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The MARS Code System User`s Guide Version 15(2014)

1. Y1l ne Y2 SUBROUTINE MHSETU SET UP HISTOGRAM ARRAYS HISTOGRAM ENTRY FOR USER DEFINED HISTOGRAMMING HISTOGRAM ID AVAILABLE 700 lt ID lt 999 HISTOGRAM TYPE IHTYP 1 COLLISION IHTYP 2 STEP IHTYP 3 ENERGY DEPOSITION IMPLICIT DOUBLE PRECISION A H 0 Z INTEGER I N REMEMBER HBOOK IS A SINGLE PRECISION ENGINE DON T FORGET THE REAL DECLARATIONS SUCH AS REAL AA ELB X1 Y1 Y1 Y2 CALL HBOOKB ID AA NEB ELB 0 CALL HBOOK2 ID TITLE NX X1 Y1 NY Y1 Y2 0 RETURN END SUBROUTINE MFILL IHTYP NREG IM JJ E1 E2 DELE W X1 Y1 21 X2 Y2 22 DCX DCY DCZ STEP TOF NI IDPRC HISTOGRAM ENTRY FOR USER DEFINED HISTOGRAMMING For neutrino scoring in MFILL only of their production vertex info HISTOGRAM ID AVAILABLE 501 lt ID lt 700 CALL TYPE IHTYP 1 COLLISION IHTYP 2 STEP TRACK LENGTH IHTYP 3 ENERGY DEPOSITION LOCAL OR ON THE STEP NREG REGION NUMBER FOR COLLISION OR STEP START STEP STEP cm El ENERGY BEFORE STEP GeV E2 ENERGY AFTER STEP GeV DELE ENERGY DEPOSITED GeV LOCALLY OR ON THE STEP W STATISTICAL WEIGHT X1 Y1 Z21 COORDINATES Al HE STEP START cm X2 Y2 22 COORDINATES Al HE STEP END
2. UCTS OF MUONS Ehi 11 FLUENCE AT IND 6 T 12 ENERGY DEPOSITION by SUB THRESHOLD hadrons 13 SURFACE CROSSING BY NEAR THRESHOLD HADRONS 14 FLUENCE BY NEAR THRESHOLD HADRONS 15 ENERGY DEPOSITION ON STEP BY NEAR THRESHOLD HADRONS 16 SURFACE CROSSING BY NEUTRAL HADRONS OR IN VACUUM 17 SURFACE CROSSING BY CHARGED HADRONS IN MATERIAL 18 ENERGY DEPOSITION ON STEP BY CHARGED HADRONS 19 FLUENCE BY HADRONS 20 ENERGY DEPOSITION BY SUB THRESHOLD e e from hadrons 21 e e vertex by muon 22 FLUENCE BY MUONS 23 SURFACE CROSSING BY MUONS 24 ENERGY DEPOSITION ON STEP BY MUONS 25 BREMS VERTEX BY MUONS 26 NUCL VERTEX BY MUONS 27 ENERGY DEPOSITION BY SUB THRESHOLD BREMS OR NUCL PROD 28 ENERGY DEPOSITION BY SUB THRESHOLD MUONS 29 ENERGY DEPOSITION BY HEAVY FRAGMENTS FROM MUON CAPTURE 30 UON DECAY VERTEX 31 SURFACE CROSSING BY EMS 32 FLUENCE BY EMS 33 ENERGY DEPOSITION ON STEP BY e and e 34 ENERGY DEPOSITION BY SUB THRESHOLD EMS 35 DELTA ELECTRON VERTEX 36 LE neutron vertex 37 LE NEUTRON FLUENCE ON STEP 38 LE NEUTRON SURFACE X ING 3 9 E NEUTRON SURFACE CROSSING AT IND 6 T 40 LE NEUTRON FLUENCE AT IND 6 T 41 LE NEUTRON LOCAL ED no new n or gamma generated 42 LE NEUTRON LOCAL ED recoil proton
3. 11 1 1 The VOLMC NON cerrar 124 11 12 The MARS OUT Hild e o eI 124 LI The MTUPE Tild a A a E a E S a pas 134 e ae bee eee eo ee oe es 134 A a a e a a E a A a 135 AE O TE 135 O RR NES 135 1122 The VERTEX PLOT fil ooo d o RE RR Ra 135 136 AR AA 136 a O kee eS Ee eo 137 TP 138 139 dditional Code Topics 150 A ee ek ee eae 150 Sg eee eS ee el oe ee ee 150 Coe ee nee oe ee eee ere ee EM ee 151 LES APR BUR OS ee ee eee 151 eb ea oe a eo ede URP 151 Seed Bee ee a eee ee ee 151 By ee ee ee ee ee be eee ee 151 bests A op Sb Led det e MEE hohe Ge Aon Ste ee EE E 151 152 TOPPED 152 CPP 152 ee CTETUR 152 owledgements 153 List of Tables 1 Neutron Enero y Groups ce ek oe a EA E RE AUS EES we eee Se 19 2 Particle Tunes 23 3 Built in Elements ee 26 Z Extended Geometry shape types and parameterd o o oo oen 68 e hae a ee ee oe ee 76 10 Histogram ID numbering ees 117 BEES ci a ia EA dd BL Qo eae oe E ret aoa ae de la List of Figures A PEE A es oe Gk Rp AR SSA 4 MARS neutron cross sectiond e ee A bee bea ee bee pe eee ee DEP paca aaa ales v 8 Model Datacomparisong es 9 Model Datacomparisons e RR es 10__ pi K yield from Deuteron nucleuscolhision e e 11 Muorn capiutel uox exeo SO ee a ee a TN RUP NS E Ure dens e
4. E E N1 NFZPEX NUMBER OF STANDARD EXTENDED REGIONS E C one time initialization section IF NE ER EQ 0 THEN NENTER 1 C Steel core both sections the same volume VOLUME N1 1 2 0DO0 XSteel 2 0DO0 YSteel ZSteel middle VOLN N1 1 UpstCore VOLUME N1 2 Volume N1 1 VOLNM N1 2 DnstCore C C The concrete around the sides of the steel core Al 2 0D0 2 0D0 YConc XConc XSteel Top and Bottom area A2 2 0DO0 YConc YSteel 2 0D0 XSteel two sides area VOLUME N1 11 Al A2 ZSteel VOLNM N1 11 Conc Znl1 C C The concrete in back of the steel core VOLUME N1 13 2 0D0 YConc 2 0D0 XConc ZConc ZSteel VOLNM N1 13 Conc Zn2 C Return C C non initialization call return the Volume for Zone N Else V VOLUME N End If C RETURN END The same parameter list used in REGI to describe the dimensions of the beam dump is also included here to calculate the volumes of the beam dump zones all volumes are cm Zone volumes are placed directly into the MARS array VOLUME these non Standard zone volumes are written with an array offset of NFZPEX just as the material content of each non Standard zone was entered into array MATIND At program startup MARS initializes all elements of array VOLUME to zero MARS then fills the Standard and Extended zone sections of array VOLUME based on settings in the MARS INP and GEOM
5. 36 IND 3 T IND 3 F IND 4 T IND 4 F IND 5 T IND 5 F IND 6 T IND 6 F IND 7 T IND 7 F IND 8 T IND 8 F IND 9 T IND 9 F IND 10 IND 10 E turns on the Extended Geometry option where a model is described using combina tions of boxes cylinders cones etc See Section I 4 for a description for using the GEOM INP input deck Extended Geometry option turned off set this switch when magnetic or electric fields are present in the geometry descrip tion This switch triggers calls to the user subroutine FIELD where field maps or components must be defined no magnetic or electric fields present turns on MCNP mode which uses the MCNP4C ENDF B VI code system for neutron transport below 14 5 MeV with corresponding low energy photon production use the MARS default neutron transport for neutrons in the 0 00215 eV to 14 5 MeV energy range using the 28 group neutron cross section library with no low energy photon treatment Switch on the mathematical expectation method to accumulate results for transported particles probabilities are used to tabulate fluence star density particle spectra and the calculations for dose equivalent rather than using the analog method to directly tabulate particle contributions This option is very powerful for deep penetration problems i e thick shielding however it can substantially increase the CPU t
6. wn ECISION A H O Z INTEGER I N jUDE cmasnsg inc PRIMI EHITX PRIMEHITY PRIMEHITZ COMMON BPRTAG XORIG YORIG ZORIG WORIG EORIG IORIG KORIG NRORIG IMORIG momentum components particle production energy and cosines source term for staging energy cosines etc for heavy ions PARAMETER CLIGHT 29979245800 D0 PARAMETER IWRTYP 1 PARAMETER IWRTYP 2 PARAMETER IWRTYP 3 IF IWRTYP EQ 1 THEN ET E PM JJ PA SORT E E 2 D0 PM JJ CTOFF CLIGHT TOFF PX PA DCX PY PA DCY PZ PA DCZ WRITE IUNIT 101 NI JJ X Y Z PX PY PZ ET CTOFF W FORMAT I8 13 3F11 3 6 1PE14 6 ELSE IF IWRTYP EQ 2 THEN WRITE IUNIT 102 N1 JJ E W X Y Z DCX DCY DCZ TOFF FORMAT 18 13 5 1PE13 5 3F14 10 1PE13 5 ELSE IF H ZA1 GT 0 DO EA E H2A1 ELSE EA E Z iw E m nb ou mp pn O Z oO IF IF IWRTYP EQ 3 TH ACOS DCZ THEN H EN E IUNIT 103 NI JJ HZZ1 HZA1 W EA TH X Y DCX DCY AT 111 17 2F8 2 5 1PE12 4 2 1PE15 7 IF ETURN 5 14 Subroutine TAGPR Particle Origin Tagging Origin tagging for hadrons muons heavy ions and electromagnetic showers EMS Particle JJ of weight W and energy E1 makes a step STEP starting from point X Y Z in
7. The xsdir file or a link to it must be present in the directory where the user runs the MARS MCNP executable This file is a set of neutron photon and electron data libraries which are included with the MCNP distribution package The user should copy the file from the MCNP installation area in the directory restricted mcnp4c data in the MARS installation area Then insert the following line at the top of the file xsdir file datapath restricted mcnp4c data The MCNP code creates three output files after the run First mcnp buf is temporary file generated at the initialization stage It is re written during each run however if problems occur a bug report is written here The second file is outp It contains information on how the mcnp code parsed it s lines from the MARS INP file and can be useful for checking the specified atomic and weight percentage of material mixtures The third file runtpe contains binary information required for a hot restart and this file can be safely deleted All physics results are printed to the usual MARS output files tabulated by zone number 112 7 FLUKA Geometry Mode MARSIS can read in an input geometry description in the FLUKA format and perform full MARS modeling in such a setup An example of a MARS model of the CMS collider detector based on a FLUKA input is shown in Fig 1 20e 03 Hi di cm 2 00e 03 1 50e 03 1 50e 03 Us Es Figure 24 Mars GUI illustration of the CMS detec
8. 117 NHSPE 1 E dN dE DIVIDED BY DEL DELTA LOG10 B FOR ALL PARTICLES IN 1 CM2 SURFACE CROSSING ESTIMATOR IHTYP S 6 SURFACE TIME SPECTRA IN TMIN TMAX INTERVAL sec HISTOGRAMS GENERATED ARE UNIFORM IN 80 BINS in nsec Table 11 Example of surfaces in MARS INP NSUR 11 RZTS 6 15 6 15 200 200 200 200 450 450 0 250 250 450 450 0 6 15 60 450 450 0 60 200 450 450 81 60 60 200 200 0 230 230 450 450 0 300 300 450 450 0 400 400 450 450 0 450 450 450 450 0 470 470 450 450 0 10 3 Other Built in Histograms There are two additional groups of the built in histograms e Histograms filled for the global energy deposition distributions initialized by the NHBK and HBKE cards for the entire system or for up to 5 materials specified on the NHBK card e Ntuple number 16 contains the normalization factors used for each histogram unity or AINT which can be re defined on line in a GUI session 10 4 XYZ Boxes or Arbitrary Mesh Tallies Flexible histograming called XYZ is implemented in boxes arbitrary positioned in a 3D system mod eled This histograming is totally independent of geometry description both type standard non standard extended and MCNP type and details including materials distribution By default the macro box detec tor axes are parallel to those of the mother volume and can be rotated using MARS2BML and BML2MARS routines The histo
9. COM ROUTINE LICIT DS COM UT EZ iD MAPS DS GRADIE FOR FOC QUADS UTPUT EVISION FI UBL ry PR ECISION A H 0 2 ELD N X Y Z BX BY BZ BBB F INT iG ER PON MAG AGNET POINT S CO E NTS IN BX BY BZ B NTS OF MAGN ETIC FIEL D IC INDEX AT ORDINATES T CM GIVEN POINT OPTIONAL G lt 0 FOR DEFOC QUADS BB IN TESLA 16 DEC 1 994 ON BLINT2 JJ KK MAG DATA RAQ BQUA G1 8 2 0 53 BX 0 BY 0 BZ 0 IF Z BX 5 IF ELSE AG THI LT 622 E Q 2 BX 5 EN CALL QUAD X Y R RAQ G1 BX BY DIPOLE X Y R RAQ BQUA BX1 BY1 BX BX BX1 BY BY BY1 CALL dd uU dd ND ND IF ETURN I N 5 8 Subroutine RFCAVT Description of Accelerating Components SUBROUTINE RFCAVT JJ VECT VOUT E TOFF NIB NIM IFLAG IMPLICIT DOUBLE PRECISION A H O Z INTEGER I N C RF CAVITY KIC C DISCRETE AT BOUNDARIES BETWEEN REGIONS WITH SPECIAL NUMB C NIB PRIOR CROSSING NIM AFTER CROSSING C INPUT JJ VECT X Y Z DCX DCY DCZ P E TOFF NIB NI C OUTPUT VOUT X Y Z DCX DCY DCZ P E IFLAG C VECT 1 VECT 7 AND E ARE RE DEFINED TO VOUT 1 VOUT 7 AND C IFLAG 1
10. PMUB F EHE INTEGER N INTEGER I DOUBLE PR bias flag 0 1 LPB HALF DATA IPRC DATA IPRC DATA PRC E EM 0 N EM 1 N NPRCE exclusive PRCEM 0 PRCEM 0 M 0 D0 hadron nucl DATA IPRC DATA PRC URN F py ND E Y HA 0 N HA NPRC vertex PRCHA 0 HA 0 D0 us PRCEM N PRCHT NP PRCEM I ECISION P PRCHT IP RCEM P RCMI RCMI DON p PMUANN PPHNUC PPBAR PRCNT NPRCHA PRCNT IPRCHA RCH DP RCMT PRCNT PRCHA Block Data HISTDUMP Histogram Bin and DUMP Region Specification BLOCK DATA HISTDU UMBERS 0 NBMA 300 DARD GE OM ETRY S ECTOR 21 NOV 2001 BY NVM 14 FEB 2002 BY NVM IMPLICIT DO COMMO COMMO BHBK BLDU ECISION A H O 2 RZ P ZBI BU 300 NBMA R Z DE T ZBIN RBIN 200 200 200 120 120 120 X Y DETECTOR BINNING XH 15 0 Recommended ECTOR BINNING at NOB 0 Recommended Recommended at NSURF 0 3 NRBIN 3 NXH NYH 96 ECTOR BINNING DATA NYH 150 Recommended C SELECTED DUMP REGION NUMBERS 0 NBMA 300 amp QO 0 20 DATA NBMA 0 DATA NBU 300 0 For example
11. 02 02 02 02 02 02 02 02 02 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 86 OOO Ot NN a E o E ee ee ee eee 61 L 04 L 04 1 04 1 03 1 04 503 1 04 1 03 1 04 04 55 55 55 909 md o e oe NON oe oe oe e oe oe oe sos C O E oe oe oe M oS oS sos O00 00000000 O0 O O t oe oe oe o oe oe AP o AP oe oe oe oN Os NON oS oS oS oM o oe 0 004 CQ 2 P2 OCW B C C0 C0 CO Y CO UY Y CO CO PO PO PO PO Po 2o PO INS PO y CQ 000 10 01 4 Q hor OO JD CO P2 E25 OC xo B QR Gm DB DB DB DB a a O 00 10 01 i C ho Ra aa a a al Ss WN PF SUBROUTINE VFAN N V IMPLICIT DOUBLE PRECISION A H O Z INTEGER I N FIND VOLUME V N CM 3 OF REGION N OF THE NON STANDARD GEOMETRY C VOLUME N ARE DEFINED IN SERV FOR N lt NFZP INCLUDE tallyl inc DATA NENTER 0 SAVE NENTER N1 NFZPEX NUMBER OF STANDARD EXTENDED REGIONS IF NENTER EQ 0 THEN Q C PUT HERE HE REAL VOLUMES CM 3 FOR ALL THE NEEDED C NON STANDARD REGIONS lt Myax I E REDEFINE ANY OF THE C PRE DEFINED V
12. Interface main features e Draw magnetic field and two dimensional geometry slice Activated by pressing Draw button or d or D key The picture of the main window is shown below 139 MARS GUI Slice fle UR AE OO UO A As UN LIS AS i HP A EU M EE M O Ee DU Lu ut E h fog f 2 Wow le h A 4 4 A A A A A A amp h 44 4 al A A A c La ha 44 4 SE SE SE oF h 4 44 F F Y Y ha TA TE i F 4 ee E RI iE FI 4 A 4 x 0 o EN FIT 9 4 4 4 X E X CA amp UA E ri 4 amp 4 4 Y AAAA A E Y 4 4 3X3 X E OX A T i Y 3 X aw Wo XM wx Md a i rite eae XX YM XXX tlh eed AA WW NNN SN AN i METER EDGE UE NON NS IS LIRE CQ ES A SS e The panel upper fields inform user about maximum field components and maximum field value 140 BH maxiT BV maxi ES max T 20 600 36 050 41 521 e User can change the minimum and maximum values for each coordinate axis together with number of points used to draw magnetic field It can be done using entries located on the right side of the interface It is worth to mention also that E NS bo o Emin cm YXmin cm E amini cm Xmax cm maz cm s maz cm 36 05 36 05 20 6 Y Z w X Z v x e User can set what axis slice will be activated It can be done using radio buttons on the right side of the interface or pressing x X y Y or z Z keys respectively Also the slice coordinate can be set using respective
13. Note DPH and DLT histograms are currently disabled In any run the total number of histograms can not exceed 300 i e a sum over all histogram types in all macro boxes detectors must be less than 300 Maximum number of voxels in any macro box bins in each histogram can not exceed 10 To save CPU time keep the number of macro boxes detectors histogram types and voxels bins as small as possible Histograms are defined in an input file XYZHIS INP where the following conventions are used 1 The first line is a textual problem description 2 The last line STOP or stop terminates the XYZHIS INP data card list i e everything after this line is ignored 3 Blank lines can be inserted between data cards for file organizational purposes 4 Comments are allowed at the line end starting from an exclamation sign 5 The data is unformatted and separated either by blank space or by one of the following delimiters D amp 6 A macro box detector is defined by a XY Z card of the following format XYZ X1 X2Y1Y2Z21Z22NX NY NZ TEXT where XY Z or xyz is a card ID X1 X2 Y LY2 Z1 Z2 are the minimum and maximum Cartesian coordinates defining the box N X NY NZ are the number of bins along each axis TEXT is a word describing the box optional 7 Macro box detector categories are nryztp 1 gt X Y ina Az slice x v y h defined by NZ 1 nxyztp 2 gt X Zina Ay slice x v z h defined b
14. p ny better description of photon induced reactions in the intermediate energy range and of radionuclide production When installed within MARS the CEM code was converted to double precision along with some other necessary modifications but is otherwise identical to the CEM2003 version Several examples of the CEM predictions compared with experimental data and results of several other models are given in Figs and 6 One can see that on the whole the code reproduces quite well not only spectra of secondary nucleons but also excitation functions for the spallation yields a much more difficult characteristic of nuclear reactions to be predicted by any theory and is consistent with other well known models 61 2 3 2 Inclusive hadron production from 5 GeV to 100 TeV An inclusive approach is the default in this energy range The hadron production model uses a combination of phenomenological models parameterizations and integration algorithms covering a hadron kinetic en ergy range of 1 MeV CE 100 TeV as described in Refs 441 62 63 An improved phenomenological model has recently been developed and introduced into MARS as the default to describe pion production in high 12 Tp 1 total i PON 2t mun ed pO tal cro To Cross section mb 3 7 m xl u Su rs a fi NR P m TOR het ue M m eee 10 i A 10 10 10 1 n ore o mea Eki
15. x amp DRIFT_FIELD_FUNC 102 ACA X A A x F x A A AX AX F F 0X F A A XA X A A F x A A AC ACA F A HF F Qk m m mo m m m RQ m m m m m m RQ e RY m m m Rm m RQ R RS m m m m m DRIFT VOL FUNC DRIFT GEO FPUNC DRIFT ZONENAME FUNC BEAMLINE ID EQ 1 THEN CALL MARS EL REGISTER 1 DRIFT NOF ZONES DRIFT NAME FUNC DRIFT INIT FUNC DRIFT GEO FUNC DRIFT MAT FUNC N D D RIFT ZONENAME FUNC CALL MARS EL REGISTER 2 RBENDEPB NOF ZONES RBENDEPB NAME FUNC RBENDEPB INIT FUNC RBENDEPB GEO FUNC RBENDEPB MAT FUNC RBENDEPB FIELD FUNC RBENDEPB VOL FUNC ELSE IF BEAMLINE ID EQ 2 RBENDEPB ZONENAME FUNC THEN CALL MARS EL REGISTER 1 DRIFT NOF ZONES RIFT NAME FUNC RIFT INIT FUNC RIFT GEO FUNC RIFT MAT FUNC O FIELD RIFT VOL FUNC RIFT_ZONENAME_FUNC VU0OUZUUOUOO CALL MARS EL REGISTER 2 RBENDEPB NOF ZONES RBENDEPB NAME FUNC RBENDEPB INIT FUNC RBENDEPB GEO FUNC RBENDEPB MAT FUNC RBENDEPB FIELD FUNC RBENDEPB VOL FUNC END IF RETURN END RBENDEPB ZONENAME FUNC 103 5 19 5 Subroutine TUNNELGEO SUBROUTINE TUNNEL GEO XLOCMAD YLOCMAD ZLOCMAD XGLMAD YGLMAD amp ZGLMAD NZ BLINDX ELINDX ELBEGINS ELLENGTH ANGLE PREVANGLE amp NEXTANGLE IMPLICIT NONE INTEGER NZ B
16. 10 5 User Defined Histograms and Ntuples Arbitrary one and two dimensional histograms and ntuples can additionally be booked in a user routine MHSETU and filled in MFILL 122 11 Output of the Simulation MARS produces many output files The main output file MARS OUT is always produced and contains startup initialization information in addition to results Other output files are produced only when certain zone types are set up or when certain histogram options are requested or when certain flags are set in the MARS INP file This section covers all these different output options how to request them modify them where possible and what the contents are MARS OUT and several other output files are flat text files which can be opened and examined with any text editor They contain tables of data which are typically but with some exceptions arranged by the MARS zone numbers These are described further below in Section 11 1 There are a few other specialized output files such as those generated by use of the TAPE card in the MARS INP file discussed in Section 11 2 While these are text files which can be opened and examined they are not intended to be used in this way but instead as input files for other programs or for multi stage running of MARS For example the TRACK PLOT file is used in conjunction with the GUI visualization tool to examine samples of generated events If the user wishes to extract particle data for h
17. 7 also defines the LC S for each shape and how it relates to the MARS coordinates also referred to here as the Global Coordinate System GC S are additional parameters describing the shape Each shape has a different number of parameters and these are defined in Table 7 The data line should hold only as many parameters as are defined for the shape If a parameter is left at it s default value and all the following parameters are also left at their defaults then they do not need to be listed on the data line otherwise all parameters used by the shape definition must be listed NSB1 NSB2 NSB3 are the numbers of optional subdivisions in LC S along corresponding di rections see shape descriptions in the above table Transformation matricies are implemented via TR cards whose syntax is TRn XT YT ZT o B 71 where TRn is the transformation matrix identifier and always starts with TR followed by an integer n 0 xn 500 Integer n is the transformation ID NTR used in the shape volume data line for shapes which utilize a transformation XT YT ZT arethe translation coordinates applied to the shape s Reference Point RP a D are the rotation angles in degrees between the shape s DC S axes and the GC S axes around x axis yaw y axis pitch and z axis roll with z direction of movement clockwise positive or counterclockwise negative If there is a rotation around more than one axis the rotati
18. CBUF 1 CBUF 2 CBUF 3 CALL flat2glob CBUF DBUF CALL mad2mars CBUF 1 CBUF 2 CBUF 3 amp MARS VEC 1 MARS VEC 2 MARS VEC 3 C COMMENT THIS DO LOOP FOR REAL WORK DO IT 1 3 MARS VEC IT BML VEC IT MARS DIR IT BML DIR IT END DO e RETURN END 5 19 3 Subroutine BLINIT SUBROUTINE BLINIT M MAX IMUN Euch x oda ues EN NUR ERE eR xuR O C MMBLB INITIALIZATION C CALLED IF IND 13 T C C AR C CREATED 2001 BY KRIOL C MODIFIED 17 OCT 2003 BY MAK E LAST CHANGE 04 DEC 2003 BY NVM E er ES Capel Ae eben deer a aui Re exer pe erae donis tere inde dU des Stand IMPLICIT DOUBLE PRECISION A H O 2 INTEGER I N INTEGER IMUN include blregl inc include tallyl inc C EXAMPLE OF REAL WORK uncomment and modify whereever needed 99 X INCLUDE SIMPLE TUNNEL INC ib INITZONE A CALL BEAMLINES_IN_USE 2 EXTENSION TO SEVERAL BEAMLINES CALL SET CURRENT BEAMLINE 1 c Angle of rotation azimuth about vertical axis MARS X axis between c Z axis and projection of the beamline direction vector onto Z Y plane c A positive angle forms a right hand screw with MARS X axis BL1_THETA 0 DO c Elevation angle i e the angle between beamline direction and its c projection onto Z Y plane If it equals to zero the beamline remains c in horizontal plane positive phi correspond to increasing X x BL1 PHI 0 DO c Roll angle about the be
19. INP input files Finally the user s code is called to fill the non Standard zone portion Also filled is character array VOLNM which holds an 8 character string name for each zone This array is initialized to hold blanks in the initialization section of subroutine REG1 In subroutine VFAN this array gets filled with zone names for each zone which gets a volume assigned These zone names are used in the non Standard zone output file MTUPLE NON and simply make it easier to locate the line holding the results for a specific zone The non Standard output file MTUPLE NON holds a table of results for all declared non Standard zones Only zones which have been properly declared will have an entry in the table of results and the trigger for 83 what MARS considers proper declaration is a non zero value for the volume of the zone So even if there is a material indicated for the zone entered into the MATIND array even if code exists within REGI or called from it which describes the boundaries of the zone and this code returns a non Standard zone number assignment no results for that zone will be reported in the output unless the zone has a non zero volume entered into array VOLUME And for the results to be correct the volume value cannot be arbitrary it must be the correct volume corresponding to the encoded boundaries of the zone As discussed in section 3 that is is particle path length which is accumulated as particles are tracke
20. Jj Q 1 IN 0 01 3 EC 160 RSEC 80 101 20 MATR MATER INP STOP U wW NWMOHWM2Z2QH EF i ti lt H n Exgeo test sphere 0 3 0 0 0 0 10 O0 2 sphere 1 3 01 b De Uu Las Zu 52 sphere2a 320 240 S90 B5 0 Ay 2 sphere2b 3 0 L0 30 15 4 10 3 ball 2b sphere 3 3 0 4 0 0 60 0 15 5 box 1 1 0 8 Le 30 I5 4 e LR 2 box 2 LO 5 23 29404 os Cis X2 30 5h box 2 cone 1 4060 0 90 2 5 6 12 20 4 cone 2 As BOY 90 064 L124 24 oe 304 6 cylO 2 E150 30w 90 Qr 2 30 2 2 0 cone 4 140 30 90 2 0 2 24 90 2 cone 3 470 0 0 00 90 0 Ze 0 6 20 cyl 1 2 0 10 0 120 0 5 40 10 10 cyl 1 cyl 2a 2 02 Oe 50 120 Jl 5 30 109 2 cyl 2b 2 0 T0 50 3120 0 1 30 1 cyl 2b cyl 3 2 0 3 9 30 X30 amp 0 5 202 4 5 cw 6yl 3 cyl 4a 2 2 4 0 40 125 0 See 25 0 Beat cyl 4a cyl 4b 2 3 350045 Ou 0v Ou uu 25k 75 2 GyL 4b TRL Or Oe Qu Sl4u32 05 gt O20 TRESL TR2 0 O 0 11 46 0 O TRE 2 TR3 Ow 00 115 I111 46 0 10 fo IRE 3 STOP 73 cm 80 o wx 0 8 C EEE 40 Figure 22 Plan View of the Extended geometry Example 74 5 User Subroutines The user subroutines are collected in the file m1514 f The default version of this file distributed as a part of the MARS code contains dummy versions of each of the user subroutines Some of the subroutines contain comments and commented ou
21. N CM2 PER INC PARTICLE AS A FUNCTION OF DEPTH DOWN AND RADIUS ACROS IN CM This table appears to be identical to the one above GRAPH NEUTRON FLUENCE AT E 1 MEV N CM2 PER INC PARTICLE AS A FUNCTION OF DEPTH DOWN AND RADIUS ACROS IN CM This table is similar to the one described above but for all neutrons below the stated energy cutoff GRAPH NEUTRON FLUENCE AT E gt 1 450E 01 MEV N CM2 PER INC PARTICLE AS A FUNCTION OF DEPTH DOWN AND RADIUS ACROS IN CM 132 This table is similar to the ones described above but for all neutrons below the stated energy cutoff 30days lday RESIDUAL DOSE RATE AT CONTACT mSv hr FOR I 1 0000E 12 P SEC The table presents arranged by Standard zone number the residual dose predicted at the surface of each Zone after a canonical exposure The exposure used is 30 days with IE primaries per second entering the model followed by 1 day of cool down decay The residual estimates are valid only for relatively thick zones those with a lateral thickness gt A n the Zone material s interaction length GRAPH 30days lday RESIDUAL DOSE RATE AT CONTACT mSv hr This table presents data values versus location in the model volume ignoring zone and region bound aries The data is instead mapped into 5 r bins and 10 z bins The maximum r and z bin values describe the maximum extent of the model the Standard zone mother volume the bins are cre ated by equal divisions between zero and
22. PPIKDEC lt 0 001 Default 1 PMUPRMT Real number specifying the parameters of the inclusive forced prompt muon production in the inelastic nuclear interaction vertex It is forced with the ap propriate statistical weight at PMUPRMT 1 forced with the Russian roulette at 0 001 lt PMUPRMT lt 1 or suppressed at PMUPRMT 0 Default 0 05 PMUBEHE Real number specifying the parameters of the inclusive forced Bethe Heitler muon production It is forced with the appropriate statistical weight at PMUBEHE 1 forced with the Russian roulette at 0 001 lt PMUBEHE lt 1 modelled exclusively at PMUBEHE 1 or suppressed at PMUBEHE 0 Al ternatively the Bethe Heitler muon production cross section can be increased 1 to 500 times with 500 lt PMUBEHE lt 1 an appropriate correction to a statistical weight assures correct results It is automatically set to 1 for KEMINCL 1 For example PMUBEHE 0 03 is recommended for most of the high energy muon collider and LHC applications Default 1 PMUGVM Real number specifying the parameters of the inclusive forced muon produc tion via vector mesons generated in photo nuclear reactions at E gt 1 5 GeV when IND 10 T default It is forced with the appropriate statisti cal weight at PMUGVM 1 forced with the Russian roulette at 0 001 lt PMUGVM lt 1 modelled exclusively at PMUGVM 1 or suppressed at PMUGVM 0 It is automatically set to 1 for KEMINCL 1 Default 0 0
23. Table 5 Source code organization File name marsmain f m1514 f m15bldt f m15bnab f m15cstuff c m15gui c m15mc c m15in1 f m15in2 f m15out f m15mareg f m15tr f m15trems f m15trneu f m15trneu mcenp f m15field f m15dedx f m15region f m15exg f ml5treem m15eve f m15evepi f m15evtgen f m15elast f m15xsec f m15ph f ml15cem f ml5neutrino f m15deutron f ml5rad f m15omega f m1 S5hist1 f m15hist2 f mi 5Sutill f m15util2 f m15tuple f m15srcterm f m15treem laqgsm f laqgsm1 6 f Content PROGRAM file User routines BLOCK DATA modules C service routines I O and initialization routines the main event processing steering routines hadronic electromagnetic and heavy ion transport neutron transport routines magnetic field and synchrotron routines DE DX routines zone identification routines event generator routines elastic collision routines cross section routines additional physics simulation subroutines CEM 2007 model routines neutrino transport and interaction routines deuteron interaction routines radiation interaction routines histogram booking and entry routines utility routines including FFREAD output routines LAQGSM routines 33 4 TheMARS INP MATER INP and GEOM INP Input Files This section describes the main input files sometimes referred to as decks used by MARS These are the native input files as opposed to user created input files which might supplement the user s own subro
