flag for choice of preprogrammed function which is line integrated 1 charge exchange source rate SIGCX 2 Hydrogen line emission source rate SIGAL 3 spectral radiance of photonic lines SIGRAD new in versions 2005 and younger 10 user supplied integrand SIGUSR this was option NSPTAL 3 in versions 2004 and older NSPSCL Flag for choice of linear or logarithmic axes in plots of spectra vs energy or wavelength resp and of source term distribution along line of sight 0 _ both axes linear 1 x axis linear y axis logarithmic 2 x axis logarithmic y axis linear 3 both axes logarithmic NSP
21. For ionization rate coefficients JZ specifies the ionization rate coefficient for the ionization process from JZ 1 to IZ i e the final charge state For recombination process IZ specifies the recombination rate coefficient for the recombination process from JZ to IZ 1 i e the initial charge state for these processes The next input decks are read only in case FILNAM PHOTON IPRFTYPE IPLSC3 IMESS IFREMD NRJPRT to be written Then JF REM D cards are read II KENN IK6 IT labelling index irrelevant KENN to be written IR to be written Note The nomenclature used in reference B has lead to a certain confusion with regard to the masses of the particles involved in a particular collision process A series of test calculations has revealed the following definitions implicit in the tables of references BI and BA For the cross section energy scale the relevant laboratory frame mass is that of the charged particle assuming an ion or electron beam incident onto a cold neutral gas at rest i e the mass in the energy scale is neither the reduced mass nor is the energy given in units energy AMU 115 For rate coefficients depending upon both the beam energy and the target temperature how ever the neutral particles are considered to be the beam particles i e their mass is the rel evant mass for the energy scale now whereas the charged particles are considered as target with their mass being the relevan
22. NVOLPL PLTSRC J J 0 DO 116 N 1 NVOLPL optional one text card starting with NSPTAL N PLTL2D N TALZMI N NSTRAI PLTL3D N TALZMA N PLTLLG N TALXMI N PLTLER N TALXMA N 180 to label the TALYMI N plot TALYMA N IF PLTL2D NTL THEN LHIST2 N LSMOT2 N DO 118 I 1 NSPTAL N ISPTAL N I NPTALI N I NPLIN2 N I NPLOT2 N I NPLDL2 N I 18 CONTINUE ENDIF IF PLTL3D N THEN LHIST3 LCNTR3 LSMOT3 LRAPS3 LVECT3 LRPVC3 LRAPS3D LR3 H LPRAD LPPOL LPTOR DO 119 I 1 NSPTAL N ISPTAL N I NPTALI N 1I IPROJ3 N J NPLI13 N I NPLO13 N 1I NPLI23 N I NPLO23 N 1I IPLANE N I 119 CONTINUE TALW1 N TALW2 N FCABS1 N FCABS2 N RAPSDEL N ENDIF 116 CONTINUE Meaning of the Input Variables for numerical and graphical Output 11A Block for numerical output written on unit 6 TRCPLT Trace back from plot routines TRCHST Printout of trajectories of selected test particle histories into geometry plots These histories are selected by the flags I1TRC and I2TRC see below sub block 11B 2 TRCNAL Trace back for non analog methods i e splitting surfaces suppression of ab sorption weighted post collision species sampling etc TRCMOD Trace back from routines for iterative mode MODUSR and p
23. ZL IMS3 A2LM A3LM A4IM A5LM A6LM A7LM ENDIF AOL IF RLBND GT M A1LM A8LM A9LM 0 AND RLBN D LT 2 THEN A2LM A3LM A4IM A5LM A6L XLI M A7LM MS YL IMS ZI A8LM A9LM IMS XLI MS2 YL MS2 ZLI MS2 ENDIF F R LBND GE Zia Pl IF Tas K GT 2 THEN THEN Pils 2y 244 P1 3 gyre B2 Ty eect 96 P2 3pas P3 1 P3 2 P3 3 P4 1 P4 2 P4 3 IF K GT 4 THEN P5 1l 2 PS 2 2 PS 3 ENDIF ENDIF ENDIF optional for non transparent surfaces ILIIN gt 0 The next 3 or 4 lines comprise the block for local particle surface interaction data in an alytic terminology the boundary condition at this surface element If they are omitted the default particle surface model is activated for this particular surface element see section ZA LREF LSPT SRS ISRC ZNML EWALL EWBIN TRANSP 1 N TRANSP 2 N FSHEAT RECYCF RECYCT RECPRM EXPPL EXPEL EXPIL RECYCS RECYCC SPTPRM this line may be omitted then default sputter model see ref sec2 6 also optional for non transparent surfaces ILIIN gt 0 read a surface interaction model identifier to link one of the surface local reflection models defined in block La below to this current surface The presence of such a link is identified by the
24. entirely wreck the performance of an only slightly different case For a general purpose Monte Carlo solver for transfer problems as EIRENE therefore no general advise can be given although the performance often could greatly be improved by adapting the method to a particular problem In particular non of these intelligent methods have been and will ever be hard wired into EIRENE EIRENE contains a set of such methods referred to as non analog methods and controlled by the flags in input block 9 see section ZA Activating those must be accompanied by a very careful statistical analysis of results not just the run time per particle nor even the standard deviation alone suffices 23 We first note here that any random distribution function f x arising during the course of gen erating the chains w particle histories can be replaced by another non analog function g x if a weighting factor w y f y gly 3 30 is included in the formula for the estimator X w y being an actual random number generated from g This choice can in some cases increase the efficiency of the algorithm The only restrictions on the choice of non analog sampling functions g x besides practical ones are if g xz 0 then f x 0 3 31 and conditions to ensure that the non analog process remains sub critical as well The condition G31 is checked in an EIRENE run whenever non analog distributions are applied and if
25. i 1 2 n Each of these surfaces is defined by a set of A equations unbounded surfaces filx y z 0 1 2 A 6 83 and optional for each unbounded surface A a subset of II inequalities e g for turning the unbounded surfaces into finite segments GAB ye lt 0 m 1 2 M 6 84 This means that for all unbounded surfaces S only the points which fulfill all corresponding inequalities 6 84 are regarded by EIRENE as valid parts of the finite surface element Assume a test particle at position r X0 Y0 Z0 moving with speed unit vector Qo VELX VELY VELZ The block then has to provide the nearest intersection r of the straight line sample trajectory G t ro to amongst all possible intersections with the surfaces S Moving the particle from ro to r and then repeating the block until the total track length as sampled from the transport kernel T l I is reached allows to generate histories with all information available along the track to evaluate the estimators mentioned in section LA In EIRENE f and g are general 2nd order with linear surfaces as special case algebraic equations of the form h z y z an ai a oan yta3 2 a r as y ag 2 ay TY ag Tz ag yz 6 85 Hence in the geometrical block nothing else but second order equations P p t q 0 have to be solved accurately and as efficiently as possible We note in passing that each of this surfaces may be
26. i e Monte Carlo code paral lelisation which are related to assignments of strata for cores in particular if the average cpu time per history strongly varies between strata In such cases the proportional alloca tion of weight to source strata discussed below is technically difficult to achieve together together with proper load balancing due to the stochastic termination of the random walks in the various strata Whereas without stratification extracting parallelism seems as trivial as constructing many independent samples in parallel This embarrassingly parallel feature of linear Monte carlo transport codes is lost and parallelisation in combination with stratified source sampling requires some attention Stratified sampling means that the primary source distribution Q r v t see Equation LIA or more generally for S x in LIJ can be decomposed into a sum of M independent sources this applies for both the source distribution S itself and the corresponding source strength s M M J Sn b gt 5 3 33 k k and the solution is obtained by linear superposition of the solutions for each sub source stra tum Sp We use again the slightly more general notation S for the inhomogeneous part of the Boltzmann equation rather than Q which is the physical source of particles objects i e a special case of S The stratified sampling technique is a well known statistical procedure from experimental planning se
27. in direction Q v v hence r r Q then the sampling distribution for is simply l T l Yi r IQ exp f ds r so o e li 3 49 0 Distances l are readily sampled from this exponential distribution using the inversion method and the cumulative distribution Gr of T l E Gr l 1 F I 1 exp f dsX r so 3 50 0 with and hence also 1 being a uniformly distributed random variable on 0 1 There fore cumulating k dsdiz r s along a flight and comparing it with In with a uniform random number provides by inversion a random sample of the free flight distance l with the proper distribution Sampling the distance l of a free flight for test particle species i with velocity v from the transport kernel 7 requires knowledge of the monochromatic mean free path A A r v along the trajectory and hence of the macroscopic cross section X U r v which also may vary along the trajectory The macroscopic cross sections X by abuse of language dimension 1 length with or without subscript k the label for the type of the collision process or subscript t for total the sum over k are defined as 1 V v _ 3 51 with the mean free path and the collision frequency v V r v i Nv Uret d Uret V vol 3 52 Here n and v are the target particle density and velocity respectively and the brackets d
28. lt NATMI NMOLI NIONI NPLSI NSPEZ is the fixed species index of the source particle No random sampling for the species index is done NSPEZ gt NATMI NMOLI NIONI NPLSI depending upon the type of the source particle the species index is sampled from the distribution DATM DMOL DION DPLS respectively The surface species distributions DATM DMOL DION and DPLS are read in the block Data for General Reflection Models see ZA 154 NSPEZ 0 the species index of the particle is directly sampled from the analog distribution WEISPZ i e no biased source species sampling WEISPZ is defined internally by the code The distribution WEISPZ is currently defined only for NUPLS TRUE sources and here only for surface recycling sources using the STEP function option in SAMSRE see further below this section and paragraph ZLI There it is set according to the local bulk ion flux composition WEISPZ may also be transferred into a run via user specified source sampling SAMUSR F see section B4 In all other cases NSPEZ must be positive NSPEZ lt 0 The surface species distributions DATM DMOL DION and DPLS are consid ered as biased source species distributions whereas the analog physical distri bution is provided automatically by the array WEISPZ from the source sampling routines SAMPNT SAMLNE SAMSRF or SAMVOL respectively An appro priate weight correction is carried out after sampling from DATM DMO
29. probability p The probability pp RPROBF Ein Oin ispez wall for the fast particle reflec tion model as specified by other flags for this surface is modified to RPROBF Ein Oin ispez wall AMIN RECYCF RPROBF RECYCT 6 5 where RPROBF was evaluated from the reflection model specified by ILREF Note the cut off at recycling coefficient RECYCT defined below The total recycling coefficient RECYCT py p is unchanged by flag RECYCF Hence by the use of RECYCE not only the fast particle reflection probability but also the probability for thermal particle emission p is altered to maintain a total recycling coefficient at this surface of RECYCT Default RECYCF 1 for incident atoms test ions and bulk ions Default RECYCF RPROBF 0 for incident molecules RECYCT Recycling coefficient must not be negative A flux RECY CT Influx is re emitted from a surface for any In flux of particles of any species where all fluxes are measured as atomic fluxes fluxes of nuclei RECYCT hence defines the sticking probability pa and hence also the pumping speed 6 6 of any surface in EIRENE for all incident species The fraction pa 1 RECYCT of incident atomic flux will be absorbed at the surface The non sticking i e the re emitted fraction RECY CT 1 p is split into a fast and a thermal component A fraction pr RPROBF see 5 of the incident particles is reflected as de
30. that part of the surface which is seen by the test particles By changing the sign of all coefficients in the algebraic equation the orientation of the surface normal vectors are reversed The intersection with the nearest surface along a trajectory is found by checking surfaces in the sequence of their input in subroutine TIMEA of the geometry block GEO3D This must be taken into consideration if there are two parts of one surface specified by different boundaries and with non empty intersection In this case always the surface later in the input sequence is seen by the test particles One can define two distinct plane surfaces as one surface of second order provided that this is compatible with the options available for surface boundaries We will refer to positive and negative directions of flights for particles intersecting a surface By positive it is meant that the angle between the trajectory of the particle and the sur face normal at the point of intersection is less than 90 degrees negative has the opposite meaning speeding up geometry calculations Checking surfaces along a test flight can be abandoned depending upon the current position of a test particle For particles in cell no NCELL all surfaces MSURF with IGJUM3 NCELL MSURF 1 are not checked For particles on surface MS all other surfaces MSURF with IGJUM1 MS MSURF 1 are not checked These matrices IGJUM1 and IGJUM3 can be set either in this block see CH1 card
31. watt T C 50 EOTPL Energy Flux incident Bulk Ions NPLS watt T C 51 SPTAT Sputtered Flux by incident Atoms NATM amp T C 52 SPTML Sputtered Flux by incident Molecules NMOL amp T C 53 SPTIO Sputtered Flux by incident Test Ions NION amp T C 54 SPTPHT Sputtered Flux by incident Photons NPHOT amp T C 55 SPTPL Sputtered Flux by incident Bulk Ions NPLS amp T C 56 SPTTOT Sputtered Flux total 1 amp T C 57 ADDS Additional Surface Tally NADS Input T C 58 ALGS Algebraic expression in surface averaged tallies NALS Input 59 SPUMP Pumped flux by species NSPZ amp Note i The tallies listed here are two dimensional arrays The 2nd index I2 is the number of the surface or the surface segment For I2 1 NLIMI the tallies correspond to the Additional Surfaces input block 3B ii For 2 NLIM 1 NLIM NSTSI NGITT the data correspond to the Non default Standard Surfaces input block 3A On each such surface of block 3A there is a spatial resolution with up to NGITT surface segments depending upon the standard grid dimensionality iii by default the sputter tallies are type and species resolved with respect to incident type and species E g the sputtered fluxes SPTAT 2 is the total sputtered flux all species sputtered by incident atoms of species ATM 2 Other conventions regarding sputter tallies are used in EIRENE versions operated at ITER IO e g SOLPS4 x see general description above iv the sputter
32. 1 5500E 01 0 0000EF 00 0O 2500E 00 0 2500E 00 6 15 121 000 30300 7 0000E 00 0 0000E 00 7 0000EF 00 0 0000E 00 As above stands for the species index of the D bulk ion Note that for reaction 6 the energy dependence of the cross section leads to a mean electron energy loss per event Ee of about 0 88 T see reference B3 This approximation is used in the default model for the electron energy loss Ea per collision and for the total kinetic energy release Ex shared by the two product atoms The reaction no 7 above AMJUEL H 8 2 1 14 provides values very close to this by an independent fit to the correct electron energy loss for this process oveBet Ea ove kT ove 3 2 din kT oy The velocity distribution of the dissociation products is isotropic in the center of mass system taken to be the system moving with the incident molecule and the dissociation energy is shared by the dissociation products so as to preserve momentum I e in case of unsymmet rical hydrogenic molecules the two dissociation products to not receive the same share of the dissociation kinetic energy release but instead this is distributed inversely proportional to their masses In case of mixed molecules such as DT HT or H D some rate coefficients are automatically split into two half and assigned to the proper product atomic particles For hydrogenic bulk ions H D 7 default volume recombination rates are available BA Further
33. 3 are updated and the particle history is stopped then 3 mirror for incident test particles I e specular reflection for neutral test particles and for charged test particles the sign of the velocity component parallel to the B field is reversed m4 periodicity surface with regard to x y or z coordinate depending upon whether this surface is a standard x y or z grid surface respectively Move particle to x radial grid surface no m m integer or to y poloidal or to z toroidal surface no m respectively and continue track from there with otherwise identical particle parameters This option is currently implemented only for Cartesian grids NLSLB and NLTRZ and for non default standard grid surfaces only The periodicity options are not fully implemented yet Please contact the author for the current status of your particular version 98 lt 0 transparent surface for example hole in one of the other additional surfaces ILSIDE 3 ILSWCH Particle and energy fluxes onto and from these surfaces do not contribute to global balances 0 Particle history is not interrupted No surface tallies are updated no switches can be operated Fastest option 1 Particle history will be stopped and restarted A switch can be operated I e this surface is used only for switching see below ILSWCH or re initializing the particle s track at the point of intersection No surface tallies are updated 2 as l
34. 3a or 3b then these variables may be made species dependent by adding an arbitrary number of lines to a SURFMOD deck each of which overwriting the specification for a particular particle species The name of the species blocks 4 and 5 must be uniquely determining one of the test particle or bulk species In the example of SURFMOD decks given above e g the first such additional line overwrites the original value of TRANSP 1 0 0 for species D2 with the value 0 5 I e all surfaces to which the reflection model modname CARB_SPT_1153K is assigned have a recycling coefficient 1 0 for all incident species except for the D2 molecules for which these surfaces are made transparent with probability 0 5 if these molecules are incident from the positive side For T2 molecules incident from the negative side this transparency is set to 0 25 The other species dependent modifications in this SURFMOD deck are self explaining 148 2 6 1 effective pumping speed The flag RECYCT described in the previous section is also used to specify surface pumping in the following way Let A be the surface area cm of a surface additional surface or non default standard sur face as seen by test particles to which a given pumping speed S is to be assigned Then the pumping speed S liters s for particles with temperature T K and mass m AMU is related to the sticking fraction pa 1 RECY CT by S A 1 RECYCT 3 638 T m A 3 6
35. 5 65 T with vr kT m the thermal ion velocity normalizing constant a and with the drift velocity V4 See Section ZZ for a description of related EIRENE input flags The superscript 38 0 indicates normalization of the flux to one particle per unit time and unit area f dv Doren y 5 66 Un gt 0 Consider now the three orthogonal velocity components v1 v2 v3 chosen such that v3 vy i e the v3 velocity component is normal to the surface target and hence also normal to the plasma sheath interface Spon V factorizes in the three uni variate distributions Doh ion TSh on 1 U1 Dh ion 2 v2 T Siionin vr 5 67 The first two factors here are simply shifted Gaussians and sampling random velocities v1 V2 from them is trivial e g Box Muller method whereas the third factor is a one sided drifting Maxwellian flux distribution 1 1 Tinen Or a2 Ur EXP z0 Vax Ur gt 0 5 68 T Ti The normalizing factor a2 for this distribution of the normal component v reads 2 2 2 az Up exp Vz 9 Vr 5 69 with Vy Var V2 vr and g x 1 y7 z 1 erf x exp z Note that the dimensionsless velocity V introduced here is related to the Mach number M by po _V Vi Tit 1 _ y VE T 1 5 70 Bm G v2 V2 with the isothermal ion sound speed c defined as cs T T m Hence V M only if T Ti It is clear that random sampling the 7 component v of v from Doh ion
36. At 34 present a discretized form of the reflection kernel Cup including all correlations between the vector components of v and v is available for the target projectile combinations listed in table LI ZNML is a target material flag set for each surface in the input file blocks 3a and 3b and is described below in block 6b Data for local reflection models These databases are essentially tables of conditional quantile functions obtained from large random samples of test particle trajectories in the solid Table 1 1 Surface reflection database TRIM Code No Projectile Target ZNML 1 H Fe 5626 2 D Fe 5626 3 H C 1206 4D C 1206 5 He Fe 5626 6 He C 1206 PVE Fe 5626 8 T C 1206 9D W 18474 10 He W 18474 11 H W 18474 12 T W 18474 13 D Be 904 14D Mo 9642 15 Ne C 1206 16 Ne Be 904 17 H Cu 6429 18 H Mo 9642 19 T Mo 9642 20 He Mo 9642 We consider these database reflection models to be the most complete option available at present and recommend to further extend the databases to additional projectile target combinations and in particular to sputtering and self sputtering data such as e g C onto C or Be etc For an INTOR benchmark case for neutral particle Monte Carlo Codes M the choice of a particular surface reflection model had no strong impact on the results This was shown
37. For I2 NLIM 1 NLIM NSTSI NGITT the data correspond to the Non default Standard Surfaces input block 3A On each such surface there is a spatial resolution with up to NGITT surface segments 249 Bibliography 1 B Braams Computational Studies in Tokamak Equilibrium and Transport PhD thesis Riksuniversiteit Utrecht June 1986 2 D Reiter H Kever G H Wolf et al Helium removal from tokamaks Plasma Phys and Contr Fus 33 1579 1991 3 D Reiter Progress in 2 dimensional plasma edge modelling J Nucl Mat 196 4 5 6 7 8 9 10 11 12 13 14 15 198 241 1992 D Reiter The EIRENE code Version Jan 92 User manual March 1992 H Gerhauser H A ClaaBen and D Reiter Contrib Plasma Phys 4 5 28 359 1988 D Reiter P Borner B Kiippers M Baelmans and G Maddison Final report on KFA NET contract 428 90 8 FU D 1991 G P Maddison E S Hotston D Reiter et al Towards fully authentic modelling of ITER divertor plasmas In Proc 18th Eur Conf on Contr Fus and Plasma Phys volume 15C page 197 Berlin 1991 J Spanier and E M Gelbard Monte Carlo Principles and neutron transport problems Addison Wesley Publication Company 1969 D Reiter Chr May et al J Nucl Mat 220 987 1994 G P Maddison and D Reiter Recycling source terms for edge plasma fluid models and impact on convergence behaviour in the BRAAMS B2 code KFA Ji
38. IN PRMSPL NIST N2ND I ENDDO DO IN 1 MAXADD READ IUNIN 66665 ID NSSPL NIST N2ND N3RD IN PRMSPL N1ST N2ND N3RD IN ENDDO WMINV WMINS WMINC WMINL SPLPAR Cards for Standard Deviation 169 N NSIGV NSIGS NSIGC NSIGI_BGK NSIGI_COP NSIGI_SPC DO 93 J 1 NSIGV GH H 93 CONTINUE DO 94 J 1 NSIGS IGHW HW 94 CONTINUE DO 95 J 1 NSIGC IGHC 1 J HC 1 J IGHC 2 J HC 2 0 95 CONTINUE Meaning of the Input Variables for Statistics and non analog Methods NLPRCA conditional expectation estimator eq 2 20 is used for atom species IATM NLPRCM conditional expectation estimator is used for molecule species IMOL NLPRCI conditional expectation estimator is used for test ion species HON not ready to use NLPRCPH conditional expectation estimator is used for photon species IPHOT in versions 2004 and younger IPRSF conditional expectation estimator is used if trajectory points towards additional sur face IPRSF IPRSF lt NLIMI the total number of additional surfaces read in input block 3B NPRCSF surfaces have that property of attracting trajectories The next lines define so called Splitting and Russian Roulette surfaces S amp R surfaces
39. ISTRAE There they may be further prepared e g normalized or scaled to other units for transfer to the external code 4 1 5 entry IF4COP post processing after one complete cycle overall balances statistics etc 4 2 Routines for cycling of EIRENE with external codes EIRSRT In this subroutine the cycling between EIRENE and external codes is controlled There are various options such as full time dependent explicit quasi stationary explicit and quasi stationary implicit 4 3 Routines for special tallies needed for code coupling UPTCOP Updating of code interface tallies COPY along the fly These tallies are specific to the par ticular background plasma CFD code hence module UPTCOP is part of the code interfacing module Apart from scoring along Monte Carlo histories in this special routine rather than in EIRENE routine UPDATE the tally COPV is scaled averaged printed and plotted as any other EIRENE tally In older versions of EIRENE before 2002 in particular momentum exchange rates i e friction terms in the direction parallel to the magnetic field have been programmed here in UPTCOP Meanwhile these have become default tallies i e scoring moved to UPDATE see chapter I Still some particular coupling tallies e g to render the coupling procedure more implicit are scored in this routine 235 4 4 Statistical noise in Monte Carlo terms for external code noise residuals STA
40. Mach number units instead The sound speed cs is taken to be the isothermal ion acoustic speed of species IPLS ABS INDPRO 4 is then used as flag for the choice of profile type Values of INDPRO 4 larger than 10 use only the last digit and only one com mon flow field is set for all bulk ion species Note the difference to the T options there the meaning of INDPRO larger than 10 was exactly opposite to the meaning here for the flow fields due to historical reasons and for backward compatibility of input files EIRENE had originally by default one single common ion temper ature but one flow field for each bulk ion species INDPRO S5 for PITCH later in initialization phase converted into cartesian unit B field vector BXIN BYIN BZIN Pitch is defined as B Biot LEVGEO 1 Bg Bio LEVGEO 2 or as Byoi Brot LEVGEO 3 where Bpa is the direction along the polygons 133 New options since 2001 In case INDPRO 5 3 flat profile the two redundant input parameters B2 B3 are used to define a constant B field strength T see below under profile type INDPRO 3 INDPRO 6 for ADIN INDPRO 7 for WGHT to be written INDPRO 12 for VOL For the profiles no 6 and 7 only the options INDPRO 5 or INDPRO 6 exist For the profile no 12 cell volumes the options INDPRO 12 4 5 6 or INDPRO 12 7 are active options For all other values of INDPRO for these latter four profiles the default profiles described above General re
41. NLPLS ISTRA TRUE e Stratum ISTRA is a surface source NLUSRF UISTRA TRUE e Number of sub strata NSRFSIUSTRA 1 e Mixed radial poloidal or x y surface type INDIM UISTRA 1 4 e Step function sampling with SORLIM ISTRA 1 104 and the step function data FLSTEP for the flux distribution entering the sheath region of the target are automatically de fined 204 e Number of step function SORINDUSTRA 1 ITARG ISTRA The other input flags for birth point sampling in input block 7 have then become irrelevant by this new settings of the modified parameters listed above The sampling of the velocity of the incident ions is as specified in input block 7 for that stratum CHGP The short cycle between EIRENE and the plasma code i e only recomputing of source term profiles in subroutine EIRSRT at each time step but no new random walks is stopped if the total volume integrated particle source rate has changed by more than CHGP per cent as compared to the previous full EIRENE run CHGEE as above but for total electron energy source rate CHGEI as above but for total ion energy source rate CHGMOM as above but for total ion parallel momentum source rate to be written May 1995 NAINB total number NAINI of additional plasma code tallies transferred onto EIRENE input tally ADIN e g in order to utilize EIRENE output facilities for plasma code data or for the options described in sub block 10c I irrelevant label
42. NSPINI NSPEND only for NSPTAL 1 Multipliers for the maximum ion temperature Ti found along line of sight for tem perature fitting The CX ion temperature is fitted from the CX line of side spectrum in the intervall NSPINI x Timar NSPINI x Timaz NSPBLC Standard mesh block number of 2nd point on line of sight NSPADD Additional cell number of 2nd point on line of sight If NSPADD 0 then this 2nd point must lie in standard mesh block NSPBLC If NSPADD 0 then the block number NSPBLC must be NSPBLC NBMLT 1 i e the second point on the line of sight is in the additional cell region EMIN1 EMAX1 for NSPTAL 1 3 10 minimum and maximum energy for spectral resolution respectively for NSPTAL 2 Parameter to identify the particular hydrogen line Emin1 and Emax are interpreted as integer principal quantum numbers n m of the lower and upper state for the transition EMINI 1 EMAX 3 Lyman beta line EMINI 2 EMAX 6 Balmer delta line EMINI 2 EMAX 5 Balmer gamma line EMINI 2 EMAX 4 Balmer beta line EMINI 2 EMAX 3 Balmer alpha line Old input version still maintained for backward compatibility of input files EMIN1 is an energy parameter to identify the particular hydrogen line and EMAX is not used EMINI is given in eV by Ry x 1 n 1 m with Ry 13 6 eV EMIN1 12 089 Lyman beta line EMIN 3 0222 Balmer delta line EMIN 2 8560 Balmer gamma line EMIN 2 5500 Balmer
43. Tally routines UPTUSR UPCUSR UPSUSR and UPNUSR Let f r v js be the distribution function in the 6 dimensional u space for particle species js S PH Photons S A Atoms S M Molecules S I Test Ions S P Bulk Ions e g 2 1 ja H D T He C O jm Ho D HD CH H20 j H CH C 0O je H Dt Het Hett se The distinction between Test Ions and Bulk Ions is problem specific see input blocks 4 and 5 The volume averaged tallies estimated by EIRENE see table EJ are profiles of responses R lt fo gt 5 evf dr g v i Fev j volume for several preprogrammed and an arbitrary number of additional user supplied detector functions g Here the summation over j is only over test particle species i e atoms molecules or test ions and not over background particles bulk ions electrons The de fault EIRENE estimators are not based upon moments of distribution function f but upon moments of the flux is r v v f s r v hence on detector functions g g v Occasionally also moments of the pre collision density U js V js r v U js r Vv are utilized then with detector functions g g v Here X dimension 1 length is the local total macroscopic cross section i e the inverse of the local mean free path length The estimators may in general be composed of a track length estimate kn 1 kn 1 Titi Ri gt Fu
44. This results in the need to sample the velocity of a bulk ion going into the collision and then to continue the former test particle with its charge increased by one the former bulk ion with its charge decreased by one i e as neutral particle in case of singly charged bulk ions The ISCDE parameters for CX processes are zero ISCDE JKLMN 00000 or 00001 which has the same meaning because the fifth digit N is presently irrelevant The second digit i e here K 0 controls the options for the velocity of the background ion going into the collision For this choice K 0 the following model is activated With respect to ions going into a CX collision the ion velocity distribution f v is assumed to be an isotropic mono energetic distribution with v V1 5 kT then shifted by VDrift 1 1 ee 42 filvi Vprist i ad Ui mo Ui Ui VU lv 4 2 The mean energy of ions undergoing charge exchange is taken to be 1 5 T plus the kinetic energy in their drift motion m 2 vp ift This is used for the corresponding part in the CX momentum and energy exchange rate coefficient The reaction rate coefficient itself is evaluated as 0 Upet O Vesp Vesp with an effective relative velocity Veff 3 2KT m Vo VDrifti This approximation to the rate coefficient for this particular choice of f is almost exact It is assuming that the effect of the scalar product v Vo in the relative velocity between ion and
45. all tallies estimated by EIRENE can be used with no risk except that evaluations of variances and covariances generally tend to slow down the code a bit few percent in case of large meshes Hence as a rule one should generally try to find the optimal setting of the non analog sam pling flags in this block and estimate the FOM from test runs and then use this setting but without evaluation of standard deviations in production runs The input flag NLANA in block 1 section L I de activates all non analog sampling distri butions This option should for example be used to derive an intuitive but physically correct picture from plots of selected particle trajectories input block 11 section Z I which oth erwise e g in case of suppression of absorption may be grossly misleading The Input Block Q Data for Statistics and non analog Methods NLPRCA IATM ATM 1 NATM NLPRCM IMOL IMOL 1 NMOL NLPRCI IION ON 1 NION NLPRCPH IPHOT IPHOT 1 NPHOT NPRCSF next read NPRCSF integers FORMAT 1216 PRSF J J 1 NPRCSF MAXLEV MAXRAD MAXPOL MAXTOR MAXADD DO IN 1 MAXRAD READ IUNIN 66665 ID NSSPL IN PRMSPL IN ENDDO DO IN 1 MAXPOL READ IUNIN 66665 ID NSSPL NIST IN PRMSPL N1ST IN ENDDO DO IN 1 MAXTOR READ IUNIN 66665 ID NSSPL NI1ST N2ND
46. also possibly particle multiplication factors e g in case of fission by neutron impact dissociation of molecules by electron impact or stimulated photon emission from excited atoms It can also include absorption in which case the post collision state must be an extra limbo state outside the phase space considered Due to both particle multiplication and or absorption the collision kernel C is not normalized to one generally If the distributions f of one of the collision partners are assumed to be given see below linear Boltzmann equation then the kernel C is linear and the expression above becomes a linear integral operator The second term on the right hand side is much simpler because the function f v can be taken out of the integral We even take the product v f before the integral The remaining integral is then just the total macroscopic cross section i e the inverse local mean free path dimension 1 length It is solely defined by total cross sections and independent of particle multiplication factors since we only consider binary collisions exactly two pre collision partners always This term is then often taken on the left hand side of the Boltzmann equation with a positive sign in the form of ot Lee pee C v gt v v f v 1 4 loss T Xlr vivi fv 1 5 linear form of Boltzmann transport equation For the linear case f given for all collision partners other than 79 and self
47. and properties are described in subsection ZZZ 2 3 1 The Input Block for Non default Standard Surfaces General remarks Some of the standard grid surfaces RSURF PSURF and TSURF may be defined as re flecting or absorbing rather than the default transparent character of co ordinate surfaces or as transparent but with other switching features cell indexing transition into additional cell region etc than the default settings E g surface averaged tallies see block ZII end of section and Table 6 3 are only evaluated on either Additional Surfaces subsection 23 2 or on these Non default Standard Surfaces whereas they are not computed for those standard grid surfaces which are not explicitly identified in this block The geometrical properties of these Non default Standard Surfaces are specified here This is described below Particle surface interaction models Although the local data for particle surface interaction models PSI models for each spe cific surface can be read in this input block their meaning is described in block LA together with the globally valid input data for particle surface interactions In any particular run there are NLIM additional surfaces see subsection 2 3 2 For many arrays containing surface properties the non default standard surfaces are stored after the additional surfaces E g FLAG NLIM 4 would store the data FLAG for non default stan dard surface
48. beta line EMIN1 1 8889 Balmer alpha line Other side on line emissivities can be obtained using the user supplied line of side inte gral SIGUSR option NSPTAL 10 and analogy to the preprogrammed options as well as the internal EIRENE hydrogen atom collisional radiative routine H COLRAD F to obtain the required reduced population coefficients for H n For the preprogrammed options these latter coefficients for n 2 3 4 5 6 are stored in AMJUEL section H12 see this web page under EIRENE AMS data files 192 ESHIFT for NSPTAL 1 3 10 options only energy shift for spectral resolution in printout and plot The line integration is carried out along a line defined by two points a pivot point Pivot and a second point Pena The second point must lie inside mesh block no NSPBLK Starting from this second point and moving in the direction towards the first point Pyivor the first intersection P with a non transparent additional or non default standard surface is computed This is the starting point for line of sight integration Then the line integration is carried out starting from this point P into the computational area until the next intersection P gt with any non transparent additional or non default standard surface is found The next card specifies the first pivot point IPIVOT only needed for NLTRA option sub block 2c 1 lt IPIVOT lt NTTRA 1 currently no available error exit number of local tor
49. block 7 are saved for later iterations or time steps L 2 EIRENE reads plasma data A amp M data from file FT13 It also reads the entire input block 7 from FT13 and overwrites the input read from this block 7 by those data Routines PLASMA XSECTA XSECTM XSECTI XSECTP are not called This option should be used if neither the plasma background nor the selection of atomic processes to be used nor the primary source model block 7 has changed as compared to an earlier run It then reduces the CPU costs for the overhead L 3 Acts as if both NFILE L 1 and NFILE L 2 Le reading background data from file and writing new background data onto file at the end of the run the time step or the iteration For continuation of iterative calculations for example L 4 Same as NFILE L 3 except primary source data input block 7 are not read from fort 13 but are taken as specified in input block 7 This allows to mod ify these primary sources parameters during iterations or time steps not only via module MODUSR but directly via input file L 6 7 8 9 Same as L 1 2 3 4 respectively but XDR file format is used K 1 EIRENE saves some data for optimizing non analog sampling and stratified source sampling on file FT14 K 2 EIRENE reads from file FT14 and tries to optimize operation for the next run time step or iteration Currently only allocation of CPU time in stratified source sampling is optimized More details see paragraph ZL below K 3
50. by running the EIRENE code with all three models Behrisch Matrix TRIM database and MARLOWE database at that time available as a third option Meanwhile the MARLOWE database is not available anymore It was found that this had little influence on global parameters as e g the pumping efficiency for the particular geometry 5 4 5 3 and 5 2 respectively On the other hand it can easily be imagined that in other cases different plasma conditions more detailed geometries the choice of the reflection kernel Cup can be more important for the result Certainly in all cases in which the results are sensitive to the neutral particle velocity distribution near 35 surfaces details of the reflection kernel matter This is for example the case for computed line shapes of certain electronic transitions Ha lines etc see e g reference Z0 36 1 5 Recycling surface sources It has been found mid eigthies of last century within INTOR framework as a result of benchmark calculations with several different neutral gas transport Monte Carlo codes EIRENE DEGAS NIMBUS DDC83 on the same input data that the main divergence in the results from the different codes tested was due to different primary source terms Q in the transport equation equations L Tall Th and L amp a although target fluxes and temperatures had been prescribed to be identical Here we describe one particular EIRENE surface source option in detail The w
51. case of linear combinations of tallies the summation over tallies k and event contributions j of a single history can be interchanged G 29 Finally the variances for R are evaluated in STATS1 reusing the procedure used for de fault tallies and the former problem specific routine STATS1_COP for variances from tal lies needed for code coupling has hence been made redundant as indicated in red color in flowchart LIJ Currently linear combination tallies R are stored on array tally COPV For them all printout and graphical output options are available One example of such linear combination tallies is discussed in section ZIJA for interfacing EIRENE with CFD codes as usually the kinetic reaction source terms provided by EIRENE to plasma fluid codes are such linear functions of default tallies Statistical independence of MC histories When the Monte Carlo histories from one EIRENE run are not strictly statistically independent as e g in case of stratified source sampling see paragraph below then a modified formula for the statistical error estimates has to be used 1 3 3 1 Sampling Non analog sampling One often encounters in literature the description of special new Monte Carlo techniques that are greatly superior to so called standard methods It is true that one can devise very intelligent methods to optimize performance but each optimization always only works well for one very particular problem it can equally well
52. collisions being excluded then this extinction coefficient X is independent of the dependent variable f fio and this term out scattering just describes the loss of particle flux of io particles due to any kind of interaction of them with the host medium With these formal substitutions the Boltzmann equation takes a form which is often more convenient in particular in linear transport theory F t e AA Ve F v d Hlev fade gt I Q r v t 1 1b 12 which in the linear case no self collisions f given externally is a linear equation for the distribution function f fi x v t for species io Clearly a computationally crucial simplification is provided in this linear case which means neglect of all interactions within the community of species 2 retaining only 7 b gt events In practice for neutral particle transport in plasmas this mostly means neglect of neutral neutral interaction retaining only neutral plasma collisions for given plasma con ditions For the status of options in EIRENE to deal with non linear self collisions to or with cross collisions io 7 amongst the species for which the kinetic equation is solved see below section L9 stationary kinetic transport equation Often the characteristic time constants for neutral particle transport phenomena are very short us compared to those for plasma transport ms We can therefore
53. define the pitch angle pro file and it is also used to set the B field strength Tesla by calling PROFS P2 P3 P5 PVAC INDPRO 4 read from input steam fort PO INDPRO 5 EIRENE calls a user supplied plasma profile routine Subroutine PROUSR RHO INDEX PO P1 P2 P3 P4 P5 PVAC NDAT NDAT data must be defined on RHO J J 1 NDAT e g by using the profile parameters PO P5 and any user supplied profile function See section BA NDAT NSURF The flag INDEX is as for the INDPRO 6 option see below and sections Ba and A It determines which of the background medium profiles has to be provided at a particular call to subroutine PROUSR PVAC is the EIRENE vacuum value for the profile in question INDPRO 6 EIRENE calls a the routine Subroutine PROFR RHO INDEX NII N1 NDAT N1I e g NPLSI profiles of NDAT NSURF data each are read onto RHO IIL J J 1 NDAT I1I 1 N1I from a work array RWK N1 e g NPLS is the leading di mension of the array PRO as specified in the calling program The data must be written onto array RWK in the initialization phase e g in subroutine INFCOP or MODUSR The location of a particular profile on this work array is determined by the value of INDEX see section below By this option plasma parameters may directly be transferred into EIRENE from other files e g from plasma transport codes NDAT NSURF is the number of cells in the Standard Mesh Parameters in the addition
54. density n 1 x 10 cm For the same conditions as above T 300 K T 0 026 eV and a pressure of 1 Pa ny 2 414 x 10 cm one then finds Agag 1 6 cm ina Dy gas For Kn lt 1 a neutral fluid model diffusion approximation Euler or Navier Stokes etc is more appropriate while Kn gt gt 1 leads to the linear free molecular flow regime in which only the linear collisions terms collisions of neutrals with surfaces and a given plasma host medium are retained 1 9 1 BGK approximation currently under development Please contact us for details and status See flowchart 9 1 figure LIB Further details can be found in Ref 22 The BGK approximation used in the the EIRENE code to model neutral neutral collisions of both monatomic and multiple species gases and its implementation via successive approxi mation of the non linear Boltzmann equation is a special case of the classical test particle method for solving the Boltzmann equation as opposed to the direct Monte Carlo Simu lation method The former was introduced in rarefied gas dynamics by J K Haviland in 1961 see J K Haviland The solution of Two Molecular Flow Problems by the Monte Carlo Method in Methods in Computational Physics Ed Alder Vol 4 1965 Academic Press An early review and comparison of different Monte Carlo methods in kinetic theory also comparing this particular test particle method with the DMCS scheme is gi
55. detector functions For example all terms in the plasma fluid equations resulting from neutral plasma interaction can be written in this way This can be seen by considering a numerical grid composed of M mesh cells spatial and or temporal for the numerical solution of the fluid equations The detector functions for many responses needed for fusion plasma applications are hard wired in EIRENE generalization to any arbitrary response by resorting to user defined detector functions is described in Section EZI for tracklength estimates and in Section for collision estimates Lets therefore define an entire set of detector functions g one for each mesh cell of an external code each including a characteristic function gm g X Chmlr t HIS 1 2 M 2 14a i e Chm r t 1 inside the numerical mesh cell or time interval labeled with the cell index m and chm r t 0 outside this cell Thus profiles of cell volume averaged responses are readily obtained in a single Monte Carlo run Estimates of surface fluxes or point estimates e g in time are also included in this concept if proper use is made of delta functions to reduce dimensionality of the response Jma 9 X Chmlr t x r t m 1 2 M 2 14b Here e g a surface cell m would discretise a surface S characterized by a surface delta function 6 Equation 2 13 shows that Monte Carlo estimates tallies fall into the category of extensive quantities nu
56. deviation profiles for volume averaged tallies to be estimated NSIGVI must be less than or equal to the parameter NSD in PARMUSR GEI NSIGSI number of standard deviation profiles for surface averaged tallies to be estimated NSIGSI must be less than or equal to the parameter NSDW in PARMUSR EI NSIGCI number of correlation coefficients between volume tallies to be estimated NSIGCI must be less than or equal to the parameter NCV in PARMUSR GEI NSIGI_BGK_ if NSIGI_BGK gt 0 then the standard deviations are evaluated for all tallies needed for the iteration procedure for the non linear BGK collision terms See subrou tine STATIS_BGK in code segment BGK F 171 NSIGI_COP if NSIGI_COP gt 0 then the standard deviations are evaluated for all tallies needed for the iteration procedure for the coupling to a plasma fluid model The rele vant tallies are selected in subroutine STATIS_COP in code segment COUPLE_ F section NSIGI_SPC if NSIGI_SPC gt Q then the standard deviations are evaluated for all surface flux spectra defined in sub block 10F below IGH Index of species for selected volume averaged tally IIH Index of volume averaged tally for which empirical standard deviation is to be calcu lated see table 5 2 IGHW Index of species for selected surface averaged tally HHW Index of surface averaged tally for which empirical standard deviation is to be calcu lated see table E3 IG
57. examples to be written 2 4 2 Neutral Neutral collisions in BGK approximation In the example considered here we have the 4 neutral neutral collision processes D on D2 D on D and D2 on D2 D2 on D In input block 4 there are three BGK relaxation rate coefficients note the rate coefficient for D2 on D is equal to the one for D on D2 hence 3 rate coefficients are sufficient 126 some 20 other reaction cards in this example 21 CONST 4H 2 EL 1 1 2 1091E 01 0 2500E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 22 CONST H 2 EL 2 2 2 0589E 01 0 2500E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 23 CONST H 2 EL 1 2 2 0357E 01 0 2500E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 In input block 4a for atoms we specify 4 collision processes for D atoms Process no 3 and 4 are neutral neutral collisions 1D 2 1 1 0 1 1 1 4 i e 4 processes to be specified for this D atom 2 other process decks e g CX and electron impact ionization 21 2014 IBULK 1001 0 111 IBGK self collision 0 00000E 00 0 00000E 00 0 00000E 00 0 00000E 00 0 00000E 00 23 2214 IBULK 1001 0 112 IBGK cross collision with IMOL 1 0 00000E 00 0 00000E 00 0 00000E 00 0 00000E 00 0 00000E 00 In input block 4b for molecules we specify 7 colli
58. field can be run without having to resort to any problem specific routines but instead by an appropriate setting of logical and numerical input flags Any user of EIRENE should be aware that this code is a moving target as is this manual Therefore it is possible that there are some inconsistencies between this description and a particular version of the code The user should always first check subroutine INPUT where most of the data are read in using hard wired formats as most input errors will lead to a rapid exit in the initialization phase of a run This manual was written by the author of the code who often may not have been able to anticipate difficulties in understanding the use of EIRENE He therefore gratefully acknowl edges any suggestions to make this manual more informative and clear than it might be at the present status This code description consists of the following parts e In the first part an introduction is given to the general linear transport problem and its solution by Monte Carlo methods Most of the terminology used in later sections is introduced there e In part two a description of the formatted input file required by EIRENE to run on a specific problem is given It mainly consists of explanations of the meanings of the various input flags e In part three the most important problem specific routines are explained At present we have restricted this part to routines for evaluation of user requested tallies na
59. for this surface The surface interaction model comprises the following information 1 pr RPROBF probability for reflection of a fast particle 0 for incident molecules 29 2 p RPROBT probability for re emission as thermal particle with surface temperature see the flags EWALL 3 Pa RPROBA probability for absorption surface sticking pumping etc 4 ps probability for physical sputtering 5 Pe probability for chemical sputtering 6 For the reflected fast particles and for the sputtered particles the type species and the distribution of energy polar and azimuthal angle of emitted particles must be specified 7 For the re emitted thermal particles the type species and only the distribution of energy must be given the angular distribution follows the cosine law by default All these data may be functions of incident energy E n of incident polar angle Oin against the surface normal and of projectile and target species The three probabilities p p and pa must add up to 1 one ps and p are sputtering yields per incident particle and thus may occasionally be larger than 1 They are called a probability here only by abuse of language All this information is contained in each of three so called Reflection Models namely the Database Reflection model see references T L9 the Modified Behrisch Matrix model references L8 B5 or the User Supplied Ref
60. for this expression is stored on ALGS ISURF and is the same for ISURF 7 8 9 10 or 11 and zero for all other surfaces 2 10 6 Energy spectra in selected cells or surfaces ISRFCLL flag to choose between surface and cell averages 0 surface averaged spectrum 1 volume cell averaged spectrum ISPSRF number of surface or cell for which spectra are to be evaluated Positive for addi tional surfaces negative for non default standard surfaces IPTYP Type of particle 0 for photons 1 for atoms 2 for molecules 3 for test ions 4 for bulk ions IPSP species index of particle within the specified type category If IPSP 0 then sum over species for this type of particles ISPTYP type of spectrum for surface averaged spectra i e ISRFCLL 0 flux spectrum ISPTYP 1 Amp eV or energy flux spectrum ISPTYP 2 Watt eV Currently only ingoing fluxes Spectra for outgoing fluxes are not yet available for cell averaged spectra i e ISRFCLL 1 case a no direction specified IDIREC 0 energy distribution ISPTYP 1 cm 3 eV energy weighted energy distribution ISPTYP 2 eV cm 3 eV velocity weighted energy distribution ISPTYP 3 cm s cm 3 eV case b direction specified IDIREC 1 velocity distribution along specified direction binned in energy units ISPTYP 1 cm 3 eV energy weighted velocity distribution along specified direction binned in energy units ISPTYP 2 eV cm 3 eV velocit
61. implementation via the USR routines e integration volumes of volume averaged tallies can now be larger than the grid cell volumes i e the plasma background and geometrical discretisation which is not very storage sensitive can be made much finer than the neutral particle volume averaged tally profile output e discretisation of general multiply connected 3D volumes by tetrahedron grids e photons as new type of test particle species The photon_dummy module allows simple photon transport one speed Boltzmann equation with spatial profiles of spontaneous emission Doppler line broadening for optically thin lines only with inclusion of mul tiple surface reflection The full photon module additionally allows for various other line broadening mechanisms and photon re absorption stimulated emission radiation trapping excitation hopping iteration with neutral gas excitation population kinetics etc EIRENE versions 2003 and younger have been compiled and successfully tested at FZ J lich on the following systems and compilers Linux Suse 11 1 and all predecessors down to Suse 6 e pgf90 Portland Compiler Version 5 2 4 10 1 e ifort Intel Fortran Compiler Version 8 1 11 1 e 1f95 Lahey Fortran Compiler Version 6 2 e nagf95 NAG Fortran Compiler Version 5 0 5 2 AIX AIX 4 3 und 5 2 e xlf95 XL Fortran for AIX Version 8 1 Windows Windows 2000 und Windows XP e Compaq Visual Fortran Version 6 6 Detlev Reiter Spr
62. in each component ISHAPE 8 Doppler broadened Zeeman Stark profile 10 Lorentzian model Rosato 2006 58 1 11 Charged Particle Transport EIRENE also follows charged particles since EIRENEj9g7 _ The particle tracing is carried out in Subroutine FOLION We refer to this ion transport model as the minimal trace ion model as opposed to refinements added only very recently The differences of the module FOLION to the module FOLNEUT for neutral particles and photons are e Motion is not along straight lines between events but instead determined by drifts and forces due to the electro magnetic fields e Time stepping is not of Poisson type but with constant increments because the equa tion of motion has to be solved numerically and this introduces already a time stepping e after each time step a Coulomb collision kernel is modelled i e a diffusive step in velocity space e after each time step a diffusion step is modelled i e a diffusive step in physical space not yet written e ionized test particles which hit a surface see an electrostatic sheath potential by which they are either reflected slowed down or accelerated depending on the sign of their charge relative to the sheath potential 1 11 1 Orbit integration Orbit integration in a magnetized plasma is carried out to various orders of the small param eter 6 p L p thermal gyro radius L spatial length scale e g gradient length etc 1 11 1 1 Particle
63. input card starting with is recognized as a comment line i e it does not contain input data These comment lines should not start with or because in this latter case EIRENE would assume that the input for the current block is completed It would expect the first card of the following block or comment lines belonging to this next block as next card Any data not read from the input file before the following block is read are set to default values An arbitrary number of such comment lines may be included in the input file but each block of comment lines must always be put at the beginning of a block or sub block I e com ment lines are only identified by EIRENE if preceded by a card starting with or indicating a new sub block or block respectively Example see section LZ below 7 Data for initial distribution of test particles this is a comment there are NSTRAI 2 strata in this run this is a comment 2 Data for first stratum this is a surface recycling source of helium ions IPLS 2 this is a comment FFFF Data for second stratum this is a hydrogen ion volume re combination source IPLS 1 FFFF 71 8 Data for some specific zones and so on In very few cases formats other than these are used They are then explicitly mentioned in this manual and in case of doubt the user should check in subroutine INPUT 12 2 1 Input data for operatin
64. interactions summed over all EIRENE species of type atom tally no 11 e PM PLis the particle source for background plasma species ipls resulting from molecule plasma interactions summed over all EIRENE species of type molecule tally no 16 e PIPL is the particle source for background plasma species ipls resulting from test ion plasma interactions summed over all EIRENE species of type test ion tally no 21 Momentum source mass velocity time volume g cm s Amp em Sm ipls icell X COPV icop icell 14 19 is icop The sum is over all strata see stratified sampling in section D COPV is the problem specific tally for code interfacing tally no 40 and it is scored in the routine UPDCOP different versions exist for different plasma fluid codes in section ELJ The sign of these sources in EIRENE is such that a gain in momentum for plasma species zpls is taken positive In the interfacing routine IF3COP of module EIRCOP the sign convention is altered to that of the plasma fluid code i e it then involves the flow direction relative to the magnetic field vector Ion energy source Energy time Volume Watt cm for total ion energy balance in lab oratory frame Spilicell gt EAP L s icell EMP Lis icell EIP Lis icell 14 20 is The sum is over all strata see stratified sampling in section D EAPL E MPL EIPL are default EIRENE tallies Table 4