24. This set is default and recommended for majority of applica tions including particle production energy deposition heavy ion projectiles nuclide inventory and DPA at energies below 8 GeV It is obviously more CPU time consuming than the previous one IQGSM 2 is currently disabled It is automatically converted to I0GSM 3 For 1IOGSM 3 exclusive modeling with the LAQGSM code is performed for all nuclear inelastic interactions from 8 GeV to multi TeV energies with the IQGSM 1 mode utilized at energies below 8 GeV It is the most CPU time hungry mode Default TOGSM 1 NEVIYPE The number of evaporated particle types to consider in each nuclear interac tion Minimum is six p n d t He t He maximum is 66 up to 4 Mg Default 17 up to 1 Be It is recommended to use NEVTYPE 6 for shield ing applications to reduce CPU time and NEVTYPE 66 if one needs pre cise nuclide mass charge distributions at 7 A 20 MCSD KMCS KDLE MCSDLE INEXDL Control of the ionization energy loss processes and scattering acting on muons charged hadrons and heavy ions nuclear elastic scattering HES at E gt 0 014 GeV for neutrons and at all energies for all other particles and multiple Coulomb scattering MCS for all charged particles This feature is primarily for study purposes to isolate and study the modeling of specific phenom ena Aside from such studies users are advised to leave these parameters at their default values although the use
25. cm DCX DCY DCZ DIRECTION COSINES AT THE STEP START TOF TIME OF FLIGHT AT THE STEP END sec NI HISTORY NUMBER IDPRC PROCESS ID IHTYP 1 E1 2E2 DELE 0 STEP 0 X1 X2 Y1 Y2 Z1 22 IHTYP 3 El ne E2 DELE gt 0 STEP 0 X1 X2 Y1 Y2 Z1 Z2 OR STEP gt 0 Xl ne X2 IDPRC PROCESS Ck Ck KC Ck CK Ck Ck CK KC Ck CK C Ck CK CC Ck CK Ck Ck CK CI C CC Ck CK CK Ck Ck KK KK KK CK Ck KK KK KK Ck Ck KA KK kk kx S KA Kk Kk ko ko ko ko 1 DPA ELASTIC AND INELASTIC 2 RECOIL NUCLEUS LOCAL DEPOSITION NON LAQGSM 3 Local deposition of heavy ions at AA vertex NON LAQGSM 4 STAR DENSITY 5 FISSION CE OCAL NON LAQGSM 6 FISSION gt 5 GE jOCAL NON LAQGSM 7 HEAVY FRAGMENTS LOCAL DEPOSITION NON LAQGSM 8d t He3 and He4 LOCAL DEPOSITION NON LAQGSM 9 SURFACE CROSSING BY HADRONS AT IND 6 T 10 STAR DENSITY AT IND 6 T 9 AOA OVA Ov QO OO C3 C2 C2 CY 4 010 004 10 90 CY C3 Q2 C1 Q0 0 20 CY C2 004110 C3 CY OQ2 C C2 O20 CY 2 a
26. dimensions in cm angle in degrees and magnetic fields in Tesla The reference system is a cartesian coordinate system where the z axis is longitudinal and the positive direction is from left to right The z axis is usually the center of symmetry and as a rule the primary particles strike along this axis in the positive direction The positive direction of the x axis of the coordinate system is up and the y axis is toward the viewer completing a right handed system Any other units used by parameters in the input deck will be specified in the list of input cards where appropriate The first card in the MARS INP deck is a line of text the remaining are data cards The order of the the data cards and their number is arbitrary The only requirement is that the first text card appear on the first line of the input deck and that the STOP data card be present to terminate the sequence of data cards Blank lines can be introduced anywhere to group similar cards together and organize the file Any given line which starts with the character C will be ignored just as in FORTRAN In general any lines after the STOP card are ignored unless the user has set switches for importing a geometry description from another program in this case a block of lines is present after the STOP card see Section 3 1 2 for more information The first line of the input deck is the Job Title card It has a FORTRAN format of A80 The user can enter any text on this line
27. large distances from each other it is recommended to run several short jobs defining the cylinders surrounding different zone groups Statistical RMS errors in the volume calculation are printed in the VOLMC NON file and can be reduced by increasing NVTRIAL Typically it takes a few tens of seconds on a typical workstation to get the above errors 1 with NVTRIALD of the order of a few millions R1 R2 Z1 Z2 Real variables for minimal and maximal radii and z coordinates NVTRIAL IVOLBML of a cylinder which contains the non standard regions whose volumes need to be calculated Default 0 RMAX ZMIN ZMAX the size of the mother Standard zone Integer or real variable equal to the number of events to run in this volume determination session Default 10 Integer variable defining the coordinate system the volume calculation cylin der defined in If IVOLBML 0 then the global coordinate system is used If IVOLBML 1 then the beamline coordinate system is used with IND 13 T Default 0 NEVT NSTOP NTIME NHIPR NITRMX IPRINM NBEGRND Integer variables which control the number of events to run and print and control the printout of a given history and of nuclear cross sections NSTOP NTIME NHIPR the number of events to generate equals incident particles thrown Can be integer or real in the interval 1 lt NSTOP lt 2 x 1016 Default 200 the number of times user routine DUMP will be called Each call
28. with the value given by the PPBAR variable in the BIAS data card Values of the RLPBR array specify antiproton production modelling It is forced with the appropriate statistical weight at RLPBR 1 1 forced with the Russian roulette at 0 001 lt RLPBR i lt l or suppressed at RLPBR 1 0 Default 0 05 RLPBR The values for the antiproton production control indexed by IM the order numbers the materials are listed in the MATER INP file 4 20 5 Standard Geometry Zone Definition ZMIN NLNG ZSEC NLTR RSEC NAZM AZIM IRFL ZMIN ZLEFT Real variable normally used if negative z coordinates are present giving the minimum left most value for the z coordinate The value can be negative if necessary The starting location for the primaries ZINI in the INIT data card may be moved to match this coordinate or placed at a larger coordinate this depends on the details of the user s model ZLEFT The left most z coordinate Default 0 NLNG LZ NLZ Integer variables which define the number of major longitudinal divisions of the MARS Standard geometry zones See Section for further discussion LZ The number of major longitudinal sections described in the accompanying ZSEC data card The allowed range is 1 L2 1250 Default 1 NLZ The number of times the major sections described in the ZSEC card are re peated Active only for NLZ 22 Default 1 ZSEC ZSE 1250 IZN 1250 IZI 1250 Real and integer variables which
29. 0 02 GeV ENERGY DEPOSITION DUE TO L E NEUTRONS GEV G P P The table presents arranged by Standard zone number the energy deposited in each zone by low energy neutrons those below the EM value set in the ENRG card the default threshold is 14 5 MeV The units are GeV per g per primary Statistical errors are not given ENERGY DEPOSITION DUE TO L E CHARGED GEV G P P 127 The table presents arranged by Standard zone number the energy deposited in each zone by low energy charged hadrons those below the EM value set in the ENRG card the default threshold is 14 5 MeV The units are GeV per g per primary Statistical errors are not given ENERGY DEPOSITION DUE TO EMS GEV G P P The table presents arranged by Standard zone number the energy deposited in each zone by electro magnetic showers this includes the ys produced by 7 which decay immediately at their production point The units are GeV per g per primary Statistical errors are not given ENERGY DEPOSITION DUE TO CH HADRONS AND MUONS GEV G P P The table presents arranged by Standard zone number the energy deposited in each zone by charged hadrons and muons with energy above the EM value set in the ENRG card the default threshold is 14 5 MeV The units are GeV per g per primary Statistical errors are not given DIRECT ENERGY DEPOSITION GEV G P P The table presents arranged by Standard zone number the total energy deposited in each zone by all cont
30. 2 Beam Dump Intense 800 GeV proton beam hits a graphite dump followed by aluminum and steel absorbers by 210 cm vacuum gap by 5 cm polyethylene slab and finally by 1 meter of a wet dirt The user is interested in energy deposition calculations in maximum amount of the output including partial distributions temperature rise and estimation of a residual dose rate in intermediate result dumps The routine REGI Section 5 4 defines the dump as surrounded with a steel shield sitting at the axis of a hypothetical cylindrically symmetrical tunnel with 30 cm thick concrete walls With these three user routines a standard MARS INP file can look as Option 1 Tevatron CO Dump 02 28 95 NDX T T 8 T EVT 500000 5 PIB 12 800 0 01 8 0 0416 0 0944 0 1 300 4 E13 ATR MATER INP z y Q U u0tuuuznu H Z lt gt pH J vn zZ LTR 9 SEC 0 03 0 1 0 3 1 3 5 10 30 150 180 LOT 5 300 450 805 C MATR C AL FE CONC CH2 MIXT 26 2 1 NLNG 7 ZSEC 350 425 475 490 700 705 805 51 14 5101325101212 32045 N R P un H O H Option 2 The geometry description is simpler and the output is more sophisticated if one uses HBOOK activated in MAIN The last lines in MARS INP can be re written as LNG 7 SEC 350 425 475 490 700 705 805 01212 320405 LTR 4 RSEC 10 30 150 180 N Z 1 N 105 6 MCNP Mode MCNP is a code package for precise simulation o
31. 3 exclusive modeling with the LAQGSM code is performed for all nuclear inelastic interactions from 8 GeV to multi TeV energies with the ILAQM i 1 mode utilized at energies below 8 GeV It is the most CPU time hungry mode Default ILAQM i 1 ILAQM The values for the model switch indexed by IM the order numbers of the materials are listed in the MATER INP file MTEG KEMIN 500 Integer variables that control the inclusive and exclusive modes in electromagnetic shower verti cies as well as in n y and other neutron interaction verticies while in the MCNP mode see the PHOT data card applied only to specific materials Any material which does not have a corresponding entry here will have the global switch KEMINCL applied as the default see the PHOT data card For KEMIN i 0 the inclusive mode is used for all electromagnetic shower verticies For KEMIN i 1 exclusive modeling is done for all electromagnetic shower verti cies five EMS bias keys see the BIAS data card are automatically converted to 1 i e to the exclusive mode For KEMIN i N 71 exclusive modeling is used for the first N generations and inclisive one for remaining higher generation levels of the electromagnetic shower KEMIN The values for the model switch indexed by IM the order numbers the materials are listed in the MATER INP file 48 LEMS LEMS 500 Integer variables that control the use of the EGS5 code for precise exclusive
32. 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 N V Mokhov and S I Striganov Beam dynamics and technology issues for u colliders in AIP Conference Proceedings page 234 Montauk NY 1995 N V Mokhov and S I Striganov Model for pion production in proton nucleus interactions 1998 N V Mokhov and A V Ginneken to be published J Ranft Phys Rev D51 1995 J Ranft Gran sasso report Technical Report AE 97 45 INFN 1997 N V Mokhov Muons at lhc part 1 Beam dumps Technical Report TIS RP TM 95 27 CERN 1995 Y Tsai Rev Mod Phys 46 815 1995 N V Mokhov G I Semenova and A V Uzunian Nucl Instruments and Methods 180 469 1981 M A Maslov N V Mokhov and A V Uzunian Nucl Instruments and Methods 217 419 1983 S I Striganov Technical Report 94 14 IHEP 1994 G W Foster and N V Mokhov Backgrounds and detector performance at a 2 x 2 tev un col lider in Proceedings of the 2nd Workshop on Physics Potential and Development of u u Colliders Sausalito California November 17 19 1994 AIP 1995 P D Group Phys Rev D50 1994 I S Baishev N V Mokhov and S I Striganov Sov J Nucl Physics 42 1175 1985 J Briesmeister Mcnp a general monte carlo n particle transport code Technical Report LA 12625 M LANL 1993 N V M M Huhtinen A cross compari
33. E El E2 PARTICLE ID JJ dl 2 3 4 5 6 Jy 8 9 TO CIL CLAS ub4 lb Lo ET 8 19 20 21 p n pit pi K K mu mu g e e pbar pid d t He3 He4 num nuam nue nuae 22 234 24 525 26 27 28 29 30 31 32 33 34 35 36 37 38 39 FF 0 F 0 F F 0X F F 0k 0X F F F 0k 0X F 0X F 0X 0 F OX F F F OX F OX X F X Ro F F F Xo RS F Xo F X F KF ox JJ is PARTICLE ID 1 40 for tabulated elementary ones 1000 21 Al Z1 for Al gt 4 IORIG IKORIG 1 projectile ID KORIG IKORIG 2 origin ID NRORIG IKORIG 3 origin region number IMORIG IKORIG 4 origin material index KORIG 0 primary beam 1 muons unstable particle decay 2 muons prompt at hA vertex 3 muons Bethe Heitler pair 4 muons e e annihilation 5 hadrons hA vertex 6 hadrons elastic 7 hadrons from muons 8 hadrons unstable particle decay 9 hadrons EMS 10 hadrons recoil LEN 11 hadrons from neutrinos 12 EMS induced by photons from pi0 decay 13 EMS induced by synchrotron photons 14 EMS induced by g et e at hA vertex 15 EMS induced by knock on electrons from muons or hadrons 16 EMS induced by g et e from unstable particle decay 17 EMS induced by prompt e e from muons or hadrons 18 EMS induced by brems photons from muon 19 EMS induced by photons from stopped muons 94 KOL KOS KO AKO LAM ALAM SIG SIGO SIG nbar KSIO KSI OM sib si0b
34. Each of these main columns holds in turn two sub columns one with the photon data and the other with the et e data Each row is an energy bin with the bin value in the left most column The data is in units dF dE 1 GeV cm The table is formatted so that the columns of data can easily be cut and pasted into an external graphics or spreadsheet program At the end of the table are three additional results obtained by combining the photon and electron positron spectra data The first result labeled TOTAL 1 CM 2 the integral of the dF dE spectra the second result is the mean energy E GEV from each spectrum the third result is the dose equivalent DEO mSv due to the leaked particles GRAPH HADRON SPECIAL REGIONS SPECTRA The special regions are user defined cylindrical volumes specified by the NOBL and RZOB cards in the MARS INP file There can be no more than three of these regions declared and there is a column printed for each filled with zeros if the region is not used Declaring a NOBL region triggers the production of HBOOK histograms of a variety of results for the zones within the region see Sec I0 T for a definition of the histograms This table holds the same data used to fill the histograms although as in this case split into the contributions from three particle types each main column for a region holds three sub columns labeled P N PI The data is dF d InE in units hadrons per cm and given in energy bins as labe
35. M Pellicioni Rad Prot Dos v 88 2000 pp 279 297 and ICRP60 This is for all the dose equivivalent distributions scored in histograms and regions of the MARS OUT and MTUPLE files The previous set based on ICRP51 is kept for reference and also used in those rare cases where the modern info is absent IFTD The control variable O for the modern definition of the Effective dose and 1 for the old ICRP51 set Default 0 DPAC IDAMEFF Integer variable which specifies the defect production efficiency DPF summarized by Broed ers and Konobeev currently for 23 materials at temperature below 6 5K Active only when IND 17 T for DPA calculations IDAMEFF The control variable 0 for no correction DPE 1 and 1 for correction at low temperatures currently 0 1 lt DPE lt 1 Default 0 4 2 8 Physics Control ALMX BIAS EMST ICEM MCSD MUON NUFR PHOT RZMN ALMX ALMAXB 6 Maximal angles on a step due to magnetic field ALMAXB 6 First five numbers are real numbers specifying the maximal angles rad allowed on a step due to magnetic field for five energy intervals A Eg E Eo 0 001 0 001 0 01 0 01 0 3 0 3 0 99 gt 0 99 The sixth parameter specifies such an angle for unstable particles in the forced decay mode PP 1KDEC gt 0 001 useful to control forced decays of an unstable par ticle beam in long drifts in presence of magnetic field Some adjustments to the angles are done for all charged particles at
36. MUERE ra m EE Pu E is 13 Sketchofboundarylocalization 2 ern 14 z sandwichexample planvieW ee 195 z sandwichexample flux mada 16 r sandwichexample plan view 222r 17 r sandwichexample cross section VieW ee 18 r sandwich example with flux map 2 re 19 Thin Window example plan view 2 RI 22 GEOM INE exatmiple e m eaea a 4 RR a BRA he a de ia a UE deo Se 2 Sketch of a simple beam dump ooo oe a a 24 Diagram of FLUKA geometry as interpreted by MAR le 79 1 Introduction The MARS code system is a set of Monte Carlo programs which simulate the passage of particles through matter All manner of particle interactions for hadrons leptons photons and heavy ions are present In teraction and production cross section modeling has been developed to match data wherever such data is available over a wide range of energies Three dimensional hadronic and electromagnetic cascades are modeled as is the transport of particles including heavy ions through matter The simulated particles are tracked through a user described geometry The users geometry model can be very simple to very complex incorporating compound materials of any shape and arbitrary magnetic and electric fields MARS tabulates the particles which pass through various portions of the geometry and produces results on particle fluxes spectra energy deposition material activation DPA and many other quantities The resu
37. NORMCO FINEXT EINT FINT2D SGINTI ISOTR 13 4 Multiprocessing A parallel processing option has been developed and implemented into MARSIS 15 It is based on the Message Passing Interface MPI libraries Parallelization is job based i e the processes replicating the same geometry of the setup studied run independently with different initial seeds A unique master process also running event histories collects intermediate results from an arbitrary number of slaves and calculates the final results when a required total number of events has been processed Intermediate results are sent to the master on its request generated in accordance with a scheduling mechanism The algorithm was tested on Unix and Linux clusters and demonstrated good performance 13 5 External Packages Required 13 6 Interfaces to Other Programs 13 6 1 STRUCT 13 6 2 ANSYS 151 14 Additional Information 14 1 MARS Web Page and World Wide Support MARS is under active development with new versions released every year or so Registered users will be sent email announcing new releases with a list of the features which have been implemented Many examples with corresponding write ups are posted on the site A question and answer sections holds user questions with expert response 14 2 Benchmarking of the Simulation Outline the bench marking to data process Refer to Data Simulation comparisons in published references 14 3 Future Developments Outli
38. RN FR RA AC TH PA U NP PU AM CM BK CE ES FM The following elements used with their standard abbreviations are treated by MARS as being in gaseous phase with density at STP H HE N O E NE CL AR KR XE RN The same elements used with the following abbreviations are treated by MARS as being in liquid phase with the stated densities LH LHE LN LO LF LNE LCL LAR LKR LXE 0 0708 0 125 0 807 1 141 1 507 1 204 1 574 1 396 2 418 2 953 Carbon element C has a default density of 2 265 g cm Carbon can also be declared as graphite by using GRPH which has a default density of 1 7 g cm substantially better with such a replacement with no effect on the oveall results Of course it makes sense only if studying effects specifically in the gaseous regions is not the purpose of the run The calculated cross section tables as well as a summary of the composition and properties of all de clared materials is written to the output MARS OUT file If the user has any questions about the detailed properties of a built in material he can declare the material and run MARS for a single event and then ex amine the information in the MARS OUT file The default densities for most elements are those at standard room temperature and pressure The general chemical makeup of the built in compounds is listed in Table 4 along with the resulting effective A and Z note effective values are not used by MARS given just for orientation The built in default de
39. THEN S call glob2flat MADVEC MADDIR else call glob2flat MADVEC MADDIR endif call mad2mars XMAD YMAD ZMAD BLPOS 1 BLPOS 2 BLPOS 3 call mad2mars WXMAD WYMAD WZMAD BLW 1 BLW 2 BLW 3 if BLPOS 3 GE 931 0626d0 THEN iS aaa 1 d0 ENDIF C COMMENT THIS MODULE FOR REAL WORK IF FIRSTCALL THEN WRITE MARS2BML IND 13 is active but transformation WRITE to the beamline coordinate system is not defined WRITE See example in MARS2BML subroutine FIRSTCALL FALSE ENDIF DO IT 1 3 BLPOS IT POS IT BLW IT W IT END DO C RETURN END 5 19 2 Subroutine BML2MARS SUBROUTINE BML2MARS BML VEC BML DIR MARS VEC MARS DIR X BEAMLINE TO MARS TRANSFORMATION C CALLED IF IND 13 T C G Sa CL a E CREATED 2002 BY IT C LAST CHANGE 08 NOV 2002 BY NVM E cr O insite Mal aig e sU fere a era ineo Cut se eue O IMPLICIT NONE DOUBLE PRECISION BML VEC 3 BML DIR 3 MARS VEC 3 MARS DIR 3 98 INTEGER IT C C EXAMPLE OF REAL WORK id DOUBLE PRECISION CBUF 3 DBUF 3 X IF BML VEC 3 GE 1234 0989 THEN 2 call set current beamline 2 K ELSE call set current beamline 1 ENDIF CALL mars2mad BML VEC 1 BML VEC 2 BML VEC 3 amp
40. UST BE RAISED C IFLAG 2 Enew lt 0 INCLUDE cmasnsg inc DIMENSION VECT 7 VOUT 7 C DO L 1 7 C VOUT L VECT L C END DO RETURN END 5 9 Fictitious Scattering ALIGN SAGIT E ERS NIB AND NIM In some applications components of the considered system can be turned or shifted with respect to each other Say the arc of any circular accelerator is built of the magnets turned by a fixed angle MARS version 88 13 95 allows an elegant way to handle such systems The user describes the geometry as the straight along the z axis Then with the help of a routine ALIGN he she creates the angular or space kicks at the required boundaries in the directions opposite to the real ones One can easily see that the resulting coordinates and angles of any particle are identical to those in the real bent geometry It is convenient to use spare NIM parameters to control such a fictitious scattering at the required boundaries with NIBZNIM as that parameter in a previous region Of course any coordinate can be used to locate the needed boundary The following example shows use of the ALIGN routine for a single kick SUBROUTINE ALIGN VECT VOUT NIB NIM IFLAG IMPLICIT DOUBLE PREC
41. and protective measures Technical Report SSCL Preprint 556 SSC Laboratory 1994 J M Butler et al Reduction of tevatron and main ring induced backgrounds in the dO collision hall Technical Report FN 629 Fermilab 1995 IEEE IEEE Standard 754 1985 for Binary Floating Point Arithmetic 1985 G Marsaglia and A Zaman Toward a universal random number generator Technical Report FSU SCRI 87 Florida State University 1988 I S Baishev Technical Report IHEP 87 149 Serpukhov 1987 F Iselin The MAD program methodical accelerator design version 8 13 8 Technical Report SL 92 CERN 1992 D M et al MAD parsing and conversion code Technical Report TM 2115 Fermilab 2000 R Brun O Couet C Vandoni and P Zanarini Paw physics analysis workstation Technical Report Q121 CERN Program Library R Brun and D Lienart HBOOK User Guide CERN Program Library y250 edition 157 108 O E Krivosheev and N V Mokhov Oo geometry engine for monte carlo simulation in Proc of Radiation Protection and Shielding Topical Meeting No Falmouths MA April 21 25 pages 487 493 1996 109 110 158
42. as described in Section 4 2 4 Details on the development of MARS particle tracking methods can be found in references 28 88 89 3 4 Materials The user declares what materials are present in his simulation in the input file for example MATER INP whose name is defined in the input file MARS INP The syntax is described in Section 4 2 4 and utilizes a 32 character string as an identifier A maximum of 500 materials can be used within any simulation An index 1 500 is assigned to each declared material according to the order in which they are listed by the user in the MARS INP file and the user must use this index when assigning a specific material to a geometric zone There can be no more than one material within a single zone A material can be declared multiple times so that different step size or energy thresholds can be applied to the same material used in different zones an example of this is given in Section 4 3 3 There are two special materials within the MARS code The first one blackhole is not included in the total number of materials and not declared in the MARS INP file The program assigns a negative material index and a zone number 0 to blackholes which are either all material outside of the simulated volume zone number 0 or any region inside marked with zone number 1 2 3 Any particle entering a blackhole zone is immediately killed it will be dropped from the tracking list and it s parameters
43. below 50 keV E1 Ep 43 LE NEUTRON LOCAL ED deuteron in non LAQGSM El Ed 44 LE NEUTRON LOCAL ED vertex non fission MCNP El Eterm 45 LE NEUTRON LOCAL ED capture on Li or B in non LAQGS 46 LE NEUTRON LOCAL ED sub threshold El En 47 LE NEUTRON LOCAL ED SUB THRESHOLD AT IND 6 T 48 LE NEUTRON LOCAL ED fission 49 LE NEUTRON LOCAL ED vertex non fission BNAB 50 FLUENCE BY NEUTRINO 51 GAS CAPTURE HE 52 GAS CAPTURE LE 53 NEUTRINO PRODUCTION VERTEX IMPLICIT DOUBLE PRECISION A H O Z INTEGER I N REMEMBER HBOOK IS A SINGLE PRECISION ENGINE DON T FORGET CONVERSIONS OF THE FOLLOWING TYPE REAL EEH WWH XL YL WH EEH REAL E1 WWH REAL W CALL HFILL ID EEH 0 WWH CALL HF2 ID XL YL WH Origin tagging for hadrons muons neutrino heavy ions and electromagnetic showers EMS moved from TAGPR RETURN 92 5 13 C2 C3 ALAA 101 102 103 Subroutine WRTSUR Custom Output UBROU INE WRTSUR IUNIT NI JJ E W X Y Z2 DCX DCY DC2 TOFF gt R R o Z ne Zz C articl PLICIT DOUBLE ICLE AT THE fort 81 fort 90 RESERVED FOR SURFACE DETECTOR FILE NTAG parameter of tally2 inc can be used as a flag for a source le to propogate it through the code to WRTSUR RAYN RAYMU etc z Q COMMON BPRIMHI UDE tally2 inc SURFACE WRITING HISTOGRAM 81 90 WRITE F DETECTOR ING ETC Eri
44. boundary localization procedure The accuracy of the geometric boundary localization process is controlled by the user using the input deck as described in Sections 4 2 2Jand 4 2 4 The pilot and minimum step sizes can be defined separately for different materials using the material dependent cards Global pilot and minimum step sizes are otherwise applied Guidelines for setting the values of these step sizes to attain the desired accuracy are also discussed in Sections 4 2 2 and 4 2 4 and the example in Section 4 3 3 discusses in detail the correct application of the step size controls Another user control over the tracking is the particle threshold energy As particles pass through matter they lose energy The user can specify an energy below which particles will be dropped from the tracking the main advantage of this feature is to reduce the computing time spent tracking particles which will have little or no effect on a particular result The specification is made via the input deck Just as for boundary localization there are global and material dependent thresholds The global energy thresholds are applied 24 in all materials although there are several of them so that each class of particle types can have a separate threshold applied as described in Section 2 3 The material dependent thresholds are applied only where those materials are present and there can separate thresholds for each class of particle type in each material
45. called then the location becomes a hole in the geometry however because there is at least one container Standard zone it typically serves as a background to all other zones and errors in the non Standard and Extended geometry descriptions can show up as being assigned to the container Standard zone rather than as a black hole An interactive GUI interface is included within MARS which allows the user to view his geometry and check items such as zone boundaries the material content of zones and the zone index number assignments An overview of the visual interface is given in SectionB 7 further details on using the interface are given in Section 2 21 3 1 1 Geometric Zone Volumes The boundaries of zones describe a geometry model to MARS and give the program the information it needs to track particles and apply physics interactions within the model But the boundaries alone are not sufficient to calculate results In order to do that MARS also needs to have the volumes of all the defined zones As particles are generated and tracked the path length of each particle type within each zone is accumulated and stored the final path length divided by the zone volume results in the flux for each particle type through each zone The particle flux is then used in turn to calculate many of the results reported by the various output files A defined zone which has a zero volume will not only have no results calculated but also the zone
46. caution when examining output results For instantaneous temperature rise due to beam then No is assumed to be the number of particles in a single instantaneous pulse For all other results contact residual dose power den sity radiation damage DPA per year No is assumed to be an average beam intensity in particles per second Default 1012 UCTR ICTR 10 Integer variables for arbitrary control in user routines ICTR The array containing ten integer numbers negative positive or zero which can be used in user routines for arbitrary control Most useful in the following routines BEG1 FIELD LEAK VFAN TAGPR WRTSUR A COM MON block BLICTR ICTR 10 is inserted in these routines Default 10 x 0 4 2 3 Beam amp Energy Thresholds IPIB BEAM INIT ENRG IPIB 10 IBEAM IZPRJ IAPRJ Integer variables to specify the incident particle type the incident beam distribution and the charge and mass for incident heavy ions If the IBEAM value is non zero then the parameters of the pro file are defined using the BEAM card Use these variables for simple uniform beam distributions More complex primary beam distributions must be modeled via the user subroutine BEG1 I0 The incident particle type see Table 2 for the index values assigned to various particles Default 1 proton IBEAM The type of incident beam distribution given by one of the four following values Default 0 laterally and longitudinally infinitesima
47. cross section libraries 84 In this regime the code models all physics processes from 0 001 eV to 0 0145 GeV such as n y reactions creation of recoil protons heavier recoils thermal neutron capture on 6 Li and B corresponding effects in hydrogenous borated and lithium loaded materials 85 etc In some cases more precise modeling of low energy neutrons is necessary particularly when predicting residual dose rates and when predicting prompt dose rates in labyrinth type geometries Residual rates are sensitive to the materials present and prompt dose rates to the n y reactions which occur when slow neutrons are stopped and captured In these cases MARS can be used coupled with the full MCNP code in a combined MARS MCNP mode In this mode MARS generates the initial neutron but sends it to the full version of MCNP for tracking and interactions to the point where the neutron is captured or to it s cutoff 18 Table 1 Neutron energy group numbers NG and lower energy boundaries EG MeV in the group at E 14 5 MeV in the 28 group representation NG 1 2 3 4 5 6 7 EG 14 10 5 6 5 4 0 2 5 1 4 0 8 NG 8 9 10 11 12 13 14 EG 0 4 0 2 0 1 4 65E 2 2 15E 2 1 E 2 4 65E 3 NG 15 16 17 18 19 20 21 EG 2 15E 3 1 E 3 4 65E 4 2 15E 4 1 E 4 4 65E 5 2 15E 5 NG 22 23 24 25 26 27 28 EG 1 E 5 4 65E 6 2 15E 6 1 E 6 4 65E 7 2 15E 7 2 15E 9 energy At that point the particle information is handed back to MARS for compilation of tallies a
48. cross sections Data compilation and interpolation algorithm for oyy with phenomenological A dependence for 0 4 are as described in 60 11 Tp total TAG lad Wee E Cross section mb 3 Ekin MeV Figure 3 MARS cross sections in comparison with experimental data c 5 and ce for m p collisions tal cro To at eee aee 10 Momentum GeV c Figure 4 MARS cross sections in comparison with experimental data o for neutrons vs beam mo as a function of pion kinetic energy mentum 2 3 Hadron Production This section needs more detail enough that the casual reader gets a better idea of what the code does a short version of sections 2 and 3 from Conf 04 053 appropriately updated would work 2 3 1 Cascade exciton model code A version of the Cascade Exciton Model of nuclear reactions as realized in the code CEM2003 53 and containing also several recent refinements is implemented as default for 1 MeV E 5 GeV The 1994 International Code Comparison for Intermediate Energy Nuclear Data has shown that CEM95 adequately describes nuclear reactions at intermediate energies and has one of the best predictive powers for double differential cross sections of secondary particles as compared to other available models Besides that it adds to MARS reliable m capture description with a few modifications e g radiative capture
49. dF d lnE per cm 2 131 This table is similar to NEUTRON LEAKAGE SPECTRA PER CM 2 table but reformatted so that the columns of data can easily be cut and pasted into an external graphics or spreadsheet pro gram SPECIAL REGIONS NEUTRON SPECTRA PER CM 2 The special regions are user defined cylindrical volumes specified by the NOBL and RZOB cards in the MARS INP file There can be no more than three of these regions declared and there is a column printed for each filled with zeros if the region is not used Declaring a NOBL region triggers the production of HBOOK histograms of a variety of results for the zones within the region see Sec 10 1 for a definition of the histograms This table holds the same data used to fill the histograms although as in this case split into three quantities each main column for a region holds three sub columns labeled NEUTRONS N UNIT LET N MEV The data is given in energy bins as labeled by the left most column note the energy bins are in MeV The columns of data are arranged to be easily cut and pasted into an external graphics or spreadsheet program At the end of the table are three additional results for each special region summed or accumulated from the spectrum data The first result is NEUTRON FLUENCE N CM 2 the second result is the mean energy E GEV the third result is the dose equivalent NEUTRON DOSE EQIVAL mSv GRAPH L E NEUTRON SPECIAL REGION SPECTRA dF d 1nE 1 cm 2
50. defaults are satisfactory for a given model except the photon energy cutoff which the user would like to raise from the default 0 0002 GeV to 0 001 GeV That variable EMIGA is the 6 of 9 listed The user would enter ENRG 06 0 001 35 into the input deck This directive will change the default value of the 6 variable to 0 001 GeV If the user next wished to also change the default value on the 4 variable EMCHR the cuttoff on charged hadrons and muons then this card entry would become ENRG 4 0 03 6 0 001 A space must separate the two equality statements but that is all that is required Finally if the user decided to additionally change the default on the 5 variable EMNEU the cuttoff on neutrons then the card becomes ENRG 4 0 03 5 0 05 6 0 001 which is equivalent to ENRG 4 0 03 0 05 0 001 For the previous example all the variables were one dimensional arrays The example would appear the same if the receiving variable was a 3 dimensional variable only one has to think about the FORTRAN conventions in the order in which the elements of arrays are filled An example of cards which are assigned multiple variables with dimensions gt 1 is given in Section 4 3 The variables associated with a card can be integer real logical represented by T or F and in one case character In general all the variables assigned to a card are of the same type but there are a few cards of mixed integer and real variab
51. directs the reader to further details in other Sections The units in MARS are energy in GeV dimensions in cm angle in degrees and magnetic fields in T esla The reference system is a cartesian coordinate system with the z axis longitudinal and the positive direction is from left to right The z axis is usually the center of symmetry and as a rule the primary particles strike along this axis in the positive direction The positive direction of the x axis of the global system is up and the y axis is toward the viewer completing a right handed system 3 Describing a Geometry by Zones The geometry description or model is seen by MARS as a contiguous array of volumes called zones The user has complete control over the size shape content and location of these zones As particles are tracked through the model MARS queries specific subroutines to determine which zone the particle is in Each zone is uniquely numbered and the zone number corresponds to an array index used by many variables in the program For example there is an array indexed by zone number which tells MARS what material is present in each zone and the material in turn is used to define manrrey parameters which affect the physics interactions which can occur within that zone As particles are generated and tracked the path length of each particle type within each zone is accumulated and stored the final path length divided by the zone volume results in the flux for each
52. entry fields Y Z w X Z v HOY ES TN e The magnetic field could be interactively turned ON and OFF by user using the button Magnetic field is ON by default il hi t Magnetic field ON i e Switch from so called Natural to separately scaled view In Natural mode program tries to pre serve the same scale over horizontal and vertical axes The horizontal axis counts as primary one 141 therefore when button Natural is pressed vertical axis boundaries will be changed to accommodate changes in horizontal axis thus keeping the same overall scale When Natural is turned OFF you can set horizontal and vertical boundaries separately Natural view is OFF by default Natural scale OFF e Checking coordinates region number material index and magnetic field module just clicking left mouse button on field geometry map It keeps the position intact and updates Point info IDE ES Point Info NREG Zem Y cm Bd o Ah T 8 513 21 466 Close e Saving the drawing as well as ran external X grabber to create a picture as Encapsulated Postscript 110 Saving the image as Encapsulated Postscript could be done by pressing Print button User will get the dialog where he or she will be able to set EPS file name You also can start external image grabber Xv by default just pressing Grab button 142 Print GEO Field Ea Directory mil AS Piles or EE E uM ISSN Cancel
53. inclusive equivalent with a single represen particle classes tative particle exiting each vertex with the given weight the inclusive approach has real advantages for a simulation there are fewer particles to handle Over many events the results from the inclusive approach for the bulk quantities of interest such as particle flux energy deposition etc match data quite well A hadronic shower can be represented the same way in the inclusive approach with a single particle usually a pion occasionally something else exiting the vertex with an appropriate weight But over time simulation software developers found that more accurate results were obtained when a certain number of particle classes were included on every vertex For MARS a hadron nucleus vertex is modeled by the inclusive method as shown in Figure 2 Five particle classes are always represented the leading particle shower hadrons electromagnetic products evaporation products from the nucleus and the nucleon The precise particle properties for each of these classes particle types weights Xp pi etc are given by a variety of cross section and production models discussed in sub sections below Which models are used depends upon the incoming particle type and it s energy The interaction type and the circumstances for use are given for each model There are a couple of important statistical techniques when using the inclusive approach having to do with the wei
54. it were positioned in this very location as defined in ICRP103 Each row contains two values the result for that zone and the statistical error on that result STAR DENSITY NO CM 3 P P The table presents arranged by zone number the star density within each zone Each row holds three values the star density due to the charged hadrons primarily protons ms and Ks the total star density and the statistical error on the total star density The standard definition of a star is a hadron with kinetic energy greater than 0 03 GeV in MARS this is the default value for the star production threshold EPSTAM in the ENRG card If this threshold is changed then the results reported in this table will likewise change and will no longer correspond to the standard definition of a star DPA DISPLACEMENTS PER ATOM P P The table presents arranged by zone number the nuclear displacements per atom within each zone which can be used to assist in estimates of radiation damage to the material located in this zone Elastic and inelastic nuclear interactions as well as electromagnetic interactions contribute to DPA in this version of the code HYDROGEN GAS PRODUCTION 1 cm 3 P P The table presents arranged by zone number the density of hydrogen gas production within each zone which can be used to assist in estimates of radiation damage to the material located in this zone HELIUM GAS PRODUCTION 1 cm 3 P P The table presents arranged b
55. lattice descriptions with the ability to generate an output file which translates those descriptions for input to MARS and can also be used as input to other tracking and CAD applications The interface system MAD MARS Beam Line Builder MMBLB reads a MAD lattice file and puts the elements in the same order into MARS geometry Each element is assigned six functions which provide information about the element type name geometry materials field volume and initialization The user specifies the element type and an optional element name If no name is specified the element is considered to be a generic one A building algorithm first tries to match the type name pair and then substitute a generic element if needed Once an element is described it is registered with the system and its name is binded with the respective geometry materials volume and field descriptions For each region search during tracking MMBLB finds the corresponding type name pair and calls its appropriate functions MMBLB calculates a local rotation matrix R and a local translation vector Then a global rotation matrix M and a position P are calculated and stored for each element Mi Mi 1 X Ri Mo U Pi Miz1 xLi Pi1 where U is the unit matrix R U for all elements except RBEND and SBEND The newest version of MMBLB was substantially enhanced and is well described in the User s Guide 16 The set of supported element types includes now almost all the elemen
56. match the conceptual sketch Figure 23 shows a sketch of a simple beam dump made from steel and concrete blocks These rectagular shapes become non Standard zones The dump is surrounded by soil and the outer edge of the soil is modeled as a cylinder this can therefore be a Standard zone specified by cards in the input deck this cylinder is not shown in the sketch Y conc bip iod Sketch of a simple beam dump ZConc Steel block surrounded by concrete block Soil surrounding the concrete User encoded non Standard Zones Steel Zones 1 10 Concrete Zones 11 20 XSteel Surrounding soil is a Standard Zone VEU Ze Material l steel 2 concrete 3 soil Figure 23 A user s sketch of a simple beam dump with dimension variables and with preliminary non Standard zone assignments The following section of code is the array and variable declaration section from subroutine reg1 corre sponding to this example of a simple beam dump The user has decided that material index 1 is steel material index 2 is concrete and material index 3 is soil and described them in the MARS INP file Consequently the material card in the input deck is set to second card is just a comment for reference MATR MATER INP C MATR FE CONC SOIL The user has set the maximum number of non Standard zones to 20 The first 10 non Standard zones will be used for steel and the second 10 for concrete SUBROUTINE REG1 X Y Z N NIM IMPLICIT
57. must always be at least one Standard zone and all the declared Extended Geometry zones must be contained within this outermost Standard zone boundary In assigning zone numbers MARS begins with the Standard zones numbered 1 NFZP the maximum number of declared Standard zones Extended zones are next numbered starting from NFZP 1 There can be no more than 100 000 declared Extended zones MARS will assign zone numbers to Extended Geometry shapes in the order in which they appear in the GEOM INP file For an introduction to zone numbering see the discussion in Section B I First line of the GEOM INP file is a title consisting of no more than 80 characters All the subsequent lines are geometric information either shape data lines or transformation data lines A shape data line is used to declare and describe a single Extended Geometry shape A transformation line describes a trans formation matrix translation and rotation which can be applied to any Extended Geometry shape Each shape can be subdivided into a number of sub regions Blank lines can be inserted between data lines for file organizational purposes and will be skipped by the routines reading the file Comments are allowed at the end of any line by starting them with an exclamation sign The Extended Geometry shape data lines can be listed in any order for example they are not required to be listed from left to right in the coordinate system however there are two important poin
58. number will not appear in any of the output results lists So the user must be certain that zone volumes are provided to the program In the case of Standard zones MARS is able to calculate most of the volumes automatically since these zones have a simple cylin drical symmetry However a container Standard zone in which other types of zones are embedded will be broken i e it is no longer a cylinder but a cylinder minus the shapes of the other zones inside of it and in this case the volume for such a Standard zone will have to be provided to the program In the case of non Standard and Extended Geometry zones the user must always provide the volumes The vol ume data is provided to MARS via user subroutine VFAN which enters zone volumes into the appropriate arrays Calculating zone volumes by hand is an option but can be tedious for complex shapes MARS has a volume MC running mode where it throws coordinate positions to the geometry subroutines and probes the boundaries of zones as it does this it forms a volume measurement of the zones The resulting volume estimates are listed in the VOLMC NON output file The user then cuts and pastes the volume values into the VFAN subroutine Section 4 2 2 gives the MARS INP settings for running in volume MC mode Sectior T I T T describes the contents of the VOLMC NON file and Section 5 5 describes the VFAN routine and the process of obtaining zone volumes in more deta
59. of ZZAAA notation The first two digits give the atomic number while the last three ones give the atomic mass Thus 92238 describes uranium 238 5010 describes boron 10 If all of the last three digits are zero then the natural mixture of isotopes for that element is assumed FraCn a real number is the proportion of this isotope in the material being described The proportions can be given by either volume percentages or by weight fractions The first are positive values the second are negative values All of the proportions for a given material must be one or the other i e a single material data card cannot mix volume and weight fractions Cy are optional parameters which select certain conditions for the material for ex ample gas 1 would indicate the state of the material See the MCNP manual for details So for example the line m1 26000 0 8 6012 0 2 is the MCNP material card describing the first MARS material by volume with 80 of atoms being natural iron 26000 and 20 of atoms being carbon 12 isotope The following line is for the same material but instead using weight fractions m1 26000 0 95 6012 0 05 The atom or weight fractions entered within a material card can be unnormalized MCNP performs re normalization by default 107 In the MCNP mode any material used by the geometry must have an MCNP material card The MCNP material data cards do not need to be listed in the same order as the materials listed on the M
60. of non Standard zones by setting NCELMX Notice that the local IMUN array where materials are assigned to non Standard zones is copied to MARS array MATIND offset in that array s space by NFZPEX Array MATIND is what MARS uses to determine the material content of each zone not IMUN However it is easiest for the user to think of his own non Standard zone assignments as being numbered 1 M MAX and fill his own local version of the materials array since the absolute zone number which MARS uses can change if the user changes the number of Standard or Extended zones in his model from one execution of the program to another All that MARS requires is that the user s version of the materials array be transfered to the MATIND array with the correct offset at some point in the REG1 initialization process Before continuing with the zone initialization process description jump ahead to the geometry definition code within REG1 for the simple beam dump example The user makes a list of parameters to hold the dimension values of his model remember the basic length unit is centimeters and all variables double precession Parameter ZConc 400 0D0 Parameter ZSteel 150 0D0 Parameter ZSteel middle 75 0D0 Parameter XSteel 30 0D0 Parameter YSteel 35 0D0 Parameter XConc 100 0D0 Parameter YConc 120 0D0 The encoding of the simple beam dump is then M 0 AX Abs X AY Abs Y C C Return immediately if we ar
61. of the mapped array correspond to the i 1 50 major sections This variable is active only when IND 2 F Default 50 0 NAZM NF Integer variable which defines the number of azimuthal divisions of the MARS Standard geometry zones This card is valid only when IND 11 T NF The number of azimuthal bins 1 lt NF lt 60 Default 1 AZIM FIB 60 Real variables which give the angular size in degrees of each azimuthal division This card is valid only when IND 11 T and NF gt 2 FIB The angular sizes O lt F IB 1 lt 360 Default 60 0 0 IRFL IRFL 3 Integer variables which control the reflection of the geometry described for the positive x y z directions to the negative ones If IRFL 1 1 the geometry description at x gt 0 is reflected to the negative x Similar reflections are done independently for y and z directions at IRFL 2 21 and IRFL 3 1 respectively In the current version only z reflection for the MCNP geometry is allowed at IRFL 3 1 Histograms are not affected by reflections because these are independent of geometry IRFL The reflection flags Default 3 0 52 4 2 6 Importance Sampling IMPT IMPZ IMPR IMPT EIMPT NIMPTZ NIMPTR Real and integer variables which define the threshold energy for hadron importance sampling and the numbers of surfaces for that See Section 3 9 The surfaces and importances are defined in the accompanying IMPZ and IMPR data cards Put these surfaces at large distances from th
62. on any of the above buttons No further change on the GUI window size is allowed further on In order to change the window size the user must terminate the current work session and restart MARS15 in graphics mode The GUI panel has been compacted leaving some space for future developments Resizing of the GUI window is inhibited Loading the geometry first by clicking on the Draw gt button is now enforced by disabling both lt LoadHist gt and lt LoadT rack gt buttons that are grayed out prior to loading the geometry Either a histogram or the tracks can be loaded In order to load the tracks when a histogram is being displayed on the canvas the user must click on the relative lt ON gt toggle Consequently the toggle turns to lt OFF gt and the button lt LoadT rack gt is enabled for selection Similarly in order to load a histogram when the tracks are being displayed on the canvas the user must click on the relative lt ON gt toggle Consequently the toggle turns to lt OFF gt and the button lt Load H ist gt is enabled for selection A button lt Hist Norm gt and relative entry have been added to the GUI panel When a histogram is loaded the entry field shows the data normalization parameter AINT or 1 applied by MARS15 when operated in simulation mode The user has the possibility to renormalize on line a histogram displayed in GUI i e to vary the current histogram data normalization by typ
63. particle tracking in accelerators have also been improved fusion with the STRUCT code 50 for multi turn particle tracking in the accelerator lattice represented by an arbitrary combination of magnetic elements and transfer matricies allowing unified approach to beam loss and radiation effects studies at modern accelerators 93 88 94 95 96 97 3 11 Getting Started This section presents an overview of the code and outlines how to create and run an executable Details on the structure and content of the input deck are given in Section 4 Details on the usage of each of the user subroutines are found in Section 5 Details on the structure and content of the input and output histogram files are given in Section IO Descriptions of the various output files are given in Section 1 MARS is primarily supported to run on SunOS and Linux operating systems with secondary support SGI IRIX IBM AIX DEC ALPHA and HP UX The MARS code system consists of a few hundred FOR TRAN77 subroutines and a few CERN service C routines organized by functionality into several files The source code file structure is listed in Table 5 The computing efficiencies of many of the MARS software algorithms have been improved and optimized over time The code runs completely in the IEEE 754 dou ble precision model 98 except for the CERN HBOOK package MARS utilizes a machine independent universal random number generator 99 The user subroutines in file m151
64. particle type through each zone Particle flux tabulated by zone number is used in turn to calculate many other results from the program In short by controlling the size location and material specifications for the zones the user controls the level of detail in the results which MARS reports The user can also tweak parameters which control some of the interactions which MARS simulates MARS classifies geometry zones as one of three types Standard Extended and Non Standard Standard Geometry zones are those whose borders are defined by quantities entered in the MARS INP input deck Standard zones always have a cylindrical symmetry with borders defined only on the z r and axes the syntax is described in Section 4 2 5 Extended Geometry zones are those whose borders are defined by the contents of the GEOM INP input deck the syntax for this deck is described in Section Extended Geometry zones are similar to the geometry description used by the Geant Monte Carlo in that they are constructed from a set of contiguous or overlapping geometrical shapes such as boxes spheres and cones Non Standard Geometry zones are those described by the user s software encoded description of a geometry there is no restriction on the type of software while the MARS user subroutines are written in FORTRAN the user can write his own modules in other languages and have these called from the MARS subroutines There is no restriction on the shape of Non Standar