65. is discussed below section LLI The familiar Boltzmann equation for the distribution function f for this species 79 reads ony Vv 4 F r v t iS vi fievt ff fow viv vylv Vi Aly 2 EA v V v W Iv VIF v fo V Q r v t 1 1a There is one such equation for each particle species 7 considered but for elastic collision without exchange between species always only two of them here to and b a directly coupled to each other Q Qio is any external source particles per unit time injected per unit volume in phase space Integrations are over the pre collision velocities v V as well as over one of the two post collision velocities V a v V v V is the differential cross section for a binary particle collision process The product of this o with the relative pre collision velocity is the transi tional probability The four velocity arguments are not truly independent the conservation laws for total energy and momentum must be fulfilled MiV HMV Moy mV 1 1 1 aio zV gio mV7 Ap 1 2 Here Ap is the exchange of internal energy in the collision on expense of the energy of relative motion Ag 0 for elastic collisions We may assume that contains appropriate delta function factors such that integrations over velocity space reduce to integrations over the lower dimensional manifolds on which these conservation laws are fulfilled The first two arguments in namely the velocitie
66. is not trivial even for this seemingly simplest sheath entrance ion velocity distribution because the cumulative distribution function F of a 1D forward drifting Maxwellian with cut off at v 0 Flom dT son lth 5 71 0 cannot be inverted explicitly Therefore in the EIRENE code we apply the Monte Carlo biassed source sampling con cept module VELOCS F We sample this component from a non analog truncated Maxwellian flux distribution see Section C3 paragraph LZZ above with zero drift in z direction but with different non analog 7 temperature T Ki T ni F Lis an 0 Note that although this non analog distribution clearly violates any Bohm criterion it is taken together with the weight correction factors described below unbiased and a fully legit imate sampling distribution because it fulfils the Radon Nikodym condition 3I Sam pling from this non analog distribution can be done by setting e g r A gt In 2 note Aq vz_ since Van 0 5 72 being a uniformly distributed random number between 0 and 1 39 In order to find the weight correction factor associated with this non analog procedure we first note that Vr 0 On Up This gives the following result for the weight correction factor w t see equation 30 to be applied for each sampled non analog velocity component z r ion r la r V T v2 Ti 1 w e exp A
67. is the distance to the nearest surface along the track of the particle The reflection kernel Cw is further decomposed it into a kernel Cup fast particle reflection Cwt thermal particle re emission and C particle absorption with respective probabilities ps p and Pa Such that Cw Cuf F Cut F Cira PpCws Cut Da its Pf Pt Da 1 4 55 Here C are as above the normalized versions of the collision kernels C We discuss in detail only the fast particle reflection model C since Cwt is generally a mono energetic and cosine angular distribution or a Maxwellian flux distribution at wall tem perature and Cwa only describes the transition into the limbo state x absorbed particle It is usual in neutral gas models to replace Cup with numerical or analytical fits to moments of Cup g Such as the particle and energy reflection coefficients Cp and Cz The particle wall interaction is often supplemented by simple assumptions on the angular distribution cosine or specular of the particles leaving the surface One has for the particle reflection coefficient Cp gt fw Cy s t v i gt v i 4 56 Note that Cp pf Cup in the terminology of equation Z10 The energy reflection coefficient is defined as 1 f 1 gt z Cs g f WV ECV gt vi Fy Ce 4 57 Here E mv 2 is the energy of the reflected particle Hence Cg E E Cp with E denoting the mean energy of the reflected particles 1
68. it is highly recommended that in addition to the information given below close interaction with scientists at FZ Juelich may be needed One also might ask for a few sample routines INFCOP which are available from the authors 232 Data are transfered from subroutine INFCOP into EIRENE via the EIRENE work array RWK Module CSPEI They are read onto the EIRENE arrays for input volume tallies by calls of subroutine PROFR in the initialization phase individually for each tally for which the flag INDPRO has the value 6 or 7 see section L5 The following addresses are foreseen on array RWK for this data transferring procedure Plasma data INDPRO 6 option TEI T D VXI VYI VZI BXI BYI BZI BEI VLI ADI 2 2A A A ae eae See J v D D D 2335353 NNNNN ve A W RW RW RW NOA BX 0 Bi ey ee Ge ee eee es eee GE eee 1 NO FP WN L 2 O x NPLS 1 NPLS NPLS 3 NPLS 4xNPLS 5 NPLS 5 NPLS 5 NPLS 5 NPLS 5 NPLS 5 NPLS Geometrical data INDGRD 6 option LEVGEO 1 or LEVGEO 2 RSURF RWK 6 5 NPLS NAI EP RWK 6 5 NPLS NAI EL RWK 6 5 NPLS NAI TR RWK 6 5 NPLS NA I PSURF RWK 6 5 NPLS NAI TSURE RWK 6 5 NPLS NAI LEVGEO 3 PGINTF RWK 6 5 NPLS NAI TSURE RWK 6 5 NPLS NAI LEVGEO 4 TRINTF RWK 6 5 NPLS N TSURE RWK 6 5
69. mode is obtained by setting the flag NTMSTP of block LIA to negative values Stationary results in this time dependent mode are obtained by launching all test flights at time tp but scoring snapshot tallies not only at t t tp DTI MV but also at tg to 2 DTIMV t to 3 DTIMV i e at all times t tp n DT IMV until the flight terminates If the source distribution and the background medium parameters are constant in time then the snapshot score contribution from time t can be interpreted as score at t resulting from the source at earlier time t i 1 DTI MV Hence this stationary snapshot score at t is in fact an integration over all contributions from earlier times t lt to When scaling the time snapshot tallies at t in this stationary mode to absolute units then an extra multiplicative factor DT MV e the time interval between subsequent scores along a particle history is applied for snapshot tallies because the stationary time averaged volume averaged tallies are scaled interpreting the stratum source strength FLUX as flux atomic particles per second whereas the snapshot tallies require this same scaling factor FLU X to be the absolute number of atomic particles flux integrated over one time interval from to tot to DTIMV Further considerations regarding the scaling factors for volume averaged tallies in EIRENE with respect to dimensionality of phase space of the p
70. modname Later in input block LE a local reflection model block with that name modname must be included This option allows quick changes of particle surface interaction parameters affecting many surfaces at once by changes in just one location of the input file SURFMOD_modname Meaning of the Input Variables for non default standard surfaces NSTSI Total number of non default standard surfaces that do not act as prescribed by the default transparent standard co ordinate surface model TXTSFL Text to characterize a surface name of the surface on the printout file ISTS irrelevant labelling index IDIMP flag to identify mesh from which this particular surface is chosen surface from the x radial standard mesh RSURF Note that for the unstructured grid options NLTRI and NLTET i e for the 2D triangular grid option or for the general 3D grids of tetrahedra all surfaces are referred to as Ist grid x or radial surfaces by abuse of language 2 surface from the y poloidal standard mesh PSURF 3 surface from the z toroidal standard mesh TSURF INUMP Number of the surface in mesh RSURF PSURF or TSURF respectively IRPTA IRPTE Only a subregion of the surface acts by the non default options specified for this particular surface This subregion is defined by these flags If JMP is a surface from the first mesh then IRPTA2 IRPTE2 and IRPTA3 gt IRPTE3 are the surface index
71. neutral velocity becomes negligible after integrating ov Vre over solid angle which would vanish indeed exactly if o x 1 Upet The velocity of the impacting ion is sampled consequently from a drifting isotropic and mono energetic distribution J weighted by o v e V e with vre the relative velocity between the two collision partners i e the sampling distribution fincx for the velocity v of ions going into a CX event depends on the pre collision test particle velocity vo as well and is finox VI vo 1 Nox o Uret Ure filvP 4 3 were the normalisation constant Nox is the rate coefficient o upel Ure Eo fi Alternatively to the weighting mentioned above a rejection method can be used to avoid the weighting and still simulate the same collision integral Currently this rejection method for each individual collision process is based upon pre evaluation initialisation phase of a run of the product o E e1 Vre in the hard wired energy range 0 1 to 1 e4 eV determination of the the maximum SGVMAX lt of that product in this energy range Then during the test 124 particle tracing a comparison on the fly and rejection if appropriate of the actual value of this product with Ranf x SGVMAX Ranf being a uniformly distributed random number If the relative collision energy of the incident test particle and the sampled bulk collision partner happens to fall outside this energy range for rejection then rej
72. no 4 xxx 34 Data for Non default Standard Surfaces NSTSI DO 31 STSI 1 NSTSI unless otherwise stated N NLIM ISTSI is the index of the following surface data for surface ISTSI TXTSFL ISTS IDIMP INUMP ISTSI IDIMP RPTA1 IRPTE1 IRPTA2 IRPTE2 IRPTA3 IRPTE3 LIIN ILSIDE ILSWCH ILEQUI ILTOR ILCOL LFIT ILCELL ILBOX ILPLG optional for non transparent surfaces ILIIN gt 0 The next 3 or 4 lines comprise the block for local particle surface interaction data in an alytic terminology the boundary condition at this surface element If they are omitted the default particle surface model is activated for this particular surface element see section LA 92 LREF LSPT SRS ISRC ZNML EWALL EWBIN TRANSP 1 N TRANSP 2 N FSHEAT RECYCF RECYCT RECPRM EXPPL EXPEL EXPIL RECYCS RECYCC SPTPRM this line may be omitted then default sputter model see ref sec2 6 31 CONTINUE also optional for non transparent surfaces ILIIN gt 0 and alternative to the local surface interaction data block mentioned above read a surface interaction model identifier to link one of the surface local reflection models defined in block La below to this current surface The presence of such a link is identified by the string SU RF MOD followed by a name
73. often neglect explicit time dependence in the equations describing the neutral particles This is done in most appli cations The extension to time dependent problems is rather straight forward and the proce dure in the EIRENE code for such cases is described in L7 below For stationary time independent problems the scalar transport flux angular flux where O x v f r v i 1 6a is sometimes used as dependent variable in preference to the distribution f z In particular for stationary O Ot 0 and force free F 0 problems as e g often encountered in linear transport theory such as neutronics radiation transport neutral particle transport in plasmas etc the transport equation then reduces to the more compact form VrO r v t Xlr v O r v Q x v t pee C t v gt v r v d lo Alternatively in computational domains with non vanishing collisionality i e if X x 0 everywhere the pre collision density W is used i e P x D a P x n x gt F x X Llr E Q i nlr 0 7 v 1 2 where again the macroscopic cross section is the total inverse local mean free path di mension 1 length and v is the collision frequency dimension 1 time This cross section can be written as a sum gt gt 4 over macroscopic cross sections for the different types identified by the index k of collision processes Further details about this macroscopic cro
74. replacement an individual particle which is on census may be sampled more than once or not at all with the likelihood for these events given by its weight warm restart This census array is either defined at the end of the previous time cycle in the same run subr TMSTEP or it is read from an earlier run from stream 15 via a call to subr RSNAP from subr INPUT in the initial phase of the run for the very first time cycle continuation of an earlier sequence of time cycles If NPTST 0 then NPTST is reset to IPRNL IPRNL is the the number of scores on the census array in the previous time cycle If NPTST lt 0 then NPTST is reset to IPRNL and the random sampling from the census array is now replaced by a one to one re launch of all particles from the census array without random sampling cold restart This option is currently used for the NLMOVIE option only movies of trajectories and leads to other modifications of the run parameters Automatically then internally NUMOVIE TRUE Default NPTST 0 NTMSTP Total number of time steps for particle tracing Each trajectory can score on census up to NTMSTP times Particle trajectories are stopped after NTMSTP time steps Default NTIMSTP 1 For convenience and by abuse of language we refer to the 3 dimensional hyper surface t tn of the four dimensional r t space as time surface and hence tallies evalu ated at fixed time t snapshot tallies
75. sheath acceleration and this increased energy comes from an additional speed component V normal towards the target surface The sheath acceleration ESH EAT Z A Te is computed from the sheath voltage A where Z is the electric charge of the sampled particle at birth point Z 0 for neutral par ticles The sheath potential drop A is given by equation in section unless overruled by parameter Sh gt 0 see ZY in which latter case ESH EAT Z Sh Te If Sh lt 0 and the sheath potential according to equation amp Z amp cannot be found either e g because V ip 0 then Sh FSHEAT MSURF the input sheath parameter for source surface no MSURF input blocks 3 and 6 is used 166 2 8 Additional Data for some Specific Zones General remarks Input data in this block permit explicit specification of plasma parameters Te Ti Di Vz Vy Vz and of zone volumes VOL in selected cells ICELL Furthermore information may be given to the geometrical block of EIRENE that some additional surfaces are invisible for a particle located in cell ICELL and therefore possible crossings need not be checked for advancing this particle at the next step Intelligent use of this option can lead to a considerable speeding up of the code less intelligent use will lead to dramatic errors All this information will be included in the EIRENE arrays after the initialization phase Subroutines INPUT PLASMA GRID VOLUME and b
76. the geometrical parameters for particle tracing and scoring of tallies are trans ferred from outside e INIUSR initialize user specified geometry block see B amp I e LEAUSR x return cell number for any given position x see e TIMUSR flight time to next cell boundary and next cell number or surface number see B amp A e VOLUSR volume of each grid cell see e NORUSR outer surface normal for any given position on a surface see In case NLGEN only a reduced set of the standard EIRENE options is available and the five user routines mentioned above and described below may have to be supplemented by some further options from the problem specific segment USER F Input block 5 only the INDPRO 3 5 and 6 options are available INDPRO 3 provides constant profiles same value in each cell Hence in case of non constant background parameters one has to resort to subroutine PROUSR INDPRO 5 or to the code seg ment INFCOP INDPRO 6 for coupling to another source code for the data of the background medium Input block 7 only the point source option is available In case of surface sources or volume sources the subroutine SAMUSR has to be called see BA Input block 11 only the printout options are available no graphics output options are avail able However subroutine PLTUSR LOG J is called from the 2D geometry plotting routine PLT2D LOG TRUE J number of surface to be plotted and from the 3D geometry plotting rou
77. the grid points or be properly rescaled in case of time dependent applications 17 1 2 1 The Green s function concept We return to Equation 2 11D where the function F v i r gt r was defined For a finite domain see ZIJ and introducing again the shortcut for r LQ v i this becomes l F l exp i ds x s x L lt lmas 2 15 0 l gt lmaz This function F is the Green s function of the left hand side the convective part of the transport equation to be written 18 1 3 Monte Carlo solution of equation 1 A statistical solution to equation LI is straight forward because it is formulated in proba bilistic terms as follows A discrete Markoff chain is defined using Q as an initial distribution and L T C order of C and T reversed compared to K as a transition probability Histories w from this stochastic process are generated according to w 0 1 2 En where x a for all j gt n and x Za for alli lt n with x being the first state after transition into the absorbing state za Xo denotes the initial state distributed as described by Q Thus the length n of the chain w is itself a random variable A random sampling procedure to generate such chains is carried out in Monte Carlo codes by converting machine generated pseudo random numbers amp Eiz into random numbers with the distributions Q T and C Having computed N chains w i 1 2
78. the one speed transport problem Major applications of EIRENE are in connection with plasma fluid codes in particular with the various versions of the B2 code M The semi implicit iterative coupling method of B2 EIRENE 2 B and it s implementation code segment EIRCOP are also described Foreword to 2nd edition The first edition of this EIRENE code user manual was published as KFA report JUL 2599 in March 1992 It basically was a collection of my notes on the meaning of the various input data options for EIRENE Over the years too many such input flags had accumulated to memorize the meaning of each individual one Since the EIRENE code became a quite popular tool also for many other users it was decided to provide these notes as a kind of user s manual in a somewhat completed and edited form In the meantime the distribution of the EIRENE code has become even wider and it seems timely to update the previous manual although most of it s content is still a relevant source of information for a user of the code Apart from several minor corrections e g of spelling errors and unclear language the major new features as compared to the previous edition are the following time dependent mode snapshot estimators section 2 13 internally consistent I integral approach for coupled neutral kinetic plasma fluid simulations partially disabled again shortly after its implementation because of oscil latory beha
79. to the overall residuals of a B2 run These are printed from IF 4COP together with the overall balances of a coupled run TRCBAL t rue Hence if the B2 estimated residuals are of the same order as these statistical noise residu als then a further convergence of the combined code can only be achieved by increasing the CPU time for EIRENE Otherwise The coupled B2 EIRENE run has failed to converge to the solution within the statistical noise This is also represented by the convergence measure of saturated residuals 236 Chapter 5 Default EIRENE tallies and selected Modules 5 1 Tables of EIRENE tallies The following three tables comprise the EIRENE tallies The term tally is adopted from neutron transport applications a more precise terminology would be response see section BJ Because of the new type of particle introduced during 2002 photon gas ITYP 0 the numbering of tallies has changed significantly Therefore the tables are given below once for the current EIRENE version 2002 and younger and once for the versions older than 2001 A further change in tally numbering and naming conventions has been carried out in early 2014 and this affects the surface sputter tallies and those surface tallies in the list after the sputter tallies These latter revisions are described in table 6 4 and only for that section of the surface tally list that has been affected Each volume averaged res
80. transparent surface ILIIN gt 0 semi transparent The probability for passing through the surface is TRANSP Hence the probability for reflection re emission etc is 1 TRANSP Default 0 0 i e fully reflecting surface Irrelevant for transparent surfaces TRANSP 2 Semi transparency for particles incident from the negative side on a non transparent surface Default 0 0 i e fully reflecting surface Irrelevant for transparent surfaces FSHEAT surface sheath potential factor The sheath potential is FSHEAT Te with Te the electron temperature at the point of incidence This sheath potential is applied if ions test ions or bulk ions hit a non transparent surface If FSHEAT lt 0 0 then a sheath potential computed from the local background plasma flow conditions is used function SHEATH assuming ambi polar flow a Boltzmann distribution for electrons and zero secondary electron emission See section L5 In case of zero undefined background plasma flow velocity at the place of incidence a default of FSHEAT 2 8 is used corresponding to Te T and a single ion species D plasma flowing at ion acoustic speed parallel to the B field into the sheath 145 Default FSHEAT 0 0 RECYCF RECYCT Multiplier for reflection probability RPROBF Particles can be re emitted from surfaces by either the fast reflection model or by a thermal emission model Flag RECYCE controls scales the fast particle reflection
81. user supplied Subroutine SAMUSR is called to sample all 3 initial co ordinates X0 Y0 Z0 see section BA If SORLIM gt 0 then the preprogrammed option is used SORIND identifies volume recombination reaction IRRC for bulk plasma species IPLS as specified in input block 5 reaction decks for bulk ions E g to distinguish between effects from three body radiative and di electronic recombination SORIND KREC IRRC If more than one recombination process is specified for bulk ion species IPLS then IRRC is the number of one particular such process counted by the sequence of input in input block 5 See printout activated by the TRCAMD flag block 11 for the correct value of IRRC in case of doubt In case SORIND 0 the sum over all relevant IRRC for the selected background species IPLS is taken as recombination source for IPLS Only for EIRENE version 2001 or younger Note Both the source strength FLUX and the relative weight of subregions if any SORWGT are automatically determined from the volume source data on the atomic data array TABRC1 IRRC ICELL SORAD1 parameter for user supplied sampling routine SAMUSR SORAD2 parameter for user supplied sampling routine SAMUSR SORAD3 parameter for user supplied sampling routine SAMUSR 160 SORAD4 parameter for user supplied sampling routine SAMUSR SORADS5 parameter for user supplied sampling routine SAMUSR SORAD6 parameter for user supplied sampling routine SAMUSR
82. variable e g polarization in case of radiation transport fi v fi l v whichever is more convenient As noted above further generalizations to include particle splitting absorption or fragmen tation into more than two post collision products are straight forward but can more conve niently be formulated in the C collision kernel formulation introduced above and used below to relate the transport equation to a Markovian stochastic discrete time process 1 2 The linear integral equation for the collision density Y By formally integrating the characteristics for Ld the same transport equation can also be written in integral form This formal procedure is outlined below in paragraph LZI The resulting integral equation is often most conveniently written for the collision density Y LZ rather than for transport flux U x S x fawno K a gt 2 1 1d This equation has the general form of the backward integral equation of a Markovian jump process and it is therefore particularly well suited for a Monte Carlo method of solution The formal relation between the integro differential form LIQ and this integral form is very 14 useful to generalize the Monte Carlo procedure e g to time dependent equations and to Boltzmann Fokker Planck equations which contain diffusive contributions or diffusive ap proximations for some processes in addition to the jump processes described by the Boltz mann collision integral
83. x exchanged I e now the x coordinates of the points P P gt are the boundaries of the surface ay bz c 0 in x direction 2 8 Complement to RLBND 2 7 3 plane triangle defined by the corners P P2 P3 P P1 1 P1 2 P1 3 P P2 1 P2 2 P2 3 P3 P3 1 P3 2 P3 3 3 5 complement to RLBND 3 only The plane surface outside the triangle is seen by the test particles 4 plane quadrangle surface inside the polygon Pi Po Pa P3 Pi Here P P2 P3 are as in the RLBND 3 option and P4 P4 1 P4 2 P4 3 Thus this surface is the union of the triangles with vertices P Pz P gt and P gt P4 P respectively 4 5 complement to RLBND 4 only the part of the plane surface outside the quad rangle is seen by the test particles 5 plane quint angle surface inside the polygon Pi Po Pa Ps P3 Pa Pi Po P3 Pa as RLBND 4 and P P5 1 P5 2 P5 3 5 5 complement to RLBND 5 only the part of the plane surface outside the quint angle is seen by the test particles RLBND lt 0 KL The surface is bounded by L linear inequalities and by K second order inequalities ALIMS XLIMS x YLIMS y ZLIMS xz lt 0 L inequalities ALIMSO XLIMS1 x YLIMS1 y ZLIMS1 z XLIMS2 x YLIMS2 y ZLIMS2 2 XLIMS3 xy YLIMS3 2z2 ZLIMS3 yz lt 0 K inequalities The meanings of the input variables for the local reflection model are described below see Z8 Input Data for Surface Interaction Models The meanin
84. 1 1 _ 5 82 the latter equality 82 follows after insertion of 80 into the former If we let furthermore the net electrical current be zero jp 0 and zero secondary electron emission Ys ee 0 we then find the classical result 1 27Me Ti eA kT smf F F 1 Hence e g for a pure hydrogen plasma and for Te T we have eA kT 2 5 and 2 84 for a pure deuteron plasma 42 1 5 3 The magnetic pre sheath In most situations when EIRENE is applied to plasma surface interaction studies the ion plasma flow velocity V is predominantly parallel to a B field Vj V and it is this par allel ion flow velocity which is usually available from CFD plasma simulations via boundary conditions specified for the momentum balance equation at the entrance of the magnetic pre sheath M P rather than at the entrance of the electrostatic sheath S The sheath model of EIRENE then is supplemented by a model PRE SHEATH for the tran sition of currents and V mp to V s i e in particular to derive the currents j and flow components V 5 entering the electrostatic sheath from jmp and V wp to be written 43 1 6 Combinatorial description of geometry EIRENE is a Monte Carlo Code Defining geometry in a Monte Carlo code is complex and laborious Of the three typical options for definition of the target geometry in Monte Carlo Codes e Constructive solid geometry CSG e boundary represe
85. 1 n2 to m2 are considered invisible for a particle located on this current surface ILIMI Intersection of trajectories starting from surface ILIMI with those invisible surfaces is not checked CH2 ILIMI n1 m1 n2 m2 Only for second order surfaces ILIMI nl m1 The first of the two possible intersections is ignored for particles located on surface no ILIMI General Data for Surfaces RLBND flag for different options to define the boundary of the surface RLARE Area in cm of the surface element which is seen by the test particles Default 666 0 needed only for scaling of non default surface averaged tallies If RLARE is not specified here i e if a value less than or equal to zero is read then EIRENE tries to evaluate this area itself For some surfaces this is still not possible automatically RLWMN lower weight limit for space weight window for particles crossing the surface in positive direction not in use RLWMX upper weight limit for space weight window for particles crossing the surface in positive direction not in use ILIIN defines the type of surface gt 0 non transparent surface 1 reflecting partly or purely absorbing surface local reflection model has to be specified unless default model is to be used all surface tallies see Table 6 3 are updated and a switch can be operated 2 purely absorbing surface surface tallies for incident fluxes i e POT and EOT tallies in Table 5
86. 1 10 Radiation transport photon gas simulations The extensions of EIRENE towards radiative transfer problems and also the material in this present short description is largely based on the monograph by Oxenius Z4 The theory of light and its interaction with matter is one of the best that physics can offer and can predict virtually every observed phenomenon with great accuracy Feynman 1985 QED The strange Theory of Light and Matter Princeton University Press Princeton In our sim ulations of radiation transport with the EIRENE code we assume a geometric optics model i e essentially particle theory of light which is sufficient for all our purposes Light is emitted scattered reflected and absorbed but moves on straight lines between these events I e a continuously varying index of refraction is not allowed and we ignore most properties of light that depend on a wave or quantum model for their explanation e g diffraction or interference However the linear wave optics phenomenon of polarization and the linear quantum optics phenomenon of fluorescence absorption of a certain wavelength line and re emission at another wavelength line can be added to our linear geometric optics model We are concerned with the kinetic theory of interacting particles and photons where the be haviour of each species is governed by a kinetic equation the kinetic equation for photons being nothing else but the well known equation of r
87. 12 4 Line of sight charge exchange spectrum Line of sight line emissivity Line of sight line shape Line of sight user defined integral 194 2 13 Data for nonlinear and time dependent Options General remarks The data in this block are used to define a discretisation in time and the test particle self interaction effects These latter options are based upon the Bird s Direct Monte Carlo Sim ulation DMCS procedure and are currently not in use see Z3 for a detailed description of its implementation in EIRENE They can be activated by replacing the current dummy routine STOSS which is called after each time step from subroutine EIRENE by a routine that reads the particle population from the census arrays described below and which then carries out the binary self collisions modification of the individual particle velocity vectors The rest of the code for time dependency and the DMCS algorithm is the same and described in this section Note that currently with the use of a dummy routine STOSS non linear self collision effects can still be simulated in BGK approximation by using the iterative mode of operation NITERI NITERE input block 1 see section LA As for the time dependence options it is important to note that there are two kinds of time steps One is the so called time cycle Each time cycle is a more or less complete EIRENE run in its own even if several NTIME see section L I such time cyc
88. 2 M 9 RECYCC is a free model parameter which can be used in the user supplied sputter model for any particular surface element Default RECYCC 1 SPTPRM_ free model parameter for user supplied sputtering models N 3 M 3 Default SPTPRM 0 Note All data in a block for local reflection data are in general independent of the type and species of the incident particle Some are however copied identically NPHOTI NATMI NMOLI NIONI NPLSI times onto appropriately dimensioned arrays with the same names This is currently done for the parameters ISRS ISRC TRANSP 1 TRANSP 2 RECYCF RECYCT RECPRM EXPPL EXPEL EXPIL RECYCS RECYCC SPTPRM The first index is the species index the second index is the surface number Overwriting local reflection data for some specific incident particle species can be done via a call to the entry RFOUSR of the user supplied reflection routine REFUSR This entry is called in the initialization phase of an EIRENE run from subroutine REFLEC Likewise the entry SPOUSR of the user supplied sputter routine SPTUSR is called in the initialization phase from subroutine SPUTER For further details on user supplied surface interaction routines see section For example RECYCT 3 5 is the recycling coefficient for incident species 3 onto surface no 5 If surface models are defined in input block 6 by the SURFMOD_modname label rather than individually for each surface in blocks
89. 22 D Reiter Chr May M Baelmans et al J Nucl Mat 241 243 342 1996 23 Th Behringer Einflu nichtlinearer Effekte auf den Neutralgastransport in Tokamaks KFA Jiilich Report J l 2637 Forschungszentrum J lich June 1992 Dissertation 24 Oxenius J Kinetic theory of particles and photons Springer Berlin Heidelberg 1986 25 W D Langer Nuclear Fusion 22 6 751 1982 26 D L Book NRL Plasma Formulary NRL Publication 0084 4040 Washington DC 20375 1987 27 Trubnikov B A Reviews of Plasma Physics Vol 1 Consultants Bureau New York 1965 28 D Reiser and D Reiter Nuclear Fusion 38 2 165 1998 29 D Reiser Zur Anwendung der driftkinetischen Theorie in Monte Carlo Studien zum Verunreinigungstransport in Tokamak Plasmen KFA Jiilich Report J l 3508 Forschungszentrum Jiilich February 1998 30 T Takizuka and H Abe Journal Computational Physics 25 205 219 1977 31 R K Janev W D Langer K Evans Jr et al Elementary Processes in Hydrogen Helium Plasmas volume 4 of Springer Series on Atoms Plasmas Springer Verlag 1987 32 A B Ehrhardt and W D Langer Collisional processes of hydrocarbons in hydrogen plasmas Princeton report PPPL 2477 PPPL September 1987 33 D Reiter Atomic and Plasma Material Interaction Processes in Controlled Thermonu clear Fusion Elsevier Science Publishers 1993 34 Gordeev et al Pis ma Zh Ehksp Teor Fiz 25 223 1977
90. 251 35 A Nicolai and D Reiter J Comp Phys 55 1 129 153 1984 36 Nuclear Fusion Special issue 1984 Data Compendium for Plasma Surface interactions 37 W Eckstein Garcia Rosales C J Roth et al Sputtering data MPI Garching Report IPP 9 82 MPI Garching February 1993 38 J Roth and C Gracia Rosales Nucl Fus 36 12 1647 1996 39 J Roth J Nucl Mater 266 269 51 57 1999 40 S H Miiller et al Plasma Phys Control Fusion 51 105014 2009 252
91. 3 Tl 92 VYDENPL momentum density y direction Photons NPHOT g cm s cm 3 Tl 93 VZDENA momentum density z direction Atoms NATM g cm s cm 3 Tl 94 VZDENM momentum density z direction Molecules NMOL g cm s cm 3 Tl 95 VZDENI momentum density z direction Test Ions NION g cm s cm 3 Tl 96 VZDENPL momentum density z direction Photons NPHOT g cm s cm 3 Tl 242 Table 5 2 continued No Name Macroscopic quantity 1 Dim Units Estim 97 MAPL parallel momentum source rate Bulk Ions NPLS amp g cm s cm 3 TPM 98 MMPL parallel momentum source rate Bulk Ions NPLS amp g cm s cm 3 TPM 99 MIPL parallel momentum source rate Bulk Ions NPLS amp g cm s cm 3 TPM 100 MPHPL parallel momentum sources rate Bulk Ions NPLS amp g cm s cm 3 TPM Note Source means if the sign is positive it is a gain for the specified type of particles if it is negative it is a loss The specified type of particle is coded by the last two letters of the name of a tally AT ML IO EL PL PH respectively as well as by the corresponding 1st dimension species NATM NMOL NION NPHOT NPLS and 1 one for electrons e g MAPL parallel momentum source sink for bulk particle plasma background due to atom plasma interactions Estimators EIRENE resorts by default to tracklength estimators G 19 Default tallies are updated scoring in routine U
92. 38 T m 6 6 If the surface area is given in m S in m s then the numerical factor becomes 36 38 Note the first two factors define an effective exposed area A across which particles with a thermal velocity would be removed The remaining factors are the thermal effective velocity of particles lost across this area 5 A vp volume time The pump throughput pumped flux mass flow rate Q is the product of pressure P in front of surface A and pumping speed S Qpump P S and for a given type of gas m and gas temperature 7 the pump throughput is given e g in flux units 1 s or Amp or as mass flow with dimension pressure times volume per time The temperature 7 and type of gas given by m are part of the specification of S e g to be found from the technical specification of the pump may also depend on the pressure for some pumps S S P T m However in the molecular flow regime S may often assumed to be a constant independent of pressure for a given temperature and type of gas But normally even in this case the specified pumping speeds S for vacuum pumps do not follow the T7T m dependence in equation 6 6 for different types of gas E g pumping speeds for H vs He of real pumps for same temperatures are usually not simply related by a factor 1 2 and those for Dy and He may not be identical either In a simulation of a gas mixture then a species dependent flag RECYCT to produce a specie
93. 4 TI5 1 NPLS ENDIF F INDPRO 3 LE 5 THEN DIO I DI1 I DI2 1 DI3 I DI4 DI5 1 NPLS ENDIF F INDPRO 4 LE 5 THEN VXO I VX1 I VX2 I VX3 I VX4 I VX5 1 NPLS VYO I VY1 I VY2 1 VY3 I VY4 1 VY5 1 NPLS VZO I VZ1 I VZ2 I V2Z3 1I VZ4 VZ5 1 NPLS ENDIF F INDPRO 5 LE 5 THEN BO Bil B2 B3 B4 B5 ENDIF F INDPRO 12 LE 5 THEN VLO VL1 VL2 VL3 VL4 VL5 ENDIF Currently option INDPRO 6 and INDPRO 7 are not available for cell volumes input tally no 12 Meaning of the Input Variables for Plasma Parameters The meaning of the variables in the bulk ion species cards is as in block 2 4 for the test particle species cards specified there New options since 2003 However after the ID3 flag there may be 2 additional input flags only for Eirene2o93 and younger oS ine CDENMODEL NRE Format 1X A10 1X 12 These flags if included control additional options to set the density temperature and flow field of the selected species IPLS If the string CDENMODEL is found here for a species IPLS then after reading the species and reaction cards for IPLS one default or NRE further input cards are expected CDENMODEL Multiply docu to be written CDENMODEL Constant docu to be written CDENMODEL fort 13 Read data for this species from file fort 13 The additional card only one reads format 216 SP TP 131 ISP is the number of
94. 4 1 The Behrisch matrix reflection model One model the matrix model due to Behrisch L8 is hardwired in EIRENE and in many other codes such as AURORA BALDUR TRANSP This model has been used as a standard option in many benchmarks L The model is based upon a table of values for Cp E and a stochastic matrix B for the transition E E for H atoms striking a stainless steel target 33 at normal incidence For other incident angles V n the moments are modified in EIRENE by the relations Cp Bin 1 1 Cp cos Bin 4 58 and Ce Vin 1 1 Cp lt cos Vin 4 59 This latter moment equation can be satisfied by modifying the tabulated stochastic matrix B E E in many different ways In EIRENE we first sample E from B given E and then set E F E E cos Vin 4 60 The linearity of E in gives an expectation value E with E E Cp 0in Ce Vin with Cp and Cp as given by equations 58 and 4 59 respectively To describe the angular distribution of re emitted particles let ez y define an orthonor mal basis at the strike point of a test particle on a surface Here let e be the unit vector parallel to the outer surface normal and let the incident particle travel in the local xz plane Furthermore let V and p be the polar and azimuthal angles sampled from a cosine distribu tion around e The speed unit vector Q of the reflected particle in EIRENE
95. 7 NHD3 5 NHD4 NCHEN DY NFL ONS NPLS NALS NRPI NHD4 5 NHD5 5 NAI NH D6 C 1 IGJUM FLAGS FOR SPEEDUP OF GEOMETRICAL CALCULATIONS C C NOPTIM REDUCES IGJUM3 ARRAY IGJUM3 NOPTIM NLIMPS C NOPTIM N1ST N2ND N3RD NADD NO STORAGE OPTIMIZATION C SPEEDUP OF GEOMETRICAL C CALCULATIONS IS POSSIBLE C BY CH3 FLAGS C NOPTIM 1 MINIMAL STORAGE NO SPEEDUP OF C GEOMETRICAL CALCULATION C DEFAULT PARAMETER NOPTIM C C NOPTM1 BIT ARITHMETIC INTEGER E G 32 FOR IBM RISK 46 FOR CRAY C DEFAULT NOPTM1 1 NO STORAGE OPTIMIZATION C DEFAULT PARAMETER NOPTM1 C 2 EXTERNAL GEOMETRY C NGEOM_USR 1 gt EXTERNAL GEOMETRY ROUTINES USR LEVGEO 10 C NO STORAGE FOR GEOMETRY DATA IN EIRENE C NGEOM_USR 0 gt ELSE NO STORAGE OPTIMIZATION C DEFAULT PARAMETER NGEOM_USR C C 3 SUM OVER STRATA C NSMSTRA 0 gt SUM OVER STRATA IS NOT PERFORMED C NSMSTRA 1 gt SUM OVER STRATA IS PERFORMED C DEFAULT PARAMETER NSMSTRA C C 4 CALCULATION OR STORAGE OF ATOMIC DATA Cc C NSTORAM 0 1 2 8 9 0 MINIMUM STORAG
96. 9 EI 0 4 4 HYDHEL H 1 5 3 1 CX 4 4 5 HYDHEL H 1 6 3 1 CX 4 4 NEUTRAL ATOMS SPECIES CARDS NATMI SPECIES ARE CONSIDERED NATMI 2 1D 2 1 Or es 0 2 iE 115 14 O 00000 1 3600E 01 0 0000E 00 2 x14 111 x14 00000 0 0000E 00 0 0000E 00 0 0000E 00 2 He A 2a de G DB 22k Qe 33 3 115 x14 o 00000 2 4588E 01 0 0000E 00 4 x14 211 14 00000 0 0000E 00 0 0000E 00 0 0000E 00 5 xxx14 211 14 00000 0 0000E 00 0 0000E 00 0 0000E 00 Here x is the species index of the D bulk ion in input block 5 xx is the species index of the Het bulk ion in input block 5 and x is the species index of the Het bulk ion in input block 5 If a corresponding background species is not found in block 5 then the corresponding default process is de activated 123 Hence D and He atoms are ionized by electron impact using the Corona data 2 1 5 and 2 3 9 respectively from reference BI and with constant electron energy loss per ionization of 13 6 and 24 588 eV respectively D atoms also undergo resonant charge exchange with D ions utilizing the cross section data for reaction 3 1 8 loc cit The assumptions for processes labelled as CX are pure electron capture from the neutral by the ion exchange of identity in symmetric charge exchange scattering angle 7 in center of mass system zero exotermicity i e perfect conservation of kinetic energy before and after collision
97. ATES OF EMITTED PARTI CLE T AL LE USER SUPPI F iD REFLECT ON MODEL ENTRY RFOUSR DEFINE SPEC ES DEPEN DENT RECYCL NG COEFF C ENT HERE RECYCT 1 RETURN SPZ MSURF ENTRY RF LUSR XMW XCW XMP XCP IGASF IGAST ZCOS RPROB EOTERM RETURN RETURN E IRENE STANDAR THERMAL MOLECULE D ANG ULAR ZS N EXP DISTR BUTION MODEI RETURN RETURN A wN RETURN THERMAL ATOM MODEL DEP DEP ON ON IGAST IGAST ABSORB PARTI CLE AT THIS SURFACE T AL ZE USER SUPPLI ENTRY SPOUSR E D SPUTTERING MODEL DEF NE SPEC ES DEPEN DENT PHYS DEP ON EXPI EOTERM EOTERM RECYCS ANI SPZ MSURF D ALSO CHEMICAL SP RECYCC SPZ MSURF UTTERING COEFF CAL SPUTTERING COEFF C ENT HERE C ENT ENTRY SP1USR RETURN END 223 3 4 The user source sampling routine SAMUSR General remarks This subroutine is called from the point source sampling routine SAMPNT the surface source sampling routine SAMSRF or from the volume sampling routine SAMVOL if the flag SOR LIM N ISTRA input blo
98. Acts as if both NFILE K 1 and NFILE K 2 J 1 Only for time dependent option see block 13 EIRENE writes census data at the end of last time step onto file FT15 J 2 EIRENE reads census data from file FT15 and uses it as initial distribution for the coming next time step 75 J 3 Acts as if both NFILE J 1 and NFILE J 2 NITERO Initial iteration number Default NITERO 1 Irrelevant parameter Only needed for book keeping and printout EIRENE labels the iterations from NITERO to NITER NITER Number of iterations if EIRENE runs in iterative mode gt 0 EIRENE calls user supplied subroutine MODUSR after completing the run some model parameters may be modified here for the next iteration step and some results from the previous step may be saved on a file gt 1 EIRENE recalls itself but does not read from the formatted input file again This recalling is repeated NITER times including the first iteration The CPU time NTCPU is used for each iteration Hence the true CPU time then is NTCPU NITER NTIMEO Initial time cycle number default NTIMEO 1 Irrelevant Only needed for book keeping and printout EIRENE labels the time steps from NTIMEO to NTIME NTIME Total number of iterations cycles in time carried out in one single run The total time per cycle is defined as NTMSTP DTIMV see below input block 13 After each time cycle the subroutine TMSTEP is called In this routine the census arrays
99. B total number of additional EIRENE surface tallies transferred to B2 code e g in order to allow re scaling in B2 such that total number of particles neutrals and ions is conserved NAOTS not in use NAOTT not in use 2 14 2 Version B2 EIRENE 2000 and younger The first thing to note is that due to introduction of photons as a forth type of test particle for radiation transfer simulations the numbering of tallies source rates to be transferred from EIRENE into B2 has changed For example the particle source rates PAPL PM PL PIPL are now default EIRENE tallies listed in Table 5 2 in section ELI rather than in Table 5 4 e PAPLis the particle source for background plasma species ipls resulting from atom plasma interactions summed over all EIRENE species of type atom tally no 14 e PM PLis the particle source for background plasma species ipls resulting from molecule plasma interactions summed over all EIRENE species of type molecule tally no 20 e PIPL is the particle source for background plasma species ipls resulting from test ion plasma interactions summed over all EIRENE species of type test ion tally no 26 206 Default tally no 32 might be added here as well once photo ionization processes are acti vated in an EIRENE run Analogous statements apply for the other source rates as compared to those described above in Z142 One further difference is that momentum so
100. B IPLS Hence IFLB lt NFLA otherwise error exit FCTE bulk ion density and flux multiplication factor The EIRENE bulk ion den sity and fluxes for species IPLS are obtained by multiplying the corresponding plasma code profiles for species IFLB IPLS with the factor FCTE This option is needed e g if the plasma code treats one ion species of mass 2 5 AMU while EIRENE treats D ions and T ions separately The drift velocity vector for all EIRENE species IPLS is set identical to the drift velocity of the plasma code species IFLB IPLS Only one common ion temperature is available from B2 B2 5 code runs even for multi species applications The bulk ion temperature TIINUPLS for all EIRENE species IPLS which are read from the plasma code data files i e for all species with IFLBUIPLS gt 0 202 lt 0 The plasma density flow field and temperature field for EIRENE species IPLS is read from the input stream fort I with II IFLB Currently only II 13 This file fort 13 must be available e g from a previous EIRENE run in which NFILEL 1 or NFILEL 3 options have been used to produce that file see input block 1 This option permits iteration on some species which are not treated in the plasma code e g for neutral neutral interactions The corresponding bulk ion species IPLS in EIRENE has zero density i e bulk ions of this species are not present in this EIRENE run Note the issue re electron density and qua
101. BLM_ Global particle and energy balance for molecules is printed TRCBLI Global particle and energy balance for test ions is printed TRCBLP Global particle and energy balance for bulk ions is printed TRCBLE Global particle and energy balance for electrons is printed TRCBLPH Global particle and energy balance for photons is printed TRCTAL Print list of activated and de activated tallies The default settings eliminate some tallies from storage and estimators which are likely to be irrelevant in a particular run e g all photon related tallies are deactivated automatically if no radiation trans fer calculation is included in a run These default settings are overruled by the flags NTLVOUT and NTLSOUT at the end of this sub block 11A see below TRCSRC ISTRA ISTRA 0 NSTRAI The selected global volumetric and surface crossing tallies are printed for those strata for which TRCSTRUSTRA TRUE In case TRCSTR O TRUE the results after summation over all strata is printed for these tallies Note printout for individual strata is only possible if the data for strata have been saved on file NFILE N 1 2 option input block 1 Otherwise only the last stratum currently on storage arrays mostly sum over strata is available NVOLPR Total number of volume averaged tallies to be printed NPRTLV Index of the tally to be printed first column in table ET or EJ If the tally has a species index it is printed for all species for which the in
102. Distribution in velocity space Together with a position and time ro to of a source particle also a specific vector C in velocity space is selected e g a surface normal vector for surface sources or a preferential direction of emission from a point source or volume source etc Let C Cx Cy Cz be this direction unit vector defined together with the point of birth of the test particle Furthermore a set of local background plasma data at the birth point ni ip r t Te 1 tp r t Vilip r t Filip r t Sh 7 9 for ion density electron and ion temperature ion flow velocity mean incident ion energy and target surface sheath potential respectively is either set in case of step function sampling FUNCTION STEP or provided in case of user source sampling SAMUSR i e if SORLIM lt 0 or computed from the known cell numbers and the input background tallies at the place of birth Depending upon the value of the flag NEMODS the following energy distributions f E ro to are available Note that f may also depend upon the input parameters SORENI SORENE SORVDX SORVDY SORVDZ and on the birth position and time ro to of the test particle via local plasma parameters Teala N T Vi and E may be different for different background ion species IPL The choice of IPL is described below digit K of the NEMODS flag Furthermore let Vy and V be the components of the velocity drift vector V normal and paralle
103. E MAXIMUM CALCULATION Cc 9 MAXIMUM STORAGE MINIMUM CALCULATION C DEFAULT PARAMETER NSTORAM C C 5 SPATIALLY RESOLVED SURFACE TALLIES C C NGSTAL 0 gt NO STORAGE FOR SPATIALLY RESOLVED SURFACE TALLIES C NGSTAL 1 gt SPATIALLY RESOLVED SURFACE TALLIES ARE COMPUTED C DEFAULT PARAMETER NGSTAL Meaning of the Parameter Variables and Defaults N1ST Maximum number of standard mesh points in x radial direction block 2a N2ND Maximum number of standard mesh points in y poloidal direction block 2b N3RD Maximum number of standard mesh points in z toroidal direction block 2c 214 NADD Maximum number of additional zones defined by the additional surfaces block 2d NTOR Maximum number of toroidal segments for approximation of torus by cylindrical segments block 2c NLIM Maximum number of additional surfaces block 3b NSTS Maximum number of non default standard surface models block 3a NPLG Maximum number of points in one polygon block 2a NPPART Maximum number of valid parts in one polygon block 2a NKNOT Maximum number of knots for mesh of triangles block 2a NTRI Maximum number of triangles block 2a NCOORD Maximum number of knots for mesh of tetrahedrons block 2a NTETRA Maximum number of tetrahedrons block 2a NSTRA Maximum number of strata sources block 7 NSRFS Maximum number of sub strata in one stratum block 7 NSTEP Maximum number of different step functions u
104. E see Section 2 2 These volume discretisation meshes VOXELS can be read into EIRENE from external files For example the mesh in B2 CFD plasma fluid code is read into EIRENE directly from the CFD grid gen erator in coupled B2 EIRENE applications Wall meshes are build from these by assigning a surface reflection model to some of the voxel surfaces Section 2 3 1l whereas internal grid surfaces remain transparent for flow of test particles Note added in 2008 An attempt has been made in 2008 to use CAD files directly for 3D wall surfaces This was done via the already existing CAD MCNP interface We had then tried to turn the CSG input for MCNP see above into a BREP form for EIRENE In principle this works But in practice the de tour via the CSG concept leads to prohibitively complex BREP input for EIRENE A direct CAD BREP interface seems now much more efficient to us and more natural any way and has meanwhile 2011 been established by an intermediate code step the ANSYS code which first converts CAD output into a triangulation of surface elements and then each triangle in 3D space is taken as additional surface BREP concept into EIRENE Very large sets of triangles required optimisation procedures which have also been implemented in EIRENE module timea f on the basis of OCTREE concepts adopted from ray tracing procedures used in image processing 44 A complete set of surfaces in an EIRENE geometry may consist of
105. E EQ 0 THEN NAINI NCOPI DO IAIN 1 NAINB NAINS IAIN NAINT IAIN TXTPLS IAIN 11 TXTPSP IAIN 11 TXTPUN IAIN 11 ENDDO ELSEIF NMODE NE 0 THEN LSYMET LBALAN NFLA NCUTB NCUTL MSHFRM NTRFRM NFULL DO 20 IPLS 1 NPLSI FLB IPLS FCTE IPLS BMASS IPLS 20 CONTINUE NDXA NDYA NTARGI NTGPRT IT IT 1 NTARGI DO 30 IT 1 NTARGI DO 33 IPRT 1 NTIGPRT IT x 198 NIFLG NPTC NSPZI NSPZE 33 CONTINUE 30 CONTINUE CHGP CHGEE CHGEI CHGMOM NAINB DO 40 IAIN 1 NAINB NAINS IAIN NAINT IAIN TXTPLS IAIN 11 TXTPSP IAIN 11 TXTPUN IAIN 11 40 CONTINUE NAOTB DO 50 IAOT 1 NAOTB NAOTS IAOT NAOTT IAOT 50 CONTINUE 2 14 1 Version B2 EIRENE 1999 and older B2 solves a set of continuum equations for electrons and ions and EIRENE solves a set of kinetic transport equations for other species not in the continuum description e g neutrals radiation trace ions In this case the EIRENE code provides volumetric particle parallel momentum and electron and ion energy sources Sn Smij S Fi Sze respectively from those kinetic species for the B2 continuum equat
106. EIML Energy Source Molecules from test ion plasma coll 1 watt cm 2 T34 35 EHO Energy Source Test Ions from test ion plasma coll 1 watt em 3 T35 36 EIPL Energy Source Bulk Ions from test ion plasma coll 1 watt cm T36 37 ADDV Additional volume av Tally Track length estimated NADV see UPTUSR TRL 38 COLV Additional volume av Tally Collision estimated NCLV see UPCUSR COL 39 SNPV Additional volume av Tally Snapshot estimated NSNV see UPSUSR SNP 40 COPV Tallies for coupling to ext code see Subr UPTCOP NCPV see UPTCOP COP 41 BGKV Volume averaged tallies for BGK self collision terms NBGV see BGK T41 42 ALGV Algebraic expression in volume averaged tallies NALV Input ALG 43 PGENA Generation limit Atoms NATM amp cm Tl 44 PGENM Generation limit Molecules NMOL amp cm Tl 45 PGENI Generation limit Test ions NION amp cem 3 Tl 46 EGENA dito Energy flux Atoms NATM watt cem 3 Tl 47 EGENM dito Energy flux Molecules NMOL watt em Tl 48 EGENI dito Energy flux Test ions NION watt em 3 Tl 49 VGENA dito momentum flux Atoms NATM as COP Tl 50 VGENM dito momentum flux Molecules NMOL as COP Tl 51 VGENI dito Momentum flux Test ions NION as COP Tl Note Source means if the sign is positive it is a gain for the specified type of particles if it is negative it is a loss 248 Table 5 7 Surface Averaged Tallies Output Common CESTIM
107. ELL g is assumed to be a constant in this cell in this example In more general cases when detector g varies along the track the product g is to be replaced by the line integral f g dl along this track 3 2 2 Collision estimated volume tallies UPCUSR The default collision estimated contributions R are updated in subroutine COLLIDE Sub routine COLLIDE is called from the particle tracing subroutines FOLNEUT and FOLION defaults Non default collision tallies are updated in UPCUSR WS IND additional user supplied tallies called from COLLIDE Here we have WS vE In EIRENE variables WS WEIGHT SIGTOT WEIGHT VEL ZMFP IND 1 indicates a call before sampling from the collision kernel and IN D 2 indicates calls with the parameters velocity weight of the particle emerging from the collision At each collision the subroutine UPCUSR is called once before and once after the collision Then in order to estimate a response for a detector function g on additional tally number ICOLYV a statement in subroutine UPCUSR should read 218 COLV ICOLV ICELL COLV ICOLV ICELL WS g Here g is evaluated at the point of a collision which is known to have taken place in cell ICELL in this call to subroutine UPCUSR We note that track length estimates ADDV reduce to collision estimates COLV if ADDV is updated at the points of collision only and if the EIRENE variable ZMFP local mean free path len
108. EPHAT Energy Source Atoms from photon plasma coll 1 watt em 3 T33 53 EPHML Energy Source Molecules from photon plasma coll 1 watt em 3 T34 54 EPHIO Energy Source Test Ions from photon plasma coll 1 watt em 3 T35 55 EPHPHT Energy Source Photons from photon plasma coll 1 watt em 3 T35 56 EPHPL Energy Source Bulk Ions from photon plasma coll 1 watt em 3 T36 57 ADDV Additional volume av Tally Track length estimated NADV_ see UPTUSR TRL 58 COLV Additional volume av Tally Collision estimated NCLV see UPCUSR COL 59 SNPV Additional volume av Tally Snapshot estimated NSNV see UPSUSR SNP 60 COPV Tallies for coupling to ext code see Subr UPTCOP NCPV see UPTCOP COP 61 BGKV Volume averaged tallies for BGK self collision terms NBGV_ see BGK T41 62 ALGV Algebraic expression in volume averaged tallies NALV Input ALG 63 PGENA Generation limit Atoms NATM amp cm T1 64 PGENM Generation limit Molecules NMOL amp cm T1 241 Table 5 2 continued No Name Macroscopic quantity 1 Dim Units Estim 65 PGENI Generation limit Test ions NION amp cm 3 Tl 66 PGENPH Generation limit Photons NPHOT amp cm Tl 67 EGENA dito Energy flux Atoms NATM watt cm 3 Tl 68 EGENM dito Energy flux Molecules NMOL watt em 3 Tl 69 EGENI dito Energy flux Test ions NION watt em 3 Tl 70
109. FWL NPLS WEISPZ NSPZ 224 l NITIALIZE SAMPLING FOR SUBSTRATUM ISR OF STRATUM ISTR ISR NUMBER OF SUBSTRATUM SEE INPUT BLOCK 7 ISTR NUMBER OF STRATUM ENTRY SMOUSR RE ENTRY SM1USR TURN ISR istr soradl sorad2 sorad3 sorad4 sorad5 sorad6 TSR X0 10 20 SORAD1 SORAD2 SORAD3 SORA D4 SORA D5 SORAD6 IRUSR IPUSR ITUSR IAUSR IBUSR TIWL TEWL DIWL VXWL VYWL VZWL EFWL SHWL WEISPZ FIND BIRTH POINT COORDINATES SUBSTRATUM ISR IF STRATUM ISTRA HAS ALREADY BEEN IDENTIFIED ISTRA IF NEEDED IS IN MODULE COMPRT NITIALIZE THOSE VARIABLES WHICH ARE NOT SET BELOW XO 0 _DP Y0 0 _DP Z0 0 _DP IRUSR 0 IPUSR 0 ITUSR 1 IAUSR 0 IBUSR 1 TEWL 0 _DP SHWL 0 _DP TIWL 0 _DP DIWL 0 _DP VXWL 0 _DP VYWL 0 _DP VZWL 0 _DP EFWL 0 _DP WEISPZ 0 _DP HERE COMES THE PROBLEM SPECIFIC DEF ON OF BIRTH POINT SAMPLING RETURN END Note The parameters EFWL SHWL have been introduced in 2005 Note Correction in May 2006 In previous versions of this manual the parameters TEWL and TIWL have been interchanged with respect to the calling statem
110. For test particles emitted from source surfaces or generated from incident bulk ions after reflection or sputtering the call is UPSUSR WEIGHT 2 For bulk ions ITYP 4 incident onto a source surface the call is UPSUSR WEIGHT 1 Therefore the tallies ADDS include the direct source contribution if the source is a surface source whereas the default surface tallies don t 221 3 3 The user surface reflection model REFUSR General remarks This subroutine is called in the initialization phase of an EIRENE run at entry RFOUSR from subroutine REFLEC and at entry SPOUSR from subroutine SPUTER At these en tries the user supplied reflection models and sputtering models if any respectively may be initialized Later during the Monte Carlo sampling phase it is called via entry RF1USR whenever a test flight intersects a surface NLLI for which the fast particle reflection model flag I LREF NLLI has been set equal to ILREF NLLD 3 Furthermore if for a certain surface NLLI a user specified sputter model is activated by the flag ILSPT NLLI 3 then REFUSR is called at the entry SP1USR whenever this surface is intersected by a test flight Format of subroutine aaa AaAAA Q QAaaAaAND SUBROUT NE REFUSR USER SUPPLI INPUT OUTPUT E CO ORD CO ORD CALL PARMMOD D SURFACE NTERACT ON ROUTINE INATES OF NC DENT PARTI CLE IN
111. HC1 HHC1 IGHC2 WHC2 Species and tally index for first and second tally respectively between which the cor relation coefficient is evaluated Note On printout the NSIGVI and NSIGSI standard deviations are printed as relative stan dard deviations in percent The standard deviations for the two tallies involved in the NSIGCI arrays are printed as absolute tallies i e with the same units as the two tallies themselves 172 2 10 Data for additional volume and surface averaged tal lies General remarks There is a large number of preprogrammed default volume or surface averaged tallies which have been selected mainly to allow assessment of global particle and energy balances for all test particle species as well as coupling of neutral gas and plasma transport equations These tallies are estimated at each EIRENE run unless they are explicitly abandoned by the surface crossing switches ILSWCH section 2 3 2 or are turned off in input block ZII There is however a very general option to allow for estimation of many more moments of the test particle u space distribution function by resorting to appropriately prepared problem specific routines UPTUSR UPCUSR and UPSUSR These are described in more detail in section LJ Furthermore there are options to form algebraic expressions from tallies and since Eirene2993 also for particle and energy flux spectra evaluated from the fluxes on selected surfaces or in selected cells of the computa