65. region N REG Both this point and the step fully belong to the region N REG with material index M Particle energy at the end of the step is 93 E2 The current history number is NJ STEP 0 for sub threshold particles E1 E2 for neutrals and in vacuum This particle JJ is not 9 10 or 11 or the EMS JJ is 9 10 or 11 was originated by parti cle with ID JORIG of energy EORIG and weight WORIG in the process KORIG at the point XORIG YORIG ZORIG in the region N RORIG with material index ZMORIG STEP gt 0 for tracking while ST EP 0 for local energy deposition AE El E2 SUBROUTINE TAGPR NREG IM JJ W E1 E2 X Y Z STEP Origin tagging for hadrons muons heavy ions and electromagnetic showers EMS Particle JJ of weight W and energy El makes a step STEP starting from point X Y Z in region NREG Both this point and the step fully belong to the region NREG with material index IM Particle energy at the end of the step is E2 The current history number is NI STEP 0 for sub threshold particles El E2 for neutrals and in vacuum This particle JJ is not 9 10 or 11 or the EMS JJ is 9 10 or 11 was originated by particle with ID IORIG of energy EORIG and weight WORIG in the process KORIG at the point XORIG YORIG ZORIG in the region NRORIG with material index IMORIG STEP gt 0 for tracking STEP 0 for local energy deposition Delta
66. sib AKSIO ksib omb 20 EMS induced by photons from low energy neutrons 21 muons vector mesons E SD G CREATED 11 AUG 2003 BY NVM o 28 APR 2006 BY NVM E LAST CHANGE 26 APR 2007 BY NVM iC RUE aes ae or xr ETT TE IMPLICIT DOUBLE PRECISION A H 0 Z INTEGER I N COMMON amp BPRTAG XORIG YORIG ZORIG WORIG EORIG IORIG KORIG NRORIG IMORIG amp HIST NI NSTOP NUPRI NHIPR C C Example C if nreg eq 9 then E write 1 100 NI NREG IM JJ W E1 E2 STEP C amp XORIG YORIG ZORIG WORIG EORIG IORIG KORIG NRORIG IMORIG C 100 format NI NREG IM JJ W E1 E2 STEP i7 15 213 4 1pell 4 C amp XORIG YORIG ZORIG WORIG EORIG IORIG KORIG NRORIG IMORIG C amp 5 1lpell 4 213 2i5 C end if RETURN END 95 5 15 Subroutine TAGGING Energy Deposition Tagging 5 16 Subroutine KILLPTCL Selective Particle Destruction 5 17 Block Data BLPROCESS Biasing Control CG E C CQ CY sO C2 162 263 HO 163 637 103 BLOCK DATA BLPROCESS IPRCEM K IPRCEM K IPRCEM 0 0 exclusive 1 inclusive with a probabili global control ty PRCI EM K Global bias control is currently done via BIAS card with parameters in COMMON BLBIAS PPIKD in process inc in process inc in process inc process inc INCLUDE cems 12 set 3 EMS global EC PMUPRMT
67. tables which hold data on low energy neutrons those with energy below A few single data values are given here the total neutron collisions per primary the total energy leaked due to this class of particles and the number of low energy neutron which exit the model volume TOTAL FLUENCE AT E 14 5 MEV N CM2 The table presents arranged by Standard zone number the low energy neutron flux in particles per cm Each data value is accompanied by it s statistical error ENERGY DEPOSITION AT E 14 5 MEV The table presents arranged by Standard zone number the energy deposited by low energy neutrons in units of GeV per gram No statistical errors are given NEUTRON LEAKAGE SPECTRA PER CM 2 This table presents the energy spectra for the low energy neutrons which have leaked out of the model The data are arranged in 3 main columns for the 3 labeled directions UPSTREAM DOWNSTREAM SIDE Each ofthese main columns holds in turn 3 sub columns labeled NEUTRONS for the overall spectrum N UNIT LET for and N MEV for The rows are bins in energy with the indicated values At the end of the table are three additional results integrating the results to a single value for each of the three leakage directions The first result is NEUTRON FLUENCE N CM 2 the second result is the mean energy E GEV the third result is the dose equivalent NEUTRON DOSE EQIVAL mSv due to the leaked neutrons GRAPH L E NEUTRON LEAKAGE SPECTRA
68. the maximums The left most column gives the mean z coordinate in each bin the top two rows give the lower and upper r range for each of those bins The data is identical to that in the table described above but re binned MUON FLUENCE MUON CM 2 AT E 0 00020 GEV The table presents arranged by Standard zone number the muon flux in each Zone for muons above the stated energy cut off Each main row holds four sub rows the first tabulating only u the second tabulating only p the third tabulating all muons and the fourth being the statistical error on the total muon flux The table presents arranged by Standard zone number No statistical errors are given The table presents arranged by Standard zone number No statistical errors are given The table presents arranged by Standard zone number No statistical errors are given The table presents arranged by Standard zone number No statistical errors are given The table presents arranged by Standard zone number No statistical errors are given The table presents arranged by Standard zone number No statistical errors are given The table presents arranged by Standard zone number No statistical errors are given The table presents arranged by Standard zone number No statistical errors are given The table presents arranged by Standard zone number No statistical errors are given 133 The table presents arranged by Standard zone number N
69. the shapes are always analyzed in the order they appear in the GEOM INP file Shapes defined first have a higher priority than shapes defined in subsequent lines MARS enters the Extended Geometry module with the location of some particle x y z at the first shape encountered which contains that x y z the code exits the geometry description handing MARS the zone number corresponding to that shape At the next entry with a new location the geometry description code begins again at the top of the GEOM INP file The user needs to think about descriptions where shapes overlap and order them appropriately so as to obtain the final desired zone shapes and numbers MARS must be provided with the volumes of all Extended Geometry zones In the special case of no overlapping shapes and when optimization is turned on then the Extended Geometry module will calculate the shape volumes and hand the results to MARS In all other cases the user has to provide the volumes of shapes either by hand or by running MARS in volume MC mode described in Sections 3 and 4 2 2 4 4 1 Example of Extended Geometry Given here is an example of an Extended Geometry description First is a simple MARS INP file used in conjunction with the example Following is a GEOM INP containing a sampling of shapes The GUI picture corresponding to this file is shown in Fig 72 nded geometry test 10 22 12 3 T H ZK Dod EX 0 5 8 5 0 001 z
70. the threshold EM set in the ENRG card the default threshold value is 0 0145 GeV The statistical errors are also given 126 HEAVY ION FLUENCE AT E gt ETH HADRONS CM2 The table presents arranged by zone number the flux of heavy ions in each zone for ions with a kinetic energy greater than the value of the threshold EMCHR set in the ENRG card default value 0 0002 GeV OR with a kinetic energy greater than EM if EM has been set to greater than it s 0 0145 GeV default value The statistical errors are also given ELECTRON FLUENCE AT E gt ETE ELECTRONS CM2 The table presents arranged by zone number the flux of electrons and positrons in each zone for those particles with a kinetic energy greater than the value of the threshold EMIEL set in the ENRG card default value 0 0002 GeV OR with a kinetic energy greater than EM if EM has been set to greater than it s 0 0145 GeV default value The statistical errors are also given GAMMA FLUENCE AT E gt ETG GAMMAS CM2 The table presents arranged by zone number the flux of gammas in each zone for those particles with a kinetic energy greater than the value of the threshold EMIGA set in the ENRG card default value 0 0002 GeV OR with a kinetic energy greater than EM if EM has been set to greater than it s 0 0145 GeV default value The statistical errors are also given MUON FLUENCE AT E gt ETM MUONS CM2 The table presents arranged by zone number the flux of muons in each zone for tho
71. usually a short title to describe the problem and perhaps the date such as Cu target in Area B with design 1 a shielding March 15 2004 This line of text is read into character variable MTEXT in the code and is written to the MARS OUT output file The rest of the MARS INP file consists of data cards The CERN FFREAD package is used to read these data cards in the MARS routine BEGINN The cards are format free in the sense that they can appear in any order and the qualifiers within each card can be listed in any order However there are structural conventions which must be followed for the cards to function properly The structure of all these cards is the same KEYWa 1 a 2 Ny b 1 b 2 Na c 4 c 5 KEYW is a keyword assigned to a group of variables a 1 b 3 and c k The variables are mapped onto a one dimensional array A 1 3 k Within array A Np is the location where element b 1 is located Nes is where element c 4 is located The numerical values listed after KEYW will be loaded sequentially into array A until a N is encountered Once detected the filling of array A will jump to the location given by N and continue filling sequentially from there For example there is a data card with keyword ENRG which controls the primary energy and energy threshold cutoffs below which particles will not be tracked ENRG is assigned to nine variables All of these thresholds have default values For this example all of the
72. vector mesons indexed by IM the order numbers the materials are listed in the MATER INP file BIAN RLANN 500 Real variables specifying the parameters of the inclusive forced e e put annihillation events applied only to specific materials Any material which does not have a corresponding entry here will have the global parameter applied as the default with the value given by the PMUANN variable in the BIAS data card Values of the RLANN array specify ete utu event modelling It is forced with the appropriate statistical weight at RLANN i 1 forced with the Russian roulette at 0 001 lt RLANN i lt 1 modelled exclusively at RLANN i 1 or suppressed at RLANN i 0 It is automatically set to 1 for KEMIN i 1 Default 0 03 RLANN The values for the control of e e annihillation events indexed by IM the order numbers the materials are listed in the MATER INP file BIGA RLPHN 500 Real variables specifying the parameters of the inclusive forced photo nuclear events applied only to specific materials Any material which does not have a corresponding entry here will have the global parameter applied as the default with the value given by the PPHNUC variable in the BIAS data card Values of the RLPHN array specify photo nuclear event modelling It is forced with the appropriate statistical weight at RLPHN 1 1 forced with the Russian roulette at 0 001 X RLPHN i lt 1 modelled exclusively
73. will not be accumulated to any built in results or histograms The negative zone number is also however a trigger to calling the user subroutine LEAK which can then be used for special scoring or for forming a source term For example a blackhole zone is created in a particular quadrant of a geometry so that every particle entering it can be recorded onto a special set of histograms defined by the user Or past a certain Z plane a blackhole zone is defined and any hadron crossing this plane gets recorded to an output file which is then in turn used as the primary beam input for a separate run of MARS which contains the geometry downstream of the one used in the first run breaking the model up into two or more such stages can save CPU time by dropping uninteresting particles at strategic points Details and examples are given in Section 5 TI which describes the LEAK subroutine The easiest way to convert any material in MARS INP to a blackhole is to define its density on the MTDN card to be gt 107 The second special material is vacuum MARS uses material index IM 0 for the global vacuum where global means that the global values for tracking step lengths and energy thresholds are applied If the user wishes to control these values for areas of vacuum then the material name VAC can be used in the MATR input card list This material gets assigned an index IM 0 just as for other materials and then the user can assign different step para
74. 076 GeV for charged hadrons muons and heavy ions and 1074 GeV default or 1076 GeV EGS5 mode for electrons and photons Note that for accurate calculation of energy deposition the user must keep all the threshold energies below 0 0145 GeV They can be arbitrary high if one studies fluxes spectra yields star densities etc but the code issues a warning on screen and in most cases disregards particles falling below a threshold energy if it is greater than 0 0145 GeV EO The incident particle kinetic energy kinetic energy per nucleon for incident heavy ions It must be gt 1071 GeV for neutrons 107 GeV for charged hadrons muons and heavy ions and 1074 GeV currently for electrons and photons Default 100 0 GeV EM The hadron threshold energy This parameter induces different behaviours for settings above or below the default Default 0 0145 GeV For values less than the default the threshold affects only flux and spectra tabulation and not energy deposition For example 7 s decay and deposit their energy as y s at their point of generation and this process will be modeled even for n s below the EM setting For values greater than the default however the threshold value becomes global and is applied to all particles and not just hadrons In this case energy deposition will be affected and all flux results biased but the CPU time will have decreased significantly This feature is useful in models which study shield
75. 2 con tinuous dE dx after Global cutoff energies Charged particles 0 1 MeV the larger of 3 MeV and the user defined value Photons 0 1 MeV the larger of 1 MeV and the user defined value Value for boundary localization variable STE User defined larger of 0 3 cm and user EM see SMIN card typically 0 01cm E a o 0 0 CS 1 0 ELEMS parameter for EMS control LEMSGL parameter for EMS control Omoa 0 LUG parameter for EMS control Optional o SSCS independent and they cannot be used concurrently Details on using the GUI visualization in terface are in Section and details on using the event generator in stand alone mode are in Section IVIS When IVIS 0 MARS will run in it s normal simulation mode If IVIS 1 then the MARS GUI interface is activated No events will be generated and the GUI X window will pop up when the executable is run The size of the GUI window is defined interactively in an dialog menu Default 0 IEVT If TEVT gt 1 then regardless of the value of IVIS MARS will run in it s stand alone event generator mode The primary particle energy and type are spec ified using the ENRG and IPIB cards and these interact on nucleus type IEVT IM where IM is the index of the selected material as listed in the MATER INP file The generator is run for NSTOP events as given in the NEVT card Default 0 IVOL If IVOL 1 then regardless of the value of IVIS or of I
76. 2 when the primary beam particle is photon electron or positron 10 9 10 or 11 on the IPIB card otherwise it is 0 005 at E gt 20 GeV or 0 at E lt 20 GeV PMUANN Real number specifying the parameters of the inclusive forced ete Fu annihillation events It is forced with the appropriate statistical weight at PMUANN 1 forced with the Russian roulette at 0 001 lt PMUANN lt 1 modelled exclusively at PMUANN 1 or suppressed at PMUANN 0 It is automatically set to 1 for KEMINCL 1 Default 0 03 PPHNUC Realnumber specifying the parameters of the inclusive forced photo nuclear events It is forced with the appropriate statistical weight at PPHNUC 1 forced with the Russian roulette at 0 001 lt PPHNUC lt 1 modelled exclu sively at PPHNUC 1 or suppressed at PPHNUC 0 It is automatically set to 1 for KEMINCL 1 Default 0 02 PELNUC Real number specifying the parameters of the inclusive forced electro nuclear events It is forced with the appropriate statistical weight at 58 PELNUC 1 forced with the Russian roulette at 0 001 lt PELNUC lt 1 modelled exclusively at PELNUC 1 or suppressed at PELNUC 0 It is automatically set to 1 for KEMINCL 1 Default 0 003 when the primary beam particle is electron or positron 10 10 or 11 on the IPIB card oth erwise it is 0 003 at E lt 300 GeV or 0 at E gt 300 GeV PPBAR Real number specifying the the parameters of the inclusive fo
77. 2 Nb35n SC coil SCC 8 500 0 24Nb3Sn 0 70CuSn 0 06T a GFRP 5 682 0 33STST 0 21Cu 0 1SCC 0 2He 0 16610 BITR 8 146 Magnet bitter coil 0 9C u 0 1 water HOLW 5 50 Hollow conductor 0 19water 0 25M gO 0 56C u 9 void LMT 2 85 Dolomite with 15 water by volume GTIL 2 90 Glacial till with 30 water by volume SHTC 2 24 Shotcrete NYLN 1 13 Nylon Type 6 NH CH3 5CO H C NO NDFB 8 00 NdFeB magnet 0 06B 0 82Fe 0 12Nd LIH 0 82 LiH MRBL 2 70 Marble CaCO3 S316 7 92 Stainless Steel 316 S347 7 92 Stainless Steel 347 STCA 7 82 Carbon Steel continued on next page 27 Table 4 table continued Abbr p g cm Compound Name Formula CAST 7 31 Cast Iron NBS2 7 00 Nb35n SC cable ISOB 0 002493 Isobutane C4 Hio gas OILM 0 769 Mineral Oil ACRL 1 1388 Acrylic SCI 0 7903 Scintillator SCIG 1 3753 Gadalinium Loaded Scintillator DEUT 0 1624 Deuterium liquid TRIT 0 0709 Tritium gas D20 1 0177 Heavy Water BEO 3 01 Beryllia Ceramic CSI 4 51 CsI Scintillator SMCO 82 SmCos magnet FERR 5 0 STO x 6Fe203 Ferrite 28 3 5 Tabulation amp Results Results are accumulated or tallied zone by zone in the modeled geometry The zones can be volumes defined by the user s encoded geometry or volumes and surfaces where histograms have been defined A description of standard mars output information and how to use the results is given in Section 1 1 1 2 Geometry and phase space tagging options used intensively in stu
78. 26 27 28 T K K XU ROL E Xt 31 32 33 34 35 36 37 38 m 2 y i XP OP g Heavy ions with A gt 4 have the following indexes ID 1000 x Z1 Al Z1 Uy ae e e as gt o 3 3 Tracking The methods used to simulate the passage of particles through matter are a large part of any physics Monte Carlo system and MARS is no exception The path any particle takes through matter has both discrete and continuous components An example of a discrete process is nuclear collisions an example of a continuous processes is the trajectory of a particle through a magnetic field In the MARS simulation a particle s trajectory is approximated by a series of connected line segments The possibility of a discrete interaction occurring or the effect of a magnetic field is evaluated at the ends of a segment the length of each segment and the magnitude of the change in direction from segment to segment are what control the overall accuracy of the tracking simulation Therefore the first thing MARS does when tracking a particle is determine the size of the next line segment There are four main parts to this determination First MARS calculates the mean distance to the next discrete process Dgi c where the set of these discrete processes consists of nuclear inelastic and elastic interactions particle decay and energy loss due to knock on electrons This distance depends upon the particle type and energy and on the material the particle is passing thro
79. 4 are the collection of routines which can be customized for a particular simulation While these routines are FORTRAN the user can of course write his routines in other languages and have them called from the appropriate locations within the m1514 f routines Input decks are also made available to the user for customization the input decks consist of format free plain text data cards which are read by the CERN FFREAD package The output of MARS consists of several files a few of which are always created and others which are created only when requested by the user via the input decks many are text based tables some are HBOOK files and some are a specialized format for use as input in multi step jobs The code is installed at many accelerator laboratories and universities The code must be installed by the author on request and is not available for self installation via anonymous ftp For the latest information a list of installation locations code status platform availability comments and other related questions visit the official MARS Web site http www ap fnal gov MARS or contact the author at mokhov fnal gov In general the MARS code system is installed into a directory structure as shown below dat linux sun GEOM INP GNUmakefile MARS INP XYZHIS INP MATER INP m1514 f marsmain f xsdir The user has access to the source code only of the user subroutines in file m1514 f all other source code is built into librari
80. 700 7 00000 0 01746 15 99900 8 00000 0 00552 39 94800 18 00000 0 00030 1 00794 1 00000 0 00002 7 CONC c Identical to material 44 8 Quartz QUAR 2 64 2 15 9994 8 0 5325651 28 0855 14 0 4674349 C NREMA 8 in this example STOP 5 Borated poly BCH2 implicit rho 0 95 5 1 00794 1 0 116 10 5 0 00945 LL 5 0 04055 12 0110 6 0 612 15 9994 8 0 222 The NREMA value defines to the program the number of active array elements in the variables assigned to the MTCH MTNE MTEM MTSM MTSH MTQG MTEG LEMS BIDC BIPR BIBH BIGV BIAN BIGA BIEA BIAP data cards The special material blackhole is not included in the total number Material blackhole is tagged with a negative IM material index value use of this material in conjunc tion with user subroutine LEAK is described in Section 5 11 The global vacuum tagged by material index IM 0 is also not included in the total number of materials The global vacuum has global step sizes and global energy thresholds applied If the user wishes to control these parameters in certain vacuum regions then the built in material VAC should be declared in the MATER INP file and then the material dependent cards can be utilized Each of the materials has an index 1 lt IM lt NREMA following the number order assigned in MATER INP The material dependent energy thresholds and step lengths in the MTCH MTNE MTEM MTSM MTSH data cards use the same IM index Reminder for
81. A n and IND 17 T IND 17 F The DPA algorithms are not activated and DPA distributions and histograms are not calculated IND 18 T Not used currently IND 18 F Not used currently IND 19 T Enables the ROOT system geometry and visualization mode IND 19 F The ROOT system geometry and visualization mode is not activated 4 022 Run Control CTRL RZVL NEVT SEED SMIN VARS UCTR CTRL IVIS IEVT IVOL IHIS IDTR Integer variables which control running modes the normal Monte Carlo session GUI visualiza tion mode stand alone event generator mode and volume calculation mode Each of these is 38 Table 6 Values of parameters set by using the IND 15 switch default setting IND 15 T setting Charged hadron multiple Coulomb scattering Always on On for 1 3 generations of B NNNM Charged hadron nuclear elastic scattering at Always on On for 1 3 generations of E AAA Knock on electron production by hadrons Always on On for 1 3 generations with modeling of induced electromagnetic of cascade tree continuous showers dE dx after Knock on electron production by muons with Always on On for muons with E E0 gt modeling tinue ceeromugnicshonen D2conimiec d d afer L Direct e e pair production by muons with Always on On for muons with E gt 5 modeling of induced electromagnetic showers GeV and E E0 gt 0
82. ATR card The index IM must simply match between the two Vacuum regions are identified in MARS by either the material index M 0 or by a VAC entry in the MATR card If the geometry contains vacuum in the region of interest to MCNP then VAC should be listed on the MATR card The corresponding MCNP material card must comply with the syntax but the data values entered will be ignored and at the preprocessing stage MCNP will be given vacuum for that material The following is the Z sandwich Standard zone geometry example from Section and shown in Figure A with MCNP material data cards added which correspond to the materials declared on the MATR card ARS15 Example Z sandwich geometry with MCNP material cards NDX 2 T 5 T 6 T EVT 1000 NRG 100 0 05 0 05 PIB 33 EAM 5 0 5 0 0 1 0 1 IN 0 2 5 ATR MATER INP MATR FE AIR CONC LNG 3 SEC 50 150 350 1252 4 4 2501 2 1 3 LTR 1 SEC 100 51 4 TOP CNP START m1 6000 0 001 14000 0 001 25055 0 004 26000 0 982 28000 0 010 29000 0 002 cond 1 m2 7014 0 78443 8016 0 21076 18000 4 671E 3 6000 1 39E 4 gas 1 m3 1001 0 006 6000 0 030 8016 0 500 11023 0 010 13027 0 030 amp 14000 0 200 19000 0 010 20000 0 200 26000 0 014 MCNP END 0 UHdtkBzuHu XNUN V ZNZO The file xsdi r which is installed with the MCNP package contains the library of material data How ever it can contain several references to different evaluate
83. D 400 IHTYP 2 5 SURFACE ENERGY SPECTRA 1 CM2 DEL 401 ID 500 IHTYP 6 SURFACE TIME SPECTRA 1 501 ID 600 116 Table 10 Default histogram ID at NOB 1 Particle Vertex Fluence Energy Dep Spectrum n 1 101 301 h 2 102 302 w o p p 203 303 Total stars 3 y 104 304 e 105 305 Total EM 6 106 206 u fromEMS 307 u total 8 108 208 308 Total ED 210 GeV g Total ED 211 GeV cm PARTICLE INTERACTION CLASS ICL 1 HADRON ICL 2 ELECTROMAGNETIC ICL 3 MUON CHARGE CONTROL NSG 0 NEUTRONS PHOTONS NSG 1 CHARGED PARTICLES NSG 2 TOTAL VOLUMETRIC HISTOGRAM ID NUI NSG 3 ICL 1 100 IHTYP 1 1000 NRE 1 10 2 Built in Surface Histograms These histograms are filled for the plane and cylindrical surface detectors for the NSURF surfaces defined in the MARS INP file and initialized by presence of non zero NSUR and RZTS cards there There is also a possibility to write down parameters of particles crossing these surfaces into the files defined on the RZTS cards with formats and various filters of the WRTSUR routine SURFACE HISTOGRAM ID NUI NSG 3 ICL 1 100 IHTYP 1 1000 NSUR 1 NUI 1 DEFAULT PARTICLE SPECTRA HISTOGRAMMING IN 80 BINS 75 LOG 5 LIN NEUTRONS 28 1 E 11 0 0145 52 0 0145 E0 GEV OTHERS 80 5 E 4 E0 GEV NHSPE 0 dN dE DIVIDED BY DEL DELTA E IN 1 CM2 GEV E dN dE DIVIDED BY DEL DELTA LOG10 E FOR NEUTRONS IF IND 14 T IN 1 CM2
84. D 5 T applies Default 0 0 RMAX 0 0 ZMAX RMINTR RMAXTR ZMINTR ZMAXTR The cylindrical region where particles are recorded Default 0 0 RMAX 0 0 ZMAX 4 2 9 Termination STOP STOP no parameters Terminates the normal MARS data card list Any cards given after this are meaningless unless one runs in a mode which uses an imported geometry description and which places the appropriate data lines after the STOP card See Section for a summary of imported geometries which can be used 4 3 Examples Using MARS INP Parameters The following examples use only the MARS INP input deck to fully describe the modeled geometry The user subroutines are not utilized and left as dummies In truth most problems of interest will involve more complex geometry descriptions however these examples serve to outline the basics of the input deck More complex examples which utilize the user subroutines in conjunction with parameters in the input deck are given in Section 5 20 4 3 1 Z Sandwich Geometry z sandwich geometry is one where the same material extends outward for all values of r The material changes only along z boundaries r sandwich geometry is one where the same material extends along the z axis and the material changes only at concentric r boundaries The user must choose either one or the other to represent the Standard zones in his model Figures I4 and I5 show a simple z sandwich Standard geometry The pictures are prod