112. HOVJ J 1 NDAT These are e INDEX 0 Electron temperature eV e INDEX 1 Ion temperature eV NPLSI calls one for each ion species I e 227 DO IPLS 1 NPLSI CALL PROUSR HELP 1 0 NPLSI TIO IPLS NSURF CALL RESETP TIIN HELP IPLS 1 NPLS NSURF ENDDO INDEX 1 NPLS Ion density em NPLSI calls one for each ion species INDEX 14 2 NPLS Ion drift velocity x direction cm s NPLSI calls one for each ion species INDEX 1 3 NPLS Ion drift velocity y direction cm s NPLSI calls one for each ion species INDEX 1 4 NPLS Ion drift velocity z direction cm s NPLSI calls one for each ion species INDEX 1 5 NPLS Magnetic field x component AU INDEX 2 5 NPLS Magnetic field y component AU INDEX 3 5 NPLS Magnetic field z component AU INDEX 4 5 NPLS Magnetic field magnitude T INDEX 5 5 NPLS Cell volume cm INDEX 6 5 NPLS Additional tally NAINI calls one for each additional quantity 228 3 7 User supplied post processed tally routine TALUSR to be written SUBROUTINE TALUSR ICOUNT VECTOR TALTOT TALAV TXTTL TXTSP TXTUN ILAST 3 8 User supplied general geometry block The following routines have to be provided for the general geometry options LEVGEO 10 option NUGEN TRUEB in which no specific geometry data are available from EIRENE input and all
113. ID3 notin use IREAC Identification flag for collision data IREAC IR and IR is the labelling index from the reaction card see above The next three flags control number species and type of particles involved in this particular collision process IBULK pre collision bulk particle identifier NLM M type flag ITYP for impacting bulk particle electron ITY P 5 or bulk ion ITYP 4 irrelevant defaulted to M 4 for bulk ion impact collision and defaulted to M 5 for electron impact collisions L irrelevant defaulted to L 1 because number of pre collision bulk particles is known from the type CRC of each collision process N Species index of pre collision bulk ion corresponds to IPLS in bulk ion species cards see block 5 Irrelevant for electron impact collisions CRC EI ISCD1 first heavy secondary particle group identifier IJKLM M type flag ITYP for these first secondaries group atoms ITYP 1 molecules ITY P 2 test ions ITYP 3 or bulk ions ITYP 4 L number of secondaries of this type and species JK Species index of secondary ATM IMOL ION or IPLS two digits I relative importance of this first secondary group as compared to the second secondary group If J lt 0 Lis defaulted to I 1 currently not in use 119 ISCD2 _ second heavy secondary particle group identifier IJKLM Same as ISCD1 but for second secondary group Note The number of secondary electrons if any need not be spec
114. ILIIN 0 option from that side as 1 but with the opposite direction of the surface normal as 2 but with the opposite direction of the surface normal as 3 but with the opposite direction of the surface normal IJKLMN i e six digits I J K L M and N 99 0 no switch is operated N EIRENE flag ITIME N 1 The calculation of the step sizes in the standard mesh is abandoned for a particle which crosses the surface in the positive direction and is reactivated if the particle strikes in the negative direction N 2 as 1 but with the direction of the surface normal reversed for this option M EIRENE flag IFPATH M 1 Abandon the calculation of the collision rates entry into the vacuum for a particle which is striking the surface in the direction of the surface normal For particles incident from the other direction evaluation of collision rates is reactivated M 2 as 1 but with the direction of the surface normal reversed L EIRENE flag I UPDTE L 1 Abandon the updating of volume averaged tallies for a particle which is striking the surface in the direction of the surface normal For particles inci dent from the other direction updating of volume averaged tallies is reacti vated L 2 as 1 but with the direction of the surface normal reversed for this option I J K flags for switching cell numbers at transition into a different mesh cell K for particles in an additional cell i e not in one of the standard mesh blocks
115. IRENE vacuum data are defaulted in subroutine PLASMA to DVAC 1 0000E 02 cm TVAC 2 0000E 02 eV Furthermore zero plasma drift velocities are set in cells which are treated as vacuum zones VVAC 0 0000E 00 cm s for all three cartesian components and for all NPLS background particle species Note A cell can be considered a vacuum cell with respect to electrons LGVAC NPLS 1 TRUE without being a vacuum cell for all background ions This is because by abuse of language also neutral particle species may be used as background ion species NCHARP 0 to include neutral neutral collisions e g by the iterative option NITER input block 1 The Input Block S Data for Plasma background NPLSI DO 51 J 1 NPLSI read NPLSI species blocks with P ISPZS TEXTS NMASSS NCHARS NPRTS NCHRGS ISRFS ISRTS ID1 NRCS NFOLS NGENS NHSTSS ID3S format 1I12 1X A8 1X 12 12 1X 51 CONTINUE End of NPLSI species cards reading INDPRO J J 1 12 130 F INDPRO 1 LE 5 THEN TEO TE1 TE2 TE3 TE4 TES ENDIF F INDPRO 2 LE 5 THEN TIO I TI1 I TI2 T TI3 1 TI
116. L TRUE Geometry level LEVGEO 2 Mesh of nested but not necessarily concentric or confocal elliptical flux surfaces The equation for the radial surface is x EP y EL r The radial coordinate r is discretized by setting r7 RSURF I 1 NRIST 84 EP and EL may vary with coordinate r These parameters are stored in the arrays EP I EL I 1 NRIST which now are used in addition to RSURF to define one co ordinate surface in the first radial or x grid RHOSRF as in NLCRC option Note RHOSRF and RSUREF may differ in this case NLTRI TRUE Geometry level LEVGEO 2 to be written triangularity in mesh of nested closed algebraic surfaces NLPLG TRUE Geometry level LEVGEO 3 The mesh in the x y plane is described by NRIST polygonal arcs of length NRPLG each A polygon may consist of several valid and invalid parts to account for grid cuts in CFD meshes The invalid parts of a polygon are not seen by test particles and are allowed for in EIRENE only in order to facilitate index mapping in case of runs coupled to plasma transport models which resort to computer generated meshes including grid cuts The polygons must not intersect each other In this case RHOSRF 1 0 and RHOSRF D is the area enclosed by polygon number 1 and polygon number I NLFEM TRUE Geometry level LEVGEO 4 The mesh in the x y plane consists of NRIST triangles composed from NRKNOT knots In
117. L DION or DPLS respectively in subroutine LOCATE Note If a step function function STEP see below is used for sampling the start po sition of a test particle on a surface then the species index NSPEZ automatically also fixes the choice of the index ISPZ for the spatial step function STEP UISTEP ISPZ selected by the flags SORLIM and SORIND ISTEP see below This default can be overruled when SORIND has three digits Distribution in physical space NLPNT TRUE Point Source NLLNE TRUE Line Source not ready NLSRF TRUE Surface Source NLVOL TRUE Volume Source NLCNS TRUE Initial conditions source sampling from census array for time dependent mode of operation see input blocks 1 and 13 One and only one of these 5 variables must be TRUE Point source Flags for the distribution in physical space not mentioned here are irrelevant for point sources NSRFSI NPNTSI Total number of different points over which the starting points for this stratum are distributed corresponds to sub strata option for surface and volume sources there to facilitate sampling of spatial coordinates The next deck of 4 input cards is read NSRFSI times one deck for each sub stratum 155 INUM irrelevant labelling index for sub strata SORWGT Relative frequency for starting point labelled INUM The sum of SORWGT for all NPNTSI points is normalized to one internally NRSOR gt 0 x or radial ce
118. N see table B I if any are specified here Otherwise the data in this block are read from the code interfacing subroutine INFCOP at entry IFOCOP rather than from subroutine INPUT They may be used to modify or complete the model defined by the formatted input file so far For example by this option the entire geometry specification blocks 2 3 can be modified or overwritten by a few geometry pa rameters without rewriting input blocks 2 and 3 This allows rapid geometry optimization geometry parameter studies which otherwise would require to generate a large set of dif ferent geometry input blocks As this routine is problem specific it must be written by the user and therefore input can be from any file and in any format chosen there Subroutine INFCOP is also used for interfacing with other codes such as plasma transport codes By use of the flags INDGRD block 2 INDPRO block 5 and INDSRC block 7 data may be transferred from subroutine INFCOP into EIRENE geometry arrays background medium arrays and source distribution arrays respectively in a preprogrammed format This is described in section Hin general terms Here we give examples for one frequently used option namely the coupling of EIRENE to the 2 dimensional plasma transport code B2 M the B2 EIRENE code system Q B A corresponding version of INFCOP is available from FZ Jiilich The Input Block 14_ Data for interfacing Subroutine INFCOP IF NMOD
119. NATM watt T C 27 ERFAAT Energy Flux emitted Ats Atoms NATM watt T C 28 ERFMAT Energy Flux emitted Mls Atoms NATM watt T C 29 ERFIAT Energy Flux emitted T Atoms NATM watt T C 30 ERFPHAT Energy Flux emitted Pht Atoms NATM watt T C 31 ERFPAT Energy Flux emitted B I Atoms NATM watt T C 32 EOTML Energy Flux incident Molecules NMOL watt T C 33 ERFAML Energy Flux emitted Ats Molecules NMOL watt T C 34 ERFMML Energy Flux emitted Mls Molecules NMOL watt T C 35 ERFIML Energy Flux emitted T I Molecules NMOL watt T C 36 ERFPHML Energy Flux emitted Pht Molecules NMOL watt T C 37 ERFPML Energy Flux emitted B I Molecules NMOL watt T C 38 EOTIO Energy Flux incident Test Ions NION watt T C 39 ERFAIO Energy Flux emitted Ats gt Test Ions NION watt T C 40 ERFMIO Energy Flux emitted Mls Test Ions NION watt T C 41 ERFIIO Energy Flux emitted T I Test Ions NION watt T C 42 ERFPHIO Energy Flux emitted Pht Test Ions NION watt T C 43 ERFPIO Energy Flux emitted B I Test Ions NION watt T C 44 EOTPHT Energy Flux incident Photons NPHOT watt T C 45 ERFAPHT Energy Flux emitted Ats Photons NPHOT watt T C 46 ERFMPHT Energy Flux emitted Mls Photons NPHOT watt T C 47 ERFIPHT Energy Flux emitted T I Photons NPHOT watt T C 48 ERFPHPHT Energy Flux emitted Pht Photons NPHOT watt T C 49 ERFPPHT Energy Flux emitted B I Photons NPHOT
120. NBMLT 1 see section refsec2 2 and the proper value of NACELL IVLSF 2 to be written Distribution for the species index NLATM TRUE Atomic source History starts in subroutine FOLNEUT with type index ITYP 1 species index ISPZ IATM and initial weight NPRTA IATM see block 4A NLMOL TRUE Molecule source History starts in subroutine FOLNEUT with type index ITYP 2 species index ISPZ IMOL and initial weight NPRTM IMOL see block 4B NLION TRUE Test ion source History starts in subroutine FOLION with type index ITYP 3 species index ISPZ IION and initial weight NPRTI IION see block 4C NLPHOT TRUE Photon source History starts in subroutine FOLNEUT with type index ITYP 0 species index ISPZ IPHOT and initial weight NPRTPH UIPHOT see block 4D Not all options for direct photon sources are fully programmed Currently we mostly use the bulk particle volume recombination source see next to simulated radiative decay from excited states as birth profile for bound bound line photons NLPLS TRUE Bulk ion source Initial co ordinates of a bulk ion with species index ISPZ IPLS and initial weight NPRTP IPLS see block 5 are generated then a surface reflection model or a volume re combination model is called and atoms molecules or test ions with species index either IATM IMOL or ION are created One and only one of these five variables must be TRUE NSPEZ Species index of the source particle 1 lt NSPEZ
121. NEW Flag for the choice whether a spectrum is plotted on the same picture as the previous one NSPNEW 0 or onto a new graph otherwise NSPCHR if gt 0 then automatically all cells along chord are identified and energy re solved spectra input block 10f are computed in all these cells by automatically aug menting input block 10f correspondingly These spectra are line of sight spectra in the direction of the chord specified here direction SPCVX SPCVY SPC VZ in augmented input block 10f is taken to be a unit vector along this present line of sight NSPSTR_ Index for stratum which is to be used for line integration NSPSTR 0 sum over strata NSPSPZ Incase NSPTAL 1 Index for atomic species IATM with IATM lt NATM for which charge exchange spectrum is to be computed NSPSPZ 0 sum over atom species index In case NSPTAL 2 Number of contribution to line intensity as programmed in Subr Ba gipna Bagammas Ly Beta etc Currently up to 6 contributions for each H atom spectral line and the total 1 coupling to ground state H 1s 2 coupling to continuum H 3 coupling to H 4 coupling to Hy 5 coupling to H7 6 coupling to H new in versions 2012 and younger 7 total was 6 in versions 2011 and older 191 In case NSPTAL 3 Index for photon species line i e for IPHOT with IPHOT lt NPHOT for which side on spectrum is to be computed NSPSPZ 0 sum over photon species index not ready
122. NPLS N LEVGEO 5 THINTF RWK 6 5 NPLS N 4 1 1 entry IFOCOP Geometry data INDGRD 6 option In the LEVGEO 3 option 2D grid of quadrangles PGINTF is an array of length NPMAX which contains all relevant information to generate a 2D mesh of polygons in the x y plane It is equivalenced to the common block CPOLYG via the statement EQUIVALENCE PGINTF 1 XPLG 1 1 In the LEVGEO 4 option 2D grid of triangles TRINTF is an array of length NTMAX which contains all relevant information to generate a mesh of triangles in the x y plane It is equivalenced to the common block CTRIA via the statement AI AI AI Z 2 2 2 2 2 w FF F F UVUVUTVTV VV VCC CU 233 GUUUCU UD U J U J J J J J J J J J J J J J J 1 NSBOX J 1 NSBOXx I 1 NPLS J 1 NSBOX I 1 NPLS J 1 NSBOX I 1 NPLS J 1 NSBOX I 1 NPLS J 1 NSBOX I 1 NPLS J 1 NSBOX J 1 NSBOX J 1 NSBOX J 1 NSBOX J 1 NSBOX J 1 NSBOX I 1 NAIN J J NIST 4 J J 2xN1ST 4 J J 3 xNIST 4 J J AxN1ST 4 J J 1 4xN1ST N2ND J J 1 J J 1 NPMAX NPMAX J J 1 N3RD J J 1 NTMAX NTMAX J J 1 N3RD J J 1 NHMAX 1ST 1ST 1ST 4m ae Z N 1ST 2ND 3RD EQUIVALENCE TRINTF 1 XT 1 In the LEV GEO 5 option 3D grid of tetrahedo
123. ORCTY SORCTZ if this vector is not zero or else by the surface normal vector in case of surface sources or else by the default 1 0 0 point line or volume sources By this option for example the main direction of emission from a surface can be influenced The new distribution of the polar angle is then not necessarily centered around the inner surface normal vector any longer in case of surface sources In all pre programmed cases the azimuthal angle around the axis C is equally distributed from 0 to 360 2 7 1 Piecewise constant Step functions for sampling The statement A STEP NSPZI NSPZE NSMAX ISTEP ISTEP initializes step functions for random sampling by the inversion method and the statement B STEP1 IINDEX ISTEP RNF ISPEZ converts a uniformly distributed random number RNF into a random number sampled from such step functions Sampling of the birth point of a trajectory is sometimes done from piecewise constant func tions ETRENE function STEP e g if one digit of the flag SORLIM has been set to the value 4 The random sampling of a coordinate u is from the step function FLSTEP RRSTEP There is storage for up to NSTEP see PARMUSR such step functions RRSTEP i ISTEP i 1 NSMAX ISTEP 1 is a discrete set of abscissae u at which the piecewise constant step function has a jump to FLSTEP RRSTEP i The final interval ends at RRS
124. PDATE All default estimators are constant within a cell m i e depend only upon the cell index m but not on the position r in the cell g s const m Hence they also do not depend on the position s along the track within a cell UPDATE calls templates UPTUSR in which any further quantity can be scored by programming the path integral of any function g s see section BA In some instances still collision estimators B I are employed but we are gradually remov ing them and plan keep them in the code only to provide independent checks for code verification runs TD Tracklength particle density g 1 v v VEL the test particle s velocity Note that the path integral of g along a trajectory in a cell is equal to the time spend by that history in a cell TPM Tracklength parallel to B field momentum source sink 243 Table 5 3 Surface Averaged Tallies Output Module CESTIM No Name Macroscopic quantity 1 Dim Units Estim 1 POTAT Particle Flux incident Atoms NATM amp T C 2 PRFAAT Particle Flux emitted Ats gt Atoms NATM amp T C 3 PRFMAT Particle Flux emitted Mls gt Atoms NATM amp T C 4 PRFIAT Particle Flux emitted T I gt Atoms NATM amp T C 5 PRFPHAT Particle Flux emitted Pht Atoms NATM amp T C 6 PRFPAT Particle Flux emitted B I gt Atoms NATM amp T C 7 POTML Particle Flux incident Molec
125. Pa 760 mTorr 1 mBar Further momentum is in g cm s and a momentum flux or momentum rate of change is in g cm s Amp per cell and the momentum source density in the EIRENE tallies for interfacing with plasma codes is then in g cm s Amp cm Hence conversion from g cm s Amp into Pa m momentum source per cell in plasma momentum balance equations in SI units is done by firstly multiplying with 10 then kg m s Amp and then dividing by 1 6022 1071 hence kg m s After dividing by 70 the cell volume m the momentum source is in Pa m or N m force density Input format The format statement numbers in subroutine INPUT start with 666 for reading and with 777 for writing The following conventions are used Standard Fortran naming conventions i e variable names starting with the letters I J N are Integer all other variables are Real In addition to these standard convention the following rules are employed Character strings start with the letter C or with T Logical variables start with NL LG or with TRC The format for a card containing only real variables 6E12 4 The format for a card containing only integer variables 1216 The format for a card containing only logical variables 12 5L1 1X The format for a card containing text A72 The format for a card containing K K lt 6 integer variables first and then up to 6 K real variables next K 16 6x 6 K E12 4 An
126. SR 0 002 220 B3 The user surface reflection mode REFUSR 222 3 4 e user source sampling routine SAMUSR 00 224 jst Goes Gah ee a eG we ah ee Se 226 B 5 e user geometry data routine OUSR 2 2 0 004 226 4 Koutines for interfacing with other codes EIRCOP 232 4 Routine for interfacing INFCOR oaoa 2 00084 232 4 JOOP e pue paie deg le ele o Rk a a 233 4 4 Statistical noise in Monte Carlo terms for external code noise residuals SALIS COB ge cee GU a Re a ee g e Be howe eee a A 236 5 Default i NE tallies and selected Module urrent status incl photon gas tallies Eirenesoo2 and younger 6 1 Tables of EIRENE fallied 5 1 D I old version w o photon gas tallies References Irenes991 and Older 237 237 239 247 Introduction and General Information This manual describes the input required by the EIRENE code to run a Monte Carlo study for a fully 3 dimensional simulation of linear transport 1 e of test particles in a prescribed background medium Although the geometry of the problem and the interaction between test particle species and the background are in principle not subject to any restrictions the aim of code development was to provide a tool for investigating neutral gas transport in tokamak plasmas Consequently the choice of preprogrammed options has been made mainly with this application in mind A large variety of problems in this
127. TEP NSMAX ISTEP ISTEP Let RNF be a uniform random number on the interval 0 FLSTEP RRSTEP 1 to FLSTEP RRSTEP NSMAX or on a sub interval thereof By calls to the entry STEP1 IINDEX ISTEP RNF ISPEZ of Function STEP the ran domly sampled index i DEX is returned as well as a coordinate u sampled from an uniform distribution on the i increment Au RRSTEP i 1 RRSTEP i u STEP1 In case of LEVGEO 1 or LEVGEO 2 u has the simple meaning of one of the spatial coordi nates in an EIRENE run However u need not necessarily be one of the 3 spatial coordinates RRSTEP can also stand e g for an arc length along a polygon LEVGEO 3 or for the cumulated length of an element in a selected list of sides of triangles LEVGEO 4 or for the cumulated area of a surface element in a selected list of surfaces of tetrahedrons LEVGEO 5 In these latter cases only the index I INDEX is used and a point from an uniform distribution on the line or surface element to which DEX points must still be sampled zZ Z 164 FLSTEP is taken as cumulative sampling distribution hence it is monotonically non decreasing It is set in function STEP from a piecewise constant distribution function e g from a surface flux density distribution by integration over RRSTEP and normalization These step functions h
128. TIS_COP As pointed out in Section for all primary not derived EIRENE tallies the empirical standard deviation can also be obtained if requested by setting proper flags in input block 9 The considerable CPU penalty for doing this was avoided at least for volume averaged tallies in EIRENE versions 99 and younger by major code optimization indirect addressing in these parts In versions 2012 and younger the same optimization was carried out also for surface averaged tallies In Versions 2012 and older some standard deviation tallies of special interest for code inter facing such as total summed over species source rates have been implemented in a special routine in the code interfacing module STATIS_COP This routine has now been made redundant because all tallies needed for interfacing includ ing sums differences of default tallies are now available as COPY tallies for which standard deviations are available by default Version 2012 and older Subroutine STATIS_COP provides these estimates for those tallies which are specific to a particular coupled case Usually these will be source terms for particle momentum and energy balance equations summed over all donor species At entry IF 4COP see section above these may be further processed For example in case of coupling to the B2 plasma fluid code these noise estimates are integrated into global quantities dimension 1 time and represent the contribution of statistical noise
129. TRCBLPH TRCTAL TRCSRC J J 0 NVOLPR DO 101 TRCNAL TRCREF TRCSOU TRCBLI TRCREA TRCFLE TRCREC TRCBLP TRCSIG TRCAMD TRCTIM TRCBLE NSTRAI J 1 NVOLPR NPRTLV J NFLAGV J NSPEZV J 1 NSPEZ 101 CONTINUE NSURPR DO 102 J 1 NSURPR NTLS NPRTLS J NFLAGS J NSPEZS J 1 NSPEZ V J 2 S J 2 102 CONTINUE optional unless block 11B starts NLTVOUT NUMTAL J J 1 NLTVOUT 12 NLTSOUT NUMTAL J J 1 NLTSOUT values per card val 12 ues per card 11B Data for graphical output 11B 1 Data for 2D and 3D Geometry plot PLIST PLCUT 1 PLCUT 2 PLCUT 3 PLNUMV PLNUMS PLARR PL2ND PL3RD PLADD PLBOX PLHST PLSTOR FORMAT 1216 FORMAT 1216 NTLVFL J NTLSFL J NPLINR NPLOTR NPLDLR NPLINP NPLOTP NPLDLP NPL DO 1140 J 1 5 INT NPLOTT NPLDLT PL3A J TEXTLA J IPLTA J IPLAA J I P LEA J I PLTA J 1140 CONTINUE DO 1141 J 1 3 PL3S J TEXTLS J IPLTS J IPLAS J I P LES J I PLTS J 1141 CONTINUE CH2MX CH2MY CH3MX CH3MY ANGLE1 ANGLE2 T1TRC I2TRC CH2X0 CH3MZ CH3X0 ANGLE3 ISYPLT J CH2Y0 CH3Y0 CH22Z0 CH3Z0 J 1 8 L NIE 11B 2 Data for plots of volume tallies
130. The EIRENE Code User Manual including B2 EIRENE interface Version 11 2009 D Reiter EIRENE THE GREEK GODDESS OF PEACE The Greek author Hesiodos wrote a genealogy of the gods The Theogony in the 8th century B C According to him EIRENE and her sisters Eunomia and Dike were the daughters of Zeus and Themis These sisters were called the horae the Greek word for the right time hora Abstract The EIRENE neutral gas transport code is described This code resorts to a combinatorial discretization of general 3 dimensional computational domains It is a multi species code solving simultaneously a system of time dependent optional or stationary default linear kinetic transport equations of almost arbitrary complexity A crude model for transport of ionized particles along magnetic field lines is also included EIRENE is coupled to external databases for atomic and molecular data and for surface reflection data and it calls various user supplied routines e g for exchange of data with other fluid transport codes The main goal of code development was to provide a tool to investigate neutral gas transport in magnetically confined plasmas But due to its flexibility it also can be used to solve more general linear kinetic transport equations by applying a stochastic rather than a numerical or analytical method of solution In particular options are retained to reduce the model equations to the theoretically important case of
131. WMINV minimum weight used for suppression of absorption at collisions survival bi assing If a particle goes into a collision with weight less than WMINYV then sup pression of absorption or any other non analog weight correction is abandoned and the analog game is played WMINV acts only for events in the volume including volume source birth events but not for events at surfaces WMINS Same as WMINYV but for surface events including surface source birth events WMINC minimum acceptable weight for conditional expectation estimators by abuse of language More precisely WMINC is the minimal acceptable probability for a test flight to reach a particular cell without collision If this probability is smaller than WMINC the particle track is stopped and restarted E g for WMINC gt 1 the es timator used in the NIMBUS code results ref 4 whereas for WMINC 0 each particle path is integrated according to equation B 20 until the nearest non transparent surface along the track is reached regardless of any collisions Periodicity surfaces are regarded as transparent in this context Note strictly speaking this is not a non analog method but rather a particular choice of an unbiased estimator Hence the flag NLANA in input block does not affect flags for conditional expectation estimators WMINL to be written SPLPAR splitting parameter for default radial splitting option MAXRAD lt 0 NSIGVI number of standard
132. X format 13 1X A6 1X A4 Axxx A3 213 3H12 4 ENDDO from external A amp M data files such as FILNAM HYDHEL METHAN AMJUEL H2VIBR for polynomial fits or other data files of appropriate format For collision reaction rates electron cooling rates etc from the so called ADAS database format AFD11 or any other properly tabulated data source i e for FILNAM ADAS an additional card is read containing variables ELNAME IZ for each IR entry see below to identify the species and ion charge state within the ADF11 file 106 IR ADAS H123 REAC CRC MASSP MASST DP format 13 1X A6 1X A4 Axxx A3 213 E12 4 ELNAME IZ format 4X A2 1X I3 For photonic emission and absorption data line shapes i e for FILNAM PHOTON the line is shortened to R FILNAM H123 REAC format 13 1X A6 1X A4 Axxx for reading from the spectroscopic line shape database PHOTON but additional lines are needed to specify the line broadening options See below There also exist an option for specifying constant or very simple functional dependencies cross sections reaction rate coefficients reaction rates etc directly via the input file without resorting to an external database This has proven useful for testing purposes e g compar ison with simple analytic or numerical solutions In this case FILNAM CONST further details see below Later EIRENE will assig
133. XTR ENDIF ENDIF ELSEIF NLPLG THEN XPCOR YPCOR ZPCOR PLREFL NPOINT 1 K NPOINT 2 K K 1 NPPLG DO 21 I 1 NR1ST XPOL I J YPOL I J J 1 NRPLG 21 CONTINUE ELSEIF NLFEM THEN XPCOR YPCOR ZPCOR NRKNOT XTRIAN I T 1 NRKNOT YTRIAN I T 1 NRKNOT DO ITRI 1 NR1ST NVERT 1 ITRI NVERT 2 ITRI NVERT 3 ITRI NEIGH 1 ITRI NSIDE 1 ITRI IPROP 1 ITRI NEIGH 2 ITRI NSIDE 2 ITRI IPROP 2 ITRI NEIGH 3 ITRI NSIDE 3 ITRI IPROP 3 ITRI ENDDO ENDIF ENDIF ENDIF 82 xx 2B y or poloidal grid surfaces NLPOL NLPLY NLPLA NLPLP NP2ND NPSEP NPPLA NPPER F INDGRD 2 LE 5 THEN YIA YGA YAA YYA ENDIF xx 2C z or toroidal grid surfaces NLTOR NLTRZ NLTRA NLTRT NT3RD NTSEP NTTRA NTPER F INDGRD 3 LE 5 THEN ZIA ZGA ZAA ZZA ROA ENDIF xx 2D mesh multiplication NLMLT NBMLT IF NBMLT GT 1 VOLCOR NM NM 1 NBMLT xx 2E additional cells outside standard mesh NLADD NRADD IF NRADD GT 0 VOLADD NM NM 1 NRADD Meaning of the Input Variables INDGRD This index controls the meaning of input variable
134. Z NJUMP NEWCEL TIM ICOS IERR Input NRCELL Actual cell number for which the intersection to the cell boundary has to be found If NJ UMP 0 i e for the first call of a new trajectory e g after a collision the starting point X0 Y0 ZO must be in that cell In later calls for the same trajectory NJUMP gt 0 NRCELL has been automatically updated i e it must not necessarily contain the starting point X0 Y0 Z0 X0 Y0 Z0 Cartesian coordinates of the starting point of a trajectory VELX VELY VELZ unit speed vector pointing in the direction of the flight Output NJUMP 0 this is the first call for a particular trajectory 0 this is a later call for a particular trajectory The initial position and speed unit vector are the same as in the previous call Hence the geometrical parameters depending only on those need not be evaluated again 230 NEWCEL lt 0 trajectory has intersected one of the non default surface input block 3a ABS NEWCEL is the number of that surface corresponding to running index ISTSI in input block 3a gt 0 number of next cell in which the flight would continue if no collision event stops the track already earlier I e cell number of the neighbor cell in the direction of the flight TIM distance cm from X0 Y0 Z0 to the nearest intersection of the trajectory with a bound ary of cell NRCELL ICOS only relevant if the trajectory has intersected a non default su
135. a bulk species on the file fort 13 e g written in an earlier EIRENE run see NFILEL option in input block 1 The parameters fields of density tempera ture flow velocity for species IPLS are set from those of species ISP on fort 13 ITP is the type of the particle i e always ITP 4 for this option Internally set ITP 4 bulk particle type independent of input value for ITP CDENMODEL fort 10 Read data for this species from file fort 10 The additional card only one reads format 316 SP TP STR ISP ITP is the number and type of a test particle species on the file fort 10 respectively from stratum no ISTR i e written onto fort 10 either in the present run or an earlier EIRENE run see NFILEN option in input block 1 The parameters fields of density temperature flow velocity for species IPLS are derived from from those of species ISP ITP ISTR on fort 10 Note at the end of a full EIRENE run the corresponding bulk particle profiles are reset to those evaluated in this run for further use in post processing routines such as the diagnostic module see Section LII printout plotting or iterative mode input flags NITERI NITERE and user subroutine MODUSR see Section LI CDENMODEL Saha Set parameters from Saha equilibrium of ionization states The additional card only one reads SP ITP ISTR to be written CDENMODEL Boltzmann Set parameters from Boltzmann eq
136. a combination of both standard surfaces hence defining standard grid cells voxels and additional surfaces defin ing a general BREP discretisation additional cells A more complicated situation arises when additional surfaces intersect standard grid voxels EIRENE model geometry for TEXTOR radial standard mesh inside vessel additional surfaces for pumping stations TEXTOR vesse TM pump 3000 17s Figure 1 3 same as left Figure but Figure 1 2 Early example a combi BREP part only and EIRENE re run with nation of BREP and VOXEL discretisa more modern 3D visualisation graphics tion around 1985 for ALT II pumplimiter program 2009 studies at TEXTOR Discretisation in side the TEXTOR tokamak vessel torus VOXEL supplemented by about 100 BREP first and second order surfaces for ALT II scoops pumping ducts and in ner structures such as probe supports get ter pumps etc If these surfaces are transparent they can be used to conveniently measure fluxes at any position But if they are reflecting or absorbing e g to define a complex shaped bounding surface in an otherwise simple grid then some care is needed because the automatic cell volume evaluation which is available in EIRENE for standard grid cells voxels may not correspond anymore to the cell volume accessible for test particles Cell averaged quantities divided by cell volume may then not necessarily be scaled properly For
137. a distance RFPOL out side the polygon NRIST and then NRIST is increased by one irrelevant if RFPOL lt 0 NPOINT 1 J Index of the first point of the valid part number J same for each radial polygon Default NPOINT 1 1 1 NPOINT 2 J Index of the last point of the valid part number J same for each radial polygon Default NPOINT 2 1 NRPLG XPOL K I x co ordinate of the polygon point number K on polygon number I YPOL K D y co ordinate of the polygon point number K on polygon number I if NLFEM TRUE NRIST number of triangles for discretisation in x y plane XPCOR YPCOR shift whole mesh by that vector in x y plane NRKNOT There are NRKNOT knots by which the triangles are defined XTRIAN YTRIAN x and y co ordinates of the knots respectively NVERT LITRD Each triangle ITRI is defined by 3 points P Pz and P from the set of NRKNOT knots NVERT LITRD is the number of point Pr I 1 2 3 in the set of knots for triangle ITRI 87 NEIGH LITRI The three sides of each triangle S1 S2 S3 are defined such that S4 connects P and P S connects P gt and P and S3 connects P and P3 NEIGH I ITRI is the number of the neighboring triangle at side S for I 1 2 3 NSIDE L ITRI NSIDE CLITRD is the number 1 2 or 3 of the side of the neighboring triangle which corresponds to side S of the triangle ITRI to be written IPROP LITRI ISTS ABSCUPROP is the integer by which a particular surface
138. a possible work around see NLERG option in input block 1 section Z I From the above it follows than in an EIRENE model surface elements building up the wall can be defined as bounded algebraic surfaces with triangles as special case i e as additional surfaces BREP or can be bounding surfaces of the voxels if the grid of voxels extends up to the real wall or a combination of both As can be seen from the flowcharts all the geometrical calculations needed for tracing test flights and for estimating volume and surface averaged tallies are compiled in a geometry block which can easily be exchanged In most cases e g all installations of EIRENE outside FZ Jiilich we load the most complete fully 3D block GEO3D which allows fully 45 3 dimensional spatial resolution Lower dimensional OD 1D or 2D are contained as special cases e g by choosing only grid surfaces with proper symmetry There is in general not a very large CPU benefit from running EIRENE with simpler spe cialized and geometry optimized blocks such as GEO2D or GEOI1D for 2D or 1D models respectively because the saving in CPU costs in most cases is only around 10 20 so these options have not been supported since the late eighties of the last century anymore The geometry module of EIRENE The following operations have to be executed by the block Suppose the three dimensional computational volume is discretized by a mesh of n surfaces Si
139. a to those described in previous sub section 2 14 1 are read basically to ac count for non orthogonal grids and for direct transfer of surface recycling boundary condi tions into EIRENE From input stream FORT 29 two angles are read for each cell 1 ALPHXB angle of B field against R coordinate x coordinate in EIRENE radians evaluated at B2 x surface East West surface centered 2 ALPHYB angle of B field against R coordinate x coordinate in EIRENE radians evaluated at B2 y surface North South surface centered Then there are 14 arrays for definitions of boundary conditions stream FORT 31 or Common BRAEIR in order to achieve full symmetry of boundary condition options between east west and north south cell faces This is in particular useful for cases with wide grids up to the real vacuum vessel in which boundary conditions on strongly inclined surfaces are defined 1 v_par x parallel velocity m s x surface across field East centered 207 Figure 2 1 Definition of angles a ALPHXB and a ALPHYB respectively for inclined non orthogonal B2 grids to be used in EIRENE code 10 11 12 13 14 v_par y parallel velocity m s y surface along field North centered v_rad x plasma ion density m s x surface across field East centered v_rad y poloidal velocity m s y surface along field North centered d par x x surface across field East centered de par y y surface along field North ce
140. ace and time DA 1 INGRDE 1 SOREXP SORIFL NLPNT NLLNE NLSREF NLVOL NLCNS NSRFSI DO 75 J 1 NSRFSI INUM NDIM NSOR INGR INGRI INGRI SORWGT SORLIM SORIND NRSOR NPSOR NTSOR SORAD1 SORAD2 SORAD3 75 CONTINUE Distribution NBSOR NASOR SORAD4 SORAD5 in velocity space SORENI SORENE SORCOS SORMAX 70 CONTINUE SORVDX SORVDY SORCTX SORCTY 151 SORVDZ SORCTZ DA 2 INGRDE 2 DA 3 INGRDE 3 NISOR SORAD6 Meaning of the Input Variables for primary sources NSTRAI Number of different sources Strata which are computed one after the other and are linearly superimposed at the end of the run NSTRAI lt NSTRA see Parameter Statements INDSRC INDSRC ISTRA 0 5 the input data for stratum ISTRA are read here but may be modified in some user routine SAMUSR or interface routine INFCOP at entry IFRCOPUSTRA INDSRC USTRA 6 no input data for stratum ISTRA are read here The definition of this stratum must be entirely in some problem specific routine IF2COP etc See section B 4 for one such example namely the default surface recycling source model as specified in coupled B2 EIRENE runs INDSRC UISTRA 1 the input data for stratum ISTRA are read here and no attempt is made to modify these I e IR2RCOPUSTRA is not called ALLOC Allocation of CPU time to stratum weighted as 1 ALLOC NPTS ALLOC FLUX TXTSOU Text to c
141. acoustic speed of ion species 7p i e cs ip y T T ip mj ip 7 11 The mean incident ion energy ELST EP E corresponds to that resulting from the NEMOD 2 3 options with FE 3 07 0 57 and the sheath potential SH STEP Sh is set to the sheath potential flag for the non default surface FSHEAT see input block 6 Note that by setting SHSTEP and hence parameter Sh the evaluation of the full sheath po tential function A in energy sampling options NEMODS digit N 3 5 7 and 9 is overruled by using A Sh instead 2 7 2 Electrostatic sheath acceleration For surface sources and ionic source particles test ions or bulk ion with charge Z an acceleration of the sampled velocity vector vo towards the surface in the direction normal to the target surface may be added I e the velocity space sampling described above NEMODS options digit N is regarded to provide the velocity at the entrance of the electrostatic sheath in front of a target surface Energy sampling options NEMODS N 3 5 7 9 add this sheath contribution to velocities sam pled from the corresponding options N 2 4 6 and 8 respectively Let vo Vo This sheath acceleration is achieved by setting a new velocity V1 Vi Vo Vs Vs Vs C and Vs evaluated such that mi Vs WoC Tive ESH EAT m ni To 7 12 i e the energy E of the particle is increased from Eo to by the amount ESHEAT eV as compared to the option without
142. adiation transfer i e the strangely nor malized photon Boltzmann equation In contrast to plasma radiation e g Bremsstrahlung the radiation processes studied here are due to single uncorrelated particles such that emis sion and absorption of the plasma is obtained by simple summation of all contributions of all individual particles We therefore consider all particles as uncorrelated and in well defined 56 one particle states For continuum radiation bound free or free free the frequency of the photon in the atoms rest frame may be replaced by the frequency in the lab frame because all cross sections are slowly varying functions of frequency By contrast for line radiation due to bound bound transitions the Doppler effect must be taken into account in all quantities that vary rapidly as function of frequency such as cross sections line profile or redistribution functions The key atomic parameters for radiation transport are the Einstein or Einstein Milne co efficients Amn Bmn and Bam of spontaneous emission induced stimulated emission and absorption respectively We will discuss them here first for a gas of stationary atoms and include Doppler and other line broadening effects later For a thermal radiation field temperature T in a gas of atoms with density n lower state and n upper state the rate equation expressing balance between emission and absorption reads mByR T n2 Ao Ba R T R T is a speci
143. al and electronic excitation as well as rates needed for radiation trapping calculations AMJUEL supplement to HYDHEL and METHAN for neutral gas transport Monte Carlo codes e g multi step reaction rates etc CONST reaction IR is a collision process with explicitly specified fit coefficients for cross sections or reaction rate coefficients depending upon input flag H123 e g constant power law etc These fitting coefficients are directly read from the formatted input file rather than from an external file ADAS Collisional radiative rate coefficients from files tabulated in the same format as ADAS adf11 files which must be located in a directory the path to which is specified in input block 1 section Z I by one of the CFILE cards described there CFILE ADAS path adf11 PHOTON H123 Identification flag for the type of data interaction potential parameters cross section rate coefficient momentum loss rate coefficient energy loss rate coefficient etc case 0 FILNAM CONST currently available only for H123 H 1 H 2 H 5 or H 8 i e only for single parameter fits in case IFTFLG 10 110 210 single parameter constant collision param eter One more line F 0 REAL is read For all other values of IFTFLG including the default IFTFLG 0 two more input lines with 9 fitting coefficients F I 0 5 REAL F I 6 8 REAL are read in subroutine SLREAC from the forma
144. al cell region ICELL NSURF 1 NSURF NRADD are set to the EIRENE vacuum values For further details of subroutine INFCOP see ZI Input Data for operating mode input variable NMODE and sections and for an example INDPRO 7 Same as INDPRO 6 option except that NDAT NSBOxX rather than NDAT NSURF Hence in this case background data are read from RWK also for the additional cell region ICELL NSURF 1 NSURF NRADD 135 2 5 1 Derived Background Data Given the data describing the background medium plasma in each cell on common block COMUSR a set of further derived background data profiles is computed and stored also on COMUSR This is done by a call to subroutine PLASMA_DERTIV The following quantities are defined there DEIN Electron density cm 3 derived from all NPLSI ion densities and the charge states NCHRGP IPLS of each ion species EDRIFT Kinetic energy eV in drift motion for each background species IPLS derived from the mass MASSP UPLS and the flow velocity VXIN VYIN VZIN LGVAC Vacuum flag logical to identify regions in which no collision data for all or cer tain background species are computed i e the collisionalities are set to zero in these cells for those background species See also explanation above with respect to the EIRENE vacuum data TVAC DVAC VVAC NSTGRD flag for special treatment of some selected cells 0 default This cell is a dead cell not to be seen by the part
145. and additionally if a particle is crossing the surface in the positive direction one sided sur face tallies are updated e g by default partial particle and energy currents J Amp and K Watt These are stored in the POT and EOT tallies of Table A If the particle crosses the surface in the direction opposite to the surface normal then negative partial particle and energy currents J Amp and K Watt are updated These are stored in the PREF and ERF tallies of Table E3 3 Net currents e g J J are evaluated and stored on the POT and EOT tallies see Table 6 3 The PRF and ERF tallies are empty for these surfaces lt 4 Not in use Currently same as ILIIN 2 option both sides of the surface act as described by ILIIN option default particles incident on the surface in the negative direction will be absorbed i e ILIIN 2 option from that side particles incident on the surface in the negative direction will be killed and the message ERROR IN ADDCOL or ERROR IN STDCOL will be printed The contribution of these particles to the particle and energy flux balances will be called PTRASH and ETRASH respectively This option should be used for geometry testing whenever the user expects particles incident only from one side particles incident on the surface in the negative direction will not see the surface i e this surface acts like a semi transparent surface
146. and atoms or if neutral neutral collisions are relevant In this latter case so called BGK approximations to the full collisions integral are employed and the non linearity is dealt with by successive linearisation i e by iteration The strongest non linearity in EIRENE applications is typically the back reaction of the plasma background the host medium on the neutral gas and radiation fields This how ever is dealt with in an operator splitting cycling procedure see section between a plasma solver diffusion advection sub module solver for given reaction term and EIRENE re action part solver for given diffusion advection solution i e for given background medium in which EIRENE within each single cycle may still be operated in linear mode The term j1 space in this report refers to the phase space of a single particle The quantity of interest is then the one particle distribution function f fr v i t o F t 2 0 4 1 or f x where the state x of the u space is characterized by a position vector r a velocity vector v a species index 2 i stands for e g H D T D2 DT He CH and the time t The number density n r for species 7 then reads nilr t ee f x v 4 t Instead of v we sometimes utilize the kinetic energy E E m 2 v and the unit speed vector Q v v in the direction of particle motion Hence f r d v f E Q dEdQ where d v v7dvdQ and dO sin 6d d and
147. and summing over all species i is the distribution of birth species index obtained by integrating over all velocities and conditional on the already sampled spatial birth point S 3 v finally is the velocity distribution at the birth point of the trajectory conditional on the already sampled species index 7 and birth point location x This procedure is employed for all types of sources namely for re sampling from a stored census array e g initial condition in time dependent mode for point sources line sources surface sources and volume sources If the sampled species 7 belongs to the background species t rather than to the test particle species community then after completion of sampling from S an appropriate col lision is carried out e g with a wall surface in case of surface sources until a test particle species 7 results I e formally a sampling from kernel C x v i i is carried out at the place of birth x to produce initial test particle coordinates Stratification of sources has been described in section L3 3 2 1 3 4 1 time census sources 1 3 4 2 Point sources 1 3 4 3 Line sources 1 3 4 4 Surface sources and see special section on plasma surface recycling source sampling L5 1 3 4 5 Volume sources special case volume radiative or threebody recombination of plasma ions and electrons to neutrals Also used for spontaneous photon emission source in radiative transfer simula
148. angle limits this operator to either isotropic background velocity distributions or at least to distributions which are symmetric around the B field line but which may deviate from being Maxwellian in the B field direction e g to accommodate thermal force effects see also Thesis J Seebacher Univ Innsbruck 2009 B binary Monte Carlo collision procedure A procedure similar to the Abe Takizuka Coulomb collision algorithm frequently used in PIC codes BU is employed This procedure consists in random sampling a bulk background collision partner and then to carry out an effective binary collision between these two particles It hence can be viewed as Monte Carlo randomization of the algorithm A in which the integration over background distribution is carried out deterministically Thesis B Berberich Univ Duesseldorf soon to come 62 1 12 EIRENE flow charts The EIRENE Code INPUT FILE formatted I O unit 50 grid data optional optional optional dump files A amp M data files I O units 10 15 HYDHEL METHANE background data Surface data files units 29 32 TRIM SPUTER direct access AMJUEL optional USER user supplied subroutines EIRENE GEO3D GEO3DTRC Geometry block COUPLE code interfacing Printout PLOT DIAGNO I O unit 6 GR Plotsoftware Processing of results into experimental diagnostic data Figure 1 8 Structure EIRENE code 63 Program EIRENE Set constants and de
149. ansport kernel T then reads as follows 1 Q r r T l T v i r gt r amp r v 2 exp f ds amp r sO v 7 0 A R r 6 N8 r r FO 4 2 11a Blr v i F v ir ar 0 lt 1 lt 2 11b with H x 0 if x lt 0 and H x 1 if x gt 0 the Heaviside step function the unit step function The two remaining delta functions restrict the motion to a path in the direction of the initial velocity v Thus although strictly being a conditional on x distribution in phase space for an infinite medium T can be interpreted as the distribution density for the distance l for a free flight starting from r to the next point of collision r r l Q We shall frequently omit the arguments v 7 to simplify notation because neither initial velocity nor species change during a free flight For a finite medium this distribution can be generalized to writing shorter l for r 19 v i D L exp i ds s y C lt lna Tl 5 lmaz 1 Iman exp i dsEx s isis 2 12 Here lmar denotes the distance along the flight direction from r to the boundary for the computational domain to any internal surface at which the test flight shall be stopped e g for scoring surface fluxes there or even to the cell boundary The Transport Kernel T has dimension 1 Dimension of phase space T x x dz is a probability The function F Dimensi
150. application runs in particular those carried out at IPP Garching Ralf Schneider et al and AEA Culham Laboratories Geoff Maddison have lead to identification of many critical issues and limitations of the code and to permanent improvements until these days Typical convergence behaviour of the combined code sys tem saturated residuals is described in the new section L written in collaboration with G P Maddison AEA Culham Laboratories Detlev Reiter Spring 1998 Foreword to 3rd edition During the year 2001 a major revision of the EIRENE code has been carried out largely in or der to implement a somewhat more modern FORTRAN structure into the code EIRENE code versions from this particular year 2001 then have sometimes been referred to as EIRENE FACELIFT EIRENE 9 in the notation of this manual In particular a dynamical allocation of storage rather than the hitherto necessary pre assignment of storage in the PARAMETER statements collected in the previous PARMUSR file is now in place This dynamic memory management has led to a replacement of the previous Common Blocks now by Modules and to the entire elimination of the Equivalence statements used for storage economy in earlier versions Further main upgrades are related to e incident species dependent surface interaction models pumping speeds sputter mod els etc can now be controlled by input flags rather than the previous quite difficult
151. asma coll NMOL amp em T14 18 PMIO Particle Source Test Ions from molecule plasma coll NION amp cm T15 19 PMPHT Particle Source Photons from molecule plasma coll NPHOT amp cm T15 20 PMPL Particle Source Bulk Ions from molecule plasma coll NPLS amp cm T16 21 PIEL Particle Source Electrons from test ion plasma coll 1 amp cm T17 22 PIAT Particle Source Atoms from test ion plasma coll NATM amp cm T18 23 PIML Particle Source Molecules from test ion plasma coll NMOL amp cm T19 24 PHO Particle Source Test Ions from test ion plasma coll NION amp cm T20 25 PIPHT Particle Source Photons from test ion plasma coll NPHOT amp cm T20 26 PIPL Particle Source Bulk Ions from test ion plasma coll NPLS amp cm T21 27 PPHEL Particle Source Electrons from photon plasma coll 1 amp cm 3 T17 28 PPHAT Particle Source Atoms from photon plasma coll NATM amp cm T18 29 PPHML Particle Source Molecules from photon plasma coll NMOL amp cm T19 30 PPHIO Particle Source Test Ions from photon plasma coll NION amp cm T20 31 PPHPHT Particle Source Photons from photon plasma coll NPHOT amp cm T20 32 PPHPL Particle Source Bulk Ions from photon plasma coll NPLS amp cem T21 240 Table 5 2 continued No Name Macroscopic quantity 1 Dim Units E
152. ate to a total energy loss gain rate and vice versa The use of flag DP is the same as in case of the AMJUEL database or any other exter nal database Default EIRENE energy source tallies then may have a different meaning depending on the choice of input flag DP and the particular database used ADAS or AMJUEL etc case 3 FILNAM PHOTON to be written REAC Name or number of the reaction as used in the file FILNAM If FILNAM METHAN or AMJUEL or HYDHEL or H2VIBR REAC is the number label of a cross section or of a rate coefficient fit E g REAC 2 15 2 in file METHAN for the reaction e CH gt CH H e If FILNAM CONST then REAC can be used to input the flag IFTFLG Whether or not REAC is to be interpreted as IFTFLG is identified by presence of the string FT e g gt REAC FT 110 would lead to IFTFLG 110 for this reaction If FILNAM ADAS then the character string REAC identifies the particular file within the directory identi fied by the path given for ADAS files in input block 1 see card CFILE DBHANDLE DBFNAME in block Z I For example REAC SCD96 then the file SCD96_h dat is read in this example this is for ionisation rate coefficients of H atoms In this latter example the additional input species identifier ELNAME reads H for hydrogen In Module eirene_read adas f called from SLREAC f the corresponding data table is then read into EIRENE If FILNAM PHOTON to be writ
153. ature T which is a quan tity given with dimension pressure times volume divided by time to a particle flux source strength given in 1 time one utilizes the universal gas law P x V N x kpgT to convert from pressure times volume typically at standard temperature T 273 15 K to the number N of particles For example x sl min standard liters per minute first divide x by 22 4 then mol min at standard conditions normal pressure 1013 25 mbar and normal temperature To Next multiply by Avogadro s no N4 6 0221 10 i e then particles per minute then divide by 60 then particles per second and finally multiply by the elementary charge 1 6022 10 then Ampere as used for particle fluxes in EIRENE Gas mass flow rates given in other units e g Torr m s are converted correspondingly Another frequently used dimensional quantity is the effective pumping speed S and also conductance L which both have dimension volume time e g litres sec i e these are volumetric flow rates rather than mass flow rates Multiplying these volume flow rates by the entrance gas pressure or by the pressure difference in case of conductance produces the pump throughput a mass flow rate again i e at given temperature a pumped particle flux 1 s Pumping speeds and conductances typically depend on pressure themselves and on temper ature T and the type of gas mass m In the molecular flow regime the pr
154. ault Standard Surfaces Z4 Input Data Tor Species Specification and Atomic Physics Modulg Neutral Neutral collisions in BGK approximation NI N NJ NJ DJ 2 4 2 3 Input for Plasma Background Derived Bac soe ce 2 1 Piecewise constant Step functions for sampling NO oq Additional Data for some Specific Zoney 2 9 Data ftor Statistics and non analog Methods 2 10 Data for additional volume and surface averaged tallies 4 0 1 Additional volume averaged tallies tracklength estimator 2 10 2 Additional volume averaged tallies collision estimato 2 10 3 Algebraic expression in volume averaged tallies 2 10 4 Algebraic expression in surface averaged tallies Algebraic expression 1n surface averaged tallies 2 10 6 Energy spectra in selected cells or surfaces Data for numerical and graphical Output Data for Diagnostic Module I N zo S Nn 48 54 55 56 56 57 59 59 59 60 60 60 62 63 69 73 79 79 80 81 91 92 92 95 106 123 126 127 129 136 137 149 150 164 166 167 169 173 174 175 176 176 176 177 179 190 B Problem specific Routines 211 bra E ORT as age ae eh ere 213 Additional Ta routines UPTUSR UPCU R 217 pa geegues os 218 B Z ollision estimated volume tallies UPCUSR 218 B Z napshot estimated volume averaged tallies UPNUSR 219 ees a Bo eRe a a n a 219 a a oe oes 220 3 2 4 urface averaged tallies UPSU
155. ave to be set in the initialization phase by calls to function STEP from SAMUSR INFUSR etc The initialization call to function STEP reads FLUX STEP NSPZI NSPZE NSMAX ISTEP ISTEP This call will initialize the step function no ISTEP for species ISPZ NSPZI NSPZE In function STEP the distribution density FLSTEP is converted into a cumulative distribution by ra FLSTEP ISPZ ISTEP i RRSTEP j FLSTEP ISPZ ISTEP j for each species index separately This cumulative flux distribution is then in Amp The cumulative distribution of the sum over the species index is stored on FLSTEP 0 ISTEP i i 1 NSMAX ISTEP After this FLUX FLSTEP 0 ISTEP NSMAX is returned The cumulative distributions FLSTEP themselves are stored in module CSTEP f the nor malized invers of the cumulative distributions which are needed for random sampling are only stored locally in function STEP Default initializations of functions STEP are carried out in the initialization of surface source sampling routine SAMSRF entry SMSRFO Random sampling using such step functions STEP is done e g from surface source sam pling routine SAMSRF entry SMSRF1 In addition to the value of the distribution FLSTEP i in each interval some further quanti 66599 ties may be defined as function of the interval index i 6659 1 TESTEP electron temperature at t
156. ay lead to strong par ticle momentum and or energy sources for the balances governing the background medium and these chemical sources may even be the dominant terms for the global flow problem at least in some parts of the computational volume e g typically in the divertor of fusion reactors Original diffusion advection equations for a background medium there may turn into diffusion advection reaction type equations and even change their mathematical charac teristics For such type of background medium models often Navier Stokes like or related then special interfacing procedures between the kinetic Monte Carlo component EIRENE and the numerical background model are required For the EIRENE code such procedures have been developed in the late eighties originally for the SOLXY 2D plasma code B but have then been transferred for the rather well established at that time 2D multi fluid plasma solver B2 The EIRENE modules developed for code interfacing are described in this section original references are Reiter E and first applications 1991 and the most detailed discussion probably still is the FZ J lich report JUEL 2872 Maddison Reiter L0 1994 The names of all routines in the interfacing block end with COP 4 1 Routine for interfacing INFCOP To write an interfacing routine INFCOP in order to couple EIRENE to another code is already a quite formidable task a new scientific challenge and