85. DATA NBMA 6 DATA NBU 115 116 117 921 1050 4380 294 0 END 5 19 MAD MARS Interface User Routines Routines used to assist the Mars Mad beamline builder 5 19 1 Subroutine MARS2BML SUBROUTINE MARS2BML POS W BLPOS BLW o Sia ceive C MARS TO BEAMLINE TRANSFORMATION E CALLED IF IND 13 T C G A us c E CREATED 2002 BY IT e LAST CHANGE 22 APR 2003 BY NVM E Go Sut dtes sepe vus ee BAe d e SOS HEUS s a ES ee eue er ee e ae e IMPLICIT NONE DOUBLE PRECISION POS 3 W 3 BLPOS 3 BLW 3 LOGICAL FIRSTCALL DATA FIRSTCALL TRUE SAVE FIRSTCALL INTEGER IT C EXAMPLE OF REAL WORK m INCLUDE beamOffset inc DOUBLE PRECISION MADVEC 3 DOUBLE PRECISION XMAD YMAD ZMAD EQUIVALENCE XMAD MADVEC 1 YMAD MADVEC 2 ZMAD MADVEC 3 x DOUBLE PRECISION aaa id DOUBLE PRECISION MADDIR 3 DOUBLE PRECISION WXMAD WYMAD WZMAD A EQUIVALENCE WXMAD MADDIR 1 WYMAD MADDIR 2 WZMAD MADDIR 3 call mars2mad POS 1 POS 2 POS 3 XMAD YMAD ZMAD 97 call mars2mad W 1 W 2 W 3 WXMAD WYMAD WZMAD oe if POS 3 GT NuMI_2_Z0 then call set current beamline 2 else i call set current beamline 1 endif M if MADVEC 3 GE 11894 92D0 AND MADVEC 3 LE 11894 94D0
86. DOUBLE PRECISION A H O Z INTEGER I N INCLUDE blregl inc 79 INCLUDE tallyl inc C SAVE NENTER DATA NENTER 0 C C Put actual max local non standard zone number here PARAMETER MN MAX 20 PARAMETER MN MAX1 MN MAX 1 Don t touch C CHARACTER 8 VNAME VNAMEBUE DATA VNAMEBUF ff C DIMENSION IMUN 1 M _MAX1 local array for material indicies DATA INCREM 1 DATA IMUN Ly Li ly Lj ds dd dy d gt 0 The local array IMUN is declared and sized to M MAX 1 The contents of IMUN are the materials assigned to each of the M non Standard zones with the value being the index of the material given by it s order in the input deck list In other words IMUN M is the material index for the M th gone where M 1 MMAX a local zone number The actual zone number in the MARS program array space depends on how many Standard and Extended Geometry zones have also been declared The following section of subroutine REG1 initialization code demonstrates this IF NENTER EQ 0 THEN CALL REG3 NCELMX NFZPEX M MAX NENTER 1 IF M MAX EQ 0 INCREM 1 IF M MAX GT 0 THEN INUG 1 WRITE There are non standard zones M_MAX M MAX DO L 1 M_MAX INCREM ATIND NFZPEX L IMUN L VOLNM N
87. EVT MARS will run in volume calculation mode It will generate coordinates within the values set by the RZVL card and probe the boundaries of the zones defined within that space tallying the volumes of those zones The results go into an out put file VOLMC NON in the format ready for inclusion into the user routine VF AN Statistical errors for the calculated volumes are also included to see if a number of events NVTRIAL is sufficient to get a good estimate of the zone 39 IHIS IDTR volumes This mode is useful to obtain the volumes of oddly shaped objects As discussed in Sections 4 2 5 and 5 4 MARs must know the volumes of all zones to be able to calculate results such as particle flux Default 0 Currently not used If IDTR 1 then the DETRA code is called to solve decay and trans mutation equations for all nuclides generated in the materials specified by the NCLD and IMNC cards After such a MARS run is done the corresponding out put files are processed by running the MARS executable again with IDTR 2 Default 0 RZVL R1 R2 Z1 Z2 NVTRIAL IVOLBML Variables which define a cylinder containing zones non standard MCNP extended or overlaped whose volumes a user wants to have calculated By default this cylinder is the mother Standard zone but in general one should define a smaller cylinder around specific regions to get better statistics If the overall geometry is large and contains many smaller non standard zone objects at
88. FZPEX L VNAMEBUF END DO VTEST 1 CALL VFAN NVTEST V ELSE INUG 0 WRITE There are no non standard zones in this run RETURN END IF END IF The non Standard zone initialization process is one of the few places where the user directly sets variables held in a MARS program common block Variable NCELMX and others are passed between routine REGI and the rest of MARS viablregl inc which contains various MARS parameters and common blocks The line NCELMX NFZPEX M MAX is how MARS is informed of the number of declared non Standard zones The total number of all zones Standard Extended and non Standard is held in variable NCELMX All of the arrays which hold accumulated MARS results are one dimensional and indexed by NCELMX The one dimensional arrays are logically divided into three blocks holding first the results for Standard zones then Extended then non Standard The boundaries of these three blocks are defined by additional variables which are the total numbers of zones of each type The total number of Standard zones is held in variable NFZP the total number of Extended zones is in NEXG2 the total of Standard and Extended zones together is given by variable NFZPEX MARS calculates NFZP NEXG2 and NFZPEX during its startup initialization 80 based upon the declarations made in the MARS INP and GEOM INP input decks On the first call to routine REG the user declares the total number of all zones and the number
89. IM G EO ME TRICAL x EVISION Q2 Q OQ UG 640 GAO 41 400 0 0 IF M 5 IF 00 R SQRT X X Y Y Ry BT 10 R LT 150 STEEL SH IF Z LT 490 E IE 28 FEB 1995 RETURN THI THI LDING zZ m m z N M 1 TUNNEL IF SE R GT 30 N M 2 ETE SH ELL SUBREGION NUMBER OUT OF TH SYSTE O lt NI 5 5 Subroutine VFAN Specifying Zone Volumes The code calculates volumes in arbitrary overlapped regions in a short Monte Carlo session once one puts CTRL 3 1 in the MARS INP file As described in Section 4 these regions are contained in a cylinder defined by the the RZVL card The results go into an output file VOLMC NON in the format ready for inclusion into the user routine VFAN Statistical errors for the calculated volumes are also included to see if a number of events NVTRIAL in this session is enough Here is an example of a VOLMC NON to be included in VFAN VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME 1 0 8712684D 02 8 0 8915421D 02 gj 0 8840023D 02 10 0 8766300D 02 11 0 8761274D 02 l2yo 0 8754572D 02 1 3 0 8628908D 02 14 0 8806513D 02 85 1 39 1 37 1 38 1 38 1 38 1 38 1 39 L 38 0 JO OP WN RA VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VO
90. ISION A H O Z INTEGER I N C FICTITIOUS SCATTERING C DISCRETE AT BOUNDARIES BETWEEN REGIONS WITH SPECIAL NUMBERS NIB AND NIM C NIB PRIOR CROSSING NIM AFTER CROSSING C VECT VOUT X Y Z DCX DCY DCZ P C VECT 1 VECT 6 CAN BE RE DEFINED TO VOUT 1 VOUT 6 C NORMALLY AT IND 4 T C IF SO VOUT 1 VOUT 6 MUST BE FILLED AND IFLAG 1 MUST BE RAISED DIMENSION VECT 7 VOUT 7 C DO L 1 6 C VOUT L VECT L C END DO RETURN END SUBROUTINE SAGIT CHARGE STEP VECT VOUT NREG IFLAG IMPLICIT DOUBLE PRECISION A H O Z INTEGER I N C FICTITIOUS SCATTERING C ON STEP IN REGION NUMBER NREG C VECT VOUT X Y Z DCX DCY DCZ P C VECT 1 VECT 6 CAN BE RE DEFINED TO VOUT 1 VOUT 6 C NORMALLY AT IND 4 T C IF SO VOUT 1 VOUT 6 MUST BE FILLED AND IFLAG 1 MUST BE RAISED DIMENSION VECT 7 VOUT 7 C DO L 1 6 C VOUT L VECT L C END DO RETURN END The same method is used in MARS to handle objects with saggita i e continuously bent Fictitious scattering defined in a user subroutine SAGIT as an anti kick at every step along charged and neutral particle trajectories simplifies the geometry description and makes a precise correspondence to the real bent objects 5 10 Edge Scattering EDGEUS If the edge scattering problem is considered with IND 9 T and the geometry includes non standard insertions defined with REG and REG2 the user should supply a subroutine EDGEUS X Y Z DX DY DZ U V It finds the distanc
91. L VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL VOL In a standard geometry sector the volumes of the regions needed for example to compute energy deposition density in GeV g are calculated at the final stage in the SERVN subroutine The array of volumes VV of the non standard regions M should be provided by the user in a subroutine VFAN N V The same subroutine can be used in specific activity and residual dose rate calculations at IND 13 T The VFAN E E E E E E E E E E E E E E E E routine can look as 4 4 4 4 4 4 4 4 4 4591919 4 4 4 4 4 4 4 4 4 QvoQ O C QVO Q 0 0 OD O Q QO OOS O0 Q 00 0 0 70 0 OOO Or O0 G Qo CO OG O O CO OQ oO Oo coco 8917097 8922123 8677498 8863480 8769651 8774678 8752896 8853427 9057840 8818241 8972389 8778029 4521213 606161 611858 583374 584715 570305 621576 569300 548021 573154 571311 592087 649390 573824 620738 534784 571981 580358 558744 1557392 1562921 1551360 1569288 1539464 1565435 1562586 1573310 1549015 1559905 5464025 5460674 5474246 5488823 J GO G O G Ss Ul 02 02 02
92. LINDX ELINDX DOUBLE PRECISION XLOCMAD YLOCMAD ZLOCMAD XGLMAD YGLMAD ZGLMAD amp ELBEGINS ELLENGTH ANGLE PREVANGLE NEXTANGLE RETURN END 5 20 User Subroutine Examples 5 20 4 Simple Model of Beam on a Target Example 1 Calculate antiproton production with 9 cm long 1 cm diameter copper target irradiated with 120 GeV proton beam Beam R M S spot size is 7 0 005 cm and o 0 007 cm In addition to forced antiproton production the user is interested in energy deposition calculation including knock on electron and ete pair production by hadrons To create a file of antiprotons generated on the target in a given phase space the user adds in MAIN OPEN UNIT 9 FILE PBAR OUT STATUS UNKNOWN and a few statements in the LEAK routine Section 5 11 The geometry and scoring is described in the standard mode The MARS INP file can look as Pbar Cu Target sigx 0 005 02 Nov 2012 T 5 T 12 T EVT 100000 120 F 1 2 EAM 0 005 0 007 IN 0 001 3 MATR MATER INP 2 Jg gt Z Q QU H El Z H U H w ZSEC 9 51 3 NLTR 5 RSEC 0 002 0 005 0 01 0 1 5 STOP The geometry is very simple here completely adequate to the standard mode Instead of the above bining and writing to a file PBAR OUT one can use HBOOK see MAIN for analyses of energy deposition and generated antiprotons Then the solid target can be described just as ZS RS C 9 C 0 5 p pd 104 5 20
93. MJET hadron event generator the MCNP code for low energy neu tron transport the ANSYS system for thermal and stress analysis physics analysis and graphics packages the MAD accelerator lattice description via a universal MAD MARS beam line builder the STRUCT program for tracking particles in accelerator lattices with beam loss recording the DETRA code for nuclide decay and transmutation calculations the EGS5 code for precise modeling of low energy electromagnetic showers and the ROOT system for description and visualization of arbitrary geometries Use of the code in a multistage mode coupled with event generators DPMJET with the STRUCT program for tracking particles in accel erator lattices with beam loss recording and with physics analysis and graphics packages is demonstrated with typical input and output examples Contents 2 1 Basic Monte Carlo Method rh A eu eee dae de LU 2 2 1 Hadron nucleoncrosssections e bight ude te amp re sa e aii e BO 22 Hadron nucleus cross sections 22e i Mw eae Oe ea A Ae ee E Uo Aree ee a He Ge ee he A au 2 3 1 Cascade exciton modelcodd 22s 2 3 2 Inclusive hadron production from 3 GeV to 100 TeV llle eRe pee been Fetes eee Bee 2 3 4 Quark Gluon String Model code LAOGSM2012 o T RR eres T Pr ee Oo EEA bea eats eka A A eee eee eee eee eee eee eee 2 6 1 Electromagnetic interactio
94. N output file Therefore the boundaries of the user s non Standard zones will correspond to various regions of interest where specific results are desired For example two separate zones of soil on either side of a beam dump can be set up so that one can compare the star densities in the two locations Or set up several zones 78 within an irregularly shaped target holder assembly so that energy and heat deposition patterns resulting from the beam target interaction can be studied There are of course a few requirements which must be met for the proper use of the subroutine The non Standard zones must be enclosed within or have boundaries equal to the outermost Standard zones Each zone of any type can hold one and only one material Each zone must have a value for it s volume The initializations concerning the material content and volumes of the non Standard zones are performed on the first call to routine REGI A simple example will serve to illustrate the non Standard zone initialization process as well as the geometry encoding process It is strongly suggested that the user create a conceptual sketch of his geom etry before starting to encode it filling in the zone boundary locations materials zone numbers and zone volumes as this will assist in the coding process Once a geometry is encoded the user is advised to utilize the MARS GUI visual interface to check that the zone boundaries and the zone number and material assign ments
95. NP zones volumes are known their values can be listed in the VFAN subroutine with the other Non Standard zones Section 5 5 or they can be listed via MCNP volume data cards which are grouped with the MCNP material data cards The syntax is vol V Va Ya Vn where vol identifies this as a MCNP volume card and the V are the volume values for each MCNP zone listed the order in which the zones are listed An example of a simple MCNP geometry description is given below 110 MCNP START 10 1 0 00129 1 2 3 imp n p 1 202 7 87 1 2 3 4 imp n p 1 90 0 1 2 4 imp n p 0 pz 0 pz 100 ez 5 Qux Die B WN FP ml 7014 0 7494 8016 0 2369 18000 0 0129 1001 0 0008 m2 26000 1 vol 7854 640 9 MCNP END The sample represents a segment of a beam pipe filled with air Material 1 is air and material 2 is iron The surface cards define four surfaces two planes and two cylinders Both planes are orthogonal to the z axis with the first plane at z 0 and the second at z 100 Both cylinders are aligned on the z axis and are infinite in length with the first having a radius of 5 and the second a radius of 5 2 Zones 10 and 20 use the surface IDs to define two cylindrical regions 100 cm long situated from O up 100 cm along z axis In radius the zones extend from 0 to 5 cm and from 5 to 5 2 cm The two zones are filled with air and iron respectively The third zone is defined to lie outside of the outer cylinder and contains bl
96. Next the settings of the cards from the MARS INP file are echoed with the first few lines as follows here is an entry for each card even those which have been left at their default value and are not listed by the user in the MARS INP file The materials declared in the MARS INP file are not merely echoed but appear along with the energy thresholds and tracking step sizes that will be applied to each material and additional information such as the radiation length The global thresholds and step sizes appear at the start of the materials list labeled as the material global vacuuum At the end of the materials data list is a table listing each element used by the model Following that are tables of calculated material dependent quantities After the materials the echoing of the MARS INP cards continues and concludes Additional tables of calculated material dependent parameters can be requested by setting the value of IPRINM on the NEVT card 1 Tables of hadron and photon nuclear cross sections and of dE dx are printed out for each material and as a function of energy Output Tables The first output table in the MARS OUT file is a mapping of the MARS Standard zone numbers to their r z and if used locations Nearly all subsequent data tables list results by their Standard zone number So for example the following lines in a MARS INP file set up a set of Standard zones This is a z sandwich geometry INDX 2 T so the material
97. OLUME L 0 DO C For example C VOLUME N1 2 PI RCOL RCOL 180 D0 C VOLUME N1 3 PI 400 D0 RCOL RCOL 60 DO C VOLUME N1 365 VOLUME N1 3 END IF V VOLUME N RETURN END 5 6 Subroutine REG3 Standard Zone Re numbering In some cases it is convenient to re define a few material and or magnetic indices assigned to the standard or extended regions at the initilization stage This can be easily done in a user routine REG3 e g UBROUTINE REG3 PLICIT DOUBLE PRECISION A H 0 Z INTEGER I N E DEFINES IM AND MAG FOR STANDARD SECTO N EQ 137 IM 14 N EQ 2503 IM 2 TURN A HAHHDH NH Z iw 5 7 Subroutines FIELD amp SUFI Description of Magnetic amp Electric Fields To describe the magnetic field components BX BY BZ in the regions with parameter MAG ZO the user puts IND 4 T and provides a subroutine FIELD The same routine is used to describe an electrical field One can use a corresponding map or analytical expressions to find the field components in the point X Y Z Parameter MAG defined in REG2 can speed up the search It indicates the type of the field in the region The unit for magnetic field is Tesla A 2 D or 3 D field map is read in a user routine SUFI at the initilization stage and transfered to the routine FIELD via appropriate COMMON block An example of the FIELD subroutine is 87 CC 0o Oo O 0 Y OQOHyxH RI O
98. P Nikitin Passage of High Energy Particles through Matter AIP New York 1989 N V Mokhov S I Striganov and A V Uzunian Technical Report 87 59 IHEP 1987 I L Azhgirey N V Mokhov and S I Striganov Antiproton production for tevatron Technical Report TM 1730 Fermilab 1991 N V Mokhov The mars12 code system in Proceedings of the SARE Workshop Santa Fe New Mexico 1993 S L Kuchinin N V Mokhov and Y N Rastsvetalov Technical Report 75 74 IHEP Serpukhov 1975 I S Baishev S L Kuchinin and N V Mokhov Technical Report 78 2 IHEP Serpukhov 1977 M A Maslov and N V Mokhov Particle Accelerators 11 91 1980 N V Mokhov Energy deposition in targets and beam dumps at 0 1 5 tev proton energy Technical Report FN 328 Fermilab 1980 N V Mokhov Technical Report 82 168 IHEP Serpukhov 1982 154 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 N V Mokhov The mars10 code system Inclusive simulation of hadronic and electromagnetic cascades and muon transport Technical Report FN 509 Fermilab 1989 N V Mokhov and J D Cossairt Nucl Instruments and Methods A244 349 1986 I S Baishev I A Kurochkin and N V Mokhov Technical Report 91 118 IHEP Protvino 1991 I L Azhgirey I A Kurochkin M A Maslov V V Talanov and A V Uzunian Technical Report 93 19 IHE
99. P Protvino 1993 D C Wilson C A Wingate J C Goldstein R P Godwin and N V Mokhov Hydrodynamic calculations of 20 tev beam interactions with the ssc beam dump in Proceedings of the 1993 Particle Accelerator Conference IEEE pages 3090 3092 1993 J Ftacnik and M Popovic Parallel version of mars10 and mars12 codes in The 1994 April APS Meeting 1994 O E Krivosheev and N V Mokhov A new mars and its applications 1998 N V Mokhov et al Mars code developments 1998 N V Mokhov Mars code developments benchmarking and applications in Proc of ICRS 9 Interna tional Conference on Radiation Shielding October 17 22 1999 volume 1 pages 167 171 Tsukuba Ibaraki Japan 2000 J Nucl Sci Tech N V Mokhov and A V Ginneken in Proc of ICRS 9 International Conference on Radia tion Shielding October 17 22 1999 volume 1 pages 172 179 Tsukuba Ibaraki Japan 2000 J Nucl Sci Tech N V Mokhov and O E Krivosheev Mars code status 2000 O E Krivosheev and N V Mokhov Status of mars electromagnetic physics 2000 N V Mokhov S I Striganov and A V Ginneken Muons and neutrinos at high energy accelerators 2000 I Baishev A Drozhdin and N Mokhov Struct program user s reference manual Technical Report SSCL MAN 0034 SSC Laboratory 1994 P D Group Phys Rev 1998 V S Barashenkov Particle and nucleus cross sections Technical report Dubna 1993 155 60 61
100. S Standard geom etry zones See Section 4 3 2 for further discussion LR The number of major radial sections described in the accompanying RSEC data card The allowed range is 1 lt LR lt 50 Default 1 RSEC RSE 50 IRN 50 IRI 50 Real and integer variables which define the locations of the major radial divisions of the MARS Standard geometry zones and the number of sub sections within each The materials in those zones are also specified by this card when IND 2 F which is for a r sandwich type geometry see Section 4 3 2 for further discussion Recall from the discussion in Section A T that the three variables of dimension 50 are mapped onto a single array of dimension 150 The boundary divisions are contiguous no gaps and must be listed in ascending order The maximum r coordinate in the model RMAX is the outer boundary of the last declared division or the last RSE value listed RSE i Ther coordinate real number of the outer boundary of the it radial section The inner coordinate of the 1 section is assumed to be 0 These values occupy elements 1 50 of the mapped array Default 5 0 49 0 IRN j The integer number of minor subsections within a given major section El ements j 51 100 of the mapped array correspond to the i 1 50 major sec tions Default 50 1 IRI k The material index value IM of each major radial section The minor sub sections must be of the same material as their major section Elements k 101 150
101. The MARS Code System User s Guide Version 15 2014 Nikolai V Mokhov and Catherine C James Fermi National Accelerator Laboratory P O Box 500 Batavia Illinois 60510 July 17 2015 This is a draft manual for the MARS15 code released in July 2015 Section 4 on the input files is up to date All other sections still need further update This manual along with recent principal papers listed below describe new and upgraded features of the MARS15 code and all can be downloaded from the MARS web site http www ap fnal gov MARS e N V Mokhov P Aarnio Yu I Eidelman K K Gudima A Yu Konobeev V S Pronskikh I L Rakhno S I Striganov I S Tropin MARS15 code developments driven by the intensity frontier needs Fermilab Conf 12 635 APC Presented paper at the 12th International Conference on Radiation Shielding September 2 1 2012 Nara Japan 0 e V S Pronskikh A F Leveling N V Mokhov I L Rakhno Calculation of residual dose around small objects using Mu2e target as an example Fermilab FN 0930 APC 2011 2 e N V Mokhov Recent Mars15 developments nuclide inventory DPA and gas production Fermilab Conf 10 518 APC 2010 B e P Aarnio Decay and transmutation of nuclides CMS NOTE 1998 086 CERN 1998 al e A Isotalo Modifications to DeTra Technical Report September 18 2008 5 e N V Mokhov I L Rakhno and S I Striganov Simulation and verification of DPA in materials in Applic
102. The program calculates and prints distributions of e e and photon fluxes and of energy deposition density e and related values dose equivalent instantaneous temperature rise AT at given initial temperature T9 TEMPO and number of particles per beam Ny AINT see VARS and contact dose due to induced radioactivity at No beam intensity Other values discussed in Section 11 1 2 are calculated independently of the IND 1 meaning 11 1 4 The MTUPLE NON File If the user defines geometrically complex insertions defined with REGI routine as a supplement to the standard and extended geometries additionally the program prints in a compact form most of the above quantities with corresponding statistical errors for all non standard regions 134 11 1 5 The MTUPLE EXG File 11 1 6 The MTUPLE MCNP File 11 2 Other Data Output Files have a less portable format which is fixed by non user MARS routines which cannot be modified a few files to be used by graphics packages and others GRA PLOT and to be used in a consecutive run in a multi stage case the files are defined in the 11 2 4 The TRACK PLOT file 11 2 2 The VERTEX PLOT file 135 12 Graphical User Interface A Graphical User Interface MARS GUI SLICE has been developed It is based on Tcl Tk and is linked in to the user s executable however it is active only when specific flags are set in the input file When the interface is active no events are generated but the user s
103. The user gives MCNP the information it needs on materials via MCNP data entry cards appended to the MARS INP file after the STOP card However if the user already has a MCNP geometry description file then the model geometry can be described using that syntax which is also appended to the end of the MARS INP file Both these modes of using MCNP are described below in Section 6 1 Using MARS with the full MCNP code requires that the user obtain and install the MCNP code library The code is obtained from RSICC 86 the Radiation Safety Information Computational Center at the Oak Ridge National Laboratory on the web at www rsicc ornl gov or from the NEA Databank in Europe 87 The code package includes the manual which is not available online Once the code library is installed the GNUmakef ile distributed with MARS must be used to link to the MCNP libraries and produce the non default MARS MCNP executable To run the executable the user must set up pointers to the MCNP data library See Section 6 2 for installation and compile build run details 6 1 Setting up MARS INP for use with MCNP Switches must be set on the INDX card in the MARS INP file to activate the calling of the MCNP mod ules even if the executable has been built against the full MCNP libraries MCNP data entry cards are then appended to the end of the MARS INP file after the STOP card Which switches and data cards are used depends on which of the two MCNP sub modes is b
104. This table is similar to the one described above being data accumulated in the volumes specified by the NOBL and RZOB cards The data here is the low energy neutron spectrum dN dE in units per GeV cm plotted in energy bins as labeled by the left most column The columns of data are arranged to be easily cut and pasted into an external graphics or spreadsheet program GRAPH LOW ENERGY NEUTRON FLUENCE N CM2 PER 1 PPP AS A FUNCTION OF DEPTH DOWN AND RADIUS ACROS IN CM This table presents data values versus location in the model volume ignoring zone and region bound aries The data is instead mapped into 5 r bins and 10 z bins The maximum r and z bin values describe the maximum extent of the model the Standard zone mother volume the bins are cre ated by equal divisions between zero and the maximums The left most column gives the mean z coordinate in each bin the top two rows give the lower and upper r range for each of those bins The data in this table is the low energy neutron flux in units of neutrons per cm per incident primary particle The columns of bins and data are arranged to be easily cut and pasted into an external graphics or spreadsheet program GRAPH TOTAL NEUTRON FLUENCE AT E 1 000E 01 MEV N CM2 PER INC PAR TICLE AS A FUNCTION OF DEPTH DOWN AND RADIUS ACROS IN CM This table is similar to the one described above but for all neutrons below the stated energy cutoff GRAPH NEUTRON FLUENCE AT E gt 0 1 MEV
105. User s guide Technical Report Fermilab FN 738 rev 2004 S I Striganov On the theory and simulation of multiple coulomb scattering of heavy charged parti cles Technical Report Fermilab Conf 04 056 2004 N V Mokhov Nauka in Proc IV All Union Conference on Charged Particle Accelerators volume 2 page 222 Moscow 1975 N V Mokhov and V V Phrolov Sov J Atomic Energy 38 226 1975 R P Feynman Phys Rev Lett 23 1415 1969 A V Ginneken Weighted monte carlo calculations in thick targets Technical Report FN 250 Fermilab 1972 A V Ginneken Casim program to simulate transport of hadronic cascades in bulk matter Technical Report FN 272 Fermilab 1975 W R Nelson H Hirayama and D Rogers The egs4 code system Technical Report SLAC 265 Stanford Linear Accelerator 1985 A Fasso A Ferrari J Ranft and P Sala Fluka92 in Proceedings of the SARE Workshop Santa Fe New Mexico January 1993 volume A349 Nucl Instruments and Methods 1994 A V Ginneken Calculation of the average properties of hadronic cascades at high energies casim in Computer Techniques in Radiation Transport and Dosimetry edited by W R Nelson and T M Jenkins 1978 N V Mokhov Sov J Part Nucl 18 408 1987 N V Mokhov Inclusive simulation of hadronic and electromagnetic cascades in the ssc components Technical Report SSC SR 1033 SSC Central Design Group 1988 A N Kalinovsky N V Mokhov and Y
106. VOLMC NON file for a simple beam dump geometry is given here In this example there is a single container Standard zone in which all the other non Standard zones are embedded this is zone 1 The Standard zone s volume is calculated along with the other zones and the message explains that the container s actual volume is likely not to be that of a simple cylinder due to the presence of the embedded zones Following the text message are the volumes for the non Standard zones stated as VOLUME nnn 0 rrrE nn The text after the gives the error on the volume calculation the assigned non Standard or Extended Geometry zone number and the zone name The entire statement can be pasted directly into the VFAN user subroutine 11 1 2 The MARS OUT File The MARS OUT file is always produced even when MARS is run in GUI mode or in volume MC mode where in both cases no particle interaction simulations are performed This is because the MARS OUT file records startup and initialization information in addition to the simulation results for Standard zones Initialization Information At startup Mars echos many of the settings in the MARS INP file to the MARS OUT file The user should always take a look at these to check that the program settings were as expected The first few lines give the Mars code version the date and time the program was started and the users title exactly as taken from the first line of the MARS INP file