157. ay the source is modelled by EIRENE allows consistency with kinetic bound ary conditions for plasma fluid equations at plasma facing surfaces To describe this we first write the volumetric source Q particles per unit time and per unit r v phase space volume in terms of a surface flux T and a surface delta function The surface wall flux T thus has dimension particles per unit time per velocity space unit and per unit area Cult v i Pt v i w T 5 62 where 7 is a coordinate normal to the surface Sw m r 0 i e e V 7 r pointing away from the computational volume We see that l specifies the ingoing transport flux introduced in L amp a at the boundary of the computational domain We will henceforth use the notation I rather than Q in case of surface sources I is a kinetic microscopic surface source flux density distribution backward directed into the computational volume i e only v lt 0 To convert from a forward directed ion flux distribution I sp ion v at the plasma sheath in terface Ssn to a neutral flux distribution back from the wall surface Sw we fold Iga ion with a magnetic plus electrostatic sheath transmission kernel Ts and with the surface reflection incl sputtering kernel Cu equation Z54 Taulr v i E dr Bu Bu T shionlt v i Torli r v gt r v Culr v i gt v i 5 63 The summation over 7 is performed over all ion species entering the
158. boundary function STEP ISTEP see section ZLI as well as the distribution in velocity space The step function itself and the total source strength FLUX ISTRA however are defined in IF2COP using data from input block 14 see LIA for target recycling source ITARG In this case the sampling range from the spatial surface distribution and the species distribution specified in input block 7 must be equal to or a subrange of the the step function for target recycling source ITARG defined from the data in input block 14 if INDSRC UISTRA 6 then the input flags described in section are used to define the entire surface recycling source automatically The corresponding data in input block 7 for this stratum are not used and may be omitted Stratum ISTRA corresponds to the target recycling source ITARG from block 14 4 1 4 entry IFJCOP UISTRAA ISTRAE Return data at the end of an EIRENE stratum At this entry data are transferred back from EIRENE to the interfacing module and from there after possibly further processing to the external code This entry is called from the strata loop in subr MCARLO after all trajectories for a particular stratum ISTRA have 234 been sampled and after all volume and surface tallies have been scaled and processed to their final form The call to IF3COP is controlled by the flag NMODE input block 1 At entry IF3COP to module INFCOP data are expected for all strata ISTRA in the range ISTRA ISTRAA
159. can be reproduced exactly for which the same number of test flights is computed as in a previous run If NINITL 0 no initialization of random numbers for the particular stratum In case of the first stratum the default initialization is used Runs can only be reproduced if the same number of test flights is computed for each stratum Somewhat weakened correlation between subsequent runs as compared to the NINITL gt 0 option If NINITL lt 0 truly random initialization determined by machine clock These runs cannot be reproduced exactly Subsequent runs are uncorrelated E g recommended for stochastic approximation procedures in nonlinear applications NEMODS Flag to select one of the preprogrammed source energy conditional distributions given the source particle s position and species See distribution in velocity space below NAMODS Flag to select one of the preprogrammed conditional source angular distributions given the position species and energy of the source particle See distribution in velocity space below FLUX SCALV SCALV 0 default FLUX Source strength in Ampere FLUX is the scaling factor for all surface or volume averaged tallies FLUX is an atomic flux or an atomic ion flux Each source particle may carry a different flux NPRT ISPZ initial weight depending on the species ISPZ see below distribution for the species index NPRT is specified in the blocks 4 and 5 The t
160. case of the NLPLG option mesh in x y plane generated by a set of polygons for sim plicity and by an abuse of language we sometimes refer to the polygons themselves as ra dial surfaces or radial polygons RSUREF and refer to the polygons obtained by connecting all points with a particular index along the various radial polygons as poloidal polygons PSURE No use is made in EIRENE of the arrays RSURF and PSURF in connection with the polygon mesh option The NLPLG option permits to run EIRENE on 2D computer generated meshes with grid cuts in one direction Furthermore TSURF 1 TSURF 2 TSURF NT3RD are grid points in toroidal or z direction sub block 2C A co ordinate surface is labeled 3 JT and is defined by the equation PT xr y z constant TSURF IT In addition to these grids and depending on the geometry options chosen EIRENE then com putes further derived grid arrays for example a radial surface labeling grid RHOSRF which may or may not be identical to the RSURF grid and a zone centered radial surface labeling grid RHOZNE IR defined by RHOZNE IR 0 5 RHOSRF IR RHOSRF IR 1 These grids may be used for the input of closed form radial or x direction plasma profiles or as abscissae in plots of e g poloidally or y and toroidally or z averaged tallies We have found it convenient to allow for several NBMLT identical copies of such standard meshes separated and bounded by arbit
161. cedure The noise level for collision estimators increases with smaller time steps Hence avoid all collision estimators in t dependent mode Please contact us for an update on this situation if you wish to use that option 47 1 8 non linear effects coupling to plasma fluid models The section is currently rewritten Please refer to the report Jiil 2872 Feb 1994 by G Maddison and D Reiter for details ref L0 The back reaction of the host medium plasma on the neutral test particle kinetics renders the combined plasma neutral transport problem non linear already for the Monte Carlo solu tion of the linear Boltzmann equation This non linearity is not in the collision integral but in the dependence of the collision parameters collision rates mean free pathes on the plasma parameters It can be dealt with by iterating a solver for the host medium plasma and for the kinetic equation neutrals Such a CFD solver for 2D plasma flows is e g the B2 BRAAMS code and its iterative coupling to the Monte Carlo kinetic code EIRENE was developed in the late eighties and early nineties of the last century under NET KFA con tracts involving three EFDA associates the EIRENE group at FZ J lich formerly KFA the CCFE formerly AEA Culham edge modelling group as well as ERM Brussels The historically oldest option is the semi implicit scheme see fig L3 because of the severe CPU time constrains in the late eightie
162. centre currents supplemented by the divergence free mag netisation currents are one important component of the plasma currents 1 11 2 Coulomb Collision Models 1 11 2 1 Simple Coulomb Collision Models Strongly simplified Coulomb collision models are usually sufficient for molecular ions be cause of their very short lifetime until further fragmentation dissociative excitation disso ciative recombination etc to neutral products In order to roughly account for thermaliza tion effects and background plasma cooling or momentum transfer the energy parallel and perpendicular velocity of such ions can be modified continuously during particle orbit inte gration hence approximating the velocity space diffusion Fokker Planck equation by mean values of energy and momentum of the test particle There are two classes of simple collision models deterministic and stochastic A Deterministic relaxation in velocity space The energy and or velocity of charged test particles are modified in a fully deterministic way along the particle trajectory I e along with orbit integration also energy or certain velocity components are evolved according to ordinary non stochastic differential equations using appropriate relaxation times Al Only energy relaxation The simplest Coulomb Collision model is an averaged BGK type relaxation of energy of test particles to the mean energy of the Maxwellian background ions In the earliest versions of
163. ch fewer sputter tallies SPT BC were available i e only one type identifier in the name of these sputter tallies And BC and the corresponding species index could either mean i resolution wrt incident flux species summing over all sputtered flux species and types same as in incident surface flux tallies or ii resolution wrt sputtered flux summing over all incident species and types depending on code version Type ii convention was used in EIRENE versions operated at ITER IO e g in SOLPS4 3 all other EIRENE versions had convention 1 The extension of Jan 2014 now combines i and ii by providing the resolution wrt emitted type and species as ii did and simultaneously keeping the resolution wrt incident type i as needed for proper scaling of particle balances see option NLSCL input block 1 If temporal resolution has been requested input block 13 then NSTSI is increased by one NSTSIP NSTSI 1 and the last tally I2 NLIM NSTSIP corresponds to the Time Surface the census array then 238 5 1 1 Current status incl photon gas tallies Eirene2 992 and younger Table 5 1 Input Tallies for Background Input Module COMUSR No Name Macroscopic quantity 1 Dim Units Estim 1 TEIN Plasma Temperature Electrons 1 eV 2 TIIN Plasma Temperature Bulk Ions NPLS eV 3 DEIN Plasma Density Electrons 1
164. ck 5 e For electric fields needed only for charged particle transport only input via external files is possible Default 0 239 Table 5 2 Volume Averaged Tallies Output Module CESTIM No Name Macroscopic quantity 1 Dim Units Estim 1 PDENA Particle density Atoms NATM cem T1 2 PDENM Particle density Molecules NMOL cm T2 3 PDENI Particle density Test Ions NION cm T3 4 PDENPH Particle density Photons NPHOT cm T3 5 EDENA Energy density Atoms NATM eV cm 3 T4 6 EDENM Energy density Molecules NMOL eV cem 3 T5 7 EDENI Energy density Test Ions NION eV em 3 T6 8 EDENPH Energy density Photons NPHOT eV em T6 9 PAEL Particle Source Electrons from atom plasma coll 1 amp cm T7 10 PAAT Particle Source Atoms from atom plasma coll NATM amp cm T8 11 PAML Particle Source Molecules from atom plasma coll NMOL amp cm T9 12 PAIO Particle Source Test Ions from atom plasma coll NION amp cm T10 13 PAPHT Particle Source Photons from atom plasma coll NPHOT amp cm T10 14 PAPL Particle Source Bulk Ions from atom plasma coll NPLS amp cm T11 15 PMEL Particle Source Electrons from molecule plasma coll 1 amp em T12 16 PMAT Particle Source Atoms from molecule plasma coll NATM amp cm T13 17 PMML Particle Source Molecules from molecule pl
165. ck 7 for the spatial distribution of birth points on sub stratum N for stratum ISTRA has a negative value This subroutine returns to EIRENE the cartesian coordiantes of the birth point X0 Y0 Z0 cell index information IRUSR IPUSR ITUSR IAUSR IBUSR as well as local plasma background data at this place of birth TIWL TEWL DIWL VXWL VYWL VZWL EFWL SHWL WEISPZ The input parameters EIRENE input block 7 for primary sources SORAD1 SORAD2 SORAD3 SORAD4 SORADS SORAD6 can be used in this problem specific routine Dimensions Precision Format of subroutine SUBROUTINE SAMUSR ISR X0 Y0O Z0 SORAD1 SORAD2 SORAD3 SORAD4 SORAD5 SORAD6 IRUSR IPUSR ITUSR IAUSR IBUSR TIWL TEWL DIWL VXWL VYWL VZWL EFWL SHWL WEISPZ USE PRECISION USE PARMMOD MORE MODULES IF NEEDED MPLICIT NONE NTEGER INTENT IN ISR ISTR REAL DP INTENT IN SORAD1 SORAD2 SORAD3 SORAD4 SORAD5 i SORAD6 REAL DP INTENT OUT X0 Y0 Z0 NTEGER NTENT OUT IRUSR IPUSR ITUSR IAUSR IBUSR NPLS NUMBER OF BULK ION SPECIES IN EIRENE INPUT BLOCK 5 NSPZ TOTAL NUMBER OF PARTICLE SPECIES NSPZ NPHOT NATM NMOL NION NPLS SEE INPUT BLOCKS 4 AND 5 REAL DP INTENT OUT TEWL SHWL TIWL NPLS DIWL NPLS VXWL NPLS VYWL NPLS VZWL NPLS E
166. cm 4 DIIN Plasma Density Bulk Ions NPLS cm 5 VXIN Plasma Drift Velocity x component Bulk Ions NPLS cm sec 6 VYIN Plasma Drift Velocity y component Bulk Ions NPLS cm sec 7 VZIN Plasma Drift Velocity z component Bulk Ions NPLS cm sec 8 BXIN Magnetic field unit vector x component 1 9 BYIN Magnetic field unit vector y component 1 10 BZIN Magnetic field unit vector z component 1 11 BFIN Magnetic field strength 1 Tesla 12 ADIN Additional input tally NAIN see INFCOP 13 EDRIFT Kinetic energy in drift motion Bulk Ions NPLS eV 14 VOL Zone Volume 1 em 15 WGHT Space and species dependent importance NSPCMC 1 16 not in use 1 17 not in use 1 18 EXIN electric field unit vector x direction 1 19 EYIN electric field unit vector y 1 20 EZIN electric field unit vector z direction 1 21 EFIN electric field strength 1 V CM Note e DEIN and EDRIFT are derived input tallies internally computed from the ion den sities quasi neutrality and the flow field respectively e Magnetic field input is needed only for photon transport with Zeeman line shapes or in case of charged particle transport Subr FOLION Only quite rudimentary prepro grammed input options for magnetic field are available usually it is expected to receive B field information from external files see INDPRO options for magnetic field tallies in input blo
167. ctory In this latter case one must add a volume source to launch these secondaries via a proper spatially distributed source in the next iteration By using this option carefully and combining it with the stratified source sampling technique coupling to external codes models can be made either more or less implicit Some care is needed here to avoid double counting Next EIRENE expects one so called species block for each test particle species Later in input block 5 it will also expect one species block for each of the heavy background particles i e for the bulk ions A species block has the format ISPZS TEXTS NMASSS NCHARS NPRTS NCHRGS ISRFS ISRTS ID1 NRCS NFOLS NGENS NHSTSS ID3S format 1I12 1X A8 1X 12 12 1X Default for ID1 is ID1 0 In case ID1 lt 2 i e two or less post collision particle not counting electrons DO K 1 NRCS IREACS IBULKS ISCD1 S ISCD2S SCDES ESTM IBGKS EELECS EBULKS ESCD1 S EDUMMY FREACS FLDLMS ENDDO New option in 2006 In case ID1 3 i e three post collision particles not counting elec trons needed for some more complex chemical reactions such as particle rearrangement collisions p CH gt CH H H etc DO K 1 NRCS IREACS IBULKS ISCD1 ISCD2S ISCD3 ISCDES ESTMS IBGKS EELECS EBULKS ESCD1 S EDUMMY FREACS FLDLMS ENDDO
168. d out which options precisely are available or contact the EIRENE team at FZ Juelich Only in case of additional surfaces the information on this deck is always fully used SORAD1 Left endpoint a of interval a b for x or radial co ordinate SORAD2 Right endpoint b of interval a b for x or radial co ordinate SORAD3 as SORAD1 for y or poloidal co ordinate SORAD4 as SORAD 2 for y or poloidal co ordinate 159 SORADS5 as SORAD1 for z or toroidal co ordinate SORAD6 as SORAD2 for z or toroidal co ordinate The direction unit vector C for the velocity space distribution is by default the positive outward normal vector of surface INUM at the birth point by default thus need not be specified for the surface source option see Standard Mesh Surfaces and or Additional Surfaces Volume source Flags for the distribution in physical space not mentioned here are irrelevant for volume sources NSRFSI Total number of subregions of the standard mesh in which the starting points for this stratum are distributed sub strata to facilitate sampling of spatial coordinates The next deck of 4 input cards is read NSRFSI times one deck for each sub stratum INUM irrelevant labelling index for sub strata INDIM INSOR not in use for volume sources INGRDA INGRDE same as IRPTA IRPTE flags in input block 3a Defines subregion of standard mesh on which the source is distributed SORLIM if SORLIM lt 0 the
169. d L3 By default the following conventions are used and can be overruled by calls to subroutines REFUSR SPTUSR only see section B3 ISRF fast particle reflection species flag gt 0 If ISRF lt NATMI then ISRF IATM the species labelling index for the re flected fast atom If ISRF gt NATMI not in use warning and error exit 0 no fast particle reflection for this species pr 0 lt 0 notin use warning and error exit ISRT thermal particle re emission species flag incident atoms test ions and bulk ions gt 0O If ISRT lt NATMI then ISRT IATM the species labelling index for the re emitted thermal atom If ISRT gt NATMI then IATM is sampled from the distribution DATM IATM 0 no thermal particle re emission for this species p 0 lt 0 molecule is re emitted and ISRT is used to identify the species labelling in dex IMOL for the re emitted molecule exactly as described above for re emitted atoms The relevant sampling distribution for species index IMOL in case ISRT gt NMOLI is DMOL IMOL This option can e g be used to specify the dis tribution of vibrationally excited molecules H v emitted from a surface after bombardment by incident H atoms the so called Eley Rideal mechanism Sur face with implanted H H gt Ho v incident molecules gt 0 If ISRT lt NMOLI then ISRT IMOL the species labelling index for the re emitted thermal molecule If ISRT gt NMOLI then IMOL is sam
170. d in the report L0 In the final section of this introductory chapter L9 the non linear BGK formalism and the di rect simulation method DMCS for self collisions between neutral particles as implemented in the EIRENE code is described 1 1 The linear Boltzmann equation for the distribution func tion f EIRENE solves a multi species set of coupled Boltzmann type equations in arbitrary 3D geometries Strictly speaking it is the Boltzmann equation generalized from its original single species form with bi linear collision kernel for elastic collisions to a far more complicated collision integral which also represents chemical reactions This generalisation is also often referred to as Wang Chang Uhlenbeck WCU equation in literature LI In this present section we start with the Boltzmann equation We then deal with linearisations of collision kernels by fixing the phase space distribution of one of the two collision partners which we refer to as bulk or background or even simply plasma species Generalization to the full WCU type multi species collision kernels which in the same linearised form provide the mathematical description of the equations solved by EIRENE is then discussed next section LLI Relaxation of the linearisation is needed only when there is self interaction amongst the species considered by EIRENE as it is required e g when radiation transfer is included coupling between photons
171. d off error margin used for geometrical computations In case NUACH 1 the error tolerated in the geometry routines is EPSGEO 1 D 10 and EPSGEO 1 D 6 for all other values of NMVACH NMODE Operating mode 0 EIRENE run as stand alone code Code coupling segment couple _Dummy f may be used Input block 14 has a fixed format see section ZIA 73 0 EIRENE calls the code coupling subroutine INFCOP in the code coupling seg ment couple _Name f where Name is a character string identifying the particular external code to which EIRENE is to be coupled e g Name B2 Name DIVIMP Name U file Name FIDAP Name EMC3 Name OSM etc Hence the routine INFCOP is called by EIRENE for communication with exter nal data sources e g other codes The calling program for the first 3 entries of INFCOP is subroutine INPUT and the call to subroutine INFCOP is after reading 13 blocks from the formatted input file READ IUNIN A 14 block of the input file is read from subroutine INFCOP with the format if any specified there At entry IFOCOP geometrical data are provided overruling corresponding data in input block 2 At entry IF1COP plasma profiles more generally background medium data are defined overruling the background data specified in block 5 Any other data e g surface or volume source distributions overruling the data in input block 7 are expected from entry IF2COP gt 0 If NMODE gt 0 subroutine INFCOP is cal
172. e any textbook on statistics or Monte Carlo methods It sometimes can significantly affect the efficiency of a Monte Carlo run This can go both ways depending upon the particular problem and the particular stratification used Therefore as with the non analog options no general recommendation can be made The effects of source stratification however are usually more easy to assess predict than those resulting from general non analog methods In order to make connection with the textbooks in which stratified sampling is often dis cussed in connection with Monte Carlo integration procedures the Monte Carlo solution of the transport problem is interpreted as a Monte Carlo integration and the stratified sam pling in Monte Carlo integration becomes a stratified source sampling in transport prob lems in this interpretation To see this we need to note here only the following based on Fredholms alternative for the linear Boltzmann operator EIRENE provides estimates of linear functionals moments responses g s 5 95 3 34 As described above g is the detector function weighting function s is the solution to the kinetic transfer equation Boltzmann equation in which S was used as inhomogeneous source term 7 is the solution of the corresponding adjoint equation with g as source term and S as weighting function 25 The above equation means that EIRENE estimates can simply be
173. e averaged tallies as in sub block 10C but for surface averaged tallies rather than volume averaged tallies The corresponding tally numbers are listed in table EA There is one generalization available here compared to the options for volume tallies which permits algebraic expressions not only between different complete surface tallies expression evaluated for all NLIMPS surfaces but also between different individual surfaces If the first index I is out of range i e larger than the first dimension N1 of the tally J as listed in table 6 3 then the operant lt I J gt identifies the following estimate surface index ILIM PS I N1 1 N1 1 species index I SPZ I ILIMPS N1 The other way round in order to identify species ISPZ and surface no ILIMPS for a partic ular tally J on must set first operand J ILIM PS N1 ISPZ second operand J The algebraic expression is stored on the ALGS tally for all surfaces ILIMPS which occurred in at least one of the operands 176 Example let there be up to 3 atom species NI NATM 3 and assume that additional surfaces 7 8 9 10 and 11 comprise the pump Let furthermore IATM 2 stand for helium atoms The total pumped flux of helium atoms from these surfaces is evaluated by the string lt 23 1 gt lt 23 2 gt lt 26 1 gt lt 26 2 gt lt 29 1 gt lt 29 2 gt lt 32 1 gt lt 32 2 gt lt 35 1 gt lt 35 2 gt The value found
174. e for total heat fluxes from drifting Maxwellians yg 2 449 V 5 V as it must We conclude that the above scheme is both an accurate and efficient random number generator for truncated shifted Maxwellian flux distributions of particles incident onto or emitted from surfaces Of course after having generated v with the weight w v and before reflecting the particle via the kernel C the acceleration of an ion in a sheath potential in direction 7 normal to the target surface as formalized in the sheath transmission kernel Ts mentioned above in Eq 4 63 can easily be included yn 2 V 4 hb 05 5 76 Vo 5 77 40 1 5 2 The electrostatic sheath The electrostatic sheath potential in front of a target surface is derived from assuming a given net electrical current 7 and a known ion particle current i e 7 q I electrical ion current entering a plasma target boundary layer the sheath with q eZ being the ion charge e the elementary charge and Z the ion charge number flowing over the target sheath edge Both these currents and the electron current j7 qel el are taken to flow parallel to the B field at the plasma sheath edge more generally forming an angle Y 4 90 degrees with the target surface normal 7 Often but not necessarily it is assumed jp jt j7 0 i e locally ambipolar flow conditions We start with a Maxwell Boltzmann density distribution ne x for the electr
175. e history to be traced in printout and or 2D or 3D plot ISYPLT J J 1 8 Indices to plot symbols along the particle tracks for different events Up to 8 different events can be picked in any order in the array ISYPLT no symbol symbol at particle s birth point at primary source symbol at the point of an electron impact collision event symbol at the point of a hard elastic collision event symbol at the point of a charge exchange event symbol at the point of a soft elastic collision event symbol at an intersection with a non default or additional surface symbol at a non analog particle splitting point o y HD Nn FW NY symbol at a non analog particle killing point Russian Roulette 9 symbol at a periodicity surface intersection point 10 symbol at restart after splitting 11 symbol at collision point saved for conditional exp estimator 12 symbol at a continuation of track for cond exp estimator 13 symbol at a particle stopped at time limit t dep mode 14 symbol at a particle stopped at generation limit t dep mode 186 15 If an error is detected by default a symbol is always plotted Plotting this symbol cannot be abandoned ILINIE connect two successive events by a straight line If a continuation of a track is computed for the conditional expectation estimators this part is represented by a dotted line see eq 1 2 5 0 only symbols if any selected will be plotted along the his
176. e standard mesh NACELL 0 For the cells in the additional cell region 1 lt NACELL lt NRADD and NRCELL 0 NPCELL 1 NTCELL 1 The last radial or x cell number NRIST for any NPCELL NTCELL inside the standard mesh is not a real geometrical cell It is used to store the radial or x average of the volume averaged tallies Likewise the last poloidal or y cell number NP2ND is not a real geometrical cell but used to store the poloidal or y average of the volume averaged tallies for any NRCELL NTCELL inside the standard mesh NTCELL NT3RD analogically A particular cell can be specified in one of two possible ways Either by giving the 5 cell numbers NRCELL NPCELL NTCELL NBLOCK NACELL or alternatively by giving the position in the 1 dimensional cell array NCELL The relation between these two options is NCELL NRCELL NPECLL 1 NR1IP2 NTCELL 1 NP2T3 NBLCKA with NBLCKA NBLOCK 1 NSTRDT NRADD 91 2 3 The Input Block for Surfaces Grid surfaces may be assigned special properties e g reflecting absorbing periodicity modified cell index switching etc Their definition is described in subsection 2 3 11 In addition to these grid surfaces also additional surfaces can be seen by the histories vacuum boundaries special surfaces for scoring fluxes diagnostic surfaces Such surfaces can be general linear or second order surfaces in 3D space Their definition
177. each stratum can be further subdivided into a sum of substrata Qk eT with normalisation Y weg 1 7 8 J J There are NSRFSI substrata and the weights wxj 7 1 NSRFSI is used for first determining a particular substratum jo and then sampling from distribution Qk jo v t t as described above The total CPU resources and storage for the census array see section 2 13 are distributed over the strata This distribution is controlled by some of the input flags in this input block as described below EIRENE stops working on a particular stratum if either the assigned CPU time for this stratum has been reached Message No further CPU time for this stratum 150 or if all requested histories have been calculated Message All histories for this stratum completed or in case of time dependent problems if the storage on the census array of this stratum has been filled up Message Census array filled for this stratum The Input Block xxx 7 Data for primary sources NSTRAI INDSRC ISTRA ISTRA 1 NSTRAI ALLOC DO 70 ISTRAI 1 NSTRAI TXTSOU NLAVRP NLAVRT NLSYMP NLSYMT NPTS NINITL NEMODS NAMODS FLUX SCALV VLSF ISCLS ISCLT SCL1 ISCL2 ISCL3 ISCLB ISCLA xSpecies index distribution L NLION NLPLS NLPHOT NLATM NLMO NSPEZ Distribution in physical sp
178. ection sampling is abandoned and the sample is accepted Check in subr VELOCX to find out which of the two physically equivalent methods are in use Default reactions 5 3 1 and 6 3 1 added in April 2006 to simplify input for pure He plasma simulations are the two resonant charge exchange processes He He He He He Hett Hett He The weighting or rejection technique was absent in versions younger than 99 for this par ticular type of default charge exchange collision integral approximation which strictly speaking had therefore led to a slight violation of the second law of thermodynamics H Theorem due to an inconsistency between the in scattering term determined by ocx and the out scattering term determined by cv in the Boltzmann CX collision integral al though mass and energy had been strictly conserved in each collision Alternative to the choice ISCDE 00000 made in the default model one may also use ISCDE 01000 with all the rest kept identical In this case the rate coefficients are evaluated in the same way as described above but neutrals emerging from CX collisions are sampled from the local drifting Maxwellian distribution of ion collision partners rather than from a drifting mono energetic distribution default model for hydrogenic molecules H and isotopomers and their ions For hydro genic molecules H2 D2 HT or molecular ions H4 D HT default dissociation io
179. ed according to the fast particle reflection model Hence same as EINTEG 1 0 not ready to use Fixed independent of energy and angle of incidence momentum reflection coef ficient This choice replaces the angle random sampling procedure in the fast particle reflection model by a momentum reflection assumption such that on average Vout Vin AINTEG Default no modification of angular distributions in reflection model for fast par ticle reflection 141 lt 0O notin use Note Some General Reflection Model data of input block 6A are copied identically NLIMI NSTSI times onto appropriately dimensioned arrays with the same names in order to make them dependent upon the surface labelling index as well The first index is then the species index the second index is the surface number Presently this localization option is available for the flags to be written RFOUSR or SPOUSR of the user supplied reflection routine REFUSR RFOUSR and SPOUSR are called in the initialization phase of an EIRENE run see section B3 By a similar strategy some of the species independent flags in the next sub block 6B can be made species dependent See for example RECYCK RECYCT RECYCS and RECYCC below 6B Data for Local Reflection and Sputtering Models The next 3 or 4 lines comprise the sub block for local reflection data Such sub blocks can be included in each surface deck block 3A 3B to overwrite the defaul
180. ed tally which is to be replaced by this tracklength estimated tally If either IADVS or IADVT is out of range no default tally is replaced by this additional tally IADVR If automatic re scaling of volumetric tallies is performed i e if NLSCL TRUE then re scale this tally with EIRENE recommended factor FATM IADVR 1 FMOL IADVR 2 or FION IADVR 3 see block 1 for the flag NLSCL and the variables FATM FMOL FION TXTTAL Text to label tally on numerical or graphical output TXTSPC Text describing the species of particles contributing for this tally in output rou tines TXTUNT Text describing the units of this tally in output routines 2 10 2 Additional volume averaged tallies collision estimator ICLVE as IADVE above for collision estimated tally subroutine UPCUSR ICLVS species index of default volume averaged tally which is to be replaced by this col lision estimated tally In case of tallies with no species index ICLVS must be set equal to 1 ICLVT number of default volume averaged tally which is to be replaced by this collision estimated tally If either ICLVS or ICLVT is out of range no default tally is replaced ICLVR as IADVR above for collision estimated tally subroutine UPCUSR TXTTAL TXTSPC TXTUNT as above 175 2 10 3 Algebraic expression in volume averaged tallies ALSTRNG character string which is interpreted as an algebraic expression in some volume averaged tallies An operant lt i j
181. ee below to the x coordinates of the poloidal mesh RSURF PSURF The radial shift of the poloidal mesh RMTOR of the approximated torus is computed from ROA such that the volume inside radial surface NRIST is exactly equal to the volume of an exact torus with poloidal cross section defined by the shifted radial grid first standard mesh RSURF Due to the approximations made by defining a torus by NTTRAM NTTRA 1 straight cylinders this condition is fulfilled only approximately for the other radial sur faces RMTOR converges to ROA with increasing NTTRA NTTRA 30 is already a very good approximation Default NLTRA FALSE NLTRT TRUE torus co ordinates R PHI THETA Presently being developed for NLSLB NLPLG and NLTRI options Not ready for use NT3RD Number of grid points in z or toroidal direction default NT3RD 1 i e no grid is defined 89 NTTRA only needed in case NLTRA and NOT NLTOR See above ZIA ZGA ZAA ZZA ROA The 3rd grid ZSURF is defined in the same way as the x grid using the parameters ZIA ZGA cm instead of RIA RGA In case of NLTRZ TRUE a z grid is defined ROA is irrelevant In case of NLTRA TRUE ZIA and ZAA are toroidal angles in degrees A grid of toroidal angles is defined For example use ZIA 0 0 and ZAA 360 0 for a full torus In case NLTOR this grid also defines the toroidal resolution If NOT NLTOR then periodicity at the endpoints ZIA and ZAA is automatically enf
182. efficients and or the resulting distributions in post reflection energy and angle respectively These flags only apply to incident particles of type 1 3 4 and 5 i e not for incident molecules because for those RPROBF 0 by default RINTEG lt 0 EINTEG lt 0 AINTEG gt 0 gt 0 Fixed independent of energy and angle of incidence particle reflection co efficient The fast particle reflection probabilities RPROBF are set to pp MIN 1 Pa RINT EG regardless of the reflection model selected by the flag ILREF in block 6B pa is kept as specified and p is then recomputed as p 1 py pa RINTEG gt 1 p enforces the fast particle reflection model for all un pumped incident particles i e RINTEG is internally reset to 1 pa Default fast particle reflection probability as defined by the reflection model chosen The fast particle reflection probabilities RPROBF are set to 1 0 i e even pump ing is turned off as distinct from the choice RINTEG 1 0 which would preserve the pumping speed at a surface gt 0 Fixed independent of energy and angle of incidence energy reflection co efficient This choice replaces the energy random sampling procedure in the fast particle reflection model by an reflection assumption Eout Ein HINT EG Default no modification of energy distribution in the reflection model for fast particle reflection elastic Eout Ein reflection for all particles reflect
183. efore setting the derived profiles De flux surface labelling grids The Input Block Data for some specific zones NZADD DO 81 IZADD 1 NZADD comment optional card N NE then read an arbitrary number of cards each starting with either T D V M VL or CH3 in any order 81 CONTINUE The following specifications are applied to each cell with cell number ICELL in the range INI lt ICELL lt INE CH3 cards format 3A 69A arbitrary number of strings n m separated by blanks n and m must be integer vari ables 1 lt n m lt NLIMI By default EIRENE assumes that any additional surface is visible from any cell of the computational box A string n m or n m has the effect that during particle tracing possible crossings of additional surfaces number n to num ber m are not checked whenever a track starts in cell ICELL By n m these surfaces are activated again in principle this option is not needed due to default setting A particle history can be forced to stop and then to restart in a cell e g by making appropriate use of the ILIIN 1 option for additional or non default standard surfaces T cards T IDION TEADD TIADDUDION format 1A 116 6X 2E12 4 plasma temperatures T and T in cell ICELL are reset to TEIN ICELL TEADD TUN IDION ICELL TIADD UIDION D cards D IDPLS DIADDUIDPLS format 1A 116 6X 1E12 4 plasma ion density D for specie
184. either in the present run or an earlier EIRENE run see NFILEN option in input block 1 The parameters fields of density temperature flow velocity for species IPLS are set from those of species ISP ITP ISTR This model then constructs a background species IPLS which is the sum of NRE species in collision radiative equilibrium with these ISP ITP ISTR particles INDPRO Flag array for the type of profile The last digit between 1 and 9 controls the type of profile A second digit and or the sign control further options as described below INDPRO is an array of length 12 Each element in this array controls one particular input tally namely INDPRO 1 for TEIN INDPRO 2 for TIIN By the default 0 lt INDPRO 2 lt 10 one common T profile for all bulk ion species is set I e read only one profile card New options since 2001 Values of INDPRO 2 larger than 10 use only the last digit and one 7 profile card must be read for each bulk ion species IPLS For example IVDPRO 2 15 or 25 means one separate ion temperature must be specified for each bulk ion species and the profile type is 5 UNDPRO 2 5 would do the same INDPRO 3 read NPLSI cards for DIIN IPLS 1 NPLSI INDPRO 4 read NPLSI cards for VXIN VYIN VZIN IPLS 1 NPLSI New options since 2001 By the default 0 lt INDPRO 4 lt 10 one separate flow field for each bulk species is set velocity is given in cm sec Negative value of INDPRO 4 means
185. elled INUM The sum of SORWGT for all NSRFSI surfaces is normalized to one internally SORLIM KLMN if SORLIM lt 0 the user supplied Subroutine SAMUSR is called to sample all 3 initial co ordinates X0 Y0 Z0 see section BA if SORLIM gt 0 then one of the preprogrammed options is used the digits L M and N are relevant only for surface sources In this case N Index to select one of the preprogrammed distributions in radial or x direction on the surface M Index to select one of the preprogrammed distributions in poloidal or y direction on the surface L Index to select one of the preprogrammed distributions in toroidal or z direction on the surface K Index to select one of the preprogrammed distributions for the starting time M N L 0 The respective co ordinate is computed from the 2 others and from the equation for surface number INSOR Thus one and only one of these 3 digits must be equal to 0 because the birth point for a surface source is determined already by two co ordinates and the labelling o index of the surface 157 If INDIM 0 any one of the 3 digits can be the 0 depending upon the particular equa tion for the surface ASURF INSOR In case INDIM 1 one has to set N 0 is now done automatically and the poloidal or y and toroidal or z co ordinate is sampled according to the flags M and L Correspondingly in case INDIM 2 one must specify M 0 and in case INDIM 3 the flag L 0 has to be set is redundant
186. enote averaging with the velocity distribution f r vp of the background medium species b 29 a is the total scattering cross section o 0 Vrei Hence e g for all isotropic target distributions f one has v v r E Qi and D DDr E Ni Furthermore let f be a drifting Maxwellian with temperature T and drift Vp fe fa Tr Vo Then v V Ty v Vel i Finally if the thermal speed v in this Maxwellian vthe T m is very large compared to typical values of v V i e nearly incompressible flow conditions then v V Tp 0 7 n o v e and here v is the usual Maxwellian rate coefficient for the collision process taken at temperature T of the background particles species b and at zero velocity of the test particles species 7 For example in case of neutral atom or molecule collisions with electrons this approximation is usually valid From the point of view of electrons or ions colliding with a cold background of neutrals or ions T 0 we have the opposite case v gt gt vi er and then the rate coefficient reduced to the simple product o v v with v being the test particle velocity 1 3 5 1 Alternative fixed time step or constant path length increment If the particle orbit between two events the Green s function is not given explicitly e g not as simple straight line then the orbit has to be integrated numerically using small time steps At or path
187. ents in the EIRENE code Thanks to Jose Guasp CIEMAT Spain for pointing this out 225 3 5 The user routines to overrule input data 3 5 1 The user geometry data routine GEOUSR to be written 226 3 5 2 User supplied background data routine PLAUSR to be written 3 6 The user routines for profiles PROUSR General remarks This subroutine is called from the subroutine PLASMA if the input flag INDPRO input block 5 has the value INDPRO IPRO 5 for a particular background tally IPRO Only the data for cells from the standard mesh ICELL 1 NSURF are used Default vacuum data are set for all cells in the additional cell region ICELL NSURF 1 NSBOX PROUSR is called furthermore from subroutine INPUT to provide cell volumes for all cells ICELL 1 NSBOX if the input flag INDPRO 12 has the value INDPRO 12 5 Format of subroutine SUBROUTINE PROUSR RHO INDEX P0O P1 P2 P3 P4 P5 PVAC NDAT CALL PARMMOD F INDEX EQ 0 THEN C DATA FOR TE PROFILE NDAT NSURF DO ICELL 1 NDAT RHO ICELL ENDDO ELSEIF INDEX EQ THEN ELSEIF INDEX EQ 5 5 NPLS THEN C DATA FOR VOL NDAT NSBOX ELSE WRITE 6 INVALID INDEX IN PROUSR CALL EXIT ENDIF RETURN END Depending upon the value of INDEX one has to specify a background tally on the array RHO R
188. ere INDPRO 6 5 7 only It also applies to the space and species dependent weight function WGHT to be used for non analog sampling techniques INDPRO 7 which is defaulted to 1 0D0 for all cells and all NSPZ species and it furthermore also applies to the zone volume array VOL cm 129 INDPRO 12 Defaults are the cell volumes computed in EIRENE subroutine VOLUME from the standard mesh data Plasma data in the additional zones IADD IADD NSURF 1 NSURF NADD outside the standard mesh are defaulted to the EIRENE vacuum data given below Plasma data other than these vacuum values meaning no collision processes in such cells in these zones have to be specified either explicitly in input block 8 see below or in the user supplied subroutine PLAUSR or with the INDPRO 7 option see below this section Cell volumes in the additional cell region are defaulted to 1 0 cm unless IN DPRO 12 4 5 6 7 A standard mesh zone ICELL is automatically identified as a vacuum zone with regard to plasma species IPL no collisions with the bulk particles IPL there LGVAC ICELL IPL TRUE for electrons IPL NPLS 1 if at least one of the following conditions is met for electrons IPL NPLS 1 TEIN ICELL lt TVAC DEIN ICELL lt DVAC for bulk ion species IPL IPLS TUN ICELL IPL lt TVAC DIIN CELL IPL lt DVAC and for all background species IPL 0 LGVAC ICELL T TRUE for I 1 NPLSI and for I NPLS 1 The E
189. es are needed only if PLTL3D TRUE LHIST3 make a 3D histogram plot LCNTR3 make a contour plot LSMOT3 make a surface plot in a 3D cube LRAPS3 produce files for RAPS graphics system If additional surfaces are to be indicated in these blocks PLSTOR TRUE see sub block 11B1 LVECT3 make a vector field plot NSPTAL must be 2 in this case The first of these 2 tallies is taken as field of x coordinates of the vector field to to be plotted and the second tally is the y coordinate field LRPVC3 produce files for RAPS graphics system for vector field plot Co ordinates of vectors as in LVECT3 option If additional surfaces are to be indicated in these blocks PLSTOR TRUE see sub block 11B1 LPRAD3 radial x co ordinate is fixed Plot tally versus poloidal y and toroidal z co ordinate See IPROJ3 flag below 188 LPPOL3 poloidal y co ordinate is fixed Plot tally versus radial x and toroidal z co ordinate LPTOR3 toroidal z co ordinate is fixed Plot tally versus radial x and poloidal y co ordinate ISPTAL species index of tally to be plotted ISPTAL 0 means sum over species index NPTALI Index of tally to be plotted IPROJ3 in case of 3d calculation IPROJ3 is the index of the mesh cell of the grid for which the corresponding co ordinate is fixed See LPRAD3 LPPLO3 LPTOR3 flags above NPLI13 NPL013 NPLI23 NPLO23 TALW1 first viewing angle for 3D plot TALW2 second viewing angle for 3D
190. essure dependence in S L diminishes and S L can be written as product S L Ag v of an area and veloc ity with v x T m Implementation of a specified volumetric flow e g a given effective pumping speed at pumps in EIRENE is via effective surface area and sticking probabilities see section 2 6 1 input flag RECYCT All densities are in cm All velocities are in either cm s or in isothermal Mach number units All geometrical data are in cm Note consequently e g energy densities are in eV cm and energy fluxes are given in eV Amp i e in Watt Hence In order to convert from EIRENE energy density units e V cm into pressure units in N m i e Pascal Pa one must multiply by 1 6022 10 19 eV to Nm and multiply by 10 cem m Check 1 Pa gas at 300 K corresponds to about 2 7 1014 x 0 026 eV em3 7 10 eV cm or a gas pressure P in Pa at gas temperature T Kelvin corresponds to a gas density n with n m P kgT with kg 1 38 107 the Boltzmann constant in J K units At 300 K and 1 Pa the corresponding gas density is n 2 415 10 m 2 415 10 tem For example energy densities as computed by EIRENE defaults tallies 5 6 7 and 8 see table EJ must be converted into temperature densities a factor 2 3 if one neglects the energy of the directed motion and then be re scaled to pressure units as described above For further scaling to other pressure units note e g 101 3
191. est Ions NPHOT amp T C 65 SPTIPL Sputtered Flux Bulk Ions by incident Test Ions NPLS amp T C 66 SPTPHAT Sputtered Flux Atoms by incident Photons NATM amp T C 67 SPTPHML Sputtered Flux Molecules by incident Photons NMOL amp T C 68 SPTPHIO Sputtered Flux Test Ions by incident Photons NION amp T C 69 SPTPHPHT Sputtered Flux Photons by incident Photons NPHOT amp T C 70 SPTPHPL Sputtered Flux Bulk Ions by incident Photons NPLS amp T C 71 SPTPAT Sputtered Flux Atoms by incident Bulk Ions NATM amp T C 72 SPTPML Sputtered Flux Molecules by incident Bulk Ions NMOL amp T C 73 SPTPIO Sputtered Flux Test Ions by incident Bulk Ions NION amp T C 74 SPTPPHT Sputtered Flux Photons by incident Bulk Ions NPHOT amp T C 75 SPTPPL Sputtered Flux Bulk Ions by incident Bulk Ions NPLS amp T C 76 SPTTOT Sputtered Flux total 1 amp T C 77 ADDS Additional Surface Tally NADS Input T C 78 ALGS Algebraic expression in surface averaged tallies NALS Input 79 SPUMP Pumped flux by species NSPZ amp Note This extended set of sputter tallies has now species naming conventions SPT A BC fully identical to those for volumetric source rates as well as those for emitted particle and energy fluxes from surfaces The full terminological equivalence leads to presence of quite strange sputter tallies e g bulk ion fluxes sputtered by incident photons tally 70 but redundant tallies and related storage are automa
192. etry plot The following 5 cards specify up to 5 groups of additional surfaces to be plotted on the 3D geometry plot Each group may consist of subgroups and each subgroup is defined by an interval of additional surface labeling indices ILIMI from the full range of all i e NLIMI additional surfaces 185 PL3A_ logical flag indicating if the additional surfaces specified in this card are to be plotted or not If PL3A FALSE the rest of this card is irrelevant TEXTLA text written onto plot characterizing this group of additional surfaces IPLTA number of different subgroups of additional surfaces comprising this group IPLAA IPLEA each subgroup consists of additional surfaces ranging from _ no IPLAA J to IPLEA J J 1 IPLTA The following 3 cards reading PL3S specify a group of standard mesh surfaces to be plotted on the 3D geometry plot The meaning of the flags in each card is the same as above for the additional surfaces The first card refers to the first x or radial standard mesh the second card refers to the second y or poloidal standard mesh the third card refers to the third z or toroidal standard mesh Each group may consist of subgroups and each subgroup is defined by an interval of standard surface labelling indices ISURF from the full range of all G e NRIST NP2ND or NT3RD resp standard surfaces I1TRC Number of first particle history to be traced in printout and or 2D or 3D plot I2TRC Number of last particl
193. eviations are printed if available The format for this extra output stream is specified in subroutine PRTTAL in code segment EIRASS NSURPR Total number of surfaces for which surface averaged tallies are to be printed NTLS Index of the surface to be printed By default all tallies listed in table 3 are printed for this surface NPRTLS J NFLAGS J NSPEZS J 1 NSPEZS J 2 These next flags are only needed for those surfaces for which a further spatial resolution within one surface is provided this is enabled by providing storage through setting the flag NGSTAL 1 in input block 1 Their meaning then corresponds to the meaning of flags NPRTLV J NFLAGV J NSPEZV J 1 NSPEZV J 2 for volume tallies respectively If the NPRTLS flags are not specified i e default 0 then no spatially resolved surface tallies are printed NTLSFL J The spatially resolved tallies if any and or the flux energy spectra if any see input block 10F are printed on additional output stream fort NTLSFL J for this surface The next optional input cards can be used to overrule the default choices of tallies which are available in a run The logical flag TRCTAL described above can be used to print a list of all activated and deactivated tallies NLTVOUT total number of volume averaged tallies to be explicitly abandoned or enabled 183 NUMTAL J Number of a tally from table EZ e g NUMTAL J 1 for neutral atom density tally PDENA The tally w
194. f Target Projectile Specification Cards of the format A_on_B Up to NHD6 see PARAMETER statements section B I data files for different Target Projectile combinations can be read in EIRENE versions older than 2001 No such limitation exists in more recent versions due to dynamic allocation of storage If no Path Card has been specified or after the Target Projectile Specification Cards continue reading general species sampling distributions used for source particle species sam pling as well as for sampling post surface event species as part of the surface reflection mod els DATD I 1 NATM DMLD I I 1 NMOL DIOD I I 1 NION DPLD I I 1 NPLS DPHT I I 1 NPHOT ERMIN ERCUT RPROBO RINTEG EINTEG AINTEG Note that the species index distribution cards must always be read even if NATM NMOL NION or NPLS are zero In this latter case at least one irrelevant parameter must be read E g if NION 0 i e no test ion species in particular run then still one card with the irrel evant parameter DIOD 1 must be read An exception from this rule is the photon species distribution DPHT this card is only read if there are photonic test particles in the run i e if NPHOT gt 0 This exception was necessary for backward compatibility of input file format after introducing photons as new type of species around 2001 Next optionally an arb
195. f coupled B2 EIRENE runs seems to be the loss of exponential decaying residuals errors in B2 balances down to machine precision which in stand alone B2 runs is a signature of having achieved convergence When coupled to EIRENE at least with uncor related EIRENE trajectories between subsequent EIRENE calls e g between time steps in the explicit coupling code residuals only saturate The level of the saturated residuals then scales only with the square root of the number of EIRENE trajectories used per EIRENE cycle Other convergence criteria then have to be defined see L0 for an early discussion of this still unsettled subject The typical behaviour of residuals in coupled B2 EIRENE runs saturated residuals is depicted in Figure LZ Note strong strict convergence exponentially decaying residuals down to machine pre cision can be achieved even in the presence of Monte Carlo noise as is regularly seen in simplified and dedicated test cases and actually in the very first applications of EIRENE in coupled plasma neutral transport problems in the late eighties of the last century B there to TEXTOR limiter configurations This however seems to require the activation of the corre lation sampling options of EIRENE in order to provide positive statistical correlation between successive time steps or iterations Presently the level of positive correlation implemented via the EIRENE flag NLCRR input block 1 seems to be too low
196. face PSURF NP2ND 2 at the center of the computational interval in this co ordinate This option has historical reasons The very first B2 EIRENE runs ever have been performed for upside down symmetric ITER double null configurations Reiter et al 1991 2 In more recent versions this option may not be available anymore FALSE no such symmetry is enforced LBALAN TRUE Global particle and energy flux balance is performed and printed at the end of an EIRENE stand alone run steady state or single time step and at the end of a short cycle between a plasma transport code and EIRENE These balances compare plasma particle and energy fluxes at the boundaries volume sources in plasma balance equations and neutral plasma interaction sources and sinks FALSE no such balances are computed NFLA Number of different bulk ion species in plasma code NCUTB Number of mesh cells in each grid cut in plasma code specific to grid generator used in connection with B2 fluid code NCUTL Number of mesh cells in each grid cut in EIRENE Note if NCUT 4 NCUTL the index mapping routines INDMAP and INDMPI are called at each call to the interfacing routines MSHFRM NTRFRM NFULL new flags available only since 2013 see section I irrelevant labelling index for EIRENE bulk ion species IPLS runs from 1 to NPLS IFLB gt 0 labelling index of bulk ion species in plasma code EIRENE bulk ion species IPLS corresponds to plasma code species IFL
197. fault parameter T is the local ion temperature for bulk ion species IPL IPL is determined such that the mass and charge number and the charge state of the source particle ION match the mass charge number and charge state of the bulk ion IPL If no such bulk ion is found T 0 These default choices of IPL can be overruled by the K digit of this input flag see below In case of not CNLPLS or NLION T 0 162 M 1 The local ion temperature T is replaced by the input constant SORENI eV and T is replaced by the constant SORENE eV in options N 4 to N 7 M 2_ notin use M 3 T is the local electron temperature and 7 is the local background ion tem perature of ion species IPL K K is the fourth digit of the NEMODS flag see below The choice of velocity parameters V in the energy distributions N 4 5 6 or 7 is con trolled by the third digit L of NEMODS L 0 In case of NLPLS the parameter V is the local ion drift velocity for bulk ion species IPL IPL is the species index of the source particle In case of NOT NLPLS V 0 L 1 The local drift velocity vector V is replaced by the constant vector SORVDX SORVDY SORVDZ cm sec regardless of the point of birth L 2 The local drift velocity vector V is replaced by the constant vector SORVDX SORVDY SORVDZ CS where CS is the ion sound velocity for the species and at the temperatures chosen above cm s Therefore SORVDX SORVDY SORVDZ are now understood as Mach nu
198. faults read formatted input file check input data for inconsistencies and set geometrical and plasma data Set cross sections and reaction rates Set data for non analog sampling methods Plot geometry Monte Carlo Particle Loop numerical and graphical output process volume averaged tallies into line integrated diagnostics signals save output data and modify input data iterative mode Figure 1 9 Flowchart Program EIRENE 64 Subroutines SETPRM SETCON SETTXT INPUT XSECTA XSECTM XSECTI NONALG PLT2D PLT3D MCARLO OUTEIR PLTEIR DIAGNO MODUSR 2 Subroutine INPUT Is this the first and or only iteration no yes Initialize data 2 1 Read from formatted input data file 13 blocks 2 13 unit 50 Check for inconsistencies correct input data compute further flags from input data read further input from interface 2 14 input block 14 unit 50 Compute standard grid and cell volumes Data for additional cell region Set background profiles 1 99 100 199 200 299 1200 1299 2000 3000 4000 IFOCOP IF1COP IF2COP GRID VOLUME MULTIG SETFIT TIMEAO ADDUSR SETEQ PLASMA PLASMA_DERIV Figure 1 10 Flowchart 2 Subroutine INPUT 65 6 Subroutine MCARLO TEETE STATSO 6 1 initialize subroutines REFLCO Initialize data 1 10 yes read output data RSTRT from earl
199. fic function characterizing the wavelength and temperature dependence of the thermal radiation field i e the Planck function For example the specific intensity 1 energy area time solid angle frequency interval is often used or the angle integrated in tensity J f I dQ or the specific energy density u 1 cJ energy volume frequency interval etc Also the wavelength dependence may be given either using frequency v Hz w rad s wavelength or energy E hv hw Depending upon all these choices the numerical factors in the definitions of the Bam coef ficients sometimes even in the Anm differ in the literature For our purpose Monte Carlo solution of the full radiation transfer equation we need to define monochromatic mean free pathes for photons rates and rate coefficients and cross sections for the individual processes In order to take advantage of the analogy between radiation and particle transport equations as much as possible we will choose the numerical constants in the Einstein coefficients such that these parameters have the same meanings and even the same units in both cases of radi ation and particle transport I e we will use the absorption coefficient better extinction coefficient if scattering is allowed a no invers monocromatic mean free path which directly corresponds to the total macroscopic cross section dimension 1 length defined earlier for particle transport problems
200. follows atoms molecules or test ions in a 3 dimensional computational box This box is discretized by zones mesh cells the boundaries of which are defined either by regular standard mesh surfaces i e co ordinate surfaces which are described here and or by zones whose boundaries are defined more generally by additional surfaces see below block 3B As long as test particles travel inside the standard mesh all cell indexing computations are done automatically At transition into the more general additional mesh and inside these additional cells this indexing has to be specified by the flags ILSWCH ILCELL etc by the user in input block 3B There are up to 3 sets of standard surfaces defined by the arrays RSURF PSURF and TSURF Here RSURF 1 RSURF 2 RSURF NRIST are grid points in the radial or x direction depending on the geometry level see below defined by the input data in sub block 2A Le there are NRISTM NRIST 1 cells in radial or x direction With regard to the terminology in LG eq 6 83 a corresponding co ordinate surface is labelled with a double index 1 IR and is defined by the equation HIR x y z constant RSURF IR PSURF 1 PSURF 2 PSURF NP2ND are grid points in the poloidal or y direction sub block 2B and there are NP2NDM NP2ND 1 cells in this direction A corresponding co ordinate surface is labelled 2 ZP and is defined by the equation fr y z constant PSURF IP In
201. from the Monte Carlo estimate by stratified sampling This fact is the reason for the EIRENE option of proportional allocation of CPU time described in input block 7 Section ZZ In principle one can even optimize the CPU performance i e minimize the variance per CPU time for any given stratification Sp by choosing the allocation N to strata in an even more intelligent way involving a priori knowledge of the variability within strata o e g estimated from a previous iteration But these options are likely to be quite sensitive to the choice of the particular tally response f In a typical EIRENE application many such responses for a large variety of detector functions g are estimated simultaneously in one single run Therefore this optimal allocation schemes are not currently implemented 27 1 3 4 Source sampling Source sampling in EIRENE is carried out in routine LOCATE F This routine converts uni form random numbers into random numbers with distribution Sx the k stratum part of the inhomogeneous term S Again sequential sampling G 32 from conditional distributions is applied In LOCATE F the following sequence is used stratum no istra k is set in calling pro gram S S x x So t x x S3 v x i 3 45 with Si x gt f d vS x i v being the cumulative distribution of the spatial coordinate x of the birth point of the trajectory obtained by integrating the source term S over all velocities