107. While making the value large has a modest effect on the time per event log STEPH STEPEM The recommendation is to set STEPH min A l where A is the mean inelastic length for hadrons and is the length of the zones of interest in the direction which most particles pass through those zones Default 10 cm VARS EFF DLEXP TEMPO AINT Real variables which control miscellaneous aspects of the model EFF The point like target efficiency which is active only when IND 7 T 0 Abs EFF lt 1 This provides a forced nuclear inelastic interaction of a primary beam if EFF gt 0 This provides a forced nuclear sampled inelastic or elastic interaction of a primary beam if EFF lt 0 Default 0 41 DLEXP An exponential transform factor which allows an increase DLEXP gt 1 or decrease DLEXP lt 1 in the effective hadronic mean free path X Ax DLEXP This feature is useful where the deep penetration problem applies and for compact restricted models Recommendation 0 3 lt DLEXP lt 3 Default 1 TEMPO The initial temperature T in Kelvin of the model for all zones It can be overwritten for the specific materials in the MATER INP file The allowed range is 1 8 lt Ty lt 1800 Default 300 AINT The number of particles No in a given pulse of beam which is used for two types of normalization The format is 4 1 0e12 The units for the value are different for temperature rise results than for other results so use
108. X Y Z in the system it determines the corresponding physical region number N each with its own material index and if one wishes the subregion number NIM The last parameter can be used in a subroutine FIELD to determine the type of magnetic field uniform dipole quadrupole etc in the region N Default MAG 0 no magnetic field in the region By convention the region outside of the global volume has a number N 0 and properties of the black hole In some applications it is useful to tag and to score the leakage out of the non standard regions into the black holes labeled with N lt 1 to use these negative tags in a user routine LEAK The user must pay a special attention to careful programming of the subroutine REGI because the geometrical modules consume 84 usually about 80 of the CPU time as is typical of cascade Monte Carlo programs A simple example of subroutine REGI is ROUTI NE REG1 X Y Z N N DOUBLE DARD G PRECISION EOMETRY HU I IN N al PLACE YSICAL REGION NU NFZP 1 EXGM NVOLUM AX 10000 Y Z B STANDARD IM A H 0 2 ODULE INT EGER I N END EXT L D EFIN ED OF GIVEN POINT IN THE SYSTE ER NMIN lt N lt NMAX ES NUMB ERED L EAKAGE z NON STANDARD SEC OR ZHZZH_ZO Z ZOH ZHU H 0
109. a tions of High Intensity Proton Accelerators World Scientific Proc pp 128 131 2010 6 e I L Rakhno Modeling heavy ion ionization energy loss at low and intermediate energies Fermilab FN 0835 APC 2009 7 e N V Mokhov S I Striganov MARS15 Overview Fermilab Conf 07 008 AD 2007 8 e N V Mokhov K K Gudima S G Mashnik et al Physics Models in the MARS15 Code for Accelerator and Space Applications Fermilab Conf 04 269 AD 2004 9 e S G Mashnik K K Gudima A J Sierk M I Baznat N V Mokhov CEM03 01 User Manual LANL LA UR 05 7321 2005 10 http www rsicc ornl gov codes psr psr5 psr 532 html e N V Mokhov E I Rakhno I L Rakhno Residual Activation of Thin Accelerator Components Fermilab FN 0788 AD 2006 11 e I L Rakhno N V Mokhov S I Striganov Modeling Heavy Ion Ionization Loss in the MARS15 Code Fermilab Conf 05 019 AD 2005 12 e N V Mokhov K K Gudima C C James et al Recent Enhancements to the MARSIS5 Code Fermilab Conf 04 053 2004 113 e N V Mokhov K K Gudima S G Mashnik et al Towards a Heavy Ion Transport Capability in the MARS15 Code Fermilab Conf 04 052 2004 14 e M A Kostin and N V Mokhov Parallelizing the MARS15 Code with MPI for Shielding Applications Fermilab Conf 04 054 2004 115 e M A Kostin O E Krivosheev N V Mokhov I S Tropin An Improved MAD MARS Beam Line Bu
110. accurate calculation of energy de position the user must keep all the threshold energies below 0 0145 GeV Materials can be single elements or complex compounds Tables B and d list all the elements and built in compounds used by MARS with their identifying abbreviations These abbreviations are the character strings to use in MATER INP A particular material can be listed more than once for cases where MARS variables applied to that 46 material need to have different values in different regions of the geometry For example a model might have both steel shielding and thin steel vacuum pipe both specified as material FE For the steel shielding a large STEPEM and STEPH could be specified using the global step control parameters assigned to the SMIN card The thin steel pipe could have a smaller step parameters applied by using the MTSM and MTSH cards The material FE would be listed twice so that two IM indexes are assigned The shielding zone and the pipe zone would have a different material IM index assigned so that the appropriate step length properties get applied by the code See the example in Section 4 3 3 MTCH RLCTCH 500 Real variables giving the charged hadron heavy ion and muon energy threshold applied only to specific materials They must be less than 0 0145 GeV if one wishes to calculate energy deposition correctly Any material which does not have a corresponding entry here will have the global threshold applied as the d
111. aces A colon separating two surface ID numbers implies an OR operation to form a union of the spaces Intersections are performed first and then unions Complicated structures where the hierarchy of the boolean operations are nested are allowed The main restriction on these operations is that the entire space of a zone must have the same sign relative to each of its bounding surfaces in other words the zone cannot be partly positive and partly negative relative to its bounding surfaces The zone data card syntax is ID IM p IDg string IMP 109 where ID an integer is the zone card ID number Each zone has a unique card ID number however this is not the assigned Mars zone number The card IDs do not need to be listed in order and there can be gaps in the ID numbers for a given group of cards IM the material index for the material contained within this zone This is the same index from the order materials are listed on the MATR card and the same integer as used for the MCNP material ID mJ M p the density of the material A negative value implies the units are g cm while a positive value implies units of atom density in 10 atom cm ID string a string of integers which are the defined surface IDs separated by spaces or by which define the zone boundaries according to the rules in the above para graph IMP a string of characters which define the relative importance for particles which enter this zone impo
112. ackhole material this zone has been given an importance of zero The volumes of the zones in cm have been entered on a MCNP volume card listed after the MCNP material cards 6 2 MCNP Installation The MCNP code package with corresponding libraries can be obtained from the RSICC center in the USA or NEA Databank in Europe The installation procedure for the MCNP code is described in the installation guide included with the package The MCNP manual is also included The user must run the install procedure and follow the on screen instructions carefully While configuring and installing MCNP choose the following options Dynamic memory Off with default mdas size Geometry Plotter Off Tally Plotter Off 64 Bit Data Off Multiprocessing Off After completion this procedure and successful running the built in test problems next step is library compilation To build the MCNP libraries usually only Fortran and C compilers are needed However for use in conjunction with MARS it is recommended to follow the procedure described below and in this case two additional software packages are required a GNU make from the Free Software Foundation 101 and a fsplit utility for splitting the fortran code into separate subroutines Some Linux distributions do not include fsplit therefore a free utility source code from the BSD is included in the installation package as described below All these files can be
113. actions below 0 0145 GeV JJ is particle type from Table If K 205 the particle type is neutron by default and JJ is its energy group number from Table I w is leaked particle statistical weight E is its kinetic energy X Y Z and DCX DCY DCZ its coordinates and direction cosines respectively The routine LEAK used in an example in Section to collect generated antiprotons in the file PBAR OUT looks like SUBROUTINE LEAK N K JJ W E X Y Z DCX DCY DCZ TOFF IMPLICIT DOUBLE PRECISION A H 0 Z INTEGER I N PARTICLE LEAKAGE SPECIAL SCORING IF K 205 JJ NGROUP E 0 0005 EN JJ FOR L E NEUTRONS E lt 0 0145 GEV REVISION 02 NOV 1994 DATA POPT DP0 DZ0 8 9 0 022 0 99 E N JJ 1 I AG Q QN TURN TURN 656 IF JJ NE 12 RE IF DZ LE DZ0 R P SORT E E 1 8 R 1 Y Fl DP ABS P POPT POPT F DP GT DPO TURN RITE 9 E W X Y Z DCX DCY DCZ K ETURN ND 1 E US Ej mp An 90 5 12 Subroutines MHSETU MFILL HISTODB User Histograms As AVY C263 202 QA A A A QC CQ 23 2 OO OAs OO QO 00 OQ OO QO AO OE 0 0 01
114. al and geometry card types 6 1 1 Mode 1 MCNP with Material description only To trigger the calling of the MCNP subroutines the INDX card in the MARS INP file must have 5 T in it s list of switches Next one inserts the MCNP start and stop delimiter cards after the MARS INP STOP card Between the MCNP delimiter cards the MCNP material data cards are inserted Each MCNP material data card is made up of an identifier followed by pairs of numbers each pair consisting of an integer and a real The integer identifies an isotope and the real represents the proportion of that isotope within the material being described Each number is separated by one or more spaces There can be as many number pairs as necessary but a single line cannot exceed 80 characters If the data requires more than one line then the line is terminated by a continuation character which is the ampersand amp the ampersand is included within the 80 character limit The card s data continues directly on the following line with no blank line between The material data card syntax is m M Iso Frac Iso Fraco Iso Fracyn Cn where mi M is the material identifier The prefix m is always present followed by an integer IM where this integer corresponds to the order materials are listed on the MATR card in the MARS portion of the MARS INP file Ison an integer is the isotope identifier part of each number pair Isotopes in MCNP are described in terms
115. amline direction vector i e angle between line c formed by intersection of beamline x y plane with Z Y plane and c beamline x axis A positive angle forms a right hand screw with beamline c direction vector BL1_PSI 0 DO x start 0 d0 y start 0 d0 z start 0 d0 x call buildbl opticsl amp x start y start z start amp bll theta bll phi bll psi amp InitZone di write REG1 INFO use beam Ekin amp BeamKineticE beam mass m amp BeamMass BeamKineticE 100 0d0 X BeamMass 0 93827231d0 x call setebl BeamKineticE BeamMass 5 6780d 03 X call blmaxmat nblnzmax if nblnzmax gt M MAX then write beamline 1 nblnzmax as read from blmatmax amp nblnzmax 100 A AX A 0x x A A 0x E gt AC 6 X Xo Xo Xo FF x x x amp amp amp write is greater then M MAX M MAX stop STOP else if nblnzmax lt M MAX then write beamline 1 nblnzmax as read from blmatmax nblnzmax write is less then M MAX M MAX endif if nblnzmax gt 0 then call blmat IMUN else write Number of zones for NuMI beamline lt 0 stop endif call set current beamline 2 b12 theta 0 0d0 b12 phi 0 0d0 b12 psi 0 0d0 x start 0 d0 y start 300 d0 z start 3000 d0 InitZone 2000 call buildbl opticsZ2 X Start y start z
116. ams accumulated for the materials declared by the HBKE data card There must be at least one declared material entering NHBK 1 into MARS INP when user defined histograms are used via the subroutines MHSETU and MFILL even if standard histograms are not requested NOB NSUR 0 and even if the user is not interested in the global energy deposition for the user defined histograms NHBK The number of materials 1 lt NHBK lt 5 Default 0 0 HBKE RIM i EHMIN i EHMAX i i 1 NHBK Real variables which defines correspondingly the material index lower and upper energy de position histogram boundaries for the total energy N ED GeV deposited in the entire system RIM 0 and in materials with index RIM gt 0 for histograms with 11 lt ID lt 15 Default 0 0 RIM The material index 0 lt RIM lt 500 Default 0 0 EHMIN The beginning of the energy deposition interval GeV Default 1076 EHMAX The end of the energy deposition interval GeV Default 1 5x Eo Note that for a heavy ion projectile Eo is its total energy NCLD NCLD Integer variable which sets the number of materials on the IMNC card in which detailed 2 D mass charge nuclide distributions are calculated and corresponding input files NUCLIDES IM for the DETRA code generated To calculate correctly stopped nuclides in NUCLIDES STOP IM files for millimeter and sub millimeter regions one must have global cutoff energy EMCHR or and specific MTCH for materials of those regio
117. and upper r range for each of those bins The data in this table is the total dose equivalent in units of mSv per incident primary particle The columns of bins and data are arranged to be easily cut and pasted into an external graphics or spreadsheet program GRAPH TOTAL STAR DENSITY This table presents data values versus location in the model volume ignoring zone and region bound aries The data is instead mapped into 5 r bins and 10 z bins The maximum r and z bin values describe the maximum extent of the model the Standard zone mother volume the bins are cre ated by equal divisions between zero and the maximums The left most column gives the mean z coordinate in each bin the top two rows give the lower and upper r range for each of those bins The data in this table is the total star density in units of stars per cm per incident primary particle The columns of bins and data are arranged to be easily cut and pasted into an external graphics or spreadsheet program GRAPH DIRECT ENERGY DEPOSITION This table presents data values versus location in the model volume ignoring zone and region bound aries The data is instead mapped into 5 r bins and 10 z bins The maximum r and z bin values describe the maximum extent of the model the Standard zone mother volume the bins are cre ated by equal divisions between zero and the maximums The left most column gives the mean z coordinate in each bin the top two rows give the lower an
118. annot be run simultaneously Details on using the GUI interface are given in Section I2 3 8 Statistics Guidelines needs further update Some of the Rules of Thumb should just be moved here 3 9 Variance Reduction and Biasing needs further update Algorithms for splitting and Russian roulette at hA vertices statistical weights and in particle transport particle trajectories Phase space and particle type biasing exponential conversion of path length Mathe matical expectation for deep penetration problems in complex highly non uniform geometries algorithms for scoring probabilities rather than real particle crossings or interactions now take into account all possible processes for both stable and unstable particles and charged as well as neutral hadrons 28 The user can now choose between sampling and forcing 7 K and u decays Algorithms for splitting and Russian roulette at hA vertices and in particle transport are also further improved For deep penetra tion problems in complex highly non uniform geometries algorithms for scoring probabilities rather than real particle crossings or interactions take into account all possible processes for both stable and unstable 29 particles and charged as well as neutral hadrons Use of accelerating field RF cavities is now optional in the code 3 10 Interfaces needs further update Interfaces to the ANSYS code for thermal and stress analyses and to the STRUCT code for multi turn
119. ape each with one half probability There is also added a third component in which the p or m interact only quasi elastically with the nucleons These are simulated using conventional MARS algorithms exactly as for protons except that the fastest nucleon emerging leading particle from the collision is identified as its antiparticle 2 10 Neutrino Interactions A special weighted neutrino interaction generator has been developed and incorporated into MARS This model permits the selection of the energy and angle of each particle v e js and hadrons emanating from a simulated interaction These particles and the showers initiated by them are then further processed in the code in the usual way Four types of neutrinos are distinguished throughout v 7 Ve V and the model identifies all possible types of neutrino interactions with nuclei The corresponding formulas for these processes as well as results of Monte Carlo simulations for muon colliders and storage rings are described in 2 11 Low Energy Neutrons The default low energy E lt 0 0145GeV neutron model in MARS is sufficient for most applications It uses a 28 group cross section library which in turn is derived from data on a set of 14 materials BNAB The cross sections are extrapolated to cover other materials not in the initial set of 14 Alternatively one can use so called the MCNP mode in MARS where neutron interactions at E lt 0 0145GeV are described using the ENDFB
120. ased upon the order in which the shape definitions appear in the GEOM INP file Each Extended Geometry shape is specified by a single line of data the data is unformatted and sepa least one non standard region described in REG1 rated by blank spaces The syntax of an Extended Geometry shape volume description line is VNAM NT NTR where VNAM NT NTR IM XR YR ZR C1 Cn IM XR YR ZR C1 C2 Cn NSB1 NSB2 NSB3 is the user s identifying name for the shape in format A8 In the current version to avoid a conflict with transformation matrix descriptions it must not start with TR is the shape type ID number an integer 1 X NT lt 6 Table 7 has the correspon dence between shapes and ID numbers If NT gt 0 the reference point RP is on the front surface as described in Table 7 If NT lt 0 the reference point RP is at the shape center not used for sphere and tetrahedron is the transformation matrix ID number 1 stands for the transformation matrix described on the TR1 card 2 stands for the transformation matrix described on the TR2 card etc enter O if this shape has no transformation applied is the material number index for the material this shape is made of This is the same material index as defined in the MARS INP deck 0 lt IM lt 500 are the coordinates of a reference point RP in the Local Coordinate System LC S for this shape Table 7 gives the location of the RP on each shape type Table
121. astic interactions see the ICEM data card applied only to specific materials Any material which does not have a corresponding entry here will have the global switch I OGSM applied as the default see the ICEM data card For TLAOM 1 0 exclusive modeling with the CEM code is done at E 3 GeV the MARS inclusive model is used at E gt 5 GeV and mix and match between these two models is used at 3 E 5 GeV If A 3 or E 0 02 GeV the LAQGSM code instead of the CEM code is used above LAQGSM instead of CEM is always used if a projectile particle is p K d t He He ni hyperon or heavy ion This mode is most suitable for shielding type simulations For ILAQM i 1 exclusive modeling with the CEM code is done at E lt 0 3 GeV mix and match between CEM and LAQGSM is used at 0 3 E 0 5 GeV exclusive modeling with LAQGSM is done at 0 5 E 8 GeV mix and match between LAQGSM and the MARS in clusive model is used at 8 lt E lt 10 GeV and the MARS inclusive model is used at E gt 10 GeV LAQGSM instead of CEM is used under the same conditions as in the previous mode This set is default and recommended for majority of applications including particle production energy deposition heavy ion projectiles nuclide inventory and DPA at energies below 8 GeV It is obvi ously more CPU time consuming than the previous one TLAOM i 2 is currently disabled It is automatically converted to ILAQM i 3 For ILAQM i
122. at RLPHN i 1 or suppressed at RLPHN i 0 It is automatically set to 1 for KEMIN i 1 Default 0 02 RLPHN The values for the photo nuclear event control indexed by IM the order numbers the materials are listed in the MATER INP file BIEA RLELN 500 Real variables specifying the parameters of the inclusive forced electro nuclear events applied only to specific materials Any material which does not have a corresponding entry here will have the global parameter applied as the default with the value given by the PELNUC variable in the BIAS data card Values of the RLELN array specify electro nuclear event modelling It is forced with the appropriate statistical weight at RLELN i 1 forced with the Russian roulette at 0 001 X RLELN i lt 1 modelled exclusively at RLELN i 1 or suppressed at RLELN i 0 It is automatically set to 1 for KEMIN i 1 Default 0 05 when the primary beam particle is electron or positron 10 10 or 11 on the IPIB card otherwise it is 0 003 at E lt 300 GeV or 0 at E gt 300 GeV RLELN The values for the control of electro nuclear events indexed by IM the order numbers the materials are listed in the MATER INP file 50 BIAP RLPBR 500 Real variables specifying the parameters of the inclusive forced antiproton production applied only to specific materials Any material which does not have a corresponding entry here will have the global parameter applied as the default
123. ation options which are collectively ap propriate when modeling thick shielding Setting this flag can provide a substantial CPU time saving for models of thick extended shielding The particular parameters and their settings are given in Table 6 As with all similar global settings any of the individual parameters in this set can be re set globally or for specific materials using the appropriate input deck parameter This mode is especially powerful if used in con junction with IND 6 T with the neutron threshold energy EMNEU gt 1074 GeV Be careful with using IND 6 T in this mode if the neutron threshold energy EMNEU is below 1074 GeV because of a possible substantial increase of the CPU time per history As always do a short timing test first IND 15 F The above items in the global parameter set for thick shielding are set to standard MARS defaults IND 16 T MCNP style geometry description is used via entries in the MCNP section of the MARS INP file and with IND 5 7T MCNP geometry description is not used Enables algorithms for accurate modeling of Displacement per Atom DPA dis tributions and histograms These algorithms are valid only if the threshold ener gies of charged particles in matter EMCHR and EMIEL and corresponding material dependent values of the MTCH and MTEL cards are below EDP Ar 0 005 GeV That is why the threshold energies for charged particles are converted to E D P Ay if they exceed ED P
124. ation s reliability and predictive power The mathematical foundation and the physical model of the MARS system and benchmarks from numerous past applications are described in many references 26 28 29 30 31 Besides the original code 7 version 19 the milestones in code development are MARS3 MARS4 33 MARS6 MARS8 B5 MARS9 36 MARS10 37 88 MARS12 31189 MARS93 40 the hydrodynamical MARS MESA SPHINX package and a version for parallel processing MARSI2 42 The purpose of this document is to be a user s guide for the current MARS Version 15 2014 Portions of the previous manual are carried over with updated sections describing the main improvements and options Section 2 gives an overview of the inclusive method and the physics models implemented in MARS The main updates from the past few years in the physics models are also described in several references 451146 47 48 49 Section 3 outlines the basics of how a geometry is described along with an overview of how MARS tracks particles and then tabulates and presents the simulation results Further details on using the program are contained in subsequent Sections Section 4 describes the syntax of the MARS input files MARS INP and GEOM INP and how these are used to control physics processes and describe simpler geometries The User Subroutines utilized to describe more complex geometries and create custom output are covered in Section 5 Section I2
125. by a corresponding radio button By clicking a corresponding button a Materials window is created with the CF displaying material index and name and select boxes SB showing color of each material in the given view on the GDP The pre set materials colors can arbitrary be modified in the corresponding SB individually for each material The colors can be reset individually or globally Changing the view automatically adjusts the material info in this window e By clicking a left mouse button at any point of the GDP a Point Info window is created with informa tion display fields IDF containing coordinates region number material name and index magnetic field module and a value of histogram see below for this point This window Keeps the position intact e Particle tracks in the given view can be displayed on the GDP by loading a PLOT file generated by MARS Similar to materials by clicking a corresponding button a Particles window is created with information similar to the Materials window particle ID name color and SB displaying color of each particle and allowing color modification A corresponding CFs allow turning ON and OFF any ID and global track visibility One can examine tracks by clicking a middle mouse button at any track point on the GDP A Track Info window is created with IDF containing the particle ID name as well as the current energy statistical weight and coordinates at the point e After the run a variety of calcu
126. can further vary the current slice rotation by acting directly on the H and V radio buttons Table 13 Default GUI rotation settings Button Y Z X Z X Y H T 0 0 V 0 0 0 12 3 Installation and usage This package requires to have Tc1 Tk installed Tc1 Tk is scripting language and graphical user interface designer developed by Dr J Ousterhout It is free software and anyone can get copy from Scriptics web 138 site 109 At least version 8 2 is required Six variables in GNUmakefile might require changes in order to accommodate local installation e TCL VER Tcl version Version 8 2 is known to work and it is the default value e TCL INC location of the Tc1 include files e TCL LOC location of the Tc1 include files e TK VER Tk version Version 8 2 is known to work and it is the default value e TK INC location of the Tk include files e TK LOC location of the Tk library files e TCLTK LST list of Tc1 Tk library files As default it consists of tcl and tk library Itk TK VER Itcl TCL VER Remember to put Tk library in linkage script before Tc1 one All interface is inside one Tk Tc1 script called mf t c1 which should be stored into MARS data directory In order to run just set second control flag CTRL to 1 in the MARS INP and run MARS executable interface window will show up Remember to set DISPLAY environment variable properly if you re working on remote computer via network 12 4 Interface features