202. fv it f r E Q i t The distribution function in the form of f clearly remains meaningful also in the case of massless particles photons i e for applications of EIRENE to radiation transfer problems 10 We start with the elastics only Boltzmann Equation 1 but by assuming additionally that collisions are discontinuous events i e finite range interaction potentials or at least that proper cut off procedures are applicable This additional assumption allows us to sepa rate in the Boltzmann collision integral the collisional loss and gain terms into two separate integrals Otherwise cases could arise in which only the net collision term fff f f f fo would lead to finite results but not the collision term in the form as given in aa below SIS EF SIS E fo Farther Lets consider only one specific species 79 now omitting this species index We as sume that there are only collisions of this species 7 with only one further species here labeled b anticipating that later when discussing linear models these species will be referred to as background species plasma species etc with an externally given distribution f x v t Restriction here to elastic collisions means that exactly one particle of each of these two species will also be present after the collision event i e chemical reactions inelastic colli sions with change of internal energy are excluded for the time being but their description
203. g mode General Remarks The variables in this block control some of the more general options in EIRENE such as over all running time usage of dump files but also a few parameters depending on the simulation model drifts included or not etc The Input Block TXTRUN I Data for operating mode first card integer flags controlling global options for the entire run NMACH NMODE NTCPU NFILE NITERO NITER NTIMEO NTIME next input line is only for EIRENE2992 and younger and optional in these versions defaults if this card is not included are given below NOPTIM NOPTM1 NGEOM_USR NCOUP_INPUT NSMSTRA NSTORAM NGSTAL NRTAL NREAC_ADD next line second mandatory line logical flags for global options NLSCL NLTEST NLANA NLDRFT NLCRR NLERG NLIDENT NLONE LTSTV next input lines are only for EIRENE 2005 and younger and optional in these versions There can be any number of these cards starting with character string CF ILE in the input file CFILE DBHANDLE DBFNAME Meaning of the input flags for operating mode TXTRUN At least one line of text to identify the run on printout and plot files Each text card must start with The first of these text lines will appear on all plots the full text will be echoed at the beginning of the printout file NMACH Code number for the computer used 1 CRAY 2 IBM 3 FACOM 4 VAX This flag is not in use any more In the past eighties of last century it only affected the roun
204. ghboring surfaces M and N must be specified by the RLBND 1 or RLBND 1 5 option The fitting is achieved by a small automatic internal modification of the surface data P1 and or P2 of surface number J in subroutine SETFIT Printout of the modifications made there is activated with the TRCSUR flag input block 11 ILCELL Parameter ILBLCK and ILACLL for the IESWCH flags described above Let ILCELL NM with N and M being integers with 3 digits each Then N ILBLCK and M ILACLL ILBOX to be written ILPLG EIRENE can write out information for a finite element mesh generator to produce a grid of triangles for a multiply connected 2D domain with cracks and holes The various inner and outer boundaries are given as polygonal lines which are composed of selected standard grid surface segments NLPLG option and or additional surfaces 2 lt RLBND lt 3 option This flag identifies closed polygonal lines composed of additional surfaces given by the 2 point option and or of standard surfaces in the x y plane For example if IEPLG I NN for surfaces I I1 I2 IN NN a positive integer then these IN surfaces form a closed polygonal line in the x y plane The region inside this closed line is part of the com putational domain By a negative integer value of NN a closed polygonal region can be excluded from the computational domain i e a hole in the domain is specified by these surfaces EIRENE writes an output file appropriate for a f
205. gs of the input variables for a transformation block are 104 ITINI ITEND The transformation defined by the next 3 cards is carried out for additional surfaces from number ITINI through ITEND The transformation is carried out as soon as this transformation deck is found Hence if such a transformation deck is found after ad ditional surface no IS then one must guarantee ITINI lt IS and ITEND lt IS XLCOR YLCOR ZLCOR Translation The origin of the coordinate system is shifted by the vector XLCOR YLCOR ZLCOR XLREF YLREF ZLREF Reflection to be written No transformation if XLREF YLREF ZLREF 0 0 0 XLREF YLREF ZLREF Rotation The vector XLROT YLROT ZLROT defines the axis of rotation ALROT is the angle of rotation in degrees No transformation if ALROT 0 or axis of rotation 0 0 0 105 2 4 Input Data for Species Specification and Atomic Physics Module General remarks EIRENE can handle up to NATM atom species NMOL molecule species NION test ion species NPHOT photon species lines and NREAC different atomic molecular or photonic reactions between these test particles and the bulk ions or electrons There may be up to NPLS bulk ion species and one electron gas derived internally from the assumption of local charge neutrality Amongst the heavy background particles the bulk ions may be species with charge state zero i e neutral particles By ab
206. gt stands for tally number j first species index 1 in tables I and EZ Note that the first index for tallies with no species index must read 1 Expressions lt c gt with an integer or real constant c are interpreted as scalars The string may contain an arbitrary but lt 20 number of operands and of operators and of properly nested parentheses E g the total electron particle source due to test particle plasma interaction in units s m can be obtained by the line lt 1 7 gt 4 lt 1 12 gt 4 lt 1 17 gt lt 16 gt lt 1 6022e 19 gt in code versions older than 2002 see tables in section ELJ and the same expressions in versions 2002 and younger i e after implementation of photons as further species type and the related default tallies tables in section LJ lt 1 9 gt lt 1 15 gt lt 1 21 gt x lt 1 e6 gt lt 1 6022e 19 gt and it would be stored on the tally ALGV with the first labelling index IALVI Note that the cell volume array VOL is regarded as a volume averaged tally by abuse of language tally number 14 see table ET TXTTAL TXTSPC TXTUNT as above 2 10 4 Algebraic expression in surface averaged tallies as in sub block 10A or 10B but for surface averaged tallies rather than volume averaged tallies Note for surface averaged tallies collision and track length estimators are identical see sec tion 2 10 5 Algebraic expression in surfac
207. gth is used rather than CLPD This fact is used by EIRENE for condensed particle species NFOLS flag in block 4 This is used for example if the motion of test ions along field lines is not followed explicitly but if instead the particles undergo a next collision immediately at their places of birth i e quasi steady state approximation QSSA for this species 3 2 3 Snapshot estimated volume averaged tallies UPNUSR By default snapshot tallies are only scored in time dependent mode see input flags in Sec tion ZIA They can however also be used as a third alternative to tracklength and collision estimators for any stationary response In particular for diffusive processes as e g ion trans port with Fokker Planck type Coulomb collision operators such snapshot averaging is the most frequent option used in Monte Carlo applications to estimate stationary moments See paragraph B below 3 2 3 1 A time dependent estimates The default snapshot estimated tallies at a fixed time t see Section LIJ are updated in subroutine TIMCOL Currently these are only the census tallies and the particle and energy fluxes at census Subroutine TIMCOL is called from the particle tracing subroutines FOL NEUT and FOLION defaults in case of time dependent mode see input block 13 Non default snapshot tallies can be scored in UPNUSR additional user supplied tallies called from TIMCOL Here we have WSNAP 0 In EIRENE variable
208. gy Flux emitted B Atoms NATM watt T C 22 EOTML Energy Flux incident Molecules NMOL watt T C 23 ERFAML Energy Flux emitted Ats Molecules NMOL watt T C 24 ERFMML Energy Flux emitted Mls Molecules NMOL watt T C 25 ERFIML Energy Flux emitted T I1 Molecules NMOL watt T C 26 ERFPML Energy Flux emitted B I Molecules NMOL watt T C 27 EOTIO Energy Flux incident Test Ions NION watt T C 28 ERFAIO Energy Flux emitted Ats Test Ions NION watt T C 29 ERFMIO Energy Flux emitted Mls gt Test Ions NION watt T C 30 ERFIIO Energy Flux emitted T I Test Ions NION watt T C 31 ERFPIO Energy Flux emitted B I gt Test Ions NION watt T C 32 EOTPL Energy Flux incident Bulk Ions NPLS watt T C 33 SPTAT Sputtered Flux by incident Atoms NATM amp T C 34 SPTML Sputtered Flux by incident Molecules NMOL amp T C 35 SPTIO Sputtered Flux by incident Test Ions NION amp T C 36 SPTPL Sputtered Flux by incident Bulk Ions NPLS amp T C 37 SPTTOT Sputtered Flux total 1 amp T C 38 ADDS Additional Surface Tally NADS Input T C 39 ALGS Algebraic expression in surface averaged tallies NALS Input 40 SPUMP Pumped flux by species NSPZ amp Note The tallies listed here are two dimensional arrays The 2nd index I2 is the number of the surface or the surface segment For I2 1 NLIMI the tallies correspond to the Additional Surfaces input block 3B
209. haracterize the stratum name of the source on the printout file NLAVRP TRUE not in use NLAVRT TRUE not in use NLSYMP TRUE Symmetrize profiles with respect to poloidal y co ordinate x i e with respect to the poloidal surface x PSURF NP2ND 1 2 in case NP2ND is an odd integer or with respect to the cell center x PZONE NP2ND 2 in case NP2ND is an even integer NLSYMT TRUE ditto but for toroidal z co ordinate i e for toroidal surface TSURF NT3RD 1 2 or TZONE NT3RD 2 respectively NPTS NPTS gt 0 Maximum number of test particle histories If there is more than one stratum NSTRAI gt 1 then the total CPU time NTIME input block 1 will be distributed proportional to NPTS to the single strata NPTS is the maximum number of test particles only if sufficient CPU time is available Otherwise a message NO FURTHER COMPUTATION TIME FOR THIS STRATUM is printed and the particle loop for the respective stratum is stopped NPTS 0 this stratum is turned off NPTS lt 0 no limitation in the number of particles The entire CPU time assigned to this stratum will be used up NPTS is reset to the largest integer on the machine Hence some care is needed here in case of multiple strata in combination with the ALLOC options to assign CPU time to individual strata 152 NINITL If NINITL gt 0 seed for initialization of random number generator The results for all those individual strata
210. he Monte Carlo procedure to solve such equations by referring to the two most often applied techniques track length and collision based estimators In the third subsection we briefly describe the treatment of boundary conditions models for interaction of the particles with surround ing surfaces and discuss some special models which are in use for the neutral gas transport in fusion plasma devices Then section L5 we discuss the most important source function non homogeneous part of the integral equation and its implementation in a Monte Carlo algorithm namely the surface source of neutral particles due to recombination of ions inci dent on solid surfaces at the boundary or inside of the computational area In section Ld we comment on the implementation of geometry within the framework of a Monte Carlo code in general terms and for the EIRENE code in particular In section LZ the time dependent mode of operation of the EIRENE code is described It merely amounts just to an increase in the dimensionality by one by adding a time co ordinate and treating it formally in a rather symmetric fashion with the other spatial coordinates See also reference Q Two kinds of non linearities may be accounted for In section the nonlinear behavior resulting from background data which depend on neu tral particle transport sources and sinks is discussed The algorithm of the B2 EIRENE code system B is described More details on this can be foun
211. he surface segment TISTEP ion temperature at the surface segment i array of length NPLS DISTEP ion density at the surface segment i array of length NPLS 66599 Ee IRSTEP cell number in 1st x or radial grid of the surface segment 66599 1 IPSTEP cell number in 2nd y or poloidal grid of the surface segment 6659 1 ITSTEP cell number in 3rd z or toroidal grid of the surface segment IBSTEP block number see section 2e 66599 1 IASTEP additional cell number of the surface segment ELSTEP ion energy flux at the surface segment 1 array of length NPLS SHSTEP electrostatic sheath potential at the surface segment 1 Default step functions Step functions for sampling the radial coordinate at a given or sampled poloidal and toroidal position INDIM 1 SORLIM digit N 4 are defined internally during the initialisation step of surface sampling routine SAMSRF if the selected step functions SORIND ISTEP has not 165 been defined externally already Also in case of unstructured grids LEVGEO 4 5 default step functions can be defined for non default surfaces In such cases the particle flux spatial sampling distribution FLSTEP of background species ip on a radial grid segment 7 or triangle side 7 or tetrahedron side 2 is computed as FLSTEP ip i nilip x cs ip 7 10 with n ip the local ion density of species ip DISTEP ip i and cs ip is the isothermal
212. he various processes taken into consideration 31 Sampling v i from C can be done along the same idea first factoring out the discrete dis tribution for the species index 7 and then by sampling v from C the conditional distribution for v given the type of the process is k and the species of the post collision trajectory is 7 Let nka U 1 Ip be the number of post collision particles of species i from process k and Nk gt D Nki Then iki i 1 Tk Nki Mk i 1 Tp is the discrete distribution for the post collision particle species 2 given a collision process of type k 1 3 7 elastic collisions 1 3 8 charge exchange 1 3 9 electron impact collisions 1 3 10 general heavy particle impact collisions 1 3 11 photon processes emission absorption scattering 32 1 4 Surface Reflection Models Within the terminology fixed in section the effects of the interaction of neutral particles and escaping ions with surfaces surrounding or inside the computational volume can be described by additional boundary conditions It is however much more convenient for Monte Carlo applications to describe this interaction as just one special type of collision process in the collision kernel C of equation 2 9 i e as k with p r 1 if r is a point on a surface and p r 0 elsewhere The transport kernel T can be modified such that the maximum length lmaz for free flight to the next point of collision
213. hen comparing with uniform ran dom number The second assumption results from Taylor expansion for sufficiently small At such that Io A lt 1 The first assumption is more difficult to justify generally 30 If the post collision test particle species is the same and its new velocity is not too different from that prior to the collision then the probability for n collisions in the same time At is roughly P Gr l and the number of missed collisions in At is _ Gp Io r ae 3 53 For sufficiently small At and hence l this error can be made small If however collisions involve change in species and or significant changes in velocity then the smallness of Jo must be guaranteed not only for the particle which is currently be ing considered but for all particle species in the system and for all possible energies of secondaries E g the excitation cross section for process A A may be small hence lo A lt 1 for species A but the de excitation quenching of state A may be very rapid Then the quenching time of species A determines the permitted time step for species A in this approximate procedure Other critical examples may be systems composed of both rather stable chemical species and short living radicals e g hydrocarbons The EIRENE code therefore only uses the correct full sampling procedure 6 50 even when particle orbits e g of ions are integrated numerically with time steps 1 3 6 Sampling fro
214. however to provide strong convergence on a regular basis and for full scale problems e g the detached ITER divertor For this consider two plasma solutions obtained with a CFD plasma code coupled iteratively to EIRENE at neighboring time steps 1 and 2 The incremental change of the plasma solu tion due to the change in the Monte Carlo reaction term in the plasma flow equations is the difference between Monte Carlo source rates evaluated at time 1 and time 2 In more general terms a Monte Carlo estimate of a difference AF between two different calculations M C and MC due to either code version differences due to a different physical incremental effects or due to iterative procedures with CFD solvers is AE E MC E MC o AE o7 E MC 07 E MC 2cou E MC E MC 8 86 This holds even for any statistical estimate of an incremental effect independent of Monte Carlo procedures Here MC is the Monte Carlo estimate of the expectation value i e it is the Monte Carlo solution to the kinetic transport equation and o is the corresponding statistical variance It is clear from 8 84 that small effects AF such as those due to slightly different code versions can only by detected when the statistical correlation quantified by the covariance of the two estimators cov between the two Monte Carlo runs is made large EIRENE option NLCRR 52 10000 Electron Energy Balance 1000 250
215. icles isolated from the computa tional domain NSTGRD ICELL 1 can be specified in problem specific routines USR or in routines interfacing EIRENE with external codes INFCOP code segment COUPLE 2 indicates that this cell belongs to a grid cut i e is not a valid cell for particle tracing 3 indicates that this cell is not a real cell but only the storage position for spatially averaged tallies E g cell no NRIST 2 NRIST etc 136 2 6 Input Data for Surface Interaction Models General remarks An outline of surface interaction models in general terms was given in section L4 As for the implementation of such models in EIRENE there are two parts to the surface interaction data block The first part contains data which are general to the EIRENE reflection model Block for General Reflection Data at all surfaces The second part may be different for each individual surface element label M SU RF and thus must be specified for each reflecting non default surface of the standard mesh and for each reflecting additional surface It is referred to as Block for Local Reflection Data If this block is missing and if the surface MSURF is neither transparent ILIIN lt 0 nor purely absorbing ILIIN 2 nora mirror surface JILIIN 3 nor a periodicity surface JLIIN gt 4 then the default reflection model i e Fe Target recycling coefficient one etc is activated
216. ier run no strata loop DO 1000 ISTRA 1 NSTRAI LOCATO Tali 7 SAMPTO 6 2 initialize subroutines SAMLNO SAMSFO a SAMVLO Initialize data 11 40 6 3 particle loop DO 100 IPART 1 NPART scale tallies 200 300 integrate tallies 300 350 replace default tallies by user supplied tallies save data for this WRSTRT stratum on file interface to external codes IF3COP strata loop 1000 finished yes 1001 2000 save data for sum WRSTRT over strata on file END Figure 1 11 Flowchart 6 Subroutine MCARLO 66 Monte Carlo particle loop in MCARLO Loop Particles DO 100 IPART 1 NPTSI check remaining cpu time optional initialize random numbers correlation sampling 6 3 1 locate particle 6 3 2 follow atoms molecules or test ions update tallies linear functions of tallies estimate standard deviations end if loop 6 3 3 Figure 1 12 Flowchart 6 3 Particle loop in subr MCARLO Default volume averaged tal lies are updated on the fly per event in routines UPDATE problem specific tallies for code code interfacing COPV e g B2 EIRENE in UPDCOP specific tallies for non linear BGK operators BGK V in UPDBGK Corresponding variances are updated per history after completion of each trajectory in STATS1 STATS1_COP STATS1_ BGK Addi tion revision in 2012 Updating of linear functions of default tallies per history in UPFCOP e g f
217. ies involved in this collision and no BGK tallies are updated for iterating the artificial background species EELEC parameter EP for electron energy loss per collision Its meaning depends on fifth digit of ISCDE flag and is described above EBULK parameter EP for pre collision bulk ion energy loss per collision Its meaning depends on fourth digit of ISCDE flag and is described above ESCD1 parameter EP for velocity space distribution of secondaries Its meaning depends on third digit of ISCDE flag and is described above EDUMMY was earlier ESCD2 in versions 1999 and older the parameter ESCD2 EP was used for velocity space distribution of the second secondaries group whereas ESCD1 was used for the first group of secondaries Now this parameter ESCD2 is not in use anymore Distribution of energy kinetic energy release EP over secondaries is now by default inversely proportional to the masses of secondary particles as follows from momentum conservation in collision For backward compatibility of input files now EP ESCD1 EDUMMY FREAC multiplier to scale the cross section and rate coefficients of this process Default FREAC 1 0 If FREAC lt 0 it is also defaulted to 1 0 To turn off this process set FREAC to a very small number e g FREAC 1 0000 E 30 FLDLM Flag for generation limit or fluid limit Default FLDLM 0 0 This flag allows to cut trajectories after a certain maximum number of CX or EL co
218. ies 1 to 24 Same as ISRS gt 0 however the species index of the sputtered particle is deter mined automatically from comparing the charge and mass numbers of the atomic species input block 4a with the corresponding data of the surface element ISRC sputtered particle species flag chemical sputtering gt 0 lt 0 ZNML KL both the sputtered particle and the reflected particle if any will be followed Their contribution to surface particle and energy fluxes is stored in surface av eraged tallies 1 to 24 i e sputtered particles are not explicitly distinguished from reflected particles in the balances Furthermore the sputtered flux sur face tallies 25 to 28 are updated The species index of the sputtered particle atom is IATM ISRC if ISRC lt NATMI or molecules IMOL if ISRC NATMI IMOL and NATMI lt ISRC lt NATMI NMOLI Hence on input ISRC lt NATMI NMOLI There is no chemical sputtering for the particular surface element and incident species note ISRC ISRC ISPZ MSURF i e pe 0 here Only the reflected particles are followed Their contribution to surface particle and energy fluxes is stored in surface averaged tallies 1 to 24 Same as ISRC gt 0 however the species index of the sputtered particle is deter mined automatically from comparing the charge and mass numbers of the atomic species input block 4a with the corresponding data of the surface element I e in case of Carbon surface
219. ified it is computed internally from charge conservation In case of collisions with only one heavy particle secondary test particle or bulk ion electron impact collision CRC EI or re combination CRC RC ISCD1 is used and ISCD2 is irrelevant In case of charge exchange CRC CX ISCD1 is used for the new state of the impacting bulk particle after the collision whereas ISCD2 controls the options for the post collision state of that particle which was the test particle prior to the collision Consistency of the particle masses of pre and post collision particles with this convention is checked in the initialization phase of each run CX collisions mean exchange of identity i e scattering angle 7 in the center of mass system Le CRC CX is used for resonant charge exchange only Non resonant charge exchange in which e g internal energy is converted into kinetic energy of products is to be treated in the CRC PI category of general heavy particle collisions In case of elastic collision CRC EL the ISCD1 and ISCD2 flags are are irrelevant because the colliding particles retain their identity by default In case of electron impact collision CRC ED the ISCD1 and ISCD2 flags are symmetric i e they can be interchanged without any effect on the calculation ISCDE flags for post collision velocity space distributions for all particles involved in the collision event Each of the five digits controls a different type of par
220. ighted rate coefficient o v My Up cm s AMU cm s as function of target temperature eV double parameter fit of target particle velocity weighted rate coefficient av m v cm s AMU cm s as function of projectile energy eV and target tem perature eV double parameter fit of target particle velocity weighted rate coefficient ov mp v em3 s AMU cm s as function of target density cm and target tem perature eV single parameter fit of target particle energy weighted rate coefficient ov m 2 v2 cm s eV as function of target temperature eV double parameter fit of target particle energy weighted rate coefficient ov mp 2 u2 em s eV as function of projectile energy eV and target temperature eV H 10 double parameter fit of target particle energy weighted rate coefficient o v m 2 v cm s eV as function of target density cm and target temperature eV H 11 single parameter fit for any other data e g to be used in special user supplied programs H 12 double parameter fit for any other data e g to be used in special user supplied programs i e not understood by EIRENE case 2 FILNAM ADAS H 4 double parameter table of rate coefficient ov cm s as function of target den sity cm and target temperature eV read from files given in ADAS adf11 format E g original ADAS file names starting with SCD ionization rate co efficients contain ionizati
221. ilich Report J l 2872 Forschungszentrum J lich March 1994 Suzuki K Yano R Formulation and numerical analysis of diatomic molecular dissoci ation using Boltzmann kinetic equation Physics of Fluids 2007 C Cercignani The Boltzmann Equation and Its Applications volume 67 of Springer Series on Applied Mathematical Sciences Springer Verlag 1988 D B Heifetz D Post M Petravic et al A monte carlo model of neutral particle transport in diverted plasmas Princeton report PPPL 1843 PPPL November 1981 J Comput Phys 46 309 1982 E Cupini A de Matteis and R Simonini EUR XII 324 9 April 1983 L Devroye Non Uniform Random Variate Generation Springer Verlag 1986 250 16 R Behrisch Plasma wall interaction In Summer School of Tokamak Reactors for Breakeven Erice 1976 17 Impurity Control INTOR Workshop Phase ITA Part 3 18 W Eckstein and D B Heifetz Data sets for hydrogen reflection and their use in neutral transport calculations MPI Garching Report IPP 9 59 MPI Garching August 1986 J Nucl Mater 145 147 p332 1987 19 G Bateman Distribution of neutrals scattered off a wall PPPL Appl Phys Rep No 1 PPPL 1980 20 D Reiter P Bogen and U Samm J Nucl Mat 196 198 1059 1992 21 V Kotov D Reiter and A Kukushkin Numerical study of the ITER divertor plasma with the B2 EIRENE code package FZ Jiilich Report JUEL 4257 Forschungszentrum J lich November 2007
222. ility theory itel N gt 86 N 3 26 For large N the variance per history variance of a single observation converges to a constant namely to o and the final Monte Carlo estimate of variance Cle E26 has the expected probabilistic 1 N scaling i e the empirical standard deviation which is the Monte Carlo error estimate scales as Gc 1 JN Multiple cell crossings One should note that except in simple 1D cases in general one single Monte Carlo history w can contribute more than once to the estimate A for a particular cell of the grid or surface segment E g test particles can cross one cell m see Z145 more than once with each cell crossing j leaving a score contribution X to estimator X w Then Ji A Xe 3 27 j l with J being the number of contributions e g cell crossings to the estimator from particle history no i The summation in 6 14 and hence also the second sum on the right hand side of 6 25 can still be accumulated on the fly while generating the Monte Carlo histories i e at no extra CPU cost However because of course x Fy X j the first sum on the right hand side of amp Z5 cannot be evaluated on the fly per event Instead here EIRENE first accumulates the sum 27 X for individual test flight i and updates the sum X X only once after each completed history in subroutine STATIS entry STATS 1 I e variance estimates are made after comple
223. in section EID e FLAPL is the ion energy source resulting from atom plasma interactions summed over all EIRENE species of type atom tally no 26 e EM PLis the ion energy source resulting from molecule plasma interactions summed over all EIRENE species of type molecule tally no 31 e IPL is the ion energy source resulting from test ion plasma interactions summed over all EIRENE species of type test ion tally no 36 Electron energy source Energy time volume Watt cm Sre icell FAEL icell EM EL icell ELEL icell 14 21 is The sum is over all strata see stratified sampling in section EAEL EMEL EIEL are default EIRENE tallies Table 2G in section ELA 200 e FFAEL is the electron energy source resulting from atom plasma interactions summed over all EIRENE species of type atom tally no 22 e EM EL is the electron energy source resulting from molecule plasma interactions summed over all EIRENE species of type molecule tally no 27 e FEI ELis the electron energy source resulting from test ion plasma interactions summed over all EIRENE species of type test ion tally no 32 The data transferred from B2 into EIRENE are either from Common BRAEIR a module common to both B2 and EIRENE or from the stream FORT 31 They are read in the follow ing sequence 14 15 16 DI plasma ion densi
224. ing 2010 Contents e neutral gas transport equation Monte Carlo terminology 9 See ee a 10 ad e WCU generalisation of the Boltzmann equation 14 OOO 14 a a Gok a e ae 18 E HO 19 3 1 Unbiased estimatord o oo a 19 poe eee ee eens a a a S 20 TERE 21 1 3 3 Statistical errors Efficiency FOM oaoa 21 3 3 N 23 Sf Se a a a ee 25 Da BGs Bede Bo ee be Peds bly Gels boos 28 3 4 time census sources o nonoa o e a ee 28 L342 _Pointsourceg o oo a 28 L343 _ MES reEg os i a a AORA a RE ERS 28 are a goat ah a a 28 ko aoe a ee oe oe eG 28 ee ee eS 28 IMENT 3 25 vs ee ee i RE ee Re ew we ee ws 30 3 6 ampling from the collisionkerneIQ 31 L3Z elastic collisions ce we ee ee ee ew ee 32 e es Be ee ee Se ee ee es 32 Re ee we ey E wee Gege 32 3 10 general heavy particle impact collisions 32 were 32 l4 Surtace Reflection Models 33 33 34 37 38 41 ee EET SIE ban or bon 43 6 ombinatorial description of geometry 2 220200 44 She Betta hee wth Be atest ha ss O beth dae 2 47 I 9 non linear effects neutral neutral collisions 1 9 2 Direct Simulation DMCS of self collisions T imple Coulomb Collision Models he Fokker Planck Colfision Model 2 1 e NLMOVIE option for making movies of trajectories 2 nput for Standard Mesh ZZI Mesh Parameters e Input Block for Surfaces o oo a a e Input Block for Non det
225. ing may be overwritten by using the INDPRO 5 flag and the corresponding input parameters see below Here either a radial or x B field pitch profile can be selected INDPRO 5 1 4 and geometry level LEVGEO 1 2 3 with pitch B2 Bi be From this a cell centered B field unit vector is internally constructed by assuming that the first set of coordinate surfaces x or radial surfaces are flux surfaces B field aligned and constant pitch The magnetic field direction then has components 0 pitch y 1 pitch in the three coordinate directions Currently only JNDPRO 5 3 profile option allows to define also the B field strength BFIN T solely by the input flags described below Alternatively and in all other options an external data source for the B field vector in cartesian coordinates I NDPRO 5 5 7 all geometry levels LEV GEO is used directly In this latter case the transfer of magnetic field data BXIN BYIN BZIN and BFIN for each cell into EIRENE proceeds from user supplied profile subroutine PROUSR JN DPRO 5 5 or from external file I NDPRO 5 6 7 via work array RWK and then from subroutine PROFR The same applies to the additional plasma profile array ADIN INDPRO 6 to permit usage of EIRENE output and graphics routines for plasma profiles such as pressure energy fluxes etc which are not directly needed in an EIRENE run but which may be available from an external plasma code h
226. inite element mesh gen erator available from FZ Juelich to produce a triangular discretization of the resulting possibly multiply connected domain This option can be used to discretize arbitrarily complex 2D domains with internal and external boundaries given by the additional or non default standard surfaces These finite element grids can be combined with the regular grids by using the problem specific geometry routines see section 3 or the code interfacing routines INFCOP see section 4 Surface coefficients and boundaries of surfaces 102 The surface equation AOLM AILM x A2LM y A3LM 2z A4LM x A5LM y A6LM 2 ATLM xy A8SLM xz A9LM yz 0 3 1 The positive surface normal nz ny nz depends upon the point of impact x y z and is defined by the vector in AILM 2 A4LM x ATLM y A8LM z ny A2LM ATLM x 2 A5LM y A9LM z nz A3LM A8SLM x A9LM y 2 A6LM z For a plane surface the following reduction is valid nz Ny Nz AILM A2LM A3LM The boundary of the valid part of the surface may be described by 4 different options de pending upon the value of the flag RLBND RLBND 0 No boundary inequalities specified i e the whole surface is seen by the test particles 0 lt RLBND lt 2 1 Only that part of the surface which lies inside the right parallelepiped defined by the two vectors XLIMS1 YLIMS1 ZLIMS1 and XLIMS2 YLIMS2 ZLIMS2 is seen by the particle
227. input file N 6 same as N 1 but only the data for the sum over all strata are written sufficient e g for BGK iterations or for post processing subroutine DIAGNO see input block 12 as long as this post processing only is to be done on total results not on contributions from individual strata 74 N 2 EIJRENE reads output data from an earlier run from files FT10 and FT11 No new particle histories are computed only the requested output is printed and plots are produced Iteration cycles or time cycles if any are abandoned N 7 same as N 2 but only the data for the sum over strata are read See N 6 option described above M 1 EIRENE writes geometry data into file FT12 These data are the output from subroutines GRID and VOLUME in the initialization phase M 2 EIRENE reads geometry data from file FT 12 The geometry subroutines GRID and VOLUME are not called This option should be used if the geometry has not changed as compared to an earlier run It reduces the CPU costs for the overhead L 1 EIRENE writes plasma data and atomic and molecular data A amp M data into file FT13 These data are output from subroutines PLASMA XSECTA XSECTM XSECTI XSECTP in the initialization phase At the end of a run some background medium data may have been modified in subroutine MODUSR iterative mode see NITER flag below In this case FT13 may be re written to prepare for next iterations Also the primary source parameters input
228. ion ZLI if M is equal to 4 or is returned from SAMUSR if SORLIM lt 0 NTSOR as for point source but additionally If NTSOR lt 0 NTCELL is found from the step function data see below Function STEP section ZLD if L is equal to 4 or is returned from SAMUSR if SORLIM lt 0 NBSOR as for point source but additionally If NBSOR lt 0 NBLOCK is found from the step function data see below Function STEP section Z LT if N is equal to 4 or is returned from SAMUSR if SORLIM lt 0 NASOR as for point source but additionally If NASOR lt 0 NACELL is found from the step function data see below Function STEP section ZLI if N is equal to 4 or is returned from SAMUSR if SORLIM lt 0 NISOR as for point source but additionally If NISOR lt 0 IPOLG is found from the step function data see below Function STEP section LLI if N is equal to 4 or is returned from SAMUSR if SORLIM lt 0 The six parameters in the next card SORAD are used to define the sampling intervals in the three co ordinate directions x y and z For some geometry options and surface types i e radial poloidal toroidal or additional these boundaries of the sampling interfaces in some co ordinates are automatically found from the specified range INGRDA INGRDE in the corresponding grid and the corresponding SORAD values are then not used for those coordinates In case of doubt see initialization phase of subroutine SAMSRF to fin
229. ions Formally these volumetric source rates arise in the particle parallel momentum and energy balances For the B2 code these are solved in conservative form laboratory system D ipls its si hick 14 14 D ipls Iti s Vi Uk D A ET 14 15 D n T V G a EE peut 14 16 D nT e 2 Be Be 14 17 D Dt denotes the derivative total or convective derivative or partial derivative and o c stands for other contributions such as e g friction forces pressure gradient forces collisional heating etc All source rates S are resolved per stratum is and per cell icell The particle and parallel mo mentum sources are also resolved with respect to receiving plasma fluid ion species ipls The source rates are given as linear functions of default EIRENE tallies Statistical variances of all sources transferred to B2 are evaluated in case specific routine STATS1_COP All printout of these sources and their variances is case specific in interfacing module EIRCOP Particle source particles time volume Amp cm Snlipls icell y PAPL ipls icell PMP Lis ipls icell PIP Lis ipls icell is 14 18 199 NDT IT IPRT NINCT NIXY NTIN NTEN The sum is over all strata see stratified sampling in section M PAPL PMPL PIPL are default EIRENE tallies Table 5g in section EID e PAPLis the particle source for background plasma species ipls resulting from atom plasma
230. ions of g and Y depend upon the problem at hand e g also on symmetry ignorable spatial coordinates or time Because the inhomogeneous part of the transport equation LId S was assumed to be nor malized to one for source sampling S r v t S r Vit s brett S r v t 3 21 s this normalization factor s has to be multiplied to estimators 214 to turn responses Rg 2 13 into estimates with correct dimensionality and in absolute units Mostly the responses of interest are intensive quantities such as density pressure collision density number of collision per unit time and volume rather than the extensive quantities obtained by the Monte Carlo phase space integration in 2 13 total energy momentum or number of particles The volume e g of a grid cell is also an extensive quantity Thus by dividing the estimate by the appropriate cell volume Vm in space time see 2 14 finally the profiles of cell averaged intensive quantities e g density profiles are obtained The final unbiased estimate in absolute units for any of the unbiased estimators X for detector function g discussed above then is N gt a S R W g RN xn X X wi N gt 1 3 22 m i 1 with N being the number of Monte Carlo histories Correct interpretation of the results of an EIRENE run hence requires knowledge of the ratio s Vm The total source strength scaling factor s i e the integral of the inhomogeneous part S of the governing Fredho
231. is irrelevant Defaults needed for scaling i e cell volumes YIA 0 YGA 0 YAA 1 YYA 1 in case of LEVGEO 1 and YIA 0 YGA 0 YAA 360 YYA 360 in case of LEVGEO 2 Data for third standard mesh toroidal or z grid TSURF 88 NLTOR A toroidal or z grid is defined Otherwise the complete block 2C may be omitted and the volume averaged tallies are then automatically integrated over this co ordinate In case NLTOR TRUE sub block 2C must be read INDGRD 3 1 standard grid option INDGRD 3 2 3 4 5 6 not in use default INDGRD 3 1 One and only one of the next four boolean variables must be TRUE NLTRZ TRUE cylindrical approximation is used i e TSURF is a grid in z direction The co ordinate surfaces are given by z TSURF L Default NLTRZ TRUE NLTRA TRUE toroidal approximation is used The coordinate line is a polygonal approximation of a circle or an angular section thereof In case NLTOR TRUE the 3rd grid TSURF is a grid of toroidal angles The toroidal segment or the full torus is approximated by NT3RD 1 straight cylindrical segements In case NLTOR FALSE there are NTTRA toroidal periodicity boundaries such that the toroidal segment is approximated again by NTTRAM NTTRA 1 straight cylin ders but without toroidal resolution in the results Note If NLTOR NTTRA NT3RD internally The torus axis of the entire mesh can be shifted in radial direction by adding a radial offset ROA s
232. is the cell area in the two remaining coordinates x y The unit length dz of an ignorable coordinate here z coordinate used in a particular run is determined by the input flags in the corresponding input block for standard grid options i e in input block 2A for the x coordinate input block 2B for the y coordinate and input block 2C for the z coordinate see Section 2 2 Note that the numerical value of source strength FLUX block 7 corresponds to the choice of e g dz If dz 1 cm then FLUX is the number of particles per unit time and per cm in z direction If dz 1 m then the same value of variable FLUX would correspond to the 100 times smaller source strength of FLUX particles per unit time and per meter All resulting volume averaged output tallies would have a value 100 times smaller A particle density might then also be interpreted as surface density particle per unit area 1 3 3 Statistical errors Efficiency FOM The efficiency for Monte Carlo Codes is the inverse of the figure of merit FOM of the calculation defined as FOM statistical variance computing cost 3 23 Note that FOM should be approximately independent of the running time because the num ber of histories generated is excluding overhead proportional to the CPU costs and inversely proportional to the statistical variance o It is one of the major advantages of Monte Carlo methods over other numerical schemes that the error estima
233. is then given by Q cos d fi Yin sin 3 sin y fo Yin Q sin cos y Q sin sin y f1 0in cos fo Vin 4 61 with sin J fi lVin sin fil9in cos Bin hea 1 fi fi In total we have defined three parameters e1 e2 e3 The first two parameters el and e2 ac count for particle and energy reflection coefficients that continuously increase with incident angle recommended el 1 e2 0 5 from comparison with TRIM code calculations see be low The third parameter e3 can be used to take into account an increasing contribution of specular reflection at near grazing incidence e3 0 gives a pure cosine distribution e3 1 reproduces the distribution given in L3 In general this model describes a fraction of specular versus co sine reflection which increases with V n and in the purely mathematical limit of Vin 90 pure specular reflection Furthermore the parameter e3 controls the speed at which the spec ular part aspec of the angular distribution a Q Ggpec QL Aeosin QQ increases with a The interaction of neutrals and ions with a solid surface for target projectile combinations other than H onto stainless steel are modelled using a reduced energy scaling 1 4 2 TRIM code database reflection models Complementary to the surface model described above EIRENE is coupled to computer gen erated reflection databases produced with the TRIM code see references L8 and I9
234. ith the macroscopic flow which are iteratively coupled operator splitting The first such couple CFD EIRENE code was SOLXY EIRENE B and had led to imple mentation of the so called correlation sampling option in EIRENE as necessary to achieve convergence measured by comparison with solution using an analog analytic neutral particle model The widely used B2 EIRENE code system is another such example of a coupled CFD Monte Carlo diffusion advection reaction code A new section describing this code coupling part of the EIRENE code has been added It de scribes the sandwich file EIRCOP which was written to permit linkage between EIRENE and a plasma fluid model one two or three dimensional Initial and boundary value prob lems can be treated in a rather self consistent manner For B2 EIRENE this code segment was developed largely under support of a KFA EURATOM contract f and first applications have been published for ITER configurations see and M Main new features in EIRENE for this project was implementation of multiply connected 2D curvilinear grids into EIRENE so that the CFD and Monte Carlo code operate on identical meshes without any interpolation necessary Also the short cycle option a semi implicit correction scheme for Monte Carlo source terms between large CFD At cycles without new or at least with strongly reduced MC runs in between was implemented Subsequently a large number of
235. ith this number NUMTAL J is explicitly enabled With an additional negative sign this tally is removed from the run and the balances e g NUMTAL J 2 would remove the evaluation and storage of tally PDENM from this run NLTSOUT to be written 11B 1 Data for 2D plot of geometry PLIST plot the x radial standard grid surfaces into a 2D geometry plot PL2ND plot the y poloidal standard grid surfaces into a 2D geometry plot PL3RD plot the z toroidal standard grid surfaces into a 2D geometry plot PLADD plot the additional surfaces into a 2D geometry plot PLHST Plot the track of some selected test particle histories into the geometry plot 2D or 3D PLCUT Flag for the choice of a plane in which the 3 dimensional geometrical configuration is plotted in case of a 2D geometry plot This plane may be defined by either x CONST y CONST or by z CONST PLCUT 1 TRUE x CONST plotting plane is the yz plane y is the ordinate z is the abscissa PLCUT 2 TRUE y CONST plotting plane is the xz plane z is the ordinate x is the abscissa PLCUT 3 TRUE z CONST plotting plane is the xy plane y is the ordinate x is the abscissa PLBOX plot box defined by surface inequalities in addition to valid part of surface PLSTOR produce file of coordinates along 2D projections of additional surfaces for later use in some graphics PATRAN format also for RAPS graphics see below sub block 11B3 The
236. itional surface can be read in this input block their meaning is described in block LA together with the globally valid input data for particle surface interactions 95 The Input Block 3B Data for Additional Surfaces NL M CHO cards format 3A 69 A may be omitted arbitrary number of strings n m separated by blanks n and m must be integer variables 1 lt n m lt NLIMI DO L M 1 NL M TXTSFL CHa l cards forn nat 3A 69A may be omitted arbitrary number of strings n m separated by blanks n and m must be integer variables 1 lt n m lt NLIMI yCH2 Gards format 3A may be omitted 69A arbitrary number of strings n m separated by blanks n and m must be integer variables 1 lt n m lt NLIMI RLBND RLARE RLWMN RLWMX LIIN LSIDE LSWCH F RLBND LT AOI M AlLM 0 LEQU LTOR LCOL LCELL LBOX LPLG THEN A2LM A3LM A4IM A5LM A6LM A7LM A8LM A9LM let RLBND KL then first read L cards ALI MS XLI MS YL MS ZI and then read K blocks next ALI ZLI MSO XL IMS1 YL IMS ZL MS IMS XLI MS2 YLI MS2 MS2 XL IMS3 ENDIF F RLBND EQ AOLM A1LM sO YL IMS3 THEN
237. itrary number of surface models labelled by the character string modname may be read SURFMOD_modname LREF LSPT SRS ISRC ZNML EWALL EWBIN TRANSP 1 N TRANSP 2 N FSHEAT RECYCF RECYCT RECPRM EXPPL EXPEL EXPIL RECYCS RECYCC SPTPRM this line may be omitted then default sputter model see below 138 next within each SURFMOD sub block there may be an arbitrary number of lines VARNAME SPZNAME VALUE format CHARACTER 8 X CHARACTER 8 Meaning of the Input Variables NLTRIM_ TRIM database is used if Database Reflection Model is specified in at least one block for local reflection data Data are read from data set FT21 no Path Card specified old option or from the domain specified by the Path Card new option see next card If the old option is used then the complete TRIM file is read containing the first 12 TRIM target projectile combination data sets listed in section L4 i e the files H_on_Fe to T_on_W If the parameter NHD6 lt 12 section B T then only the first NHD6 files are read from FT21 Path Card This card is machine specific If EIRENE finds a card containing the string PATH or path it assumes that this card specifies the path to the domain containing the TRIM surface reflection data files A_on_B Name of a particular TRIM data file in the domain specified by the path card E g H_on_Fe would include the data file for hyd
238. k 2 10 Ck gives the mean number of secondaries for this collision process The function C then is a con ditional probability density The particle absorption process can conveniently be described by adding an absorbing state x to the space generally referred to as one point com pactification of this space in the language of mathematical topology This limbo state once it is reached is never left again if the kernels T or C are employed as transition prob abilities Formally an additional collision kernel C 2 a and an absorption probability Pa a must be included in the collision kernel The quantity X comprises all collision processes with no next generation particles within the community of particles considered by the coupled set of kinetic transport equations Ionisation of a neutral atom is a loss if the resulting ion is not considered further or dealt with by a CFD code outside the Monte Carlo procedure The kernel T describes the motion of the test particles between the collision events Let again Q denote the unit vector in the direction of particle flight v v and let Q and 95 be two further unit vectors such that these three vectors form an orthonormal basis at the point r Neither velocity nor species change along the transition described by T i e v v and i i Omitting the corresponding delta functions in velocity space and the Kronecker delta 15 ii the tr
239. k or block 2 6 referred to in a particular run is not given here then these data files are expected usually with the same name in the local directory from which the calculation takes place Due to historical reasons and for backward compatibility for some data files also different default names are recognized Default file names to be used in this local directory currently are AMJUEL HYDHEL METHAN or METHANE for database name METHAN H2VIBR HYDRTC SPECTR PHOTON 78 POLARI SPUTER TRIM or fort 21 for database name TRIM For ADAS AMdata and TRMSGL Surfacedata there is an exception from this scheme In these cases no default file names are available The notation ADAS and TRMSGL here are only synonymous for any atomic or surface data file which is stored in the same format as the so called ADAS adf11 files and the TRIM conditional quantil data tables independent on whether these tables originate from ADAS or TRIM And input variable DBFNAME specifies only the path to the directory which is the root of the data tabulated in ADAS tabular format and the TRIM format data tree respectively Example CFILE ADAS home path AMdata Adas_Eirene_2010 adf11 CFILE TRMSGL home path Surfacedata TRIM The particular data file from these trees e g SCD 96 in case of ADAS or A_on_B in case of TRMSGL the chemical element and the charge stage of a particular ion Z 1 Z 1 e g C 4 a
240. l respectively to a possibly fictious surface element similar notation as in section LAI the orientation of which is locally defined at the initial position of the test particle by the above mentioned outward normal unit vector C see above In the earliest applications of EIRENE to plasma target surface recycling V corresponds then to the parallel to a magnetic field B plasma flow velocity often sonic onto a target surface which is orthogonal to the magnetic flux function e g a limiter side or divertor target NEMODS KLMN The choice of one of the following energy distributions is made depending upon the value of the first digit N of NEMODS N 1 Mono energetic source f E 6 E0 with energy EO SORENI eV N 2 Mono energetic source f E 6 E0 with energy E0 SORENI T SORENE T N 3 only for surface sources As N 2 but with added sheath acceleration see para graph below 161 N 4 Mono energetic source f E E EO with energy E0 EMAX T Vri Voi where EMAX is the mean energy from a truncated one sided Maxwellian flux at temperature T drifting by a velocity Vii Voa One obtains see amp 74 in section I by integration EMAX ygT with yg V2 2 V2 0 5804 V V and g x 1 yrz 1 erf x exp z i The normalized velocities V V V used here coincide with the isothermal Mach number if T Te see again section LST N 5 only for surface sou
241. lection model see section E3 and in several so called Sputter Models B4 B B8 These models may to some extend be modified by the input flags described here For exam ple a surface may be purely absorbing for all test particles incident onto it ILIIN 2 op tion acting like a mirror for the neutral test particles by the LJ N 3 option see section 2 3A and 2 3B or enforce periodicity e g because of symmetry conditions JILIIN gt 4 option In these two latter cases all test particles of all species are reflected with the species 137 unchanged with probability one and elastically Eout Ein In case of the mirror reflection option the normal component v of the incident velocity vector v is reversed vn gt Vn In case of a periodicity surface both the position and the speed unit vector are altered ac cording to the specific periodicity of the configuration If instead a surface reflection model is chosen J LI N 1 then some of the input flags described here RECYCF RECYCT RECYCS RECYCC as well as the flags RINTEG EINTEG AINTEG may be used to modify conveniently the otherwise rather unhandy re flection data and formulas The Input Block for General Reflection Data 6A Data for General Reflection Models NLTRIM Path Card for TRIM surface reflection files machine specific may be omitted If a Path Card is included then read an arbitrary number o
242. led once again after each completed stratum at the entry IFJ COPUSTRAA ISTRAB to return data to another code post processing The call to IF3COP is from subroutine MCARLO at the end of the DO 1000 loop over the strata One final call to the interfacing routine entry IF4COP is implemented after the calls to the EIRENE printout and plot routines e g to perform global balances etc after summation of the contributions from the individual strata NTCPU Maximum number of CPU seconds allowed for this run NTCPU must be less than or equal to the time parameter in the job card if any If more than one iteration is carried out NITER see below this section or more than one time cycle NTIME see below this section then each iteration or cycle can take up to NTCPU seconds In 2008 the definition of NTCPU was slightly changed the initialisation overhead is not any longer included in NTCPU I e this variable NTCPU now is close to the true Monte Carlo sampling time The total cpu time including initialisation overhead as well as post processing is printed at the end of an EIRENE run see total cpu time of this run in printout file NFILE Flag for the use of dump files FT10 FT11 FT12 FT13 FT14 and FT15 0 Neither reading nor saving of data is done JKLMN N 1 EIRENE writes output data from this run into files FT10 and FT11 to save them for plot or printout options in this or in later read only runs with the same
243. length increments Ax The algorithm to determine the next point of collision then is different After a free flight time At the probability of at least one collision during this period is the function Gr lo defined above with Ax lo St v t dt vAt the fixed path length for this step This follows from the definition of Gr as cumulative distribution for the free flight length 50 Clearly 0 lt Gr l lt 1 for all positive l by definition Lets now assume constant mean free path A and constant velocity v during time step At and l v At to simplify notation The procedure to find the free flight length or time is now as follows Rather than sampling by inversion as in Equation G 50 now a uniformly distributed ran dom number on 0 1 is compared with the probability Gr Jo 1 exp p A If gt Gr lo no collision has happened during this step and the next step is carried out If lt Gr lo then at least one collision has happened prior to completion of the step Strictly in this case the exact position of the first collision during this step has to be identified by inversion the time step has to be shortened and the particle has to be moved to the sampled point of collision in the interval Ax However various approximations are now usually made to simplify coding e Ignore the fact that more than one collisions could have happened during At e replace Gr lo by lo A Atvd v see above w
244. les are carried out in one single job In each time cycle a time horizon is set and the trajectories are stopped at latest if they have survived until then All relevant particle coordinates position velocity type and species cell indices etc are stored at this time horizon on the so called census arrays Each time cycle may consist of one or more than one NTMSTP see below internal time steps At the end of each of these time steps the relevant tallies are updated subroutine TIMCOL These are the volumetric snapshot tallies the default time surface tallies particle and energy fluxes and the census arrays Hence these tallies are averaged over NTMSTP internal time steps For more details on snapshot tallies see Section EZA This distinction between complete time cycles and internal time steps is particularly relevant for obtaining truly steady state results on the census arrays e g in order to continue a stationary case in the time dependent mode see below The Input Block 13 Data for nonlinear and time dependent Options NPRNLI NINITL READ NPRMUL IF NLERG AND NPRNLI EQ 0 NPRNLI 100 IF NPRNLI GT 0 THEN NPTST NTIMSTP DTIMV TIMEO xx 13A DATA FOR SNAPSHOT TALLIES NSNVI IF NSNVI GT NSNV DO 1320 J 1 NSNVI SNVE J ISNVS J ISNVT J ISNRC J TXTTAL J NTALT TXTSPC J NTALT TXTUNT J NTALT 1320 CONTINUE ENDIF
245. lights in these zones has to be specified explicitly by making use of the ILSWCH ILCELL parameters block 3B Default NRADD 0 VOLADD Volume cm of each additional zone as seen by the test particles 90 2 2 1 Mesh Parameters As stated above the computational volume in an EIRENE run is subdivided into NSBOX cells NSBOX NRIST NP2ND NT3RD NBMLT NRADD The can mesh consist two different parts The first is the so called standard mesh part VOXEL geometry defined by the grids RSURE PSURF and TSURF There may then be NBMLT copies of that mesh separated by additional surfaces see below section default NBMLT 1 The second part is the so called additional cell region Up to NRADD additional cells of ar bitrary shape are defined by their boundaries BREP geometry the additional surfaces defined in section ZZZ NRIST is the number of surfaces in the 1st radial or x grid There are NRISTM NRIST 1 cells The cell index of a particular cell is called NRCELL 1 lt NRCELL lt NRISTM NP2ND is the number of surfaces in the 2ND poloidal or y grid There are NP2NDM NP2ND 1 cells The cell index of a particular cell is called NPCELL 1 lt NPCELL lt NP2NDM NT3RD is the number of surfaces in the 2RD toroidal or z grid There are NT3RDM NT3RD 1 cells The cell index of a particular cell is called NTCELL 1 lt NTCELL lt NT3RDM For the cells of th
246. ling index NAINS species index of tally in B2 arrays NAINT flag to determine which particular quantity is put onto input tally ADIN In the current version of subroutine INFCOP for interfacing to B2 the following B2 quantities can be selected 1 lt NAINT lt 16 1 DI plasma ion density m 3 also on DIIN by IPLS species 2 UU poloidal velocity m s 3 VV radial velocity m s 6 PR plasma pressure N m 7 UP parallel velocity m s 8 RR pitch angle 1 9 FNIX Particle fluxes along the field 1 s 10 FNIY Particle fluxes across the field 1 5 11 FEIX Ion energy fluxes along the field Watt 12 FETY Ion energy fluxes across the field Watt 13 FEEX Electron energy fluxes along the field Watt 14 FEEY Electron energy fluxes across the field Watt 15 VOL cell volume m 205 16 BFELD magnetic field T 17 lt NAINT lt 30 EIRENE atomic data profiles These can be selected also in the NMODEZ 0 subroutine INFCOP not called option currently revised Do not use 17 18 19 20 21 22 recombination rate lt ov gt n 1 5 1 lt NAINS lt NPLS recombination process KREC 1 for background species IPLS NAINS 1 NPLS lt NAINS lt 2 NPLS recombination process KREC 2 for background species IPLS NAINS and so on 122 electron energy weighted recombination frequency eV s TXTPLS TXTPSP TXTPUN as described for additional output tallies in bock 10 NAOT
247. ll number NRCELL of the zone containing the point source 0 NRCELL is found automatically from the standard mesh zoning NPSOR ditto for y or poloidal cell number NPCELL NTSOR ditto for z or toroidal cell number NTCELL NBSOR standard mesh block number NBLOCK Defaulted to NBLOCK 1 if NBSOR lt 0 NASOR additional cell number NACELL if point source is located outside the standard mesh Defaulted to NACELL 0 if at least one of the variables NRCELL NPCELL or NTCELL are larger than zero NISOR polygon index IPOLG Meaningless if NLPLG FALSE SORAD1 x co ordinate of source point XO SORAD2 y co ordinate of source point YO SORAD3 z co ordinate of source point ZO SORAD4 SORADS5 SORAD6 are the x y and z coordinates of a vector C CRTX CRTY CRT Z which may be used to distinguish one particular direction for the distribution in velocity space see below Internally this vector is normalized to length 1 Irrelevant for an isotropic velocity distribution Line source to be written Surface source Flags for the distribution in physical space not mentioned here are irrelevant for surface sources NSRFSI_ Total number of different surfaces or surface segments over which the starting points for this stratum are distributed sub strata to facilitate sampling of spatial coordinates The next deck of 4 input cards is read NSRFSI times one deck for each sub stratum INUM irrelevant labelling inde
248. llisions gen erations FLDLM gt 0 0 or if the mean free path compared to a geometric dimension falls below a certain value FLDLM lt 0 0 fluid limit The precise status of this option should be inquired from the code authors 122 2 4 1 Default atomic and molecular data If default atomic data are requested for some test particle species these are activated by set ting the flag NRCM IATM 0 or NRCM IMOL 0 NRCI IION 0 resp for a particular atom IATM molecule IMOL or test ion HON and by omitting the corresponding cards IREACS and EELEC Then EIRENE tries to find automatically the corresponding species types and indices of the collision products in the species blocks It then tries to define all variables in the cards IREAC and EELEC for collision rates and collision kinetics using default assumptions default model for atomic H H D T and He test particles Assume that the bulk ion H is specified as bulk ion species no a DY as bulk species b T as bulk species c and He as bulk ion species no qd then the default atomic collision models for H and isotopes and He are identical to a model that would result from the following specifications in input block 4 For atoms D likewise for H or T e g IATM 1 and atoms He e g IATM 2 x ATOMIC REACTION CARDS NREACI 5 1 HYDHEL H 2 2 1 5 EI 0 1 2 HYDHEL H 1 3 1 8 Cx wh 3 HYDHEL H 2 2 3
249. lm integral equation is input to EIRENE variable FLUX in input block 7 see ZJ The space time cell volumes V are either automatically calculated by EIRENE in subroutine VOLUME for cells belonging to standard grid input block 2 Section 2 2 or are provided from external 20 considerations by a number of options e g input blocks 3b 5 or 8 In this latter case great care is needed however that the cell volumes are proportional to the volumes as seen by the test flights for otherwise not only unscaled profiles but even wrong biased profile shapes will be obtained 1 3 2 1 Scaling in problems with ignorable coordinates As seen in the previous paragraph the absolute values of estimates are scaled with the ratio s V of source strength to cell volume Depending on ignorable coordinates in any particular problem or on whether stationary i e time is an ignorable coordinate or time dependent transport problems are considered the dependent variable Y in the governing integral equa tion LId the source strength s and cell volume V may have different interpretations stationary time independent problems one ignorable spatial coordinate In stationary problems with one ignorable coordinate say the z coordinate the source strength s input flag FLUX is the flux particles per unit length dz in direction of z Likewise the volume V is per unit length in the ignorable direction i e if dz 1 then V
250. lock 2c if ILTOR gt 0 the surface is defined with respect to the local coordinate system of the toroidal segment with cell number ILTOR hence 1 lt ILTOR lt NTTRAM if ILTOR 0 the surface is defined with respect to any local coordinate system I e the surface equations are taken to be the same in each local system If the surface equations are z independent then this surface is toroidally symmetric within the NLTRA approximation Otherwise the surface has NTTRAM fold periodicity This flag is irrelevant for NLTRZ i e if cylindrical coordinates are used or for NL TRT Default ILTOR 0 101 ILCOL Flag for the color that is used for plotting this surface on 2d or 3d geometry plots If ILCOL lt 0 than LCOL is used and the surface area is filled in by that color on the 3d geometry plots Default ILCOL 1 ILFIT MN This option is relevant only for surfaces with one ignorable coordinate i e it only works for the 2 lt RLBND lt 3 surface boundary options It is a tool to facilitate a neat fitting of surfaces in particular for connecting curved and plane surfaces i e to avoid particle leakage due to numerical round off errors in the algebraic surface coefficients Mand N 3 digits each M may be omitted if not needed are the numbers of the surfaces which must have the same ignorable coordinate the boundaries of which should match to those of the actual surface J The boundaries of these nei
251. luding a birth point sampling routine SAMUSR one can easily model any spatial distribution of the primary source in addition to the preprogrammed options described in section LZ This is explained in section BA Some geometrical variables such as cell volumes surface coefficients etc may be re defined or modified after reading the input data This is done by a call to routine GEOUSR called from EIRENE subroutine INPUT See section BST below Similarly any background data plasma profiles may explicitly be modified in routine PLAUSR see section B 5 2 The routine for additional background profiles PROUSR called for those background tallies for which INDPRO 5 see block 5 is described in section BA It is recommended to use this 211 option if a particular closed form expression for the background profile is needed It is then more convenient than the external data file options INDPRO 6 or INDPRO 7 see section A The various routines needed for the general user supplied geometry option NLGEN LEV GEO 10 see block 2a are described in section EA Simple examples are also given there 212 3 1 Parameter Statements for ETRENE 2001 or older The deck PARMUSR is the first part of the user supplied Fortran file It contains parameter statements used in an EIRENE run and it determines the storage required to run EIRENE on a particular problem In EIRENE versions after 2001 dynamic allocation of storage is implemented the m
252. m units of g cm source strength FLUX however with FLUX converted to units 1 s rather than input units Ampere For the definition of the detector functions g and g see section B J the variable FLUX is explained in input block no 7 This scaling is default for density tallies of particles momentum and energy 174 2 scale tally per unit cell Same units as above however not per cm but per cell instead 3 same as IADVE 1 but with FLUX in Ampere rather than 1 s This scaling is default for source rate tallies e g for particle momentum and energy sources 4 same as IADVE 2 but with FLUX in Ampere rather than 1 s else no re scaling done units as chosen in subroutine UPTUSR Note scaling of EIRENE default tallies 1 to 6 particle and energy densities respectively is as for IADVE 1 option Scaling of all default source and sink terms is as for IADVE 3 option If instead also for particle or energy densities tallies 1 to 6 the scaling IADVE 3 would have been used then for example particle densities would have been in units AMP s cm atomic charge density rather than 1 cm Energy densities would have been in W s cm rather than eV cm IADVS species index of default volume averaged tally which is to be replaced by this ad ditional track length estimated tally In case of tallies with no species index IADVS must be set equal to 1 IADVT number of default volume averag
253. m bers in x y and z direction respectively L 3 V is the local background ion drift velocity of ion bulk species IPL K K is the fourth digit of the NEMODS flag see below K options The digit K unless zero is used to specify one of the background ion species IPL from which the T J PL V I PL parameters in the sampling distributions described above are taken SORCOS SORMAX Depending upon the value of the flag NAMODS various different angular distributions may be selected Each one depends upon the two parameter P SORCOS and Q SORMAX NAMODS 1 The polar angle V against the unit vector Cy Cy Cz of the source particle s ve locity is sampled from a cosine P distribution around the inner normal vector 1 0 C i e f W dd sin v cos V dv Important special cases P 0 isotropic distribution P 1 cosine distribution P gt gt 1 close to 6 distribution around 1 C NAMODS 2 The polar angle against 1 C is sampled from a Gaussian distribution with zero mean value and the parameter P now is used for the standard deviation degree of that distribution 163 The second parameter Q is the cut off angle degree for the polar angle distribution note Q lt 180 is enforced internally Q lt 90 is enforced internally for surface sources Q 0 for a beam i e for an angular d distribution at 1 C SORCTX SORCTY SORCTZ The unit vector C mentioned above is given by normalization of SORCTX S
254. m the collision kernel C The general rules for sampling from multivariate distributions outlined in Section L33 Equa tion 2 32 also apply here It is not necessary but usually most convenient and intuitively most clear to decompose the kernel C according to the physical nature of the various collision processes taken into account The collision kernel C was written as see equation 2 9 J e T i Ur C r v 07 gt v i So pC sv 2 v i gt P SK k a with summation over the index k for the different types of collision processes under consid eration and p defined as the probability for a collision to be of type k The normalizing factor i gt fav Cy r v i gt v i Ck Ck Ck 7 was the mean number of secondaries for this collision process The function C then is a conditional probability density for v i given the pre collision coordinates r v 7 Sampling from C given that a collision of some kind has occurred proceeds most conve niently by firstly sampling the type k of the process from the discrete distribution Pr k 1 K and then by sampling the post collision state of the test particle from C Finally the weight of the test flight after collision is increased or reduced by multiplying it with the normalization constant Cx The decomposition of C into sub kernels Cy is somewhat arbitrary and the criteria may also be computational aspects rather than the different physical nature of t
255. marks are set For each profile up to 6 parameters PO P5 are read e g TEO TES for the T profile TIO TIS for the 7 profile and so on Depending upon the value of INDPRO one of the profile routines PROFN PROFE PROFS etc is called from subroutine PLASMA INDPRO 1 4 NRISTM plasma data are defined on the one dimensional zone centered grid RHOZNE J J 1 NRISTM NRISTM NRIST 1 Vacuum data are specified in zone NRIST These NRIST data are copied NBLCKS times to define NBLCKS identical profiles totally NBLCKS NRIST NSURF data subrou tine MULTI Here the number of copies is NBLCKS NMULT NP2ND NT3RD see Input Data for Standard Mesh block 2 INDPRO 1 see subroutine PROFN RHOSRF 1 lt x lt P5 Po P3 P x P1 P0 P1 1 ee x RHOSRF 1 gt P x PO x P5 gt P x P1 P5 lt x lt RHOSRF NRIST P x P1 exp x P5 P4 INDPRO 2 see subroutine PROFE RHOSRF 1 lt x lt P5 P x PO exp x P1 P2 in particular x Pl P x PO P5 lt x lt RHOSRF NRIST P x P PS5 exp x P5 P4 P3 no meaning in particular 134 INDPRO 3 see subroutine PROFS PROFS P0 P1 P5 PVAC RHOSRF 1 lt x lt P5 P x PO P5 lt x lt RHOSRF NRIST P x P1 Parameters P2 P3 P4 have no meaning except for the magnetic field IND PRO 5 3 Here PROFS PO P1 P5 PVAC is used to
256. mber of particles total energy momentum etc per cell Intensive quanti ties flow velocity temperature etc obtained by dividing two extensive quantities are typically difficult estimate with Monte Carlo methods see ratio estimates correlation be tween nominator and denominator If however the extensive quantity in the denominator is known exactly such as e g the cell volume in a computational mesh then of course obtaining an intensive quantity from an extensive quantity with Monte Carlo is a trivial re scaling Monte Carlo estimates of the intensive volumetric source terms in the fluid equations due to the trace particles neutral particles but also trace ions described by the Monte Carlo procedure are such cell averages surface averages time averages or point estimates e g in time averaged over a sub manifold with reduced dimensionality This works of course only if the probability for particle histories crossing this sub manifold is not zero Surface averages in EIRENE are described in Section 2 2 4 point averages in time are described in Section LZA This option to reduce dimensionality of responses usually excludes point estimates in real space for which special estimators not mentioned here would be required Nevertheless in concluding depending upon the numerical algorithm in the fluid code one may then have to interpret these Monte Carlo estimates properly e g they may have to be interpolated to
257. mber of short cycling steps before a full EIRENE run is enforced for all strata 2 14 4 Version B2 5 EIRENE 2012 and later One distinction to the earlier versions of interfaces to the B2 plasma fluid code is that in B2 5 the energy conservation equation is solved for the internal energy only i e the thermal energy rather than for the total energy as in B2 The ion energy source term S pj internal tcell transferred from EIRENE to B2 5 in grid cell icell reads S Ei internallicell Spi torailicell UA x S icell EKIN x S icell 14 23 with Sip total Sm icell S icell being the total ion energy source rate the momentum source rate and the particle source rate respectively as defined in for the interface to the B2 plasma solver The coefficients UA and EK IN are the parallel plasma flow velocity Vj and the kinetic energy carried by the parallel plasma flow EK IN mipis 2 V This equation applies for a single plasma fluid case one single plasma species ipls Relation 14 23 for the internal energy source follows from either substituting the lower order moment equations into the total energy moment equation or by forming the energy moment equation directly by averaging the kinetic equation with velocities in the plasma frame w v V i e by averaging the kinetic equation with m 2 w rather than m 2 v with V the plasma flow velocity BQ 209 In case of multi fluid plasmas we use without proof t
258. me formally identical to collision estimators for detector functions containing surface collision delta functions Consequently a statement in subroutine UPSUSR WEIGHT IND for this surface averaged tally must read ADDS ITALS IS ADDS ITALS IS WC g_ here JS is the index of the surface which is being crossed IT ALS is the labelling number of the surface tally Furthermore WC to llv cos Q ep the detector function g is evaluated at the strike point rg and as above w is the weight of the history k after event i and before event i 1 Note WEIGHT w wir in our terminology The flag IND has the value 1 if the particle is incident onto the surface and IND 2 if the particle is emitted from the surface Some care is needed because the local surface normal unit vector e at the strike point rg is not known in subroutine UPSUSR unless the surface input variable ILIIN see input block 3 is positive equal to 1 2 3 or 4 for the surface S In all other cases this vector defined by its Cartesian components CRTX CRTY CRTZ in EIRENE has to be computed in subroutine UPSUSR at each entry if it is needed for updating the surface averaged tally Subroutine UPSUSR is called whenever the default surface tallies are updated For one sided surface tallies ILIIN 2 or ILIIN 4 therefore UPSUSR is also only called for one sided tallies only In addition to these calls UPSUSR is also called from surface source routines
259. mely the subroutines UPTUSR UPCUSR and UPSUSR Other often applied routines such as SAMUSR user supplied source sampling distribution or REFUSR user supplied surface interaction model are briefly described e In part four the package EIRCOP for interfacing EIRENE with other codes e g the B2 EIRENE package is described Here mainly the location of the storage on the EIRENE work array RWK for plasma data and geometrical information is given Also the implementation of the method of semi implicit corrections see section LJ at each plasma code time step to the terms transferred from EIRENE to plasma fluid transport codes is described here Chapter 1 The neutral gas transport equation Monte Carlo terminology General Remarks To introduce the terminology used throughout this report we briefly recall the basic defi nitions and principles of a Monte Carlo linear transport model following the lead of many textbooks on Monte Carlo methods for computing neutron transport see e g R We begin with the linear transport equation for the pre collision density written as integral equation linear non homogeneous Fredholm integral equation of 2nd kind Distinct from standard terminology in the analytic transport theory we do not discuss analytic properties of the var ious terms in the equation but instead point out their probabilistic interpretation as needed for a Monte Carlo solution of that equation Next section L3 we sketch t
260. n of 71 f2 is a conditional marginal distribution obtained from f firstly by integrating f over all but the first 2 variables x1 72 and secondly then taking the conditional distribution conditional on z i e the univariate distribution of x2 for given values of x1 Likewise f3 is a conditional marginal distribution n 3 fold integration of f and then distri bution conditional on 71 2 and so on Random sampling from f 1 2 73 then proceeds by sampling first x from the univari ate first factor in equation B 32 then x by sampling from the univariate second factor and so on One particular example of this scheme is the TRIM database surface reflection model see below section L4 2 There essentially tables of the conditional marginal distributions men tioned here are pre computed with the TRIM code For convenient random sampling these tables are stored for the inverted cumulative distribution i e as conditional quantile func tions 24 1 3 3 2 Stratified Source Sampling The EIRENE code resorts to a stratified sampling technique This technique is one the few Monte Carlo variance reducing techniques which are quite straight forward easy to imple ment and most importantly behave in a well predicable way It is therefore recommended to always use source stratification described below as much as possible There are however non trivial issues of load balancing in case of multi core runs
261. n potentials elastic processes to be written 128 2 5 Input for Plasma Background General remarks The background medium mostly plasma consists of NPLS sometimes in the code NPLST different so called bulk particle species also referred to as bulk ions by abuse of lan guage From the assumption of quasi neutrality the specified charge state of each background ion species including charge state 0 for neutral background species and the data for density n of background species labeled 7 an array of NSBOX data for the electron density n cm DEIN is computed see next subsection derived background data The background medium is described by several blocks of NSBOX data each i e one datum per grid cell so called input tallies namely e one array for the electron temperature Te eV TEIN e one common or NPLS distinct one for each bulk ion species arrays for the ion tem perature s T eV THN e NPLS arrays one for each bulk ion species ion densities n cm DIIN e one common or NPLS one for each bulk ion species arrays for the cartesian drift velocities V Vz V V VXIN VYIN VZIN either in cm s or Mach number units The unit vector b bj b2 b3 BXIN BYIN BZIN parallel to the magnetic field is set to 0 0 1 by default i e pointing in z or toroidal direction The default magnetic field strength is B 1 T in all grid cells This default sett
262. n the relevant atomic molecular of photonic processes to each test particle and also bulk particle from either this set of NREACI processes or from a small set of default processes which are hard wired in EIRENE In versions younger than 2002 each reaction in these databases can contain a string fit flag value with IFTFLG value IFTFLG is used in EIRENE to identify the type of fitting expression to be evaluated with the fitting coefficients from the database By default IFTFLG 0 for all data i e single or double polynomial fits All atomic rate coefficients and cross sections can be scaled with a constant factor FREAC see below for sensitivity studies Excluded from this scaling option are all photonic processes and those elastic collisions for which EIRENE uses an interaction potential H 0 type data because here the scaling would not have the expected effect on transport but rather it would only modify the effective small angle scattering cut off in the binary collisions Atomic and molecular processes are always of the following type a A b B 3 gt m M4 n N AE Here A B M and N are labels for the type of pre and post collision particles a b m and n are the stoichiometric coefficients and AF is the amount of internal energy transferred into or at the expense of the kinetic energy of the collision products M and N The following conventions are always in use At least one of A B M or N must stand for a
263. nization and dissociative recombination data are available EIRENE uses the 6 reaction rates 2 2 5 2 2 9 2 2 10 2 2 11 2 2 12 and 2 2 14 from the data set HYDHEL BI and again tries to identify the reaction products from the mass and nuclear charge number of the respective molecule IMOL or test ion HON In order to distinguish Dy from HT is also uses the name TEXTM or TEXTI by looking for the appearance of the character D in the name then D3 or D or for H or T then HT or HT The default reaction kinetics are set as if they would have been specified by the following species blocks x ATOMIC REACTION CARDS NREACI 7 1 HYDHEL H 2 2 2 9 EI 0 2 2 HYDHEL H 2 2 2 5 EI 0 2 3 HYDHEL H 2 2 2 10 EI 0 2 4 HYDHEL H 2 2 2 12 EI 0 2 5 HYDHEL H 2 2 2 11 EI 0 2 6 HYDHEL H 2 2 2 14 EI 0 2 7 AMJUEL H 8 2 2 14 EI O 2 125 x NEUTRAL MOLECULES SPECIES CARDS NMOLI SPECIES NMOLI T 1 D2 4 2 2 0 0 1 0 3 1 115 13 0 00000 1 5400E 01 0 0000E 00 0 0000E 00 0 0000E 00 2 115 1241 000 00000 1 0500E 01 0 0000E 00 3 0000E 00 3 0000E 00 3 115 111 x14 00000 2 5000E 01 0 0000E 00 5 0000E 00 5 0000E 00 x TEST ION SPECIES CARDS NION ON SPECIES NIONI 1 1 D2 4 2 2 1 0 1 0 3 1 4 LS 111 x14 00000 1 0500E 01 0 0000E 00 4 3000E 00 4 3000E 00 5 11 5 24 00000
264. ns THINTF is an array of length NHMAX which contains all relevant information to generate a mesh of tetrahedrons in the 3d compu tational domain It is equivalenced to the common block CTETRA via the statement EQUIVALENCE THINTF 1 XT 1 4 1 2 entry IFICOP Plasma background data INDPRO 6 option to be written 4 1 3 entry IFZCOPUSTRA Primary source data INDSRC 6 option In case of an EIRENE run in which input information is obtained from an external code e g B2 EMC3 DIVIMP the stratification of the primary source should be such that the first NTARGI see LIA strata are determined by the plasma fluxes onto surfaces recy cling surface sources In this case the surface source distribution Qs r v i t section L3 can be defined automatically from the interfacing routine using the data specified in input block 14 The remaining primary sources NTARGI 1 NSTRAI e g gas puff volume recombination sources etc still have to defined in input block 7 Whether input block 7 or input block 14 is used for a particular surface source ISTRA lt NTARGI is controlled by the flag INDSRC For sources ISTRA gt NTARGI the input flag INDSRC is irrelevant if INDSRCUSTRA lt 0 then interfacing routine IF2COP is not called Input data are used from block 7 see ZZ if INDSRCUSTRA 0 5 then the input flags described in section L7 are used to define the spatial distribution of a recycling source on a grid
265. ntation BREP e Voxel Geometry EIRENE uses a combination of the latter two concepts In CSG a solid object is constructed from the intersection union or other boolean oper ations of several half spaces Each half space in specified by a relation F x y z lt 0 typically F is a low order polynomial For example the neutronics code MCNP used e g for ITER nuclear safety studies is based on CSG In BREP geometry surfaces and volumes are build up from constituent parts These parts may be related with algebraic functions elementary BREPs or complex functions such as Bezier functions or B splines advanced BREPS Most CAD software uses BREPs in their native definition of geometry In the EIRENE BREP options surfaces are build from bounded algebraic functions These surfaces are referred to as additional surfaces see Section 2 3 2 EIRENE uses only alge braic functions up to second order some extensions to raise the order to fourth order have been started recently but are not ready to use In Voxel geometry a 2D or a 3D object is constructed from identically shaped volume el ements voxels In EIRENE these may be triangles or quadrangles in 2D or tetrahedrons in 3D New options to accommodate trilinear hexaedra as 3D voxels are currently being de veloped in connection with 3D edge codes such as EMC3 The bounding surfaces of these voxels are referred to as standard grid surfaces in EIREN
266. ntered 6 rad x x surface across field East centered e rad y y surface along field North centered 0 par x x surface across field East centered 0 par y y surface along field North centered 6 rad x x surface across field East centered 6 rad y y surface along field North centered sheath_x x surface across field East centered sheath_y y surface along field North centered 208 On any particular surface element only either the x or the y values are set depending upon whether this surface is a x or y surface One cell however may have either one or two recycling surfaces one north and one east surface 2 14 3 Version B2 EIRENE wide grid 2011 and later Further adaptations in case of wide grid option to accommodate mixed fluxes e g west and north at a single boundary element To be written Meaning of additional flags from input block 14 format see 2 14 MSHFRM three different options for reading of B2 grid MSHEFRM 0 Linda format historically oldest format default e g used in SOLPS Originates from LINDA grid generating code G Maddison mid eighties last century MSHEFRM 1 Sonnet format MSHERM 2 Carre format NTRFRM two different formats for triangular grid files are supported NTRFRM 0 old format first all x coordinates then all y coordinates NTRFRM 1 new format x y coordinate per point one point per input line NFULL Maximum nu
267. nto so called sub blocks each one starting with a card TEXT Each input block is described in one of the following 14 sections ZI to ZTA 2 1 Input data for operating mode 2 2 Input data for standard mesh 2 3A Input data for Non default Standard Surfaces 2 3B Input data for Additional Surfaces 2 4 Input data for species specification and atomic physics module 2 5 Input data for plasma background 2 6 Input data for surface interaction models 2 7 Input data for initial distribution of test particles 2 8 Additional data for some specific mesh zones 2 9 Data for statistics and non analog methods 2 10 Data for additional volumetric and surface averaged tallies 2 11 Data for numerical and graphical output 2 12 Data for plasma diagnostic module DIAGNO 2 13 Data for nonlinear and time dependent mode 2 14 Data for interfacing with external codes This last block 14 may be read in from the user supplied part with any format specified there from this same unit IUNIN but equally well from any other unit specified there e g from the subroutine INFCOP for interfacing with other codes Units cgs units are used with two exceptions All temperatures and energies are in eV 69 All particle fluxes are in Ampere i e s 1 602210 even neutral particle fluxes Since energies are given in eV units a particle flux x energy is already in Watt E g to convert a gas flow rate Q mass flow rate at temper
268. o 2m Z2Z2 an 6 8 x 10 8 h a p h 4 a 11 102 u Ha TR Ha a 1 2 1 T 2 31 2 u 2m2 Z2 ap 6 8 x 1078 P oe D Bo 11 103 E ab a 3 2 Ha T Ea a Using this decomposition and definition of in equation LL94 we find dEa eS Hb 12 D 3T asa 3 p 11 104 dt a El Ea t Ve 9 04 Hence in this limit of a lt 3 27 the solution of this linear differential equation exists in closed form edh exp He 1 pu pa t et 1 exp v t 11 105 Example hydrocarbon ions With ua 1 for protons Ha 16 for CH the Coulomb logarithm Aa 10 hence De 1 pe pal 8 8 x 1078 my T 2 np Tp in cm and eV resp which is close to the solution Eq 11 given in Z5 for thermalization of hydrocarbons in a Maxwellian hydrogen plasma And this is also exactly the approximation which was also used in EIRENE since about 1987 for all test ions traveling in a bath of background ions To be done in case of drifting Maxwellian background first transform into frame such that stationary Maxw background then relax test particle energy in this frame then transform back To be done isotropization currently the ratio v parallel to v perpendicular is pre served 61 The full expression for the energy relaxation frequency v without the approximation of slow particles a i e for all values of x is yea 2 pa MoU ae a vg 11 106 where x has been defined above relati
269. o be checked simply the same formula but with the second and third term replaced by the sum over all receiving plasma ion species X UA ipls Sim ipls icell X EK IN ipls S ipls icell 14 24 ipls ipls In any case we see that the internal energy source term can be written as linear function of default tallies listed in subsections 214 2 2143 Hence they can be scored per history in newly introduced routine UPFCOP see flowchart LIZ directly on tally COPV Therefore the statistical error estimates for code interfacing tallies Sn Sm Sei Sze are directly available using the standard printout and graphical output procedures of EIRENE see dis cussion in paragraph L3 3 on evaluation of statistical variances for linear functions of tallies Prior to implementation of routine UPFCOP such variances have been evaluated in case spe cific codes STATS 1_COP Other differences between earlier versions of EIRCOP and the one for B2 5 2012 are re lated to different interpolation schemes the cell centered vs surface centred fluxes and cell indexing in B2 5 as compared to B2 210 Chapter 3 Problem specific Routines General remarks As mentioned earlier already the hard wired options in EIRENE allow a large variety of lin ear transport problems to be studied In most cases of neutral gas transport in a prescribed background plasma the only problem specific FORTRAN that is required consists of a few parameter statemen
270. odule PARMUSR has been removed Instead from parameter statements the storage is allocated directly from input flags usually with the same name as in module PARMUSR but an addi tional letter T in the end E g NATM number of different atomic species then is identified with input flag NATMI input block 4a etc The module PARMUSR reads stands for an integer not less than 1 COMDECK PARMUSR C C Q Geometry PARAMETER NIST PARAMETER NADD PARAMETER NLIM PARAMETER NPLG PARAMETER NKNOT PARAMETER NCOORD Primary Source PARAMETER NSTRA PARAMETER NSTEP Species and Tallies PARAMETER NATM NADV 7 PARAMETER NCLV PARAMETER NCOP Statistics PARAMETER NSD N Atomic Data PARAMETER NREAC PARAMETER Surface Reflection Data PARAMETER NHD1 NHD5 e g TRIM Database PARAMETER NHD1 12 N Diagnostic Chords Data PARAMETER NCHOR Interfacing routines PARAMETER NDX N Census Arrays PARAMETER NPRNL PARAMETERS FOR STORAGE REDUCTI 213 N2ND N3RD NTOR NSTS NPPART NTRI NTETRA NSRFS NMOL NION NADS NSNV NALV NBGK SDW NCV NRRC NREI NRCX NREL NHD2 NHD3 NHD6 HD2
271. of 1 2 10 cm to be used in this Knudsen number For a gas temperature of 300 K and a pressure of 1 Pa ny 2 414 x 10 4cem7 we then obtain alcem 1 2 414 x 10 x 2 x 107 amp 2 cm 9 88 In the BGK approximation to the Boltzmann collision integral see below Section LT only an effective mean free path appears because the collision rate vga is an effective rate only chosen such that the BGK model provides a certain viscosity binary diffusion or other continuum transport coefficient in the continuum limit One default set of BGK collision parameters used in EIRENE is based upon the concept of diffusion volumes to provide a weakly temperature dependent binary diffusion coeffi cients Dj for cross collisions e g for He Hg or viscosity u for self collisions in the gas see 9 This choice results in a BGK collision rate coefficient k T koT with the constant ko derived from such continuum limit considerations and the experimentally deter mined diffusion volumes Within this concept then a BGK mean free path ZI follows as n B Vf8T rm pox om nlov nko T 25 Lo x TleV n 10 cem 9 89 54 where the proportionality factor Lo in cm is typically in the range between 7 and 20 Lo 20cm for D D self collisions Lo 9 75 cm for D D self collisions and Lo 8 7 cm for D He cross collisions Lo is the BGK mean free path in cm in a gas at T 1 eV and
272. oidal co ordinate system in which this pivot point is specified The pivot point is then given in cartesian coordinates is this local system IPIVOT 0 pivot point is given in global cylindrical coordinates XPIVOT YPIVOT ZPIVOT r z with in degrees XPIVOT lst co ordinate of pivot point for line of sight e g x YPIVOT 2nd co ordinate of pivot point for line of sight e g y ZPIVOT 3rd co ordinate of pivot point for line of sight e g z The next card specifies the second inside point The second point on the line of sight must either be inside the first radial or x mesh or the additional cell number of the mesh cell to which this point belongs must be specified by the NSPBLC and NSPADD flags For otherwise the initial point for the line integration cannot be found automatically ICHORD only needed for NLTRA option sub block 2c Meaning analogous to that of first point flag IPIVOT XCHORD 1st co ordinate of second point for line of sight YCHORD 2nd co ordinate of second point for line of sight ZCHORD 3rd co ordinate of second point for line of sight PLCHOR the lines of sight are plotted into 2D or 3D geometry plots This however is automatically turned off if other plots are done between geometry plots initialization phase and line of sight integration post processing phase PLSPEC the spectra along the lines of sight are plotted irrelevant in case of NSPTAL 2 193 2 12 1 2 12 2 2 12 3 2
273. old EIRENE ver sions without dynamic allocation of storage NSNVI must be less or equal NSNV see PARMUSR and the detector functions are user supplied in subroutine UPNUSR see Sub section BZA Default NSNVI 0 The meaning of the next three cards is the same as for the corresponding cards in block 10A 10B or 10D Census Arrays All particle co ordinates at time t for history number IHIST i e position cell indices ve locity etc are stored on arrays RPART IHIST Real and IPART IHIST Integer in subroutine TIMCOL This subroutine TIMCOL is called if a collision with the time surface t t has occurred The number of scores on the old census arrays from a previous completed time cycle in a current run or from an earlier run is IPRNL The actual number of a score in subroutine TIMCOL is IPRNLI and after the score IPRNLI is increased by one IPRNLI is set to zero at the beginning of a run The actual number of a score in subroutine TIMCOL for the present stratum ISTRA is IPRNLS and after the score IPRNLS is increased by one IPRNLS is reset to zero at the beginning of sampling for each stratum Scaling of census array fluxes to be written 197 2 14 Data for interfacing Subroutine INFCOP example General remarks Data in input block 14 control additional input for an EIRENE run In case NMODE 0 see input block 1 i e no call to interfacing subroutine INFCOP only the additional input tallies ADI
274. on length times Dimension of T defined in expression 2 115 and analogously from 2 12 for a finite medium will turn out to be the relevant Green s function for the transport problem see Section LZ The integral Q r r a r r f dsLlr sQ 0 in equation Ila is well known as optical thickness of the medium in linear transport theory The inhomogeneity S in equation Id is excluding normalization the distribution density of first collisions whereas the integral term in equation Id describes the contribution to W from all higher generations The quantity can be written as Sz f woe T x gt 2 1 6a with a source density Q As the problem is linear Q can be normalized to 1 and thus Q can be considered a distribution density in ju space for the primary birth points of particles as e g opposed to the secondary birth point distribution or post collision density x of particles after a collision event vie fee C x gt x 1 6b 16 It can be shown that a unique solution x exists subject to appropriate boundary conditions and under only mild restrictions basically on the constants c and pa to ensure that the particle generation process stays sub critical Usually a detailed knowledge of or Y is not required but only a set of responses R defined by R lt Wg gt f atle g a lt Olg gt f w0 a0 2 13 where g x g x are given
275. on LY vo N ZEZE Aab Am ue V2 11 107 and the Maxwell integral U x W 2 fp dye yy erf Vx cee 11 108 Y x dv dx er 11 109 With this more general expression for the collision frequency Equation LL94 can then only be integrated numerically along the particle trajectory However other features of the colli sion process velocity spreading isotropization have then to be taken into account as well in order to ensure equilibration of energy of test particles to 3 27 of the fixed stationary Maxwellian background Without such further velocity space effects a test particle with en ergy a corresponds to the non equilibrium situation of a plane parallel monoenergetic flux and energy exchange of this non equilibrium flux with a Maxwellian background vanishes at a critical energy c distinct from from 3 27 ZZ paragraph 19 A2 BGK Coulomb Collision operator Diploma Thesis Felix Reimold 1 11 2 2 The Fokker Planck Collision Model A The gyro averaged Fokker Planck Coulomb Collision Model which was originally de veloped for a stand alone trace impurity ion transport code DORIS 28 29 is accommodated now as collision kernel in EIRENE In its present version this collision operator ignores the difference between real particle position and the guiding center hence e g classical dif fusion terms due to finite Larmor radius effects are not taken into account The averaging over gyro
276. on rate coefficients to charge state Z Z 1 Zmaz and filenames starting with ACD contain recombination rate coefficients from charge state Z Z 1 Zmar The particular chemical element ELNAME and the value of charge state Z is specified in the next input card which is read only in case of FILNAM ADAS H 10 same as for H123 H 4 but ionisation and recombination electron energy loss rate coefficients rather than reaction rate coefficients In the original ADAS files the names PLT and PRB are used for those quantities Note distinct from the AMJUEL database convention in case of ADAS format the PLT rates W cm do not contain the potential energy loss DP x SCD and the PRB rates contain in addition to their corresponding rates from AMJUEL also a Bremsstrahlung con tribution Internally EIRENE subtracts this ADAS Bremsstrahlung from electron energy weighted PRB rates whenever such rates are read via the ADAS format i e whenever FILNAM ADAS 113 Note in general the potential energy difference DP may or may not be included in the definition of energy rate coefficients H 8 H 9 and H 10 as read from a particular database For example the energy rate coefficients may in effect be either a radiation loss rate or a total energy loss gain rate This database specific convention may be altered by EIRENE input flag DP dur ing the internal preparation of atomic data files Proper choice of DP may then turn a radiation loss r
277. onal etc state as appropriate As above linearisation will be obtained by grouping labels and l into two disjunct classes and allowing for reactions only between initially prior to the collision one member from class 2 and one member from class b If we consider then the phase space balance equa tion for a given species l then the sum in the collision integral is over velocities belonging to all pre collision labels l l and over velocities of species J more generally over all velocities except those from the one post collision label in case of more than two post collision particles 10 The cross sections in the corresponding collision integrals ae v V v V are multiple differential for scattering at a certain solid angle and post collision energies with simultane ous transition from Ji l to l l For more than two post collision objects e g fission dissociative excitation stimulated radiation emission etc this notation is readily general ized by adding more superscript labels and more post collision velocities Thus the full WCU prototypical system of kinetic transport equations then reads for two post collision particles to be written for reference purpose only not needed explicitly here 1 7 The extra discrete label l introduced here compared to the Boltzmann equation may either be regarded as species index 79 to l or as other additional discrete independent
278. ons with elec tron temperature T in the electron retarding electric field with potential x Here x is a coordinate parallel to the current flow e g the magnetic field B The electron current density along the field is then after reduction possibly due to secondary electron emission 8kT jp e 1 4 ne rvs 1 Ys ec 1 4 Ne g expleAPs r kT am ha Ise e Here Ys e e is the secondary electron emission coefficient and v2 is the average electron velocity The subscripts and 7 stand for the plasma sheath interface and for the target surface respectively and A s r is the typically negative voltage drop from the plasma sheath edge to the target In order to determine the sheath voltage drop A sr we equate the component normal to the target of this current density with the corresponding component of the net ion current density ir Jp cos W jf jp cos W jf jni Hence the cosine of the angle Y of direction of current flow e g of field line inclination against the target surface normal if the current flows parallel to B cancels out as does the elementary charge e The ion electrical current to the target j j no ion sources within the sheath region is given as Ip e X Zi nais Vrais X Zi nas Mais Ci s i i The sum is over all ion species Z is the charge state of species 7 n g is the corresponding ion density and V 5 the ion flow velocity com
279. or code coupling tally COPV This makes redundant the specific statistical variance evaluation in STATS1_COP 67 SECOND RANSET RANGET LOCAT1 SAMPT1 SAMLN1 SAMSF1 SAMVL1 FOLNEUT FOLION UPFCOP STATS1 STATS1_BGK STATS1 COP 100 10 BGK specific Iteration Routine MODUSR MODBGk read all EIRENE tallies RSTRT sum over strata from fort 10 and fort 11 identify artificial neutral i background species and mete their collision partners evaluate parameters for new background for self Been DOBO collisions BGK tallies evaluate parameters for new background for cross Boise D0130 collisions BGK tallies print residuals fill work array RWK for next EIRENE iteration 500 600 evaluate derived background data electron density DEIN PLASMA_DERIV vacuum flags LGVAC etc modify background 600 800 parameters temporarily to enforce relation between Ti12 and Ta molecular data arrays XSECTI restore all PLASMA background parameters PLASMA_DERIV write dump file fort 13 for PESAN background media Figure 1 13 Flowchart 9 1 Iterative mode for neutral neutral interactions 68 Chapter 2 Description of formatted input file General Remarks All input data from unit IUNIN are read in subroutine INPUT using formatted I O There are 14 blocks each one starting with a card eee n TEXT where n is the number of the input block n 1 2 14 Some blocks are subdivided i
280. or the pre but for the post collision density integral equation results in a track length type conditional expectation estimator X which together with X and the tradi tional track length estimator X may be used as one further option in the EIRENE code 19 This estimator X is obtained from X by extending the line integration which is restricted to the path from z to x4 in formula G79 to the line segment from z to Lena Here Zena iS the nearest point on a boundary along the test flight originating in 2 I e the line integration may be extended into a region beyond the next point of collision into which the generated history would not necessarily reach This conditional expectation estimator reads l 1 1 0 j l If Zeng is taken to be the nearest point on each mesh cell boundary then the estimator G 20 reduces as a special case to the method employed by the NIMBUS code L4 However the estimator G 20 is more general as the integration may be extended over arbitrarily many cells The length of the integration path is controlled in EIRENE by an input flag WMINC see section ZIO 1 3 2 Scaling of tallies With increasing NV the number of Monte Carlo histories the unbiased estimators X given in previous section LZ provide arbitrarily precise approximations for the responses Ry W g for detector function g and dependent variable Y equation LId The precise meaning and physical dimens
281. orced ROA is the radial shift of the poloidal cross section defined by the x y grids E g if the x y grids are given with magnetic axis as origin then ROA is the major radius If the x y grids are already given with respect to the torus axis at their origin then ROA 0 or better e g 1 0 4 ROA 1 Note ROA affects evaluation of cell volumes Note also in case of geometry and trajectory plots input block 11 this major radius offset ROA of poloidal cross sections has to be taken into account when defining plot frames Defaults NLTRA FALSE ZIA 0 ZAA 1 Data for mesh multiplication NLMLT the complete Standard mesh data are copied NBMLT times NBMLT Number of identical copies of the standard mesh Transition from one such mesh called block in EIRENE into another one has to be defined by transparent additional surfaces see block 3B VOLCOR The volumes of all cells of the standard mesh as computed by EIRENE in sub routine VOLUME are multiplied by one common factor VOLCOR for each block Data for additional zones outside the Standard mesh NLADD There are cells in the computational volume which are defined through additional surfaces as cell boundaries E g a standard mesh if there is one is augmented by additional cells in this case If NLADD FALSE the complete block 2D may be omitted and the defaults are used NRADD Number of additional zones The cell indexing along test f
282. ortional or otherwise optimal allocation to strata then requires estimates of run time per history for each stratum prior to the Monte Carlo simulation itself This information is stored in output stream FORT 14 and can be read back in into the next EIRENE run and used then for assignment of compute nodes to strata and vice versa This is controlled by the NFILE K flag described above 2 1 2 The NLERG option for cell volumes All non transparent surfaces are made perfectly reflecting mono energetic cosine distribu tion All volumetric collision processes are de activated Except possibly for the very first flight there is only either one atomic species ATM 1 or one molecule species IMOL 1 79 Unless otherwise specified in input block 13 a single time step with time limit DTIMV 1 0 s is set and up to NPRNLI 10 test flights are launched Under such conditions the particle density should be constant throughout the grid Statistically significant deviations from that constancy indicate wrong cell volumes as compared to the volumes seen by the test particles e g due to additional surfaces intersecting the grids or complicated shapes of some addi tional cells see input blocks 2 and 3 In a second run the volumes of these cells can then be set explicitly e g in input block 8 2 1 3 The NLMOVIE option for making movies of trajectories documentation to be written 80 2 2 Input for Standard Mesh General Remarks EIRENE
283. oss section Mnoniin to the total cross section C Chin T Chonlin 9 92 y ie T nonlin 9 93 Whereas Cun and Xin depend only upon parameters of the background medium bulk par ticles usually electrons and ions the kernels Choniin and the rate coefficients Xnontin May also depend upon parameters of the test particles atoms molecules test ions themselves In order to include such nonlinear interactions in a case a copy of the test particle species cards input block 4a 4b or 4c is put into the background species specification input block 5 E g if one wishes to include H H elastic neutral neutral collisions in a simulations then an artificial species of H particles has to be specified as one of the background particles bulk ions with charge state zero by abuse of language During the iterative procedure the parameters of this artificial background species density temperature drift velocities are those that have been obtained from the corresponding test particle tallies in the previous iteration One iteration steps end by overwriting these parameters at the end of a cycle with the new values in the post processing phase of each iteration cycle module MODBGK f and by preparing the new collision rate coefficients for the next iteration cycle 1 9 2 Direct Simulation DMCS of self collisions currently under development Please contact us for details and status Further details can be found in Ref Z3
284. otal atomic source particle flux for each stratum is scaled to be FLUX For example a H molecule source with NPRT p 2 is treated as if a flux of FLUX 1 602E 19 2 H molecules per second is emitted resulting in an equivalent atomic flux FLUX 1 602E 19 per second SCALV O0 The default scaling of tallies with FLUX can be overruled by this flag The IVLSF common scaling factor for all surface and volume averaged tallies is determined such that one particular tally selected by the ISCL flags described below has the prescribed value SCALYV This determines the scaling of all other volume av eraged and surface averaged tallies By this option for example one can set the neutral particle density to a prescribed value in one particular cell Hence one can prescribe the local Knudsen number for nonlinear applications including neutral neutral interactions 1 The following ISCL flags select one particular volume averaged tally 2 The following ISCL flags select one particular surface averaged tally ISCLS species index of selected tally ISCLT tally number of selected tally refer to tables L253 ISCL1 ISCL2 ISCL3 ISCLB ISCLA 153 IVLSF 1 cell numbers NRCELL NPCELL NTCELL NBLOCK NACELL respectively if NPCELL 0 or NTCELL 0 then ISCL1 NCELL the cell number in the 1 dimensional arrays see end of section 22 1 The additional cell region is specified by NRCELL 0 NPCELL 1 NTCELL 1 NBLOCK
285. pe group The second digit is irrelevant and defaulted to one only binary collisions are considered This flag controls options for non linear test particle test particle collision Let ISPZ be the species index of a test particle If the collision is a self collisions this flag IBGK must point to the species ISPZ itself Otherwise it must point to the 2nd test particle species ISPZ2 which is involved in the BGK cross collision term IBGK must be consistent with IBULK which in this case is the artificial background species result from previous iteration in the linearization of the collision operator I e if test particle species A collides with test particle species B of same or of differ ent species and type then a bulk species A B must be present in input block 5 such that species A and ABy have the same mass nuclear charge and charge numbers The density flow field and temperature of collision partner AB are iterated using either the corresponding parameters estimated for species A in case of self collisions or using parameters obtained from the formulas for nag TaB Vag see section LT for cross collisions between species A and B The flag IBULK must point to the corresponding species IPLS ABgy_x in block 5 An example for input specifications of non linear BGK collisions is given below in section Z42 Default 0 no iteration for non linearity in collision kernel no artifi cial background spec
286. pled from the distribution DMOL IMOL 0 no thermal particle re emission for this species p 0 lt 0 not in use warning and error exit species index out of range In code versions older than year 2000 this ISRT lt 0O options was also used to acti vate sampling the new species index IMOL from distribution DMOL In order to avoid un intentional species sampling at surfaces this option was disabled from year 2000 on These latter two surface species index flags are considered to be particle properties hence they are read in the particle specification blocks 24 and 2 4 The flags in the next card can be used to modify the pre programmed fast particle reflection models to some extend at least ERMIN For incident particle energies below ERMIN the fast particle reflection model is switched off Only the thermal particle model is used 140 ERCUT RPROBF These variables may be used to modify the default Behrisch Matrix reflection coeffi cients for particles incident on a surface at low energies Ein The original data L8 are used only for Ein gt ERCUT and for normal incidence 0 In the range ERMIN lt Fin lt ERCUT the particle reflection coefficient p Ein Vin 0 is replaced by a smooth cubic interpolation curve p such that p 0 RPROBF The original Behrisch Matrix is recovered by setting ERCUT lt 0 The next three flags modify the particle energy and momentum reflection co
287. plot FCABS1 FCABS2 189 2 12 Data for Diagnostic Module General remarks The data in this block are used to define a line of sight LOS across the computational do main along which line integrals Pz g l dl f g I dl 12 13 LOS Pi are evaluated This is done in subroutine LININT which is called from subroutine DIAGNO at the end post processing phase of an EIRENE run The spatial dependence of the function g l is defined as function of one or more of the estimated volume averaged tallies e g atom density and or input tallies e g plasma temperatures At present there are two version 2004 and older or three preprogrammed functions g and the option to call a user supplied integrant Firstly there are the Lyman and Balmer series volume source rates emissivity see Subr SIGAL Secondly the neutral atom charge exchange source rate can be integrated along a line of sight for a given energy of the impacting plasma ion Subr SIGCX This routine includes re absorption along the line of sight A LOS spectrum also side on spec trum of up to NCHEN energies may be obtained by this procedure Thirdly version 2005 and younger the side on radiances of selected lines photon test particle species including reabsorption can be obtained Subr SIGRAD A number of different emission line shape profiles is available for these The Input Block 12 Data for Diagnostic Module NCHORI NCHENI IF NCHORI GT 0 THEN
288. ponent normal to the target of ion species 7 Mx is the Mach number of the corresponding current component and c is the ion acoustic speed for species 2 Hence combining the three previous relations the sheath potential difference A in terms of given jp Te Ys c c and ions flows I reads omitting the subscript 7 for the components 4 normal to the target in these quantities V2 i e eA kT In I y aus Ves m Jpl e n 1 Ys e e i Ne S kTe Nes kTe Me 2 i e i C D 225 Msas m Jp i e n 1 Ys e e Ne S kT s kTe 5 79 5 78 This expression 78 is evaluated by the function SHEATH of the EIRENE code taking local plasma data for Te and n and Vr Nne from quasi neutrality at the point of impact of an ion at a wall boundary e g the divertor target plate strictly at the sheath entrance S in front of the target Special forms of 6 79 are often quoted in the literature Writing for the ion acoustic speed ci explicitly kT kT m ADM Mi y denoting the adiabatic coefficient and hence Me kT Me 1 2 a fae E 1 5 80 we recover well known expressions for simpler cases Consider e g a single ion fluid case Ne ni n with Z 1 and M 1 Bohm sheath condition for isothermal flow y 1 E reduces to e A kTe in O asy me L 1 E Ys e e kTe e n kze Me 5 81 V2T ykT i Me 1 2 Sol m fon KT
289. ponse is a spatial function averaged over a grid cell hence piece wise constant in each grid cell ICELL ICELL 1 NRAD Tally naming convention Particle source rates name P A BC with A type of incident particle A A atoms M molecules I test ions PH photons P bulk particle BC type of produced particle BC AT atoms ML molecules IO test ions PHT photons EL electrons PL bulk particles The tallies are resolved by species index of produced particle and are to be scaled NLSCL option by type of incident test particle Energy source rates name E A BC analogue to particle source rates but not resolved wrt species index of secondary particles Momentum source rates name M A BC analogue to particle source rates only available for A A M I PH and for BC PL i e currently default tallies are only available for momentum sources sinks for background plasma particles caused by test particles resolved by type of test particle name of tally and by species of bulk particle 1st index in array 237 Surface averaged responses are also spatial functions averaged over surface segments hence piecewise constant on each surface ISURF or surface segment ISURF 1 NLIMI and with some spatial resolution possible on standard mesh surfaces ISURF NLIM NLIM NSTSI incident onto surface particle and energy surface averaged fluxes are split by the type of the incident particle photons Phs a