127. ches to control exclusive generators volume and surface histogram binning and DUMP regions MARS to Beam line transformation Beam line to MARS transformation MMBLB initialization MMBLB element registration MMBLB independent tunnel description 5 1 Main Program MARSMAIN F The names of the main I O files are here and can be modified by the user 5 2 Subroutine MARS1514 Subroutine M1514 is the main steering routine which directs the running mode of the executable There are three possible running modes normal GUI interface and stand alone event generator Switching be tween these modes is controlled by the CTRL card in the input deck The default mode is normal where the primary particle interacts with the described geometry secondary particles are tracked through the ge ometry and various parameters are scored and tabulated for output The GUI interface Section I2 is very useful for checking a complex encoded geometry and for displaying results No events are generated in this mode but the user s encoding of the modeled geometry and zone and material assignment is executed and displayed The stand alone event generator is useful for 76 The three modes can be seen in the 3 way IF ELSE block within the subroutine The first segment in the block which calls STTCL is the GUI interface mode The second segment in the block which calls EVTGEN is the stand alone generator mode The third segment in the block which ca
128. content of the zones is defined on the ZSEC card The resulting map table in the MARS OUT file is The integer number is the Standard zone number and the number in parentheses is the index for the material in that zone For example for 25 0 lt z 35 0 and 10 0 r lt 124 20 0 the Standard zone number is 14 and it contains material number 2 Notice that the r and z boundaries listed in the map table are not evenly distributed but correspond to the boundaries of the declared Standard zones The tables which report results by Standard zone number are all laid out in a similar manner The table has ten columns with the columns numbered 1 10 the rows are labeled 10 20 30 etc The data being reported in the table is listed in order by zone labeled also Region Number starting at the first row through 10 columns then to the second row third and so on for as many rows are required So for example imagine if the model was a target simplified to a group of Standard zone cylinders One wishes to know the location which will have the largest energy deposition Go to the table which lists total energy deposition by zone and look for the largest value identify based on the row and column which Standard zone number the value is in Then return to the Standard zone map table to determine the r and z value which that zone number corresponds to Many results have a statistical error reported with them Please read Section 3 8 for a brie
129. d nuclear data sets for the same material By de fault MCNP reads in the first reference to the corresponding nuclear data set encountered in the file xsdi r Specific suffixes are used differentiate between the data sets and these suffixes can be appended to the iso tope identifier as a means to select a particular data set for that material For example if one listed ml 26000 42c 1 then the specified 42c nuclear data set would be used for this iron material See the MCNP manual for details 6 1 2 Mode 2 MCNP with both Material and Geometry description Just as for the material data only mode the INDX card in the MARS INP file must have 5 T in it s list of switches but in addition the 162 T switch must also be set Setting both these switches triggers calls to both the MCNP material modeling and geometry description subroutines The MCNP geometry has simularities to MARS Extended Geometry in that items are built from a col lection of geometric shapes For those familiar with MCNP MARSIS supports all of the MCNP geometry capabilities except lattices and universes The usual set of regular surfaces is present plane sphere cylin 108 der cone ellipsoid hyperboloid paraboloid and elliptical and circular torus In addition it is possible also to use so called macrobodies which are composed of the regular surfaces mentioned just like a box is composed of six different planes The following macrobodies are allowed at pres
130. d through zones and to obtain the particle flux in the zone path length is divided by the zone volume An incorrect value for the zone volume will give incorrect results for the flux and for all other results derived from particle fluxes The same local zone index is used when defining volumes can be greater than the total number of non Standard zones actually used because the declared array space does not need to be close packed M MAX is set by the user and is the size of the MARS array space being reserved for the user s non Standard zones The user can define M MAX in a DATA statement as done in the distributed REGI or via his own parameter list or common block The user must be careful to coordinate the physical outer boundaries of his non Standard volume with the Standard zone s and or Extended geometry zones defined via the input decks Non Standard zones must all fit inside Standard zones or be aligned along the same boundaries non Standard zones cannot extend beyond the outermost defined Standard zone This is because as stated above the outermost extent of the Standard zones defines for MARS the outermost extent of the entire model If the entire model is defined by the user from REGI then one must still have at least 1 Standard zone and the maximum geometrical values in the ZSEC and RSEC cards in the input deck must correspond to the maximum geometrical limits set by the user within REG1 Up to 80 of the cpu time is spent i
131. d upper r range for each of those bins The data in this table is the total direct energy deposited into the materials of the model in units of GeV per gram per incident primary particle The columns of bins and data are arranged to be easily cut and pasted into an external graphics or spreadsheet program GRAPH TEMPERATURE RISE This table presents data values versus location in the model volume ignoring zone and region bound aries The data is instead mapped into 5 r bins and 10 z bins The maximum r and z bin values describe the maximum extent of the model the Standard zone mother volume the bins are cre ated by equal divisions between zero and the maximums The left most column gives the mean z coordinate in each bin the top two rows give the lower and upper r range for each of those bins The data in this table is the temperature rise of the materials due to beam from a single pulse of 10 2 primaries in units of K it is assumed that the starting temperature of the materials is 300K unless the user changed this via the TEMPO value on the VARS card in the MARS INP file The columns 130 of bins and data are arranged to be easily cut and pasted into an external graphics or spreadsheet program GRAPH DOSE EQUIVALENT This table presents data values versus location in the model volume ignoring zone and region bound aries The data is instead mapped into 5 r bins and 10 z bins The maximum r and z bin values describe the maximum
132. d user supplied sectors CPU time grows almost linearly with the number of regions in the direction of predominant propagation of the particles 4 Use as little as possible volume detector histogramming it is rather time consuming At least mini mize the number of bins 5 Keep STEPEM 0 1Xtmin where tmin is a smallest linear size of the smallest region in the consid ered group of zones 6 Use cutoff energies for each particle class as high as possible to not damage result of course espe cially in bulk regions far from your regions of interest 7 Use IND 15 T for thick shielding calculations 8 Use IND 6 T and DLEXPX1 options for thick shielding calculations Be carefull as with any biasing techniques do short tests first 9 Use IND 1 F in a routine run to reduce amount of the output In some of these rules the code takes care of those components in some effective manner anyway but the user can reduce the CPU time drastically if he she turns off the corresponding options 13 2 Biasing and Other Control of Physics Processes This is a new section intended to describe in detail how to control or modify the physics processes applied to various particle types as they are transported for example what thresholds or other input deck settings modify which physics processes 150 13 3 Supplementary Routines Section on supplementary routines available from the MARS libraries ATNM RMA8 RNDM POISSN NORRAN
133. d zones they can have cylindrical or cartesian symmetry or can be of an arbitrary shape too intricate to render using the Extended Geometry syntax Further details on setting up non Standard zones is in Section 5 4 Geometry descriptions can be imported from a few external programs and these are referred to as imported zones and MARS will treat these areas as non Standard zones See below in Section 3 1 2 All geometry options can co exist in a setup description Only extended geometry option provides exact crossing of particle tracks with surfaces that prevents small regions within a large volume from being skipped over In other geometry options boundary localization is based on iterative algorithm 20 and user needs to take care of appropriate region numbering pilot steps and localization parameters Zone overlapping in the extended geometry mode means in particular that in this mode a user doesn t need to care about zone numbering when one large zone is filled with small objects Any type of zone can hold any material which the user has declared to be in use see Sections 3 4 and 4 2 4 But there can be only one material in each zone On the other hand a magnetic field can vary from point to point within a zone The difference between the requirements for materials and fields within zones has to do with how the tracking is handled discussed below in Section 3 3 The entire volume of the user s model must be filled by any combinati
134. ded Geometry zones are constructed from a set of contiguous or overlapping geometrical shapes which currently consists of box cylinder sphere cone tetrahedron elliptical tube toroid elliptical cone and conical sector This is similar to the geometry description method used by GEANT There can be up to 10 Extended Geometry shapes declared where each declared shape is counted as a MARS zone A single shape can be sub divided into sub zones with each sub zone counting towards the maximum limit 67 Only extended geometry and ROOT options provide exact crossing of particle tracks with surfaces that prevents small regions within a large volume from being skipped over In other four options boundary localization is based on iterative algorithm and user needs to take care of appropriate region numbering pilot steps and localization parameters Zone overlapping in the extended geometry mode means in particular that in this mode a user doesn t need to care about zone numbering when one large zone is filled with small objects The specifications for the geometric shapes are controlled by lines in the input file GEOM INP As indicated in Section 4 2 2 setting IND 3 T in the MARS INP file activates the reading of the GEOM INP file and the implementation of the Extended Geometry Zones described by it The user is reminded that the overall outer boundary of the model mother volume is set by the ZSEC and RSEC cards in the MARS INP file There
135. define the locations of the major longitudinal divisions of the MARS Standard geometry zones and the number of sub sections within each The materials in those zones are also specified by this card when IND 2 T which is for a z sandwich type geometry see Section 4 3 T for further discussion Recall from the discussion in Section A T that the three variables of dimension 1250 are mapped onto a single array of dimension 3750 The boundary divisions are contiguous no gaps and must be listed in ascending order The max imum z coordinate in the model ZMAX is the right hand boundary of the last declared division or the last ZSE value listed ZSE i The z coordinate real number of the right hand boundary of the i longi tudinal section ZLEF T in the ZMIN data card gives the left hand coordinate of the 1 section These values occupy elements 1 1250 of the mapped array Default 100 1249 0 IZN j The integer number of minor subsections within a given major section Ele ments j 1251 2500 of the mapped array correspond to the i 1 1250 major sections Default 1250 1 IZI k The material index value IM of each major section The minor subsections must be of the same material as their major section Elements k 2501 3750 51 of the mapped array correspond to the i 1 1250 major sections This variable is active only when IND 2 T Default 1250 0 NLTR LR Integer variable which defines the number of major radial divisions of the MAR
136. defined by the user as the x1 y1 z1 coordinates of the first vertex LCS identical to GCS Elliptical Tube 6 cl the inner radius along vertical x axis C2 the inner radius along horizontal y axis C3 the tube wall thickness along one of the axes C3 0 correspondes to a solid filled ellipse defined by C1 and C2 C4 the tube length NT gt 0 or half length NT 0 along the LC S z axis NZSB the number of subdivisions in LC S z default 1 RP defined as the center of the plane perpendicular to the z axis and with the minimum coordinate location LCS the LC S z axis is parallel to the GCS The z axis points from the center of the minimum coordinate location cylinder end to the center of the maximum coordinate location cylinder end Toroid 7 currently unavailable Elliptical Cone 8 C1 the inner radius along horizontal y axis at the lowest LC S z the cone base C2 the outer radius along horizontal y axis at the lowest LC S z the cone base C3 the outer radius along vertical x axis at the lowest DC S z the cone base if C3 C2 then the cone is round otherwise all other lateral dimensions are squashed appropriately the ratio C3 C2 is the scaling factor C4 the inner radius along horizontal y axis at the highest LC S z the cone top C5 the outer radius along horizontal y axis at the highest LC S z the cone top C6 the cone length NT gt 0 or half length NT 0 along the LC S z axis NZSB the number of subdivisions in LC S z default 1 NRSB the number
137. dies with MARS see e g 92 have been further improved These allow a very efficient way to study a source term Calculated are three dimensional distributions of star density total and partial particle fluences above several thresholds total and partial energy deposition densities temperature rise dose equivalent residual dose rates displacements per atom DPA one and two dimensional mass and charge nuclide distributions All of these are accumulated and presented with corresponding statistical errors as part of the standard MARS outputs in the files MARS OUT MTUPLE MTUPLE NON MTUPLE EXG MTUPLE MCNP Energy spectra in the defined zones tagged distributions and some integral values are also produced 3 6 Histogram Options The 7 O sequence as well as the histograming for surface and volume detectors is substantially improved and extended MARS native and HBOOK based histograming and analyses have been extended to include scoring of surface current flux dose equivalent particle spectra and time distributions See XYZ histograming section 3 7 Visualization needs further update See GUI Section The interactive GUI interface is invoked by setting a flag in the main MARS INP input deck The interface is very useful to visually check the geometry of the model before actually running the executable to generate events The flag must be reset to run MARS in the event generating mode as this mode and the interactive GUI mode c
138. downloaded from the secure section of the MARS web page 102 111 Create a new directory and copy from the MCNP installation directory the following components e mcnpf id e prpr e patchf Copy to the same directory the following files downloaded from the MARS web page e GNUmakefile e source patch e fsplit c e lsignal c Check GNUmake file for commands and compiler options appropriate for you system If there is no a fsplit utility on your system create it by means of the following command cc o fsplit fsplit c Now run the GNUmakefile and wait for several minutes until the procedure is complete Upon its successful completion a MCNP library called for example libmenp4Csun a on a Sun system will be created The library must be moved to the directory restricted menp4c os lib where os is sun linux dec aix or irix depending on the OS of your computer and looks like home mokhov for most MARS installations 6 2 1 Building and running MARS MCNP To create a MARS MCNP executable the user copies the distributed MARS user subroutines and GNUmakefile to his local directory as described in Section This is the GNUmakef ile which is distributed with the MARS code not the one used to build the MCNP libraries One specifies the desired non default executable by entering it s name on the command line make rmars mcnp os instead of simply using make which results in the standard Mars executable
139. e U from the given trajectory point X Y Z toa non standard surface and the projection V of the direction vector DX DY DZ to the normal to the surface which passes in its positive direction through the point X Y Z This example shows use of the EDGEUS routine for the surface Y YPL gt 0 and for the particle with 89 Y YPL and DY lt O SUBROUTINE EDGEUS X Y Z DX DY DZ U V IMPLICIT DOUBLE PRECISION A H O Z INTEGER I N C EDGE SCATTERING PROBLEM Y YPLANE Y TURN CJ E Hd y 7 G U Zz Jg 5 11 Subroutine LEAK Creating custom source terms IM 1 and region number N lt 0 to blackholes which are either all material outside of the simulated volume N 0 or any region inside marked with N 1 2 3 where entering particles are killed This feature is used for special scoring or for forming a source term for the cosequent runs both in subrou tine LEAK A user subroutine LEAK N K JJ W E X Y Z DCX DCY DCZ TOFF handles particles which escape from the system N 0 or from the non standard regions tagged with NX 1 Parameter K is the tree vertex level generation number for the hadronic part of the calculated cascade If IND 14 T then K has the same meaning as the above if given particle was generated in hA vertex at E gt 0 0145 GeV otherwise it is forced to be K 205 if the leaked neutron was produced in sequent inter
140. e User is able to load particle tracks as produced by MARS Stored tracks file usually has PLOT extension Also there is possibility to turn on or off the tracks visibility All of that can be done in main panel using Load Track button and switch Load Track ON The same as Print dialog will appear with prompt to enter track file name 143 r Directory f tel E TRACE OLD PLOT E TRACK PLOT E P rile name itn Files of type TRACK Files PLOT plot Cancel e There are two information panels can be started one for materials and another for particles Materials Particles e Materials info panel allows you to examine which material is drawn in which color turn ON and OFF interactively what material to show It can be done by pressing the buttons on the panel left The individual material color can be altered by pressing the colored square on the panel right 144 Of course if you change the view and number of materials will be changed the panel will adjust auto matically e Particles panel has the same properties and allows user to pick particular particles to show and change tracks color interactively 145 Particles Al ES Particles ID Name Modify Reset ae ee Reset Close e User can examine tracks by pointing mouse and pressing middle button panel with track information will appear and particle type energy weight and positio
141. e outside the User non Standard geometry If AX ge XConc or AY ge YConc or Z ge ZConc Return E C Is the current position in the steel core If AX lt XSteel and AY lt YSteel and Z 1t ZSteel Then If Z ge 0 0D0 and Z lt ZSteel middle Then M 1 Go to 200 Else If Z ge ASteel middle and Z lt ZSteel Then M 2 Go to 200 End If End If C Is the current position in the concrete surrounding the steel If Z lt ZSteel Then If AX lt XConc and Ay ge YSteel and AY lt YConc Then M 11 Go to 200 Else If AX ge XSteel and AX lt XConc and AY lt YConc Then M 11 Go to 200 End If C Is the current position in the concrete downstream of the steel Else If Z ge ZSteel and Z 1t ZConc Then If AX lt XConc and AY 1t YConc Then M 13 81 Go to 200 End If End If C C If all User zone area X Y Z are covered by the above statements then the C code should never get to this point If M 0 here then there is a hole in the C logic If M gt 0 and gets to here then there is a missing Go To 200 statement C Print a warning write Logical Error in Regl M Return C C Set and Return N the Mars Zone number corresponding to input X Y Z 200 Continue IF M GT 0 HEN N NFZPEX ELSE IF M LT 0 THEN Non standard blackhole N M D IF E TURN D E m on Although this code is simple there are several necessary steps w
142. e shower core to examine a deep penetration problem never in vacuum or at a boundary with vacuum EIMPT The cutoff energy for hadron weight splitting and Russian roulette De fault 107 GeV NIMPTZ The number of the z planes for hadron weight splitting and Russian roulette 1 lt NIMPTZ lt 10 Default 0 NIMPTR The number of the cylindrical surfaces for hadron weight splitting and Rus sian roulette 1 lt NIMPTR lt 10 Default 0 IMPZ ZZIMPT i WZIMPT i i 1 NIMPTZ Real variables which define the importance sampling in the z direction ZZIMPT z coordinates which define the planes for hadron weight splitting and Rus sian roulette Place them in the exponential attenuation region well beyond the shower maximum z lt z9 lt lt Zip Recommended Az Ain where A n is a material dependent inelastic nuclear mean free path In typical thick shielding case use it for neutrons of energy of several hundreds MeV Default 10 0 0 WZIMPT Importance factors at the above z planes which define the factors for hadron weight splitting and Russian roulette If Az Ain then recommended WZIMPT i z e 2 7 Default 2 0 IMPR RRIMPT i WRIMPT i i 1 NIMPTR Real variables which define the importance sampling in the radial direction RRIMPT Radii which define the cylindrical surfaces for hadron weight splitting and Russian roulette Place them in the exponential attenuation region at radii exceeding several Ain r lt ro lt l
143. e values coincide with boundaries of geometry zones This card is valid only if NOB in the NOBL card is gt 1 See Section RZO 1 i The minimum radius of the i Ox RMI RMAX Default 0 0 RZO 2 i The maximum radius of the i RMI lt RMA lt RMAX Default 0 0 RZO 3 i The minimum left hand z coordinate of the ih special region ZMI i where ZMIN lt ZMI lt ZMAX Default 0 0 RZO 4 i The maximum right hand z coordinate of the i ZMA i where ZMI lt ZMA lt ZMAX Default 0 0 th special region RMI i where th special region RMA i where th special region NSUR NSURF NTOFF NZH NRH Integer variables which give the number of surfaces where all surface type histograms will be accumulated and whether time of flight histograms will also be included See Section 10 2 for the list of the histograms and their IDs The location of each surface is given in the accompanying RZTS data card The surfaces must have cylindrical symmetry being either circles in the z y plane perpendicular to z axis or cylindrical shells oriented along the z axis Time of flight specifications are given in the accompanying TOFF data card NSURF The number of surfaces OXNSURF 100 Default O NTOFF Turns on the generation of time of flight distributions for all declared surfaces when NTOFF 1 Default 0 NZH NRH The numbers of bins in z and r directions Default 150 150 RZTS RZTSUR 4 i UNIT i i 1 100 Four real values which specify
144. ecided by comparing capture and decay lifetimes of which the lat ter is favored for light nuclei Z lt 11 A captured y then cascades down to the ground state of the muonic atom emitting photons along with some Auger electrons all of which is simulated using approximate fits to the atomic energy levels In hydrogen muon capture always produces a 5 1 MeV neutron via inverse 8 decay In complex nuclei the giant dipole resonance plays a role and results in an evaporation type neutron spectrum with one or more resonances superimposed This is illustrated in Fig T I which shows the neutron spectrum resulting from u capture on oxygen In addition smaller numbers of evaporation type charged particles and photons may be emitted Calculated with the above algorithms longitudinal dose distributions in a slab tissue equivalent phantom are shown in Fig 12lat the axis of 150 MeV proton and 75 MeV pion muon and neutron beams striking the phantom 0 4 u capture on Oxygen dN dE MeV Energy deposition density GeV g 0 5 10 15 0 5 10 45 30 Neutron Kinetic Energy MeV Depth cm Figure 11 Neutron spectrum generated in a Figure 12 Axial absorbed dose in a tissue capture on oxygen atom equivalent phantom for 150 MeV p and 75 MeV T u n beams with 1 x1 cm transverse dimen sion 17 2 9 3 Antiprotons Stopped p attach to nuclei in the same way as 7 or jz Annihilation at res
145. ectory can be regenerated randomly in BEGI rechecked and accepted only when it fits within the users specification Another example is where the beam is uniformly distributed in one view but gaussian distributed in the other view The Input Deck cards can do one or the other distribution for both views together but not separately Again the user TI would use the input deck to specify either the uniform or gaussian characteristics and then modify those characteristics as needed in routine BEGI Question if you set W 0 0 for primaries which don t fit your criteria does that eliminate that particular primary particle and force the generation of a new one Another way to use routine BEG is to read in a file which contains a list of primary beam particles The user can create such a file in any custom format it must simply contain the same parameters as the BEGI subroutine arguments or contain sufficient information to extract those parameters The user in this case must also install the code to properly open read and close the file Such a file can be generated by MARS itself using the LEAK subroutine In this case one uses MARS in two or more consecutive steps The first step generates a beam into a geometry and creates the resulting showers Within that geometry is a Zone with a specific Zone number which acts as a flag for subroutine LEAK any particle crossing into that zone will have it s parameters written to a file The parameter
146. ed in a cylindrical geometry and so display only from R 0 to R Rmax The GUI interface displays the geometry in X Z Y Z or X Y planes Thus the color maps display only in the upper half of the plan or elevation view The particular histogram shown is a map of the charged hadronic flux each color being an order of magnitude in flux density One can see the broad pion beam traversing the air green and blue color bands showering and spreading out in the steel and concrete of the beam dump and some amount of back scattered particles from the front face of the steel back into the air above the incoming beam More details on both histograms and the GUI interface are given in Sections and I2 respectively 4 3 2 R Sandwich Geometry Next examine a similar simple geometry also a beam dump type but using r sandwich geometry r sandwich geometry is one where the same material extends along the z axis and the material changes only at concentric r boundaries Again the user must choose either z or r sandwich geometries to represent the Standard zones in his model Figures I6 and I7 show a simple r sandwich Standard geometry The pictures are again produced by the Mars GUI interface Figure l6 is a color filled diagram of the Standard zones with the colors similar to the z sandwich example light blue is air orange is steel and tan is concrete Figure 17 gives a cross section view of the zone diagram Y x tis ty Figure 16 Plan View