290. property is assigned to side I of the triangle ITRI ISTS 0 stands for default grid option transparent surface cell indexing is done automatically Otherwise ISTS is the number of an additional STS lt NLIMI or non default standard NLIM lt ISTS lt NLIM NSTSD surface option as read in sub blocks 3a or 3b respectively By default the normal vector of each side of a triangle points out of the triangle In case IPROP lt 0 this vector points into the triangle This is relevant at surface options with ILSIDE 0 if NLTET TRUE Documentation not available here Make contact with the authors if NLGEN TRUE NRIST number of cells in otherwise arbitrary mesh option NLGEN Data for second standard mesh poloidal or y grid PSURF NLPOL A poloidal or y grid is defined Otherwise the complete block 2B may be omitted and the volume averaged tallies are then automatically integrated over this co ordinate INDGRD 2 1 standard grid option INDGRD 2 2 3 4 5 6 not in use default INDGRD 2 1 NP2ND Number of grid points in y or poloidal direction YIA YGA YAA YYA for the LEVGEO 1 option the y grid PSURF is defined in the same way as the x grid using the parameters YIA YGA cm instead of RIA RGA for the LEVGEO 2 option the 0 grid PSURF is defined in the same way as the r grid using the parameters YIA YGA poloidal angle in degree instead of RIA RGA for all options LEVGEO gt 2 this input card
291. r RIA see NL CRC TRUE option above EPOT Value of EP r for cylindrical surface number NR1IST with rnrisT RAA EPCH Value of EP r for cylindrical surface number NR1IST 1 with rnRisT 1 RRA irrelevant if RRA lt RAA EXEP The variation of the shift function EP r with r is given by EP r EPIN 4 0 EPOT EPIN ELIN Value of EL r for cylindrical surface number 1 with 71 RIA see NLELL TRUE option ELOT Value of EL r for cylindrical surface number NR1ST with TNRIST RAA ELCH Value of EL r for cylindrical surface number NR1ST 1 with rn RiST H1 RRA irrelevant for RRA lt RAA EXEL The variation of the ellipticity function EL r with r is given by EL r BLIN kee N ELOT ELIN if NLTRI TRUE to be written 86 if NLPLG TRUE NRIST number of polygons for discretisation in radial or x direction NRPLG Number of points per polygon NPPLG Number of valid parts on each polygon Each polygon is described by the x and y co ordinates of NRPLG points It is not necessary that all this points are used for the polygon One can cut the polygon into several valid parts interrupted by parts which are not seen by the test particles Default NPPLG 1 This option facilitates the use of 2 d computer generated meshes which contain topological grid cuts XPCOR YPCOR shift whole mesh by that vector in x y plane RFPOL if RFPOL gt 0 one additional polygon zone is defined at
292. rall CPU time This additional freedom can be used in EIRENE runs to affect the statistical error for a given CPU time Unfortunately as with non analog sampling this can go both ways Fortu nately however here a clear general recommendation can be given see below in this section proportional allocation Lets denote by 2 N the estimate for tally R as obtained only from the N samples from stratum k but scaled with the full source strength s Likewise we denote by G N the variance of estimate R per history i e for a single sample obtained by only using the Ny samples from stratum k again implying the scaling with total source strength s Then clearly S R N gt Fa Ne 3 37 k is the only unbiased weighted estimate of R obtained from summing over all strata i e from all N samples The asterisk denotes the estimate R of R obtained with stratification N WN Ny and R N is the estimate of the same quantity from a simple sample no stratification of same size NV R E R N E R N 3 38 where X denotes the expectation value of random variable X Furthermore ash 1 OF FRN TiN O N OS k s 1 52 Nz 3 39 26 where again the asterisk indicates the value obtained with stratification The right equation follows from the sum rule for variances and because the estimates for the strata are mutually statistically independent It is clear that the variance with st
293. ranges of the 2nd and 3rd mesh respectively for which this surface acts as non default surface IRPTA1 and IRPTE are irrelevant If JMP is a surface from the 2nd mesh then IRPTAI IRPTE1 and IRPTA3 gt IRPTE3 are the surface index ranges of the 1st and 3rd mesh respectively for which this surface acts as non default surface IRPTA2 and IRPTE2 are irrelevant 93 If JMP is a surface from the 3rd mesh then IRPTA1 IRPTE1 and IRPTA2 IRPTE2 are the surface index ranges of the Ist and 2rd mesh respectively for which this surface acts as non default surface IRPTA3 and IRPTE3 are irrelevant The third card ILIIN ILPLG is identical to the corresponding card for additional sur faces see block below Input Data for Additional Surfaces One exception is the flag ILSIDE which controls the sign of the surface normal vector hence the orientation of a surface In case of unstructured standard grids NLTRI or NLTET triangles in 2D and tetrahedrons in 3D there is no well defined default surface orientation and the flag ILSIDE is irrelevant in such cases The input data in the block for the local reflection model are described below see 4 Input Data for Particle Surface Interaction Models 94 2 3 2 Input Data for Additional Surfaces General remarks Internally each additional surface is defined by an algebraic equation and some algebraic inequalities specifying the boundary of that surface i e
294. rary additional surfaces Input flags for this mesh multiplication option are comprised in sub block 2D As mentioned above in addition to these regular grids one can define cells of almost arbitrary complexity by using the additional surfaces defined in sub block 3B Such surfaces are labeled 0 JA in EIRENE Appropriate cell number switching flags must be set on transparent 81 additional surfaces separating these general additional cells Data relevant for the additional cells e g the volume are read in sub block 2E The number of additional cells is NRADD Therefore the total number of cells in an EIRENE run is NSBOX with NSBOX NRIST NP2ND NT3RD NBMLT NRADD Cell volumes in the standard mesh region as well as the center of mass vector in each of these cells are computed automatically The corresponding data in the additional cell region must be specified by the user e g in the input block 2E or 8 or in the user supplied routine GEOUSR section B 4 which is called by EIRENE in the initialization phase The Input Block xxx 2 Data for Standard Mesh INDGRD J J 1 3 xx 2A x or radial co ordinate surfaces NLRAD IF NLRAD then NLSLB NLCRC NLELL NLTRI NLPLG NLFEM NLTET NLGEN NRIST NRSEP NRPLG NPPLG NRKNOT F INDGRD 1 LE 5 THEN IF NLSLB OR NLCRC OR NLELL OR NLTRI THEN RIA RGA RAA RRA F NLELL THEN EPIN EPOT EPCH EXEP ELIN ELOT ELCH EXEL F NLTRI THEN TRIN TROT TRCH E
295. ratification amp N can certainly be different from the variance N obtained from a simple random sample without strati fication of the same size N To see this we write the trivial identity M N Y N 3 40 k 1 For example in case of proportional allocation of CPU time to strata according to their source strength sx 1 Nk X sz N 2N FHLB eM 3 41 S one finds from 8 39 for the variance of the stratified sample 2 Sk 5 N X aE Ne 3 42 which can be substantially smaller than the variance from the simple sample G 40 of size N if the subdivision into strata is made such that the variability within strata o is less then the variability in the entire population o Furthermore one can show that with proportional allocation 4I the variance from the stratified sample is always less than or equal to the variance from the simple sample of same size N no matter how the subdivision into strata was done P If M N k 1 2 M then N lt 6 N 3 43 i e stratified source sampling with proportional allocation is an inherently safe working procedure for variance reduction This important inequality can be derived after some lengthy algebra leading finally to EN 8 N SOIR RON 3 44 k Clearly the second term on the right side of this equation which is the variance between strata is always positive or zero and this fraction of the variance is eliminated
296. rator Tsp is solely the acceleration in the electrostatic sheath Alternatively and in cases when the magnetic field is tilted with respect to the wall surface one may define g ion v to be the kinetic transport flux distribution entering the magnetic pre sheath i e with a drift velocity of at least ion sound speed in the direction parallel to the magnetic field B rather than normal to the wall In this case the action of the magnetic pre sheath must be accommodated in the sheath kernel Tsa which we might even consider to split into a magnetic pre sheath MP kernel and an electrostatic sheath Sh kernel Tsn Tapsn Mpshs VMpSh Yesh Vesh Tessh eshs Vesh Wall 5 64 CFD kinetic magn pre sheath 4 sheath I gt gt i Tr V I reared I j ho ds MP Figure 1 1 Transition region between fluid plasma CFD and wall surface schematic The plasma flow is specified by CFD models at the entrance surface of the magnetic presheath MP taken normal to the magnetic field B 1 5 1 half sided Maxwellian flux at electrostatic sheath entrance One of the standard options in EIRENE in particular in applications in which EIRENE is coupled into a plasma fluid code is a half sided forward drifting Maxwellian ion flux dis tribution options NEMODS 6 7 Section 277 The kinetic plasma ion flux distribution entering the electrostatic sheath is given as 1 1 Dikin a Ur EXP z 0 va oe 50
297. rces As N 4 but with added sheath acceleration see para graph below N 6 surface source The velocity vector Vo V Xo VYo V Zo is sampled from a truncated Maxwellian flux fmax T V C at temperature T and which is drifting by a velocity V The flux is across a surface element described locally by the outward normal vector C The mean energy from this sampling distribution is that given by option N 4 point or volume source The velocity vector Vo V Xo VYo V Zo is sampled from a truncated Maxwellian density distribution fmaz T V C at temperature T and which is shifted by a ve locity V N 7 only for surface sources As N 6 but with added sheath acceleration see para graph below N 8 Mono energetic source f E 6 E0 with energy E0 E with E being the local mean incident ion energy for example defined in connection with the spatial step function option see section ZZ11 N 9 only for surface sources As N 8 but with added sheath acceleration see para graph below The choice of temperature parameters T and T in the energy distributions N 4 5 6 or 7 of the plasma fluids entering the sheath region is controlled by the second digit M of NEMODS M 0 K is the local electron temperature taken from input tally TEIN on the grid In case of NLPLS the default parameter T is the local ion temperature for bulk ion species IPL IPL is the species index of the source particle In case of NLION the de
298. re are volume averaged tallies surface averaged tallies surface crossing tallies and global tallies These latter tallies are derived from the former ones by integration over the total computational volume or over all non transparent surfaces respectively Each volume averaged tally is an array TALLY V I of NSBOX data comprising the re sponses for the respective detector function gy in each zone of the computational mesh see section 22 General Remarks Each surface averaged tally is an array TALLYS I of NLIMPS data comprising the re sponses for the respective detector function gg integrated over each non default standard or additional surface Each volume or surface tally is characterized by its index ITALV or ITALS respectively augmented by a first species index in some cases The first index if there is one is always referred to as species index by abuse of language even for additional tallies ADDV or ALGV in which cases it might have a different meaning As for the volume tallies there are NTALV preprogrammed detector functions up to NADV user supplied detector functions for track length estimators tally no ITALV and NCLV user supplied detector functions for collision estimators tally no ITALV Furthermore there are NSNYV snapshot tallies tally no ITALV NCPV tallies for coupling with plasma background codes tally no ITALV and NBGV tallies for the non linear BGK collision integrals needed for
299. re detailed later in input block 4 for volumetric collision processes based on ADAS adf11 format and input block 6 TRMSGL for the surface reflection database based on TRIM see below sections Z4 2 4 respectively 2 1 1 Automated stratification optimization proportional allocation The stratified sampling in EIRENE can improve the performance measured in terms of sta tistical error per CPU time if proportional allocation of sample size N to strata source strength S can be achieved See paragraph for more information on stratified source sampling The input flag ALLOC in input block ZZ controls this allocation Monte Carlo codes such as EIRENE are in principle trivially parallelisable by just distribut ing the Monte Carlo trajectory calculation over the available compute nodes If parallelisation is activated in combination with stratified source sampling however and strata are assigned to compute nodes then load balancing may be hard to achieve together with proportional al location of weights to strata This is because trajectories from some strata may be very short e g transport into purely absorbing media for example of impurity particles until ionisation and very fast to compute while from other strata these trajectories may be very long and time consuming to compute e g in near diffusive regimes with many collisions Often volume recombination strata in cold plasma regions fall into this category Load balancing and prop
300. regarded as Monte Carlo estimates of multi dimensional integrals namely of the adjoint function 7 integrated over phase space with S defining a distribution measure in phase space us It is then obvious that one can split that integral into a sum of integrals by arbitrarily de composing the domain of integration i e by decomposing the source S into sub sources strata S with M Ry dx ds 9 8 03 So fans 8 35 k This is the concept of stratified sampling which for Monte Carlo particle transfer proce dures in particular actually turns out to be a stratified source sampling Further details about this in our particular context are given in the description of input block 7 section Z7 below As pointed out above the evaluation of statistical error estimates has to account for the stratification because with stratification the Monte Carlo histories are not strictly independent anymore Grouping the WN statistically independent test flights random samples into M strata leads to Monte Carlo particle numbers Ny sampled from stratum k i e with birth points sampled only from source Sy with S MeN M gt for k 1 M 3 36 where again we omit the subscript g for the particular tally response function from now on The choice of the N is only restricted by the normalization condition in G 34 This there fore also applies for the allocation of CPU time to individual strata for a given ove
301. relation sampling is used See discussion at end of section LA NLERG The case is automatically reduced to a case for estimating cell volumes by utilizing an ergodic property More details see paragraph below NLIDENT In multi processor calculation mode NLIDENT forces all processors working on the same stratum to use the same sequence of random numbers and hence to carry out exactly identical work This flag can be used to test the parallelized code version NLONE The case is automatically reduced to a single species and one speed transport problem not ready don t use LTSTV free flag used for testing purposes Optional input cards for pathways to external databases Their presence is identified by the starting character string CFILE of these cards DBHANDLE Name of the database which is specified in this CFILE card The format of a data file is identified in EIRENE by its name Possible database names currently recognized are AMJUEL HYDHEL METHAN H2VIBR HYDRTC ADAS SPECTR PHOTON POLARI SPUTER TRIM TRMSGL with volumetric collision databases in the first block and surface interaction databases in the second DBFNAME Absolute or relative path and name of file to be used for this database Example CFILE AMJUEL home path AMdata amjuel tex CFILE TRIM home path Surfacedata TRIM trim dat Default If the specification of an external database name and path which is later e g in bloc
302. rface In this case ICOS is the sign 1 or 1 of the cosine of the angle of incidence against the surface normal this later unit vector may e g be found in TIMUSR by a call to NORUSR IERR error flag Presently any value different from 0 will lead to an immediate end of the run See subroutine TIMER in code segment GEO3D F 3 8 4 Subroutine VOLUSR The subroutine VOLUSR is called from subroutine VOLUME in case of LEVGEO 10 The call is CALL VOLUSR N A Here N is the number of cells in this run and A is an array of length N containing the N cell volumes in cm 3 8 5 Subroutine NORUSR The subroutine NORUSR is called from subroutine STDUSR in case of LEVGEO 10 The call is CALL NORUSR M X Y Z CX CY CZ SCOS Here X Y Z are the Cartesian coordinates of a point located on non default standard surface no M The routine must return the surface normal unit vector CX CY CZ 231 Chapter 4 Routines for interfacing with other codes EIRCOP General remarks The background or host medium usually the plasma is fixed in an EIRENE run and usually either specified in input block 5 2 5 or the background volume tallies are simply ready from data files However the mutual coupling between test particle species treated by EIRENE and the back ground medium may be very strong even if the test particle density is quite low compared to the background plasma density This is because in elastic collisions m
303. rfaces is not equidistant at some poloidal position but instead such that the area enclosed between two neighboring surfaces is kept constant The input variable RGA is irrelevant in this case 3 4 5 not in use 6 Data for NRIST radial surfaces are read from the work array RWK These data must have been written onto RWK in the user supplied subroutine INFCOP By this option grid parameters may directly be transferred into EIRENE from other files e g from plasma transport codes see below section LIA Data for inter facing routine INFCOP One and only one of the next 7 logical variables NLSLB NLTET must be TRUE NLSLB TRUE Geometry level LEVGEO 1 Cartesian geometry the x co ordinate is discretized by setting x 7 RSURF D I 1 NRIST Furthermore the flux surface labeling grid RHOSRF 1 is identical with the grid RSURF J NLCRC TRUE Geometry level LEVGEO 2 Cylindrical or toroidal geometry 1D radial mesh of concentric circular surfaces Polar coordinates are used in the x y plane The third coordinate either z or toroidal angle is either ignorable or discretized according to options described below block 2c The radial surfaces are given by r x y const and radial coordinate r is discretized by setting r7 gt RSURF I 1 NRIST Furthermore RHOSRE 4 Bue T where AREA is the area inside surface number J Thus for this option one has again RHOSRF D RSURF D I 1 NRIST NLEL
304. roblem 1D 2D 3D stationary or time dependent are given in Section LZZ 3 2 4 Surface averaged tallies UPSUSR Finally we note that surface averaged tallies table E3 may be considered just as special cases of the volume averaged tallies described above if appropriate use is made of functions Let therefore p be a co ordinate normal to a surface S at the strike point 1 of a test flight from r to r with speed unit vector Q v u Le the surface is described locally by the equation p 0 at the point rg S at which we may define an orthonormal basis p p p Furthermore rs r 1 which means that one may treat surface events exactly in the same way as collisions with the background medium in our terminologies Then a surface response function gs defined as gs j r v T lp g j r v is the detector function for the same response FR as previously detector function g was but now surface averaged instead of volume averaged sa t f drost sur face volume Therefore the line integrals J in the formula given above for track length estimates equa tion ZZ now reduce to his fal 8 0 9 0 9 0 cose 9 2 5 220 if the surface is intersected during the test flight from r to r and J 0 else This can easily be seen by writing cos Q ep Tri mtl cos Q e 2 6 cos Q ep i e p rp l cos Q ep In other words tracklength estimators beco
305. roblem specific routines call from MODUSR TRCSIG_ Trace back from post processing line integral diagnostics block DIAGNO TRCGRD Printout of standard mesh surface data TRCSUR Printout of data for additional surfaces TRCREF Printout of reflection model related data In particular a list of all non perfect recycling surfaces is printed i e a list of surfaces for which there is some absorption at least for one incident particle species TRCFLE Trace back from subroutines WRSTRT WRGEOM WRPLAS writing on and reading from the dump files FT10 FT11 FT12 FT13 etc TRCAMD Trace back from atomic and molecular data routines XSECTA XSECTM XSECTI 181 DCON TRCINT Traceback from user specified interfacing routine INFCOP e g of data related to coupling of EIRENE to other codes TRCLST Printout of information during the last history of each stratum E g sampling efficiencies and other accumulated information which is only available in the history generation routines during particle tracing TRCSOU Traceback from primary source sampling routines e g from LOCATE SAMPNT SAMLNE SAMSRF SAMVOL and SAMUSR TRCREC Printout of EIRENE recommendations for next run on same case A stratified source sampling at present for proportional allocation of weights B weight windows at present to be written TRCTIM Printout cpu time information for each history TRCBLA Global particle and energy balance for atoms is printed TRC
306. rogen onto iron into the EIRENE run Up to NHD6 such Target Projectile Specification Cards may be included For a complete list of such files currently available see again section L4 Note if during a Monte Carlo simulation a projectile A hits a target B for which no TRIM data file has been specified but still NLTRIM TRUE then EIRENE searches the closest of all its TRIM data files with respect to a reduced mass argument and uses this target projectile combination together with a reduced mass scaling of incident particle energy Hence a TRIM data set is chosen such that the reduced mass scaling factor is as close to one as possible amongst the files available DATD distribution for sampling the species index of reflected or otherwise emitted atoms The NATMI relative frequencies DATD IATM IATM 1 NATMI are used to produce the corresponding cumulative distribution DATM in order to facil itate sampling inversion method Normalization of DATD such that Yaru DATD IATM 1 is carried out internally DMLD as for DATD but for molecules Cumulative distribution is DMOL DIOD as for DATD but for test ions Cumulative distribution is DION DPLD as for DATD but for bulk ions Cumulative distribution is DPLS 139 The activation of these distributions at surface events during the particle history generation process is controlled by the surface species index flags ISRF ISRT read in the species sub blocks of section Z4 an
307. rom molecule plasma coll NION amp cm T15 16 PMPL Particle Source Bulk Ions from molecule plasma coll NPLS amp cm T16 17 PIEL Particle Source Electrons from test ion plasma coll 1 amp em T17 18 PIAT Particle Source Atoms from test ion plasma coll NATM amp cm T18 19 PIML Particle Source Molecules from test ion plasma coll NMOL amp cm T19 20 PIO Particle Source Test Ions from test ion plasma coll NION amp cem 3 T20 21 PIPL Particle Source Bulk Ions from test ion plasma coll NPLS amp cem 3 T21 22 EAEL Energy Source Electrons from atom plasma coll 1 watt cem 3 T22 23 EAAT Energy Source Atoms from atom plasma coll 1 watt em 3 T23 24 EAML Energy Source Molecules from atom plasma coll 1 watt em 3 T24 25 EAIO Energy Source Test Ions from atom plasma coll 1 watt em T25 26 EAPL Energy Source Bulk Ions from atom plasma coll 1 watt em T26 27 EMEL Energy Source Electrons from molecule plasma coll 1 watt em 3 T27 28 EMAT Energy Source Atoms from molecule plasma coll 1 watt cm T28 29 EMML Energy Source Molecules from molecule plasma coll 1 watt em T29 30 EMIO Energy Source Test Ions from molecule plasma coll 1 watt cm T30 31 EMPL Energy Source Bulk Ions from molecule plasma coll 1 watt em T31 32 EIEL Energy Source Electrons from test ion plasma coll 1 watt cm T32 33 EIAT Energy Source Atoms from test ion plasma coll 1 watt em T33 34
308. rrently in use e N 0 photons versions 2004 and younger e N 1 atoms e N 2 molecules e N 3 test ions e N 4 bulk ions e N 5 electrons The Input block 4 Data for Species Specification and Atomic Physics Module Note in EIRENE 2003 or later the format of input flag REAC described below was generalized from A9 to Axxx with xxx lt 50 to accommodate the longer reaction information for photonic processes into the same format The old format A9 is of course automatically still recognized as special case NREACI DO for real particles databases FILNAM HYDHEL AMJUEL METHAN H2VIBR 109 IBGKS R FILNAM H123 REAC CRC MASSP MASST DP RMN RMX format 13 1X A6 1X A4 Axxx A3 213 3E12 4 IF RMN GT 0O READ IFEXMN FPARM J J 1 3 IF RMX GT 0 READ IFEXMX FPARM J J 4 6 for real particles database FILNAM ADAS or any table in an equivalent format as the ADAS adf11 files IR ADAS H123 REAC CRC MASSP MASST DP format 13 1X A6 1X A4 Axxx A3 213 3E12 4 ELNAME IZ format 4X A2 1X 13 i e one additional input card is read to identify the chemical element and charge state Ex trapolation flags RMN and RMX are not in use in this case and may be omitted Default hard wired extrapolation schemes are used if the plasma density and temperature is outside the tabulated range for real particles database FILNAM
309. s WSNAP WEIGHT Then in order to estimate a response for a detector function g on snapshot tally number ISNV a statement in subroutine UPNUSR should read SNAPV ISNV ICELL SNAPV ISNV ICELL WSNAP x g E g with g 1 this is an unbiased estimate of cell averaged particle density at time t t see EJ i e just counting the particle weights at t t provides an unbiased estimate of the particle density This is intuitively clear but also mathematically correct since these snapshot estimators are formally derived as special cases of tracklength collision or surface flux estimators interpreting the time horizon sub manifold as time surface by abuse of language by including in g a delta function in time g t r v 6 t g r v Subroutine UPNUSR must at least include module COMPRT for the particle weight WEIGHT Here g is evaluated at the point of time at which TIMCOL is called Scaling of snapshot tallies is done by interpreting the linear source strength FLUX scaling factor given in input block ZZ for each stratum as a total number of particles rather than as flux particles s i e FLUX is the integral of the source distribution not only over physical space but also over time interval DT MV from initial time t to time t Section LIB 219 3 2 3 2 B stationary snapshot tallies A stationary value of snapshot tallies to be compared with other tallies in stationary
310. s Le the three inequalities XLIMSI lt x lt XLIMS2 YLIMS1 lt y lt YLIMS2 ZLIMS1 lt z lt ZLIMS2 are checked at the point of intersection x y z 1 5 Complement to RLBND 1 Only the surface element outside the parallelepiped is seen by the particles RLBND gt 2 In this case the surface will be defined by the input of the coordinates of at least 2 and at highest 5 points on a plane surface If there are only 2 points the surface is parallel to one axis If there are 3 or more points then the boundary of this plane surface is a closed polygon Pi Pa Pi Therefore the correct order of points at input is relevant The orientation of the positive surface normal vector is defined by the first 3 points and it is given by the vector product P3 P1 x P3 P2 Thus the orientation can be reversed e g by interchanging P gt and P 2 1 plane surface parallel to z axis The surface equation of this plane reads ax by c 0 with the coefficients a b and c such that the points P P lie on this surface and the valid part of that surface ranges from P to P in the xy plane The z coordinates of these two points define the boundaries in z direction 103 2 2 Complement to RLBND 2 1 2 4 as RLBND 2 1 option but with z and y exchanged I e now the y coordinates of the points P P gt are the boundaries of the surface ax bz c 0 in y direction 2 5 Complement to RLBND 2 4 2 7 as RLBND 2 1 option but with z and
311. s block 4 NRRC Maximum number of re combination processes blocks 4 5 NREI Maximum number of electron impact processes blocks 4 5 NRCX Maximum number of charge exchange reactions blocks 4 5 NREL Maximum number of elastic reactions blocks 4 5 NRPI Maximum number of ion impact reactions blocks 4 5 Reflection database parameters see example above NHD6 is the maximum number of dif ferent target projectile combinations for which databases can be included NCHOR Maximum number of lines of sight for diagnostics module block 12 NCHEN Maximum number of energy values for spectra computed in diagnostics module block 12 NDX NDY NFL Problem specific in case of coupling to external code See input block 14 Otherwise stand alone mode just set to 1 NPRNL Maximum number of particles stored on census array for time dependent mode block 13 In addition to these parameters which depend upon the size of the particular problem under investigation there are a few further parameters in PARMUSR which can be used to optimize storage versus CPU performance E g atomic data can either be stored in great detail or they can be recomputed whenever they are actually needed This is controlled by the parameter NSTORAM The latter choice e g NSTORAM 0 or NSTORAM 1 may be the better one on very large meshes above say 20000 cells as are commonly encountered in 3D Stellarator applications 216 3 2 The Additional
312. s see reference B9 new flux dependence option A8 2004 M 5 not in use M 6 Haasz Davis 1998 formula for chemical sputter yield M 7 Haasz Davis 1998 formula for chemical sputter yield and multiplicative fac tor for flux dependence Roth 2004 M 9 was option N 3 in Eirene 2004 and older user supplied sputtering model see section B Entry SPTUSR to subroutine REFUSR Default ILSPT 0 143 The next two surface species index flags ISRS and ISRC control the species of sputtered particles Hence they are considered surface properties and are read in the surface specifica tion decks in blocks ZZ and or ZA ISRS sputtered particle species flag physical sputtering gt 0 lt 0 both the sputtered particle and the reflected particle if any will be followed Their contribution to surface particle and energy fluxes is stored in surface aver aged tallies 1 to 24 i e sputtered particles are not explicitly distinguished from reflected particles in the balances Furthermore the sputtered flux surface tal lies 25 to 28 are updated The species index of the sputtered particle atom is IATM ISRS Hence on input ISRS lt NATMI There is no physical sputtering for the particular surface element and incident species note ISRS ISRS ISPZ MSURF i e ps 0 here Only the reflected particles are followed Their contribution to surface particle and energy fluxes is stored in surface averaged tall
313. s IDPLS in cell ICELL is reset to DITINUDPLS ICELL DIADD IDPLS 167 V cards V IDPLS VXADDUDPLS VYADD IDPLS VZADD IDPLS format 1A 116 6X 3E12 4 plasma drift velocity in x direction Vz for species IDPLS in cell ICELL is reset to VXINCUDPLS ICELL VXADD IDPLS VYIN VZIN likewise for the drift velocities in y and z direction respectively M cards M IDPLS MXADD IDPLS MYADD IDPLS MZADDUDPLS same as V cards but drift velocity in cell ICELL is given in Mach number units VXIN MXADD ZA m being the mass of bulk ions of species IDPLS VYIN VZIN are computed in the same way from MYADD and MZADD respectively VL cards VL VLADD format 2A 1E12 4 The zone volume in cell ICELL is explicitly set to VOL ICELL VLADD 168 2 9 Data for Statistics and non analog Methods General remarks The statistical performance FOM figure of merit see equation in section L3 3 of an EIRENE run as for any Monte Carlo application in general is very sensitive to the non analog methods used by EIRENE Therefore the input parameters in this block which define the non analog setting of an EIRENE run should only be used if the user has carefully worked through the code and has a detailed knowledge of the Monte Carlo techniques acti vated by setting the flags in this block Only the Cards for Standard Deviation which allow to obtain graphical and printed output regarding statistical standard deviation for
314. s and CH3 cards described below or in some user specified problem specific rou tines e g GEOUSR ignorable coordinates Surfaces with ignorable coordinates are specified either by setting the corresponding coeffi cients in the surface equation to zero or in case of 2 point 3 point 4 point of 5 point options by setting the corresponding coordinates of the points to 1 D20 and 1 D20 respectively coordinate systems transformations All surfaces are specified in cartesian coordiantes In case of NLTRA toroidal geometry approximation surfaces must be defined in the local coordinate system of toroidal cells centered at the magnetic axis xa ya RMTOR 0 i e excluding the major radius of the torus To facilitate input of the geometrical data each single or a set of surface s can be trans formed by a Cartesian mapping after specification of the surface coefficients and boundaries in some convenient coordinate frame by including TRANSFORM cards at the end of an input block for a particular surface One such TRANSFORM deck can act on an entire range of surfaces but only on those which have been read previous to the TRANSFORM deck Hence in order to transform the entire set of additional surfaces by one deck this deck must come after the last surface no NLIMI see below Particle surface interaction models Although the local data for particle surface interaction models for each specific add
315. s dependent effective area A ISPZ has to be specified to reproduce a given ratio of pumping efficiencies for different types of gas for a particular type of pump see the Note at the end of previous section RECYCT ISPZ option to reproduce the proper species dependence and pressure dependence if any of the pumping system Probably sometimes when S S P even RECYCT has to be made dependent on the pressure P found in front of the surface A then e g by an iterative procedure 149 2 7 Input data for Initial Distribution of Test Particles General Remarks The primary source and initial distribution of test particles in time dependent mode is given as a function Q i r t v Q is the density of the probability distribution from which the species index 7 the starting point r the velocity vector v and the starting time t are sampled in subroutine LOCATE i r t v is the state of the starting particle which then will be followed traced in subroutine FOLNEUT or FOLION There are four primary types of sources Strata namely Point sources Line sources to be written Surface sources and Volume sources As the transport equation is linear various sources of test particles can be treated subsequently and the responses can then be linearly superposed EIRENE can handle up to NSTRA see PARMUSR BI different strata and it prints output from each single stratum as well as from the sum over strata The source streng
316. s following the B field Simple analytical orbit integration zeroth order in A no electric field no drifts To zeroth order in the smallness parameter p L i e for p 0 charged particle orbits are the magnetic field lines themselves The magnetic field unit vector b B B is provided as input vector in each cell of the computational grid see input block 5 section Z5 With the recent FEM option EIRENE209 and younger iso parametric elements can be used for interpolating and hence for providing a magnetic field which continuously varies inside the grid cell Default is b 0 0 1 in each cell The velocity vector of each test ion followed by EIRENE is projected onto b in each grid cell along the trajectory The velocity used for pushing the particle along its trajectory is only the parallel component v v b b B E x B drift only Only the E x B drift is included This is still zeros order in 6 By modifying the electric field in each cell into one effective E field some features of guiding centre drifts namely the grad B drift can be already captured at this level 59 1 11 1 2 Guiding centre approximation To first order in a number of so called guiding centre drifts arise Their inclusion into EIRENE module FOLION is a very recent extension and not fully operational yet Once this option is fully implemented guiding centre currents will derivable from EIRENE runs as volume tallies These guiding
317. s of different standard grid op tions INDGRD 1 for the radial or x direction grid INDGRD 2 for the poloidal or y direction grid INDGRD 3 for the toroidal or z direction grid Data for first standard mesh radial or x grid RSURF NLRAD TRUE A radial or x grid is defined Otherwise the complete sub block 2A may be omitted Depending upon the logical parameters in the next input card the geometry level variable LEVGEO is set internally LEVGEO 1 cartesian coordinates x and y LEVGEO 2 polar coordinates r and 0 LEVGEO 3 general curvilinear coordinates a full 2D mesh polygonal coordinate lines is used in the x y plane Grid cuts are permitted in the y direction LEVGEO 4 a 2D finite element mesh of triangles is used in the x y plane LEVGEO 5 a 3D finite volume mesh of tetrahedrons used 83 LEVGEO 6 a general user defined geometry block is used All geometrical calcula tions are performed in problem specific routine VOLUSR TIMUSR etc If NURAD FALSE then no spatial grid is defined and the default geometry level LEVGEO is used Volume discretisation may still be achieved by hand by defin ing additional surfaces input block 3b and appropriate cell number switching INDGRD 1 1 standard grid option the input parameters are used as described below 2 As for INDGRD 1 1 but in case of LEVGEO 2 by this option a radial grid is defined such that the spacing of radial su
318. s of the last century when B2 EIRENE was first developed see Reiter et al E Later mostly the simpler explicit scheme fig was employed in applications which although probably being much slower in code turn around time did require less attention by the person running the code i e seemed to be numerically more robust in particular in cold recombining divertor plasma conditions Since about 2009 also available but apparently not used in 3rd party applications is a com bination of both methods The selection between explicit and semi implicit iteration is made possible individually for each stratum such that now some parts of the problem can be run semi implicitly while others notably the volume recombination neutral gas source can remain explicit All these coupling schemes treat the kinetic part of the model in quasi steady state approxi mation with the plasma state This is justified as long as the gas dynamics is fast compared to the plasma dynamics the latter being roughly specified by the time step At used in the CFD plasma simulation In particular in high density low temperature detached divertor plasmas this ordering may not necessarily be correct any longer and a time dependent mode of operation of EIRENE for the coupling may be required due to CFL constrains The full exploration of this option which was implemented into EIRENE in the mid nineties of the last century for ELM simulations has not ye
319. s the local electron temperature at the point of collision for K spatially dependent bulk ion energy dependent loss 1 5 T E prift per collision where T is the local bulk ion temperature at the point of colli sion and E p f is the kinetic energy of the drift motion VXIN VYIN VZIN of the background ions see input block 5 Both contributions are evaluated for background bulk species IPLS which is the bulk collision partner in this particular reaction The local drift energy contribution E p f is added only in case NUDRFT TRUE see input block 1 D for L currently not in use 2 Currently not fully implemented Let stand for a pre collision bulk particle J or K The energy loss of the impacting bulk particle is calculated from the velocity and energy weighted rate coefficients In this case EP must be the labelling index IR of the reaction card by which these moments have been read from the data file Let now stand for a post collision heavy particle group i e L Then the velocity vector of the secondary particle is sampled from a cross section weighted and optional if NLDRFT shifted by the local drift velocity of the pre collision bulk particle Maxwellian distribution at the local ion temperature 7 The cross section is taken at the relative velocity of the impacting test particle and a particle sampled from the above mentioned shifted Maxwellian This option permits to identify one partic
320. s the sputtered particle is a C atom if such an atom has been specified in input block 4a KLMN 4 digits atomic weight of wall material Note the nearest integer of the mass number in the TRIM runs is used For example a copper target is specified in the TRIM files with an atomic weight of 63 54 and the corresponding TRIM file is used for surfaces with KL 64 144 MN nuclear charge number of wall material Example Carbon ZNML 1206 Example Molybdenum ZNML 9642 Example Copper ZNML 6429 Default ZNML 5 626E3 stands for Fe EWALL lt 0 EWALL TW is a surface temperature eV in a Maxwellian flux distribution for the thermal particle energy The resulting mean energy is Emean 2 TW gt 0 EWALL Energy of mono energetic thermal particles The relation between surface temperature TW and the mean energy of particles then reads EWALL Emean 1 5 TW 0 Energy is sampled from a Thompson distribution using the flag EWBIN see below as parameter for the surface binding energy Default EWALL 0 0388 TW 0 026 eV 300 K Note that the EW ALL gt 0 option enables EIRENE to include boundary conditions in one speed transport equation approximations which often are of great interest in general linear transport theory EWBIN see above EWALL 0 option Default EWBIN 0 0 irrelevant for Default Model TRANSP 1 Semi transparency for particles incident from the positive side Renders a non
321. s v V in the first integral correspond to the species i and b respectively prior to a collision These are turned into the post collision velocities v V again for species to and b respectively The first integral therefore describes transitions v V v V into the velocity space interval v v dv for species io and the second integral describes loss from that interval for this species 11 Furthermore m m is the particle mass and F r v t is the volume force field The right hand side is the collision integral af cor Lf there are more than just one possible type of collision partners species b then the collision integral has to be replaced by a sum of collision integrals over all collision partners b including possibly b io self collisions bf _ of bf of gain t loss 2 t Fp leon i St coll 1 3 All these collision operators are bi linear in the distribution functions fio fo The first term on the right hand side is due to scattering into the element dv of velocity space and we shall abbreviate it by defining the collision kernel redistribution function C as a proper integral over pre and post collision velocities of species b particles of ot In addition to being an integral over particle b velocity distributions the kernel C can be a quite complicated integral due to collision kinetics as is involves not only multiple differential cross sections but
322. scribed by the fast particle reflection model However by relation 6 5 it is ensured that RPROBF is always less than or equal to RECYCT The fraction p RPROBT RECYCT RPROBF will be re emitted by the thermal particle reflection model Note RPROBF 0 for incident molecules ITYP 2 by default Default RECYCT 1 i e pa 0 RECPRM_ free model parameter for user supplied recycling models ILREF 9 Default RECPRM 0 EXPPL only for ILREF 2 option angular dependence of fast particle reflection coefficient The formula R 1 1 RPROBF cos P 6 is used el EX PPL see equation L358 where 146 RPROBF Reflection probability from Behrisch Matrix model which is valid only for normal incidence Angle of incidence against surface normal R Reflection probability for particles incident with angle note R 1 for 90 and EXPPL gt 0 Default EXPPL 1 recommended from a comparison with the TRIM database EXPEL as EXPPL but for the energy reflection coefficient Default EXPEL 0 5 recommended from a comparison with the TRIM database e2 EXPEL see equations and EXPIL Index for angular distribution of re emitted atom or molecule affects both models ILREF 1 and ILREF 2 EXPIL 0 cosine distribution independent of choice of fast particle reflection model EXPIL gt 0 mixed cosine specular model In case of ILREF 1 the angular distribu
323. se coordinates are stored on arrays XPL2D YPL2D in subroutine STCOOR called from subroutine PLTADD PLNUMV print cell number into standard mesh cells PLNUMS print numbers near additional surfaces PLARR plot arrows to indicate surface normal vector CH2MX horizontal half width of 2D plot window cm 184 CH2MY vertical half width of 2D plot window cm CH2X0 horizontal co ordinate of midpoint of 2D plot window cm CH2Y0 vertical co ordinate of midpoint of 2D plot window cm CH2Z0 distance CONST of plotting plane to origin NPLINR NPLOTR NPLDLR radial standard surfaces with labels IRIST NPLINR NPLOTR NPLDLR are plotted NPLINP NPLOTP NPLDLP poloidal standard surfaces with labels IP2ND NPLINP NPLOTP NPLDLP are plotted NPLINT NPLOTT NPLDLT toroidal standard surfaces with labels IT3RD NPLINT NPLOTT NPLDLT are plotted 11B 2 Data for 3D plot of geometry CH3MX half width of plot chamber in x direction used for 3D geometry plot CH3MY half width of plot chamber in y direction used for 3D geometry plot CH3MZ half width of plot chamber in z direction used for 3D geometry plot CH3X0 x co ordinate of midpoint of plot chamber in user co ordinates 3D geometry plot only CH3Y0_ y co ordinate of midpoint of plot chamber in user co ordinates 3D geometry plot only CH3Z0 z co ordinate of midpoint of plot chamber in user co ordinates 3D geometry plot only ANGLE1 ANGLE2 First and second viewing angle for 3D geom
324. sed for primary source sampling block 7 NATM Maximum number of different atom species block 4a NMOL Maximum number of different molecule species block 4b NION Maximum number of different test ion species block 4c NPLS Maximum number of different bulk ion species block 5 NADV Maximum number of additional volume averaged tallies track length estimated block 10a NADS Maximum number of additional surface averaged tallies block 10d NCLV Maximum number of additional volume averaged tallies collision estimated block 10b NSNV Maximum number of additional volume averaged tallies snapshot estimated in time dependent mode only block 13 NALV Maximum number of algebraic tallies obtained from volume averaged tallies block 10c NALS Maximum number of algebraic tallies obtained from surface averaged tallies block 10e NAIN Maximum number of additional input tallies not needed by EIRENE but to facilitate presentation block 14 215 NCOP Maximum number of tallies for coupling to external codes block 14 NBGK Maximum number of tallies for iterative BGK scheme for neutral neutral interac tions see MODUSR below NSD Maximum number of standard deviation profiles for volume averaged tallies block 9 NSDW Maximum number of standard deviation profiles for surface averaged tallies block 9 NCV Maximum number of covariance estimates block 9 NREAC Maximum number of atomic reactions from external file
325. sheath region A typical example for Isp ion is at least sonic parallel plasma flow Mach number Mj gt 1 along the magnetic field lines entering the magnetic pre sheath In this magnetic pre sheath the ion trajectories are bend over accelerated by the electric pre sheath field such that at the entrance of the electrostatic sheath at least sound speed is already reached with respect to the surface normal M gt 1 A commonly adopted simplification is made by ignoring the typically small spatial volume between the plasma sheath interface and the wall surface Hence Tsp factorizes into a 3D delta function 6 r r and a deterministic transition kernel for the velocities v v Random numbers from I are generated conveniently by sampling firstly r v 7 from T Shion next generating r v from Tsp and then finally v i from the conditional distri bution Cw the weights velocities and species indices of re emitted neutral particles A frequently employed assumption for I g7 ion is a one sided only positive velocity com ponents into the sheath forward drifting Maxwellian ion flux distribution at the interface between plasma and electrostatic sheath Ssn In this case the bending of trajectories from parallel to B to normal to the surface sonic flow within the magnetic pre sheath is already 37 included in Isp ion g Via boundary conditions in a CFD model for plasma ion flow and the action of ope
326. short cycles 10 full histories 100 f 100 short cycles 4x105 full histories 2 10 AU Il 50 short cycles yl cN i Mi 1 6x106 full histories E 1 Ni Al i haha iy m4 Cumulative iteration hla bo 0 1 time s 0 01 10000 Ion Energy Balance 1000 100 7 kani A dl 10 PUNE E 1 i u p y iy ih i BS odoo ooz ooog 0 005 owos ooo 002 j 0 022 Cumulative iteration i 0 1 time s 0 01 10000 Continuity 1000 100 u AU pa l Z 10 lh 4 f K i NIN 3 oos opos oos one ooe 00 2 0 1 Cumulative iteration f time s h 0 01 Figure 1 7 Convergence of B2 EIRENE measured by B2 residuals Method implicit cou pling method of saturated residuals ref L0 53 1 9 non linear effects neutral neutral collisions Neutral neutral collisions make the Boltzmann collision integral non linear bi linear More generally inclusion of any binary collisions between two test particle species to Jo elastic or not have this effect Important examples are of course elastic self collisions to 70 ci 2 H Hp collisions leading to viscous effects in the gas elastic cross collisions io Jjo er such as H H collisions often leading to a heating of the molecular gas due to hot charge exchange atoms Furthermore there may be relevant inelastic binary particle colli sions io jo inet Such as Ho H H Hj which is an important channel in hydrogen pla
327. si neutrality mentioned above Note in an iterative mode all plasma species in the plasma code should also be in EIRENE There may be more in EIRENE with charge state zero see introduction to section LA but not less because otherwise the electron density computed in EIRENE from quasi neutrality and used e g for ionization mean free paths may be inconsis tent with the electron density in the plasma code BMASS Mass of plasma code species IFLB IPLS is BMASS IPLS in AMU NDXA NDYA grid size in 2D plasma code NDXA is the size of the grid tangential to the flux surfaces and NDYA is the size of the grid normal to the flux surfaces These grid sizes have to be equal to the grid sizes 1st and 2nd grid RSURF and PSURF of the mesh on which plasma code data are specified for EIRENE I e NDYA NRIST 1 and NDXA NP2ND 1 must be obeyed NTARGI Number of different surface recycling sources defined from the plasma code sur face effluxes at specified boundaries NTGPRT Number of different surface segments radially or poloidally by which this tar get recycling stratum no ITARGI is composed The following NTGPRT ITARG cards are used to specify these selected recycling bound aries and to set up the appropriate EIRENE surface source flags These flags partially overrule those specified in block ZZ surface sources see below If even INDSRC 6 for that partic ular stratum in block 2 7 then no further data must be read for this
328. sion processes for D2 Process no 6 and 7 are neutral neutral collisions 1 D2 4 2 2 0 0 1 0 7 i e 7 processes to be specified for this D2 molecule 5 other process decks 22 2114 IBULR 1001 0 112 IBGK self collision 0 00000E 00 0 00000E 00 0 00000E 00 0 00000E 00 0 00000E 00 23 2314 IBULK 1001 0 Alla IBGK cross collision with IATM 1 0 00000E 00 0 00000E 00 0 00000E 00 0 00000E 00 0 00000E 00 In input block 5 there are at least 23 bulk ion species in this example Of those species no 20 to 23 are artificial BGK species for neutral neutral self collisions specified above by IBULK 2014 2114 2214 and 2314 in blocks 4a and 4b above 19 other bulk ion species decks 20 D B 241 0 2 0 0 21 D2 B 4 2 2 0 1 1 0 0 22 DD2 B 2 1 1 021 1 0 23 D2D B 4 2 2 0 1 1 0 0 2 4 3 Fitting expressions IFTFLG The default fitting expressions IFTFLG 0 are single or double polynomial expressions as described in BI or BA for the databases HYDHEL and METHANE respectively The following options are available in recent versions of the code a for cross sections rate coefficients rates IFTFLG lt 100 rate coeff or cross section cm s or cm IFTFLG gt 100 rate density rate coeff s also used for spontaneous decay e g radiative decay mod IFTFLG 100 10 only one fitting coefficient is read i e the cross section rate coef ficient or rate is constant 127 b for interactio
329. sma chemistry and hv H 1s gt H n 2 the absorption of resonance Lyman alpha photons under non LTE conditions In large dense divertor plasmas the ratio H 1s to H n 2 may have to be calculated consistently with the radiation field photon Boltzmann equation competing electron impact collisions and neutral atom transport Two methods of solution for this non linear problem have been tested in EIRENE 1 a parametrization of the single particle distribution functions involved in non linear collision terms and an iterative scheme see next subsection BGK model collision terms and 2 a Direct Monte Carlo Simulation DMCS technique based upon a swarm simulation an oper ator splitting Streaming and Collisions and a random simulation of binary collisions in the swarm Currently only the first of these two options is still being used because despite its approximate character it proved to be much more effective than the full DMCS method for the cases relevant to fusion research applications studied so far A simple estimate for the relevance of neutral neutral gas collisions is given by the so called Knudsen number Kn Ael 1 Kn T PrE 9 87 Here Aa is the mean free path for elastic neutral neutral collisions ce is the typical collision cross section cm ny the gas density em and L is a characteristic dimension cm Fixing the hard sphere molecular diameter at d 4 1078 cm results in a typical cross section Gel
330. species cards NION DO 48 ON 1 NION read NIONI species blocks with I 48 CONTINUE and for versions younger than 2003 x 4D test ions species cards NPHOTI DO 49 IPHOT 1 NPHOTI read NPHOTI species blocks with Ph 49 CONTINUE Meaning of the input variables NREACI Total number of different reactions to be read The next block has different meanings for real particles and photons Cross section and rate coefficients are specified for particles but emission and absorbtion line shapes are specified for photons real particles An interaction potential V r cross section o plus a reaction rate coefficient ov for one process counts as one reaction but higher order rate coefficients such as energy or momentum weighted rate coefficients for the same process count as new reaction and must be labelled by a different index J R see below Storage is provided for up to NREAC different additional reactions see Parameter Statements section B T i e one must guarantee NREACI LE NREAC IR Labeling index of the reaction that is read in The condition IR LE NREACI must be fulfilled otherwise error exit FILNAM Name of the data set that contains the required reaction HYDHEL Hydrogen and Helium data BI METHAN Hydrocarbons data BJ 111 H2VIBR Data for H molecules and their isotopomeres including effects of vibra tion
331. ss section and its relation to the conventional microscopic cross sections are given below section L33 In closing this section we note All these equations LIA LIA LI4 and equation LId given below are equivalent of course as well as their WCU generalizations discussed in the next section LLI Which particular form is used in a particular discussion depends upon the issue which is considered For example the collision estimator for evaluating moments responses of the solution to the Boltzmann equation can be shown to be unbiased quite conveniently when using eq LId whereas the tracklength estimator used for the same purpose in EIRENE is most easily understood with the from LId Time dependent cases are best discussed utilizing the form LIB etc 13 1 1 1 The WCU generalisation of the Boltzmann equation The mathematical generalization from the classical Boltzmann equation for a system under going only elastic collisions to the semi classical Boltzmann equation the WCU equation LM for chemical reactions including for example vibrational relaxation or exchange of internal energy as special cases symbolized as J l l la is outlined here These species indices label both the chemical species and or the internal quantum state I e we regard two particles objects as different with a different label if either they belong to a different chemical species or they differ by their internal electronic or ro vibrati
332. standard mesh block no NBLOCK NACELL ILBLCK if the particle is striking in the positive direction or NBLOCK NACELL ILBLCK if the particle is striking in the negative direction Exit from standard mesh into additional cell NACELL NBLOCK ILACLL for a particle striking the surface in the positive direction or NACELL NBLOCK ILACLL if the particle is striking in the negative direction Specification of ILACLL and ILBLCK is via the input variable ILCELL see below I 2 asI 1 but with the direction of the surface normal reversed If a test particle history starts from a surface NLSRF option then ILSWCH acts as if this particle had struck the surface prior to the birth process in the positive direction This default setting is only available for ILSIDE 0 and can must be overruled by the SORIFL flag see section ZJ e g if a surface source needs to be defined on a surface with ILSIDE 0 ILEQUI The algebraic equations for the surfaces J and IABS ILEQUI J will be described by exactly the same coefficients up to a common sign if ILEQUI J It 0 For example a triangle can be specified by the three corners and another part of the same plane surface can be specified directly by its algebraic coefficients To avoid round off errors one should use the ILEQUI option in such cases in particular if surface J is a transparent hole in surface ILEQUI J or vice versa Default ILEQUI 0 ILTOR For NLTRA option only see b
333. stim 33 EAEL Energy Source Electrons from atom plasma coll 1 watt cem 3 T22 34 EAAT Energy Source Atoms from atom plasma coll 1 watt em 3 T23 35 EAML Energy Source Molecules from atom plasma coll 1 watt em 3 T24 36 EAIO Energy Source Test Ions from atom plasma coll 1 watt em 3 T25 37 EAPHT Energy Source Photons from atom plasma coll 1 watt em 3 T25 38 EAPL Energy Source Bulk Ions from atom plasma coll 1 watt em 3 T26 39 EMEL Energy Source Electrons from molecule plasma coll 1 watt em 3 T27 40 EMAT Energy Source Atoms from molecule plasma coll 1 watt em 3 T28 41 EMML Energy Source Molecules from molecule plasma coll 1 watt em 3 T29 42 EMIO Energy Source Test Ions from molecule plasma coll 1 watt em 3 T30 43 EMPHT Energy Source Photons from molecule plasma coll 1 watt em 3 T30 44 EMPL Energy Source Bulk Ions from molecule plasma coll 1 watt cm 3 T31 45 EIEL Energy Source Electrons from test ion plasma coll 1 watt em 3 T32 46 EIAT Energy Source Atoms from test ion plasma coll 1 watt em 3 T33 47 EIML Energy Source Molecules from test ion plasma coll 1 watt em 3 T34 48 EHO Energy Source Test Ions from test ion plasma coll 1 watt em 3 T35 49 EIPHT Energy Source Photons from test ion plasma coll 1 watt em 3 T35 50 EIPL Energy Source Bulk Ions from test ion plasma coll 1 watt em 3 T36 51 EPHEL Energy Source Electrons from photon plasma coll 1 watt em 3 T33 52
334. stratum in input block 2 7 and the full specification of that recycling source is done in subroutine INFCOP automatically from the plasma code data and the next NTGPRT input cards for this stratum IT irrelevant surface source labelling index NDT number of surface in plasma code mesh either in tangential or in normal direction If the plasma code uses cell centered indexing then the north and the east surfaces of a cell are labeled by the indices of the cell In EIRENE cell indexing the south and the west surface have the same index as the corresponding cell in the first radial and second poloidal mesh respectively Therefore NDT may be different from the surface labelling index in EIRENE input block 2 3 1 Note also that NDT refers to cell numbers after index mapping if NCUTL is not equal to NCUTB 203 NINCT 1 positive i e outer surface normal is in the positive co ordinate direction as it is the case by default for EIRENE standard co ordinate surfaces 1 positive surfaces normal is in the negative co ordinate direction NIXY 1 surface in the direction normal to the flux surface i e it belongs to the 2nd EIRENE mesh PSURF usually divertor target 2 surface is in the tangential direction i e it belongs to the Ist EIRENE mesh RSUREF usually vessel liner interface to vacuum region NTIN NTEN The surface source is restricted to the cells ranging from cell number NTIN to cell number NTEN 1 along the co ordinate s
335. string SU RF MOD followed by a name modname Later in input block LE a local reflection model block with that name modname must be included This option allows quick changes of particle surface interaction parameters affecting many surfaces at once by changes in just one location of the input file SURFMOD_modname optional read one or several blocks of five cards each for orthogonal mapping The pres ence of each such block is identified by the first card of that block containing the string TRANSFORM followed by the other four cards TRANSFORM TINI ITEND XLCOR YLCOR ZLCOR XLREF YLREF ZLREF XLROT YLROT ZLROT ALROT ENDDO end of ILIMI loop Meaning of the Input Variables for additional surfaces CH0 n1 m1 n2 m2 surfaces from the range n1 to m1 n2 to m2 are ignored by EIRENE Specifying a surface in such a CHO card is identical to taking it out from the input file It may be more convenient in some cases however to use the CHO option because the labelling index of the remaining valid surfaces is not altered then No input is read for these surfaces and the input segment for the next valid surface identified by the string text is read next 97 NLIMI number of surfaces in the input block TXTSUR Text to identify a surface name of the surface on the printout file CHI ILIMI n1 m1 n2 m2 surfaces from the range n1 to m
336. t 100 then the 3rd digit is used to select the species index from step function ISTEP Le Let SORIND LMN then MN is used to sample from step function ISTEP MN for species ISPZ L This concerns the spatial distribution The species index itself of the sampled particle is still determined by the flag NSPEZ see above SOREXP Decay length in the exponential distribution option 3 SORIFL The first of the 4 digits can be used to overrule the default orientation of the surface normal at the birth point or if ILSIDE 0 for this particular surface If this digit is nonzero a value 1 would lead to a test flight originating from the surface as if a particle has been incident onto this surface in the positive direction and the value 2 means that this imaginary particle has been striking in the negative direction The last 3 digits of SORIFL act as LMN of the ILSWCH flag described in section 2 3B assuming incidence in the positive direction 158 If any of this 3 digits equals zero than the ILSWCH flag for this particular surface is activated See also section 2 3B input flag ILSWCH NRSOR as for point source but additionally If NRSOR lt 0 NRCELL is found from the step function data see below Function STEP section ZLI if N is equal to 4 or is returned from SAMUSR if SORLIM lt 0 NPSOR as for point source but additionally If NPSOR lt 0 NPCELL is found from the step function data see below Function STEP sect
337. t a gt gt Pui f dl g 2 2 i 0 i 0 Ti and a collision estimate i R gt i 2 3 i 1 Here 2 is the weight of history number k before going into collision number 7 and w is the weight of history number k when coming out of collision number i In R the sum is over line integrals along the track of a test flight from point of collision r to the next one at rjii 2 O 1 Fn 1 whereas in Re the sum is over the points of collisions 217 r i 1 2 n Here i 0 corresponds to the point of birth and n the number of the last collision along the track i e the collision which leads into the final state absorbed particle The tallies are estimated as arithmetic means N R sore no 2 4 k 1 of the contributions of each test particle history k 3 2 1 Tracklength estimated volume tallies UPTUSR The tracklength estimators R for detector function g are updated in subroutine UPDATE defaults and UPTUSR WY additional user supplied tallies with WV w v In EIRENE variables WV WEIGHT VEL Then in order to estimate a response for a detector function g on additional tally number ITALY a statement in subroutine UPTUSR should read DO IC 1 NCOU ICELL NRCELL NUPC IC ADDV ITALV ICELL A ENDDO xNR1P2 NBLCKA DDV ITALV ICELL WV CLPC IC g Here CLPC is the length of the flight in the cell IC
338. t happened with respect to overall coupled code stability and turn around code run time The flowchart LA illustrates this mode of operation 48 explicit coupling INTERO EIRENE BRAAMS nE Histories n B time steps _ INTER1 i INTER2 Figure 1 4 Explicit coupling scheme between EIRENE and a CFD code for plasma flow After each plasma code cycle or time step a full new Monte Carlo run is carried out 49 implicit coupling INTERO INTER3 E intera L BRAAMS Biia aip each time step l INTER1 A INTER2 Figure 1 5 semi implicit coupling scheme between EIRENE and a CFD code e g BRAAMS B2 for plasma flow involving internal re iteration on sources terms without new Monte Carlo trajectories much less frequent Monte Carlo runs than in explicit mode of operation but unresolved issues still re volume recombination contribution LINDA is a grid generating tool providing a numerical discretisation mesh which is common for B2 and EIRENE 50 time dependent coupling explicit LINDA INTERO EIRENE Source 1 in At INTER1 BRAAMS 1 timestep Source 2 at t 0 from previous At ane Source1 Source2 Stratified Source Sampling Source1 homogeneous in At Source2 bootstrapping from empirical distribution at t 0 Figure 1 6 Time dependent coupling to plasma CFD code 51 A generic feature o
339. t mass for the temperature scale Following these conventions EIRENE assumes that cross sections have been measured with the charged particle as projectile and the neutral target at rest Thus MASSP is assumed to be the relevant mass number of the original data for the energy scale in cross sections H 1 and for the temperature scale in the rate coefficients H 2 H 3 H 4 If MASSP 0 MASSP is defaulted to the electron mass AMU I e MASSP is the mass number of those collision partners in the database which would play the role of bulk particles in an EIRENE run unless the automatic re scaling to the true EIRENE bulk ions mass RMASSPCUPLS of the bulk particle is carried out MASST is assumed to be the relevant mass number for the projectile energy scale in H 3 H 6 and H 9 i e for the test particles in an EIRENE run EIRENE then automatically converts the energy temperature scales in the data fits to the correct scales for the particular particles masses isotopes involved in a collision event during the simulation process if these do not happen to coincide with MASSP and MASST DP only for H 8 H 9 H 10 additional e g potential energy lost or gained which is not already included in the rates This may be needed due to the logarithmic fits used and if changes in sign arise For example in case of recombination of hydrogen ions AMJUEL H 10 2 1 8 DP 13 6 must be specified In reaction decks H 8 H 9 or H 10 in AMJUEL this val
340. t reflection model for each individual surface ILREF ILSPT ISRS ISRC ZNML EWALL EWBIN TRANSP 1 TRANSP 2 FSHEAT RECYCF RECYCT RECPRM EXPPL EXPEL EXPIL RECYCS RECYCC SPTPRM this line may be omitted then default sputter model see below An arbitrary number of such sub blocks of 3 or 4 lines each may also be defined under a certain label SURFMOD_modname and be included in the input file in block 6 directly after the ERMIN deck In blocks 3a and 3b surfaces may be assigned a particular local reflection model by a card reading SURFMOD_modname Many surfaces may then be linked to the same surface reflec tion sub block Example SURFMOD_BERYL_SPT_300K 1 2 0 0 9 04000E 02 2 60000E 02 0 00000E 00 0 00000E 00 0 00000E 00 2 80000 1 00000E 00 1 00000E 00 1 00000E 00 1 00000E 00 5 00000E 01 1 00000 1 00000E 00 1 00000E 00 1 00000E 00 SURFMOD_CARB_SPT_1153K 1 12 0 0 1 20600E 03 1 00000E 01 0 00000E 00 0 00000E 00 0 00000E 00 2 800001 1 00000E 00 1 00000E 00 1 00000E 00 1 00000E 00 5 00000E 01 1 00000 1 00000E 00 1 00000E 00 1 00000E 00 TRANSP1 D2 0 5000E 00 TRANSP2 T2 0 2500E 00 RECYCF D 0 0000E 00 RECYCT D2 0 9500E 00 SURFMOD_CARB_SPT_812K 142 E 00 E 00 E 00 E 00 1 2 0 0 1 20600E 03 7 00000E 02 0 00000E 00 0 00000E 00 0 00000E 00 2 80000E 00 1 00000E 00 1 00000E 00 1 00000E 00 1 00000E 00 5 00000E 01 1 00000E 00 1 00000E 00 1 00000E 00 1 00000E 00
341. tallies have been revised at revision svn 360 Jan 2014 to allow full resolution with respect to both incident type for scaling and emitted sputtered particle type and species see Table K4 245 Table 5 4 Sputter tallies new version svn 360 ff 2014 Output Module CESTIM No Name Macroscopic quantity 1 Dim Units Estim 51 SPTAAT Sputtered Flux Atoms by incident Atoms NATM amp T C 52 SPTAML Sputtered Flux Molecules by incident Atoms NMOL amp T C 53 SPTAIO Sputtered Flux Test Ions by incident Atoms NION amp T C 54 SPTAPHT Sputtered Flux Photons by incident Atoms NPHOT amp T C 55 SPTAPL Sputtered Flux Bulk Ions by incident Atoms NPLS amp T C 56 SPTMAT Sputtered Flux Atoms by incident Molecules NATM amp T C 57 SPTMML Sputtered Flux Molecules by incident Molecules NMOL amp T C 58 SPTMIO Sputtered Flux Test Ions by incident Molecules NION amp T C 59 SPTMPHT Sputtered Flux Photons by incident Molecules NPHOT amp T C 60 SPTMPL Sputtered Flux Bulk Ions by incident Molecules NPLS amp T C 61 SPTIAT Sputtered Flux Atoms by incident Test Ions NATM amp T C 62 SPTIML Sputtered Flux Molecules by incident Test Ions NMOL amp T C 63 SPTHO Sputtered Flux Test Ions by incident Test Ions NION amp T C 64 SPTIPHT Sputtered Flux Photons by incident T
342. tatistical precision due to the use of track length estimators EIRENE computes three factors FATM FMOL and FION such that particle balances for atoms molecules and test ions re spectively are accurately observed if NUSCL TRUE NLTEST Tests for consistency between cell numbers and geometrical data along the parti cle tracks are carried out at each point of collision If inconsistencies are detected the history is stopped and an error message is printed The contribution of these particles to the particle and energy balances is stored in the bins PTRASH and ETRASH respectively NLANA De activates NLANA TRUE all non analog sampling distributions such as bi ased source sampling splitting etc Select NUANA TRUE if particle trajectory plots are used to get an intuitive picture of what is going on physically NLDRFT Drift component in the bulk ions velocity distribution is included i e the as sumed underlying distribution in velocity space is a drifting Maxwellian for volumetric background tallies of bulk particles see input block 5 input tallies VXIN VYIN VZIN Otherwise if NLDRFT FALSE an isotropic Maxwellian distribution is as sumed for the background particles and the input for VXIN VZIN is ignored 11 This flag also affects the output tallies for energy exchange momentum exchange be tween test particles and background particles as well as sampling from linear collision kernels NLCRR Cor
343. tegral of the tally over the computational area is nonzero Otherwise the statement ZERO INTEGRAL FOR SPECIES ISPZ is printed below the header for this tally The term species index is used here in a more general sense for the first index if any for any given tally In case of some 182 additional tallies or other tallies in which the first index does not label a particle species but something else this term species index then is to be understood in a more general sense If NPRTLV 0 then the user defined post processing routine TALUSR is called GZ NFLAGV Flag to specify the level of printout print only header 0 additionally print global quantities total and block averages 1 additionally print 1D profiles if any averaged over all if any higher dimen sions 2 additionally print 2D profiles if any averaged over all if any higher dimen sions 3 additionally print 3D profiles if any averaged over all if any higher dimen sions 4 print 3D profiles but no lower dimensional averages NSPEZV_ If NSPEZV 1 0 then this tally is printed only for the species index range MN NSPEZV 1 tol2 MAX I1 NSPEZV 2 rather than for all species relevant for the specified tally NTLVFL In addition to the standard output stream fort UNOUT this tally is also printed onto output stream fort NTLVFL for all species selected and also the corresponding standard d
344. ten CRC Identification for the type of the reaction process Depending upon the value of this flag various assumptions are automatically made concerning the atomic data in the initialization phase CRC EI electron impact collision i e ionization excitation or de excitation or disso ciation In older EIRENE version CRC DS was also in use This is now automatically identified with CRC EI CRC CX quasi resonant charge exchange CRC EL elastic collision CRC PI in elastic ion impact collision not fully implemented CRC RC re combination CRC OT other 114 MASSP Mass number AMU of the first particle involved in the collision for the original data as being read from the data file EIRENE automatically re scales data according to the mass number of the actual first particle involved in this particular collision process e g if data are given for H atoms in the data file but are used for D or T atoms in an EIRENE run MASST Mass number AMU of the second particle involved in the collision for the origi nal data as being read from the data file EIRENE automatically re scales data accord ing to the mass number of the actual second particle involved in this particular collision process The next input deck is read only in case FILNAM ADAS ELNAME Name of element in ADF11 style formatted file e g Fe for iron C for carbon W for tungsten etc IZ Charge state in ADF11 file This value is always between 1 and Zmaz
345. tes empirical variances are directly provided by the method itself not requiring any further considerations The options to activate evaluation of statistical variance in an EIRENE run for any computed quantity tally are described in input block 9 section 2 9 EIRENE provides numerical and graphical output for the empirical relative standard deviation in Ggret N G N R N x 100 3 24 21 and ne is the Monte Carlo estimate for tally R based on N Monte Carlo histories ZJ properly scaled to source strength s 21 Here R may be any volume or surface averaged tally for detector function g either tracklength collision or snapshot estimated The variance o per history is obtained as the unbiased estimate empirical variance as N N N 2 1 _ 1 1 ar ai N _ gt O ap x h x 3 25 i 1 i 1 i 1 where X X w is the contribution of Monte Carlo history w to estimator X for tally R and X is the arithmetic mean X 1 N X over all histories N is the number of statistically independent Monte Carlo histories The subscript g is omitted here and from now on Note that the expression on the right hand side of G25 can be evaluated after each completed particle history i e without storing all individual contributions X first The variance per history is turned into the final estimate for the Monte Carlo variance by the law of large numbers and the central limit theorem of probab
346. th is prescribed for each stratum separately input card FLUX STRA Subdividing the total source into such strata can be useful to increase the efficiency of the code stratified source sampling see paragraph or any textbook on Monte Carlo integration or if the contribution of such sub sources is of interest by itself In order to facilitate sampling each stratum can be subdivided further into a number NSRFSIT of sub strata Random sampling is done by firstly sampling the sub stratum ISRFSI and then conditional the initial state of the test flight within this sub stratum Random numbers from the multivariate distribution Q are generated by a sequence of uni variate conditional distributions see equation B 32 Source sampling from Q in EIRENE is based on the formal decomposition Q i r t v Qi r t x Qoa ilr t x Q vli r t D dv Q r t i v x f wav t x Q vli r t 7 7 i e the source sampling routines in EIRENE samvol f samsrf f etc start by sampling the spatio temporal birth point coordinates ro to from Q r t obtained by integrating Q over velocity space v and summing over all species then next sampling the species index 7 from the conditional distribution Q i which is conditional on ro to and integrated over velocity space and finally then sampling the velocity vo from 3 v conditional on species ig and space time ro to To facilitate random sampling from Q for a particular stratum k
347. the EIRENE code mid eighties it was originally based upon the hydrocarbon ion equilibra tion model given by Langer Z5 and it is a slight generalization thereof The equation for the energy 4 of a test ion a in a background of ions b with mean energy 3 2 T is given as dEa y ey Ealt 0 e 11 94 dt This is a non linear equation because the energy exchange collision rate energy transfer rate v2 depends on itself The full expression for v2 is given below it involves the Maxwell integral Y and its derivative Y see below In the limit of small test particle velocities as compared to thermal velocities of the field particles b i e Va K V 2D m ie x pyv2 2kT lt 1 11 95 as often particularly appropriate for molecular ions a one has 24 poh Sy Sy H 11 96 60 Here the energy transfer rate v2 is given via the slowing down rate v the transverse diffusion rate v and the parallel diffusion rate vj In this limit on has for the basic Spitzer rates loc cit 1 2 1 2 V Mm Z2Z2an 6 8 x 1078 m i re 11 97 Ha Ha 1 2 Ti nZ Ze Aab 1 4 x 107 Bg ee 11 98 Ha 1 2 yor e p 6 8 x 107 Ty en 11 99 and hence using Equation LYG 1 2 1 2 1 1 1 1 Uo MZZ Aap 6 8 x 108 7p 27 2 gt fioo a b b a a a v p 11 101 with the constant and variable contribution v and v2 respectively defined as 1 2 4 1 2 1 2 v
348. the iteration procedure tally no ITALV Up to NALV algebraic expressions in these tallies tally no ITALV can be stored There is also one tally no 0 which is evaluated in subroutine TALUSR section EZ This tally is printed immediately after evaluation i e it is not put onto any storage unless explic itly done so in subroutine TALUSR The input volume tallies for the background medium are listed in table EI They are selected for printout or graphical output by the negative value of their tally number E g the choice ITALV 5 selects tally no 5 from table EZ and the choice ITALV 5 selects tally no 5 from table EI Furthermore there are NTALS preprogrammed detector functions for surface averaged tal lies and there may be up to NADS additional user supplied surface averaged tallies tally no ITALS The preprogrammed tallies and their default units are given in table volume averaged tallies and in table surface averaged tallies Table B I lists the NTALI volume tallies which are computed from the input data in block 5 and which describe the background medium plasma By an abuse of language the cell volumes cm stored in the array VOL I are also referred to as an input volumetric tally no ITALI 13 in table T The Input Block 11 Data for numerical and graphical output 11A Block for numerical output written on unit 6 IUNOUT 179 TRCHST TRCSUR TRCPLT TRCGRD TRCINT TRCLST TRCBLA TRCBLM
349. this case a flux surface labeling gird RHOSRF is not defined NLTET TRUE Geometry level LEVGEO 5 3D discretisation of volume by tetrahedrons For this grid option please make contact to the authors NLGEN TRUE Geometry level LEVGEO 10 Arbitrary geometrical configuration Mesh consists of NR1IST arbitrarily shapes cells in any dimension Particle tracing routines must be provided by user VOLUSR SAMUSR TIMUSR LEAUSR NRIST Number of grid points in the radial or x direction standard mesh if NRIST lt 1 no radial or x direction standard mesh is defined 85 NRSEP This flag is active for LEVGEO 1 or LEVGEO 2 Otherwise it is irrelevant The first x or radial standard mesh is composed by two equidistant x or radial grids of co ordinate surfaces with different grid density There are NRIST NRSEP 1 grid points in the first and NRSEP grid points in the second part The grid point RSURF NRIST NRSEP 1 belongs to both parts RIA left endpoint of standard grid internally set gt 0 if LEVGEO 2 RSURF 1 RIA RGA boundary separating first and second part of standard grid with different grid point densities RSURF NRIST NRSEP 1 RGA RAA right endpoint of standard grid RSURF NRIST RAA RRA if RRA gt RAA one additional zone is defined RSURF NRIST 1 RRA and NRIST is increased by one irrelevant if RRA lt RAA if NLELL TRUE EPIN Value of EP r for cylindrical co ordinate surface number with
350. tic energy in drift motion Bulk Ions NPLS eV 14 VOL Zone Volume 1 cm 15 WGHT Space and species dependent importance NSPCMC 1 247 Table 5 6 Volume Averaged Tallies Output Common CESTIM No Name Macroscopic quantity 1 Dim Units Estim 1 PDENA Particle density Atoms NATM cm T1 2 PDENM Particle density Molecules NMOL cm T2 3 PDENI Particle density Test Ions NION cem T3 4 EDENA Energy density Atoms NATM eV ecm 3 T4 5 EDENM Energy density Molecules NMOL eV cm 3 T5 6 EDENI Energy density Test Ions NION eV cm 3 T6 7 PAEL Particle Source Electrons from atom plasma coll 1 amp cm T7 8 PAAT Particle Source Atoms from atom plasma coll NATM amp cm T8 9 PAML Particle Source Molecules from atom plasma coll NMOL amp cm T9 10 PAIO Particle Source Test Ions from atom plasma coll NION amp cem 3 T10 11 PAPL Particle Source Bulk Ions from atom plasma coll NPLS amp cm T11 12 PMEL Particle Source Electrons from molecule plasma coll 1 amp cm T12 13 PMAT Particle Source Atoms from molecule plasma coll NATM amp cm T13 14 PMML Particle Source Molecules from molecule plasma coll NMOL amp cem 3 T14 15 PMIO Particle Source Test Ions f
351. tically removed from arun Physically irrelevant tallies are listed here only to maintain complete symmetry in notation 246 5 1 2 old version w o photon gas tallies Eirene2o and older In these older versions photon test particle tallies are not available nor are the momentum source rates MAPL and test particle momentum fluxes VXDEN VYDEN VZDEN In these versions such tallies may still have been available but then in problem specific tallies COPY interfacing to particular plasma fluid codes or in tally BGKV internal iterations due to neutral neutral collisions in BGK approximation Table 5 5 Input Tallies for Background Input Common COMUSR No Name Macroscopic quantity 1 Dim Units Estim 1 TEIN Plasma Temperature Electrons 1 eV 2 TIIN Plasma Temperature Bulk Ions NPLS eV 3 DEIN Plasma Density Electrons 1 cm 4 DIIN Plasma Density Bulk Ions NPLS em 5 VXIN Plasma Drift Velocity x component Bulk Ions NPLS cm sec 6 VYIN Plasma Drift Velocity y component Bulk Ions NPLS cm sec 7 VZIN Plasma Drift Velocity z component Bulk Ions NPLS cm sec 8 BXIN Magnetic field unit vector x component 1 9 BYIN Magnetic field unit vector y component 1 10 BZIN Magnetic field unit vector z component 1 11 BFIN Magnetic field strength 1 Tesla 12 ADIN Additional input tally NAIN see INFCOP 13 EDRIFT Kine
352. ticle Let us write JKLMN ISCDE Let then furthermore the character stand for J K L M or N respectively Then J controls electrons if any involved K controls pre collision plasma bulk particles if any involved L the secondary particles if any Flags M and N are not in use any more Each of these single integer flags controls the meaning of the energy parameters which are read in the next card EP EELEC J for the electrons involved in the collision process EP EBULK K for the pre collision bulk ions EP ESCD L for the heavy secondary particles this option is only available for CRC EI and CRC PI collisions whereas for EL CX and RC type collision processes the kinetic energy of products is determined by default models independent of the value of flags L and ESCD 0 constant loss or gain of EP eV per collision event If L and if there is more than one heavy particle secondary then the energy loss gain EP reaction exothermicity or kinetic energy release is distributed over the secondary bulk particles inversely proportional to their masses E g for reac tion e CH gt CH H e and EP ESCD 8 0 eV then the fragment C H3 would receive an extra energy of 0 5 eV and the fragment H would receive 7 5 eV both isotropically in the center of mass system of the collision 120 1 for J spatially dependent bulk electron temperature dependent loss 1 5 Te per collision where T i
353. tine PLT3D LOG FALSE J number of surface to be plotted 3 8 1 Subroutine INIUSR This subroutine is called from subroutine INPUT after reading from the formatted input file and after optional calls to interfacing routines INFCOP Any initialization including definition of COMMON blocks for the user geometry package may be done here 229 3 8 2 Subroutine LEAUSR Identify cell index from a point given by its three carthesian coordinates The function LEAUSR is called from functions LEARC1 and LEARCA in case of LEV GEO 10 The call is NCELL LEAUSR X Y Z Here X Y Z are the Cartesian coordinates of a point inside the computational domain in cen timeters LEAUSR must then return the number of the cell to which this point belongs Note see section 2 2 Any particular cell in EIRENE can be specified in one of two possible ways Either by giving the 5 cell numbers NRCELL NPCELL NTCELL NBLOCK NACELL in the first radial second poloidal third toroidal grid or additional cell region or alterna tively by giving the cell index in the 1 dimensional cell array NCELL The relation between these two options is NCELL NRCELL NPECLL 1 NR1P2 NTCELL 1 NP2T3 NBLCKA with NBLCKA NBLOCK 1 NSTRDT NRADD LEAUSR is expected to return the cell index NCELL 3 8 3 Subroutine TIMUSR The subroutine TIMUSR is called from TIMER block GEO3D The call is CALL TIMUSR NRCELL X0 YO Z0 VELX VELY VEL
354. tion given by the database is used In case of ILREF 2 the specular contribution increases according to equations o with angle of incidence and with e3 EXPIL recommended EX PIL lt 1 Default EXPIL 0 RECYCS The meaning of this flag for the physical sputtering options depends upon the value of the first digit N of ILSPT N 0 no physical sputtering YIELD1 0 RECYCS is irrelevant N 1 constant physical sputtering yield YIELD1 RECYCS N 2 RECYCS is a multiplier for the sputtered particle flux YIELD1 YIELD1 is computed from the incident species energy angle and surface parameters by the sputter model N 2 Hence the sputtered particle yield YIELD1 as computed from subroutine SPUTER is modified to YIELD1 RECYCS YIELD1 N 9 RECYCS is a free model parameter which can be used in the user supplied sputter model for any particular surface element Default RECYCS 1 RECYCC The meaning of this flag for the chemical sputtering options depends upon the value of the second digit M of ILSPT M 0 no chemical sputtering YIELD2 0 RECYCC is irrelevant M 1 constant chemical sputtering yield YIELD2 RECYCC 147 M 2 RECYCC is a multiplier for the sputtered particle flux YIELD2 YIELD2 is computed from the incident species energy angle and surface parameters by the sputter model M 2 Hence the sputtered particle flux YIELD2 as computed from subroutine SPUTER is modified to YIELD2 RECYCC YIELD
355. tion of each history inside the particle loop see flowchart LIJ The full evaluation and scaling of expression Z3 BZA is then carried out after completion of all histories per stratum in entry STATS2 of subroutine STATIS Linear functions of tallies Often algebraic functions of tallies sums products ratios are formed after a Monte Carlo run to produce further post processed output quantities see input blocks 10C and 10E in section 2 10 For those tallies standard deviations are not available in general due to statistical correlation between individual tallies obtained from the same Monte Carlo run 22 However for linear functions of tallies e g sums differences this is possible even with out resorting to the covariance estimators block 9 of EIRENE Usually this was done in problem specific modules e g in STATS1_COP for source terms arising in plasma fluid codes see section ZI In 2012 a new routine UPFCOP was added and is called inside the particle loop prior to STATS1 Let a linear function Riin of default tallies Ry be given by Riin ak Rk 3 28 k az are some constant scalar factors then after each completed history w in routine UPFCOP the sum of contributions X lwi N an Xe wi 2e aal wi 2 Le wi 3 29 k is formed to finally build the linear function tally N 1 N X X wi by averaging over all histories same as for default tallies This is possible because in
356. tional grid The input data in block 10 described here are flags for activating and controlling these routines Default If the first card in this block NADVI contains only zeros then the rest of this block can must be omitted The Input Block 10 Data for additional tallies NADVI NCLVI NALVI NADSI NALSI NADSPC 10A Data for additional track length estimated volumetric tallies DO 101 IADVI 1 NADVI ADVE IADVT ADVS IADVT ADVT IADVT ADVR IADVT TXTTAL ITADVI NTALA TXTSPC IADVI NTALA TXTUNT ITADVI NTALA 101 CONTINUE 10B Data for additional collision estimated volumetric tallies DO 102 ICLVI 1 NCLVI CLVE ICLVI CLVS ICLVI CLVT ICLVI CLVR ICLVI TXTTAL ICLVI NTALC TXTSPC ICLVI NTALC TXTUNT ICLVI NTALC 102 CONTINUE 10C Data for algebraic function of volumetric tallies DO 103 IALVI 1 NALVI ALSTRNG TXTTAL IALVI NTALR TXTSPC IALVI NTALR TXTUNT IALVI NTALR 103 CONTINUE 10D Data for additional surface crossing tallies 173 DO 104 IADSI 1 NADSI ADSE IADST ADSS IADST ADST IADST ADSR IADST TXTTLS ITADSIT NTLSA TXTSPS IADSI NTLSA TXTUNS TADSI NTLSA 104 CONTINUE
357. tions 1 3 5 Sampling a free flight from the transport kernel T The conditional sampling distribution T r r for the next point of collision event given a test flight is at position r traveling with velocity v is given by ZIA A more intuitive argument for this distribution of free flight path lengths follows from the simple attenuation law of a mono energetic beam incident on a thin slab of material thickness dl target material density n Clearly the fraction of beam particles undergoing collisions in 28 this slab is on dl with cross section o stationary target This results in the attenuation law dn nn odl gt n ngexp n ol 3 46 where n is the number of beam particles no the number of beam particles at l 0 It is then naturally supposed that p l dl exp n ol n o dl 3 47 is the probability for a first collision between and l dl and hence Pi exp n 0l nz0 dl 1 exp n ol 3 48 is the corresponding probability distribution function for a first collision at distance lt l i e the same results as derived above formally with the Green s function argument Returning to Zla we first again omit velocity and species index in the argument lists to keep the notation simple but we note that certainly the mean free path A or macroscopic cross section usually depend explicitly on the test particle energy and species Let us introduce the distance of the flight
358. toms Ats molecules Mls test ions T I or bulk ions B I and each tally is species resolved for it corresponding particles This permits scaling of these fluxes with the factors FPHOT FATM FMOL FION to eliminate statistical errors from the particle balances see NLSCL option input block 1 Naming conventions for incident surface fluxes are POT BC EOT BC with BC standing for the type of incident particle BC AT ML IO PHT or PL Emitted from surface particle and energy surface averaged fluxes are split by the type of the incident particle photons Phs atoms Ats molecules Mls test ions T I or bulk ions B I This permits scaling of these fluxes with the factors FPHOT FATM FMOL FION to eliminate statistical errors from the particle balances see NLSCL option input block 1 Naming conventions for emitted surface fluxes are analogue to those for volumetric source rates i e PRF A BC SPT A BC with A and BC having the same meaning as described above for volume tallies PREF are fluxes reflected or emitted due to incident particle fluxes of type A SPT A BC are sputtered fluxes additional fluxes of surface material Note The naming convention of surface sputter tallies SPT differs in older versions of EIRENE The full resolution wrt to incident type and emitted species is only implemented in EIRENE revisions svn 360 and later Jan 2014 see Table BA In all older versions only mu
359. tory 11B3 Graphical output of volume averaged tallies NVOLPL Total number of pictures from volume averaged tallies PLTSRC USTRA ISTRA 0 NSTRAID Profiles of the selected volumetric tallies are plotted for those strata for which PLT SRC ISTRA TRUE In case PLTSRC 0 TRUE the summation over all strata is plotted for these tallies Note graphical output for individual strata is only possible if the data for strata have been saved on file NFILE N 1 2 option input block 1 Otherwise only the last stra tum currently on storage arrays mostly sum over strata is available NSPTAL Number of different species quantities to be plotted for this tally into one picture For 3D plots NSPTAL 1 except for the LVECT3 or LRPVC3 vector field options in which case NSPTAL 2 See below PLTL2D Switch to activate a 2D plot PLTL3D Switch to activate a 3D plot PLTLLG The tally is plotted on a logarithmic scale PLTLER Standard deviation is plotted if available In case of 2D plot error bars are plotted along the curves In case of 3D plot a full standard deviation profile is plotted on a separate picture TALZMI Minimum ordinate value for the plot If TALZMI 666 0 then the minimum is searched for in the data array Even if PLTLLG log scale the true minimum ordinate value not the logarithm thereof must be specified If TALZMI 666 0 and PLTLLG ZMIN 1 E 48 is used as cut off value TALZMA like TALZMI but maxim
360. transparent purely absorbing semi transparent or partially reflecting Surface sources may be defined on each surface These surfaces may be invisible from one side and transparent absorbing or reflecting from the other and each surface can operate switches if intersected by a test flight such as abandoning the evaluation of atomic or molec ular reaction rates entrance into vacuum regions along the flight abandoning evaluation of volume averaged responses e g in some uninteresting regions or abandoning geometrical calculations for those surfaces for which it can be known a priori that they will not intersect a flight path originating at a particular surface or in a particular cell 46 1 7 time dependent mode of operation The section is currently rewritten Please refer to the J Nucl Mater paper D Reiter et al Vol 220 222 1995 987 992 Details of options available in EIRENE for time dependent problems are also given in Section ZIJ The following issues have to be considered in case of time dependent coupling schemes to external plasma fluid solvers see figure LG The coupling is explicit hence CFL type conditions for the time step have to be obeyed Here this means the time step must be shorter than the time between re ionization and sub sequent neutralization in the volume or at the targets because the fate of a particle during its intermediate ionized phase is not included in the explicit Monte Carlo pro
361. ts NMASS Mass number NCHAR Nuclear charge number NPRT Flux units carried by one particle of this type and species The WEIGHT of a test flight has dimensions atomic flux i e equivalent atoms per second For example a methane molecule C H should have NPRT oy 5 if H atoms and C atoms have NPRTy NPRIc 1 NPRT is used to convert fluxes into equivalent atomic fluxes for scaling see input flag FLUX in block 7 and for flux conservation in non diagonal species changing events at surfaces and in the volume NPRT is irrelevant for atoms and always set to one for them NCHRG Charge state irrelevant for atoms and molecules always set to zero for them ISRF Species index flag for fast particle reflection model see block 6A irrelevant for molecules ISRT Species index flag for thermal particle re emission model see block 6A ID1 notin use in versions 98 to 2002 ID1 was the sputtered species index in versions older than 98 but this species index has then become a surface property see input block 3 In versions younger than 2002 this flag can be used to increase the number of secondary test particle groups from 2 or less default to 3 if ID1 3 or to 4 if ID1 4 This option then allows more complex fragmentation processes of large molecules as compared to the default ID1 2 NRC gt 0 total number of reaction decks to be read for this species 0 default model is to be
362. ts i e the COMMON deck PARMUSR described below in section B I It defines the storage requirements for this particular case In versions ETIRENE2 02 and younger this pre assignment of storage has been removed by a dynamical allocation of storage throughout The user controllable storage options e g CPU vs storage optimization formerly un der parameters for storage reductions in PARMUSR can now be set in an additional but optional input line at the beginning of input block 1 as new second line in this block see section LI The names of all other routines in the user specified block end with USR The description of the additional tally routines UPTUSR UPCUSR UPSUSR and UP NUSR given below section BJ is meant as a guide for the more experienced users of the code only These routines allow to extend the number of responses estimated by EIRENE almost arbitrarily The number of options for fast particle surface interaction models can be increased by adding subroutines REFUSR and SPTUSR which have to provide the particle data after reflection or sputtering respectively velocity vector weight type species etc after a test particle has collided with a non transparent surface and neither absorption nor specular reflection nor the thermal particle re emission is identified as surface event by the flags and the random sampling procedure The use of this routine REFUSR is described in section BA By inc
363. tted input file The natural logarithm of cross section In a H123 H 1 or of a rate coefficient In R A123 H 2 H 5 or H 8 is computed as Ino Dymo F I In Eras and likewise a rate coefficient R is evaluated as In R Yo F I 7 Here Ezras is the relative energy of impact but with the mass of the charged particle i e for a target of neutral particles at rest see below and T is the electron or ion temperature depending on the type of impacting plasma particle This option permits specification of constant cross sections or rate coefficients only the first of the nine parameters nonzero or e g specific power law energy dependencies or temperature dependencies second of the nine parameters case 1 FILNAM HYDHEL METHAN AMJUEL H2VIBR H 1 single parameter fit for cross section o cm as function of energy ELAB eV with ELAB m 2 v2 For the definition of mz MASSP see below 112 H 2 H 3 H 4 H 5 H 6 H 7 H 8 H 9 single parameter fit for rate coefficient ov cm s as function of target temper ature eV assuming zero velocity projectile double parameter fit of rate coefficient ov cm s as function of projectile en ergy eV and target temperature eV double parameter fit of rate coefficient cv cm s as function of target density cm and target temperature eV single parameter fit of target particle momentum we
364. ty m cell centered UU poloidal velocity m s x surface across field E W centered VV radial velocity m s y surface centered along field N S TE electron temperature J cell centered TI ion temperature J cell centered PR plasma pressure N m cell centered UP parallel velocity m s x surface across field E W centered RR pitch angle 1 cell centered FNIX Particle fluxes along the field 1 s x surface across field E W centered FNIY Particle fluxes across the field 1 5 y surface centered along field N S FEIX Ion energy fluxes along the field Watt x surface across field E W centered FETY Ion energy fluxes across the field Watt y surface centered along field N S FEEX Electron energy fluxes along the field Watt x surface across field E W centered FEEY Electron energy fluxes across the field Watt y surface centered along field N S VOL cell volume m cell centered BFELD magnetic field T cell centered and thereafter index mapping units conversion are carried out to turn them into EIRENE bulk ion tallies as well as to derive recycling target fluxes and boundary conditions from them Meaning of the Input Variables for interfacing Subroutine INFCOP 201 LSYMET TRUE Upside down symmetry of all tallies transferred to external code via common block EIRBRA is enforced Symmetry plane is the PSURF 2 surface i e the poloidal or y co ordinate sur
365. ue of DP is now automatically read and overwrites the value specified here Hence in the EIRENE versions later than June96 this input flag is redundant Be careful check that this is really the case in any particular version of EIRENE The next flags control the options to extrapolate atomic data fits read from files The default data in EIRENE and some reactions in the files AMJUEL already contain that information EIRENE searches for the string ELABMIN and ELABMAX for cross section data If it finds them it uses them as RMN and RMX respectively In such cases the next card IRFEXMN and IFEXMX may also be omitted because the corresponding information is found from the atomic data file as well The extrapolation expression is that of option IFEXM 5 see below Likewise in case of reaction rates EIRENE searches for TMIN TMAX for single parameter fits H 2 H 5 H 8 and H 11 and additionally for PMIN and PMAX if H 3 H 4 H 6 H 7 H 9 H 10 or H 12 and the extrapolation parameters again are expected in the atomic data file RMN minimum energy or temperature for data as read from file Below RMN the data are extrapolated using the input card IFEXMN FPARM J J 1 3 See below and e g subroutine CROSS for the various options Some cross section data in AMJUEL already contain the extrapolation information and hence the default RNM 0 can be used there 116 RMX same as above but for high parameter range extrapolation
366. uilibrium of excited states The additional card only one reads format 316 6x 2E12 4 SP ITP ISTR G BOLTZMANN DELTA _E docu to be written CDENMODEL Planck only for background photons to be written CDENMODEL Corona Set parameters from Corona equilibrium The additional card only one reads format 316 1X A6 1X A4 A9 A3 E12 4 SP ITP ISTR FILNAM H123 REACTION CR A_CORONA ISP ITP is the number and type of a particle species either one of the already defined bulk species IPLS ISP IPLS for ITP 4 or from the file fort 10 for ITP 0 1 2 or 3 from stratum no ISTR i e written onto fort 10 either in the present run or an earlier EIRENE run see NFILEN option in input block 1 The parameters fields of density temperature flow velocity for species IPLS are set from those of species ISP ITP ISTR This model then constructs a background species IPLS which is in corona equilibrium with these ISP ITP ISTR particles 132 CDENMODEL Colrad set parameters from collisional radiative equilibrium using re duced population coefficients from atomic database The NRE additional cards read SP ITP ISTR FILNAM H123 ISP ITP is the number and type of a particle species either one of the already defined bulk species IPLS ISP IPLS for ITP 4 or from the file fort 10 for ITP 0 1 2 or 3 from stratum no ISTR i e written onto fort 10
367. ular collision partner from the background population correctly accounting for the energy dependence of the cross section 3 KREAD option description to be written see example of default hydrogen molecule reaction model below there reaction 6 and 7 In principle an energy weighted loss rate coefficient is read in a mean energy loss per collision is derived from that If this option is used for heavy particles secondaries i e the third digit of ISCDE has the value 3 than this energy is again distributed inversely proportional to the masses over all heavy particle secondaries 4 to be written 5 to be written IESTM Three digits IESTM LMN N M and L are flags for the choice of estimators for particle momentum and energy sink and source term contributions from the collision process Default 0 track length estimators In some cases when track length estimators can not be used because the corresponding momentum or energy weighted Maxwellian rate coefficients are not available in a particle run i e are missing in the preceding list of NREAC reaction data then internally a switching from track length to collision estimators is carried out and a corresponding warning is printed IBGK Three digits IBGK NML Particle identifier for BGK self and cross collisions For mat as for IBULK ISCD1 and ISCD2 species identifier flags I e it has three digits 121 pointing to the type and to the species index within that ty
368. ules NMOL amp T C 8 PRFAML Particle Flux emitted Ats gt Molecules NMOL amp T C 9 PRFMML Particle Flux emitted Mls Molecules NMOL amp T C 10 PRFIML Particle Flux emitted T I Molecules NMOL amp T C 11 PRFPHML Particle Flux emitted Pht Molecules NMOL amp T C 12 PRFPML Particle Flux emitted B I Molecules NMOL amp T C 13 POTIO Particle Flux incident Test Ions NION amp T C 14 PRFAIO Particle Flux emitted Ats Test Ions NION amp T C 15 PRFMIO Particle Flux emitted Mls Test Ions NION amp T C 16 PRFIIO Particle Flux emitted T I Test Ions NION amp T C 17 PRFPHIO Particle Flux emitted Pht Test Ions NION amp T C 18 PRFPIO Particle Flux emitted B I gt Test Ions NION amp T C 19 POTPHT Particle Flux incident Photons NPHOT amp T C 20 PRFAPHT Particle Flux emitted Ats Photons NPHOT amp T C 21 PRFMPHT Particle Flux emitted Mls Photons NPHOT amp T C 22 PRFIPHT Particle Flux emitted T I gt Photons NPHOT amp T C 23 PRFPHPHT Particle Flux emitted Pht Photons NPHOT amp T C 24 PRFPPHT Particle Flux emitted B I Photons NPHOT amp T C 25 POTPL Particle Flux incident Bulk Ions NPLS amp T C 244 Table 5 3 continued No Name Macroscopic quantity 1 Dim Units Estim 26 EOTAT Energy Flux incident Atoms
369. um ordinate value for the plot If TALZMA 666 0 then the maximum is searched for in the data array Even if PLTLLG log scale the true maximum ordinate value not the logarithm thereof must be specified 187 The following input variables are needed only if PLTL2D TRUE TALXMI TALXMA If both are zero then the radial x grid is used as abscissa for plot ting default if TALXMI TALXMA then a grid equidistant on a linear scale is used TALXMI is then the minimum abscissa value for the plot TALXMA is then the maximum abscissa value for the plot if TALXMI TALXMA and both are positive then a grid equidistant on a log scale is used TALXMI is then the minimum abscissa value for the plot TALXMA is then the maximum abscissa value for the plot if TALXMI TALXMA and at least one of them is negative then a user defined grid XXP2D_USR is used This must have been defined in one of the user routines for this figure no N IBLD i e the array XXP2D J IBLD must have been set J the grid index ISPZTL Index of the species of the tally that will be plotted If ISPZTL 0 the tally obtained by summation over its species index is plotted NPTALI Index of tally to be plotted NPLIN2 Index of the first cell that is displayed on the plot for 2D plot only NPLOT2 Index of the last cell that is displayed on the plot for 2D plot only NPLDL2 Increment for the cell indices for 2D plot only The following input variabl
370. urce terms for parallel momentum balance equa tions of plasma fluid codes have become default tallies rather than problem specific tallies COPV I e now we have compare to ZT9 SmI tpls icell M AP Lis ipls icell MMP Lis ipls icell MIP Lis ipls icell 7 14 22 The sum is over all strata see stratified sampling in section D MAPL MMPL MIPL are default EIRENE tallies Table 52 in section ELI e MAPL is the parallel momentum source for background plasma species ipls resulting from atom plasma interactions summed over all EIRENE species of type atom tally no 97 e MMPL is the parallel momentum source for background plasma species ipls result ing from molecule plasma interactions summed over all EIRENE species of type molecule tally no 98 e MIPL is the parallel momentum source for background plasma species 7pls resulting from test ion plasma interactions summed over all EIRENE species of type test ion tally no 99 The sign of these sources in EIRENE is such that a gain in momentum for plasma species zpls is taken positive In the interfacing routine IF3COP of module EIRCOP the sign convention is altered to that of the plasma fluid code i e it then involves the flow direction relative to the magnetic field vector Meaning of the Input Variables for interfacing Subroutine INFCOP input block 14 unchanged as compared to section ZI41 Additional dat
371. urface Note that NTIN and NTEN label cell boundaries hence the NTEN 1 above Note further the total number of surface cells in one surface recycling source ITARG i e summed over NTGPRT UITARG must not be larger then NRIST NP2ND see definition of parameter NGITT in Common Deck PARMMOD NIFLG This corresponds to the SORIFL flag in input block 7 and is needed only if IND SRC 6 i e if the source is specified by data from block 14 alone NPTC This corresponds to the NPTS flag in input block 7 and is needed only if IND SRC 6 i e if the source is specified by data from block 14 alone NSPZI NSPZE Species range for this stratum Only the EIRENE fluids IPLS corresponding to plasma code fluids IFL with NSPZI lt IFL lt NSPZE are sampled from this stratum See index map ILFB IPLS specified above in this same input block One geometrical target may appear several times with different species ranges This permits to apply stratified sampling within the species distribution and hence to remove statistical noise resulting from species source sampling The following automatic adjustments to input flags from block 7 are then carried out for strata ISTRA 1 NTARGI species and birth point sampling e The source strength FLUX ISTRA is reset to the value as computed from the plasma code data fluxes at the corresponding surface and the species range specified e Initial species distribution is sampled from bulk ion population
372. use of language we refer to them as bulk ions as well but we mean in this case heavy background particles i e more general objects NATM NMOL NION NPHOT NPLS and NREAC are specified in the parameter block PARMUSR see Parameter Statements section B_I below for versions EIRENE2999 and older or are determined automatically from the input file Masses in EIRENE RMASSA RMASSM RMASSI RMASSP assigned to the objects atoms molecules test ions photons and bulk ions respectively are in units of the proton mass which is taken to be 1 0073 in atomic mass units At the beginning of input block 4 EIRENE first searches for the character string INCLUDE in the input card directly following the card xxx 4 DATA FOR If such a character string is found here then the rest of input blocks 4 and 5 are skipped and a proper A amp M model data file from a pre compiled EIRENE AM library can be used If such a library AM data set is not included then the original EIRENE procedure is fol lowed to define general test particles objects atoms molecules test ions photons and assign reactions A amp M datasets to each of them from external or internal databases This is described next First EIRENE reads NREACI non default atomic data cards if any i e if NREACI gt 0 NREACI DO I 1 NREAC R FILNAM H123 REAC CRC MASSP MASST DP RMN RM
373. used no collision processes for this particle species at all NFOLS controls the motion of test particles gt 0O default test particle tracing model is to be used motion of test particle is not followed static approximation The test particle is destroyed immediately at it s point of birth by a collision A collision estimator is used rather than a track length estimator for all default volumetric tallies as described in section BZ 118 NGEN Maximum number of generations for this test particle species gt 0 For each particle history the generation counter XGENER is reset to zero at birth after surface events and after a non diagonal event modification of type and or species of a particle in a collision event It is increased at entropy produc ing events elastic and diagonal charge exchange collisions If XGENER gt NGEN after a collision no test particle secondaries are generated The parti cle flux parallel momentum flux and energy flux is put into the tallies PGENA VGENA and EGENA for atoms resp PGENM VGENM and EGENM for molecules resp PGENI VGENI and EGENT for test ions respectively and PGBENPH VGENPH and EGENPH for photons respectively 0 Incase NGEN 0 default no generation limit is activated for atoms NGENA 0 molecules NGENM 0 or test ions NGENI 0 NHSTS only in versions 2004 and younger NHSTS 1 turns off the trajectory plot for this particular species default NHSTS 0
374. ven by the report N A Derzko Review of Monte Carlo Methods in kinetic Theory UTIAS Review No 35 April 1972 University of Toronto Institute of aerospace studies April 1972 This review also includes a discussion of a third Monte Carlo scheme the so called Integral eval uation method of A Nordsieck and B L Hicks In rarefied gas dynamics problems for fusion reactor design in particular for the ITER di vertor design the Haviland method but applied to a Boltzmann equation with a non linear BGK collision integral was first developed for the EIRENE code around 1995 see Reiter et al 22 and it is routinely applied in computational divertor design studies for ITER since about 2004 by V Kotov A K Kukushkin et al The method of successive approximations employed in EIRENE is illustrated best when using the integral Fredholm form of the Boltzmann equation to be continued Consider first the elastic self collisions amongst particle species A The BGK approximation to the Boltzmann collision integral reads afa _ ot v fa f 9 90 i n _m v V f nmT s2 exp oF 9 91 General Concept Self collisions between those particle species which are followed by EIRENE i e between any two test particle species can be included by using the iter ation option NITER gt 1 input block 1 and by adding a proper collision process to the where 55 collision kernel and its total cr
375. violated an error exit with the message violation of Radon Nikodym con dition occurs Note a violation of condition B 31 can not be detected otherwise e g by monitoring over flow in the weighting factor w Of course values y resulting in a zero in the denominator of w equation B30 have sampling probability zero according to distribution g x and hence are never sampled Still the results would be biased Note when inspecting an EIRENE geometry plot with particle trajectories or even a movie NLMOVIE TRUE input block 1 in order to get an intuitive feeling for the particular transfer process considered then all non analog sampling options must first be turned off NLANA flag in input block 1 for otherwise the pictures may be grossly misleading We consider the procedures for random sampling from univariate distributions as known and refer to the many textbooks on that in particular to the random sampling library L5 If none of the direct methods apply then still either the non analog method mentioned above or the rejection method can be used Sampling from a multivariate distribution f 21 22 n can always be reduced to a se quence of samplings from univariate distributions by noting that iio sin filz fo x2 21 fs z3 1 2 Piste 3 32 Here f is the marginal distribution obtained from f by integrating over all but the first independent variables It is a univariate distributio
376. viour of derivatives of polynomial fits for rate coefficients individual background ion temperatures TI IPLS for each background species e g for neutral background particles simulation of self collisions in BGK approximation some new collision processes and data such as net re combination energy losses radi ation potential elastic neutral ion collisions multi step brake up of molecules RAPS graphics interfaces user defined geometry block In this new mode of operation geometry level LEV GEO 10 EIRENE knows nothing not even the dimensionality about the geometrical aspects of the problem Everything concerning grids cell volumes flight times within cell etc is in user supplied routines No default graphics options are available of course in this mode of operation This option is used in context with EMC3 EIRENE since about 1999 Particle tracing routines FOLATM and FOLMOL for neutral atoms and neutral molecules are combined into one routine FOLNEUT for neutral particles The particle tracing routine FOLION for charged test particles has been updated consid erably including now a simple approximation to the Fokker Planck collision operator a Krook collision operator in 1997 An increasing number of EIRENE 3rd party applications is running cases in which EIRENE is coupled to a fluid CDF plasma model Here it provides sources and sinks due to inter action of kinetic sub components w
377. x for sub strata INDIM 0 source on additional surface ASURF see block 3B source on standard surface RSURF x or radial mesh see block 2A and 3A 156 2 source on standard surface PSURF y or poloidal mesh see block 2B and 3A 3 source on standard surface TSURF z or toroidal mesh see block 2C and 3A 4 source on a surface composed of one or more segments of radial and or poloidal polygons The further details of the spatial distribution are defined in code cou pling routines i e the code coupling routine IF1COP must be called Spe cial versions of IF1COP are available e g in the code segments COU PL Epp COU PLE 5 coupling to B2 BRAAMS multi fluid plasma code COU PLEpivimp coupling to DIVIMP impurity ion kinetic transport code or COU PL Ev fite TRANSP code format The position on the surface is sampled from a piecewise constant step function defined from plasma fluxes onto that surface vs arc length The flags INSOR INGRDA and INGRDE described below are set automatically in this option and hence need not be specified INSOR number of the surface in the mesh RSURF PSURF TSURF or ASURF respec tively Redundant in case INDIM 4 INGRDA INGRDE same as IRPTA IRPTE flags in input block 3a Defines subrange on standard surfaces on which the source is distributed Irrelevant for sources on additional surfaces SORWGT Relative frequency for starting points on surface lab
378. y weighted velocity distribution along specified direction binned in energy units SPT YP 3 cm s cm 3 eV 177 IDIREC SPCVX SPCVY SPCVZ These flags are only for cell averaged spectra other wise not in use 0 no direction specified 1 cell averaged spectra are along direction SPCVX SPCVY SPCVZ The vector defining this direction is normalized internally NSPS SPCMN SPCMX Number of equidistant energy bins eV for spectra The contri butions with energies below the minimum energy SPCMN are stored in bin no 0 those with energies above the maximum energy SPCMX are stored in bin NSPS 1 SPC_SHIFT shift spectrum by SPC_SHIFT eV in printout and plots SPCPLT_X SPCPLT_Y to be written SPCPLT_SAME plot this spectrum into previous frame The surface flux spectra are printed together with the other surface averaged tallies for those surfaces which are selected for printout in sub block 11A They are all automatically plotted as soon as at least one further volume tally plot input sub block 11B 2 is selected 178 2 11 Data for numerical and graphical Output General remarks The input flags in this block control all the numerical and graphical output of an EIRENE run This comprises diagnostics during the initialization phase e g 2d and 3d geometry plots as well as selected test particle histories printed and plotted during their generation All numerical output of a run is arranged in so called tallies The

The EIRENE Code User Manual Version: 11/2009

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