147. efault with the value given by the EMCHR variable in the ENRG data card RLCTCH The values for the energy thresholds indexed by IM the order numbers the materials are listed in the MATER INP file MTNE RLCTNE 500 Real variables giving the neutron energy threshold applied only to specific materials They must be less than 0 0145 GeV if one wishes to calculate energy deposition correctly Any material which does not have a corresponding entry here will have the global threshold applied as the default with the value given by the EMNEU variable in the ENRG data card RLCTNE The values for the energy thresholds indexed by IM the order numbers the materials are listed in the MATER INP file MTGA RLCTGA 500 Real variables giving the electromagnetic energy threshold for y applied only to specific mate rials They must be less than 0 0145 GeV if one wishes to calculate energy deposition correctly Any material which does not have a corresponding entry here will have the global threshold ap plied as the default with the value given by the EMIGA variable in the ENRG data card RLCTEM The values for the energy thresholds indexed by IM the order numbers the materials are listed in the MATER INP file MTEL RLCTEL 500 Real variables giving the electromagnetic energy threshold for e applied only to specific mate rials They must be less than 0 0145 GeV if one wishes to calculate energy deposition correctly Any material wh
148. eing used The first sub mode has all the geometry description handled by MARS with MCNP handling the details of neutron interactions in this case only MCNP material correspondence data cards are appended to the MARS INP file Details on the syntax of MCNP material data cards is in Section In the second sub mode the MCNP geometry module is used to describe the arrangement of materials where detailed neutron interactions are performed So in addition to the material data cards MCNP geometry data cards are also present These data lines are defined in Section 6 1 2 In this second mode the full MARS physics modeling is still performed within the geometry described by the MCNP geometry data lines and there can be portions of the model s geometry defined by the usual MARS zones outside the MCNP geometry description where MCNP will continue to handle neutron interactions All of the MCNP data cards are located after the MARS INP STOP card and must be contained between the MCNP data delimiter lines the start card MCNP START and the stop card MCNP STOP A MCNP 106 data card either the material or geometry type is a free format input up to 80 characters on a single line a single data card can continue past a single line by using the continuation indicator amp at the end of a line Data cards of a given type must be grouped together on sequential lines and not intermixed Blank lines are treated as delimiters between the groups of materi
149. encoded geometry is probed and visually displayed The interface displays all the details of the encoded geometry showing the encoded zone numbers materials and magnetic fields it is a valuable tool for checking complex geometries before executing event generation During event generation runs the user can specify output files holding histograms and particle tracks these output files can be opened by the GUI interface post run and projected onto the visual display of the geometry 12 1 Main Features The main MARS GUI SLICE features are e Two dimensional geometry slice and magnetic field view on a graphical display panel GDP Maxi mum and minimum coordinates along each axis and maximum field components are provided for the given view in corresponding entry fields EF They are changed automatically by grabbing a desirable view box on the GDP holding a CTRL key and clicking with the mouse left button at the two diagonal box corners Alternatively the lower and upper view boundaries can be typed in the EF along with a binning of the magnetic field grid seen on the GDP There is a 1 1 scale check field CF to return to a natural scale e A slice plane is chosen by a corresponding radio button A magnetic field view can be interactively turned ON and OFF in a corresponding CF e Materials distribution in a given view is represented in a color or black and white wire frame contour mode or in a color region filled mode with the mode chosen
150. ent arbitrarily oriented orthogonal box rectangular parallelpiped sphere right circular cylinder right hexagonal prism Using these shapes to define a geometry adds two more groups of data to the MCNP section of the MARS INP file where the first group is the material data cards described in the previous Section The two added groups are to define geometric zones called cells in MCNP and to define the surfaces which bound the zones Each of the three groups of data cards is required to be present using MCNP material geometry mode data cards of each group cannot be intermixed but each sit in their own block of cards with the card groups separated by a blank line delimiter The surface data cards are a shorthand syntax of the equation f x y z 0 where equality to zero is assumed and not written Each of the cards contains a mnemonic name of the surface and numerical entries indicating the extent or location of the surface consult the MCNP manual distributed with the code for a listing of surface names and their numerical descriptors The surface data card syntax is ID Sname Val Vala2 Val where IDs an integer is the surface ID number Each surface has a unique ID number Sur face data cards do not need to be listed in order by their ID and there can be gaps in the ID number values for a given group of cards Sname a short character string which is a mnemonic name of the surface such as pz for an infinite plane ort
151. er of zones the physics results for these zones will be listed as for all non Standard zones 3 20 Particles used in MARS The list of particles which the MARS simulation produces interacts and tracks through a model is given in Table 2 Heavy ions are also transported in the code The mesons listed 1 7117 K K muons and the longer lived particles such as K A and other hyperons are allowed to decay in flight according to their 22 lifetimes if they survive interactions in matter between their production and decay points Their main decay modes are included in the simulation Short lived particle types generated at an interaction point such as n9 p w D and J V are forced to decay immediately using their most probable branching fractions these decays produce daughters which are listed in Table Each particle in Table has an index associated with it This index is used to refer to the particle type in various places in the MARS code For example the primary particle type can be specified from the input MARS INP file using this index the user histogram subroutines can utilize the index to accumulate data on a particular particle type In the MARS common blocks and the user subroutines the index value is generally assigned to variable JJ Table 2 Transported particle types and their corresponding index value 1 2 3 4 5 6 7 8 9 10 p n cU wo KY K w w e 11 12 13 14 15 16 17 18 20 er p v d t Hez Hey v Ve 21 22 23 24 25
152. es marsmain f is a short file which holds the FORTRAN Program statement the names of the main input and output files and the call to the mars1514 master code 30 PROGRAM MARSMAIN oru PET E MARS15 CODE E AA C LAST CHANGE 10 DEC 2013 BY NVM C a IMPLICIT NONE INCLUDE fnames inc EN CERE MD a INPNA MARS INP OUTNA MARS OUT HBKNA MARS HBOOK XYZTABNAM XYZHIS TAB DUMPNA DUMP MTUPLENAM UPLE MTUPLEEXGNAM UPLE EXG MTUP CNPNAM UPLE MCNP MTUPLENONNAM UPLE NON CALL MARS1514 STOP END The user is free to change the input output file names in narsmain f The user copies marsmain f m1514 f GNUmakefile and the input decks MARS INP GEOM INP and XYZHIS INP along with the MCNP file xsdir to his her own working area The user customizes the input decks and the user subroutines as needed the user is free to create additional subroutines called from the provided user sub routines The GNUmakefile can be edited by the user to include the list of all the user s local subroutine files so they will be compiled and linked to the MARS libraries to obtain an executable The executable is made by running the GNUmake file script This manual assumes the user is familiar with the syntax for compiling and linking source code using gmake or make on unix or linux systems The GNUmakefile sc
153. es symbol and the max imum minimum data values on either side of the color bar can be dragged all over the canvas by point amp click using the mouse lt Button 3 gt They are also singularly deletable by point amp click using the key stroke lt Ctrl gt lt Button 3 gt The added lt ViewFormat gt button allows for switching between the 1 1 and 16 9 canvas aspect ratios The former view is intended for working purposes whereas the latter one is useful for generat ing publications and documentations inserts Some white space at the bottom of the canvas allows the user to include some add on text strings This new GUI state is fully integrated with the other GUI features The tracks environment has been integrated with the navigation system lt lt and gt gt User s add on text strings and arrows have been integrated with the navigation system lt lt gt gt and view format The geometry display modes have been reduced to two namely lt Fill gt and lt WireFrame gt The former is currently the default at GUI start up The horizontal H and vertical V rotation radio buttons have been compacted The rotation initial default values depend upon the slice view selection according to Table I2 2 Remember MARS15 uses the right handed cartesian coordinate system Therefore the default settings shown in the table correspond to the top side and cross sectional looking along the z axis views respectively The user
154. explains how to use the Graphical User Interface a visual tool to examine a geometry and to display results Section IO describes the input and output histogram files Section IT describes the output files produced by MARS with details of the tables and values in the default output files and the contents of various special output files Other Sections describe special running modes Recent updates include extended histogram capabilities more built in materials corrected handling of longer lived hadrons and improved computational performance In addition to direct energy deposition calculations a new set of fluence to dose conversion factors for all particles including neutrinos has been built into the code MARS uses portions of the MCNP4C code for default neutron transport below 14 MeV and has the ability to fully utilize the MCNP code where more detailed simulation of low energy neutrons is needed The MARS system also includes links to the ANSYS code for thermal and stress analyses and to the STRUCT code for multi turn particle tracking in large synchrotrons and collider rings The code is available for the Unix and Linux operating systems and is distributed by the developers from Fermilab Section gives instructions on obtaining the code and basics on building an executable For re cent publications on the current MARS15 version see the official MARS Web site at http www ap fnal gov MARS 2 Physics Models MARS simulates a varie
155. extent of the model the Standard zone mother volume the bins are cre ated by equal divisions between zero and the maximums The left most column gives the mean z coordinate in each bin the top two rows give the lower and upper r range for each of those bins The data in this table is the tissue dose equivalent in units of mSv per incident primary particle The columns of bins and data are arranged to be easily cut and pasted into an external graphics or spreadsheet program GRAPH TOTAL HADRON FLUENCE IN HIGH ENERGY SECTOR This table presents data values versus location in the model volume ignoring zone and region bound aries The data is instead mapped into 5 r bins and 10 z bins The maximum r and z bin values describe the maximum extent of the model the Standard zone mother volume the bins are cre ated by equal divisions between zero and the maximums The left most column gives the mean z coordinate in each bin the top two rows give the lower and upper r range for each of those bins The data in this table is the total hadron particle flux for hadrons with energy greater than the value of EM the hadron threshold energy in the ENRG card the default threshold value is 0 0145 GeV Units are hadrons per cm per incident primary particle The columns of bins and data are arranged to be easily cut and pasted into an external graphics or spreadsheet program LOW ENERGY NEUTRON SECTOR This delimiter labels a group of
156. f certain user subroutines All histogram sets however are by default written to the same mars hbook file All these histogram sets are described further below By default MARS sorts histograms by following classes e histogram type vertex fluence energy deposition and energy spectrum e particle class hadron electromagnetic and muon e charge neutrals charged and total The main program allocates the dynamic memory for HBOOK and gives control to the whole system His togram set up and entry routines can be re defined by the user according to his her specific needs 10 1 Built in Volume Histograms These histograms are filled for the whole system or for the NOB special regions defined in the MARS INP file and initialized by presence of non zero NOBL and RZOB cards there Residual dose histogram is normalized to AINT p s and is scored for the irradiation TI RH and cooling TICH times days defined on the HTIR card default is 30 and 1 days respectively The histogram list in the file MARS HBOOK with their IDs and functional contents is obtained with the PAW command hi list The list is self explainatory Default histogram IDs are shown in Table 10 ALL HISTOGRAMS DIVIDED BY VOLUME SURFACE AREA OR AND DELTA E HISTOGRAM TYPE IHTYP 1 VERTEX STAR CM3 1 lt ID lt 100 IHTYP 2 FLUENCE AT STEP 1 CM2 101 ID 200 IHTYP 3 ENERGY DEPOSITION GEV G 201 ID 300 IHTYP 4 ENERGY SPECTRUM 1 CM2 DEL 301 I
157. f discussion on how one should use these errors as a guide to the quality of the results All results are normalized to one incident particle i e to one event except for temperature rise and residual dose which are normalized to the total incidents as declared by the value of AINT on the VARS card The following paragraphs itemize each data table in the order in which they appear in the MARS OUT file The table label is highlighted and the values it contains are defined Not all the listed tables may be present If INDX 1 T more tables will be present than otherwise If special region histograms were requested using the NOBL card then additional tables of results will be present for the declared special regions LONGITUDINALLY INTEGRATED ZMIN ZMAX VALUES This table is not arranged by zone number but as the title implies has combined the results along the z axis Each column holds the summed results for all z within the r values given at the tops of the columns Each type of integrated result is listed for those r on each row The first row SCHAR is the charged star density STOT is the total star density FL TOT is the total hadron flux ELEN is energy deposited by low energy neutrons those below the hadron energy threshold as given by EM on the ENRG card ELCH is energy deposited by low energy charged hadrons from nuclear de excitation processes EEMS is energy deposited by electro magnetic showers EDEX is energy deposited thro
158. f low energy neutrons MARS uses portions of the MCNP package by default when neutrons fall below 14 MeV however this default mode is not sufficient for certain applications In particular when predicting residual dose rates and when predicting prompt dose rates in labyrinth type geometries the full MCNP package should be used to take advantage of it s detailed models of the interactions of interest Residual rates are sensitive to the materials present and prompt dose rates are sensitive to the n y reactions which occur when slow neutrons are stopped and captured the MCNP code package excels at the simulation of both these effects MCNP code contains very detailed material handling taking into account the nuclear physics details that occur in interactions with different nuclei and this affects residual rate calculations MCNP also includes n y reactions when the neutron is finally stopped and captured These reactions affect the prompt dose calculations in labyrinth type geometries where slow neutrons are dominant MARS can be used in conjunction with the full MCNP code package MARS generates the initial neutron but sends it to MCNP for tracking and interactions Once tracked to capture or to it s cutoff energy the accumulated information is handed back to MARS for compilation of tallies and results In general the model geometry is specified using the usual collection of Mars zones and MCNP handles the details of the declared materials
159. f the default values are appropriate for the user s model then the control lines for those features do not need to be present in the MARS INP file Some problems cannot be described solely by information in MARS INP such as complex composite materials different of the built in compounds complex geometries atypical primary beam distributions or magnetic fields In these cases the appropriate user subroutines are customized to describe the problem s complexity and the use of these is discussed Section 5 However even with extensive code customization the MARS INP file parameters are a key method of specifying basic information Section I3 2 discusses some of the switches in the MARS INP file which turn on or off various physics process and the conditions under which one might wish to modify these Sections 4 T and H 2 cover all aspects of the MARS INP parameters and syntax Section H 4 describes the use of the GEOM INP file Section 4 3 holds examples showing the use of some the more common MARS INP parameters and Section has an example of Extended Geometry zones Other sections of this manual hold descriptions for other optional input files Section IO 4 describes the use of the XYZHIS INP file and the histograms it produces Section 6 describes the inputs required when using the MARS MCNP running mode Section holds instructions for generating input information using the MARS MAD Beamline Builder Section 7 describes h
160. for 5 GeV cE 100 TeV 44 This provides at least partially the features of a full exclusive event generation with all known particles in a final state and is available as a non default option which the user must specify see Section 8 2 for instructions The DPMJET code has been proven to be consistent with collider and cosmic ray data in a multi TeV energy region The two component Dual Parton Model is used with multiple soft chains and multiple minijets at each elementary interaction Within this model the high energy projectile undergoes a multiple scattering process as formulated in the Glauber approach Particle production is realized by the fragmentation of colorless parton parton chains constructed from the quark content of the interacting hadrons The code includes cascading of secondaries suppressed by the formation time concept within both target and projectile nucleus The excitation energies of the remaining 14 Tp 1 total i Sol 2t mun ed o tal cro To Cross section mb 3 m cdi t a l Hu EN yn CU etm ua m m ee 10 i i i nici Ep iiai y ee 10 10 10 j 10 10 M TRUM GeV c Ekin MeV Figure 9 missing figure from hadron production Figure 10 missing figure from deuteron nucleus section collision section target and projectile nuclei are calculated and simulation of subsequent nuclear evaporatio
161. geometrical limits The table is arranged in 3 columns labeled by the indicated directions The first row TOTAL SURFACE CHARGED CURRENT is the number of charged hadrons the second row TOTAL SURFACE NEUTRAL CURRENT is the number of neutrons This is followed by HADRON LEAKAGE ENERGY GEV a sum of the energy carried by these exiting particles in the indicated directions This table is followed by single values for the leaked energy from various particle types along with the total of all types Finally there isthe VISIBLE ENERGY BALANCE which compares the total energy detected within the geometry to a projected total energy which is defined on the following line For geometries similar to beam dumps with thick shielding one expects most or all of the energy to be contained within the model For geometries which simulate a beamline one expects a good fraction of the incoming beam energy to pass through These leakage values help one determine if the model is behaving in an expected way and help give indicators of how energy is being carried out of the model 128 HADRON LEAKAGE SPECTRA This table presents the energy spectra for different groups of hadrons which have leaked out of the model The data are arranged in 3 main columns for the 3 labeled directions UPSTREAM DOWNSTREAM SIDE Each of these main columns holds in turn 3 sub columns labeled P PBAR for p and p N NBAR for n and pn and P1 K for 1 and K The rows are bins in ener
162. ghts applied to representative particles The statistical accuracy of the results of the simulation for example the error on the particle flux through a certain portion of the geometry depends upon the weights assigned to all the simulated particles which were tracked through that portion of the geometry For very large and very small weights the divergence of these errors becomes a problem The solution within MARS is to employ a weight window particles with weights within the window are left as is but particles with weights above and below the window have special handling applied For particles with a weight above the weight window value surface splitting is applied At an arbitrary surface some distance from the actual interaction vertex a generated particle with weight W is split into n particles each with a new weight W lw For example an initial 7 with W 12 would be split into four 7 s each with W 3 The splitting increases the number of tracked particles and therefore increases the simulation cpu time but the results are statistically more stable For specialized studies the user can control the location of splitting surfaces and the particle energy at which they are applied see Section 4 2 6 Surface splitting is sometimes applied even for particles within the weight window in order to accumu late statistics in specific regions of interest This is done for example in simulations of thick shielding For rarely produced
163. grams can overlap contrary to the volume RZ and surface histograming Arbitrary voxels the smallest distinguishable box shaped part of a three dimensional space can be defined by individual binning NX NY NZ in each macro box Arbitrary cut off energies can be defined for each flux type histogram Histogram J D reserved 701 lt ID lt 1000 These histograms are normalized to AINT p s contrary to all previous histograms and most values in MARS OUT and MTUPLE which are normalized to one incident particle Residual dose histogram DRE is scored for the irradiation TI RH and cooling TICH times days defined on the HTIR card default is 30 and 1 days respectively Up to 39 different histogram types can be defined in a run as described in Table 12 First 33 types are two dimensional and can be filled 118 for particle energies above certain cutoffs e g FLN gt 0 03 DET gt 0 001 DRE gt 0 02 etc This cutoff technique is not applicable to the gas production histograms HY D H EL and T RI Defaults are 0 03 GeV for star density and energy transport cutoff energies defind on the ENRG card Last 6 types are one dimensional energy spectra Note that the DP A type histograms are calculated only if IND 17 T DET through DEE histograms prompt dose are calculated in the course of Monte Carlo from energy dependent fluxes and flux to dose conversion coefficients they can have non zero values in vacuum assuming that a tissue equivalent phant
164. gy with the indicated values Two spectra data entries are given for each row column dF dE in units per GeV cm and dF d ln E in units per cm At the end of the table are three additional results combining the specified particle groups into a single value for each of the three leakage directions The first resultis TOTAL 1 CM 2 the sum of the GF d ln E spectra the second result is the mean energy E GEV the third result is the dose equivalent HADRON DEQ mSv due to the leaked hadrons OTHER NON LEPTON LEAKAGE SPECTRA This table is similar in set up to the one described above but for different particle groupings In this table all charged hadrons are one particle group all neutral hadrons and all heavy ions Does this table include the particles from the above table just in different combination Or is it a summary of anything NOT included in the above table In my sample output this table is all zeros while the above table has some data results GRAPH HADRON LEAKAGE SPECTRA This table repeats the dF d InE data from the HADRON LEAKAGE SPECTRA table but refor matted so that the columns of data can easily be cut and pasted into an external graphics or spread sheet program GRAPH PHOTON ELECTRON LEAKAGE SPECTRA This table presents the energy spectra for photons and electrons positrons which have leaked out of the model The data are arranged in 3 main columns for the 3 labeled directions FACE BACK SIDE
165. hich apply to any use of this subroutine When REGI is called MARS passes to it the position X Y Z of the current particle There is a local variable M which is set to O on entry to REG1 M is set to a non zero value somewhere in the code s logic and it s value is between 1 and M MAX Just before exiting REGI the statement N NFZPEX Msets and returns to MARS the absolute zone number N which corresponds to the input X Y Z There are other steps in this example which while not necessary are highly recommended At the top there is a statement or series of statements which asks whether the current X Y Z is within the regions where non Standard zones are defined if not then the routine is exited Up to 80 of the program s running time is spent in geometry modules including REG1 It is far more efficient to determine immediately whether X Y Z is outside the overall non Standard zone region than to let all possible X Y Z locations fall through the code In the case where X Y Z is outside the non Standard zone region the input absolute zone number N must be returned to MARS unchanged Another recommendation is to construct the logic of the code so that satisfied conditions jump out and errors fall through In this example once a condition is satisfied and a zone number assigned the code jumps out of the conditional statements to the end where the absolute zone number N is assigned If none of the conditional statements are
166. hogonal to the Z axis Refer to the MCNP manual for the collection of names Val a string of one or more numbers integer or real depending on the surface being described The values give information on the size and or location of the surface according to the equation used to describe the surface For example in the case of a plane orthogonal to the z axis the single value 10 would be entered as this is the shorthand for the equation z 10 0 which describes such a plane located at z 10 In general surfaces are defined in the Mars global coordinate system If the surface cards are defined in a local coordinate system then a transformation matrix between the local and global systems must be supplied by the user Zones are built from surfaces Each surface has two sides a positive side where points satisfy f x y z gt 0 and a negative side where all points satisfy f x y z lt 0 To first order a zone is con structed by stating which sides of a selection of defined surfaces bound it This is done by attaching a or sign to the surface ID numbers IDs to indicate which of the sides positive or negative is assigned to the zone the is optional while the is mandatory In addition the boolean operators AND and OR are used to describe how intersecting surfaces define the zone One or more blank spaces between any two surface ID numbers implies the AND operation applied to their spaces to form an intersection of the sp
167. ich does not have a corresponding entry here will have the global threshold ap plied as the default with the value given by the EMIEL variable in the ENRG data card RLCTEM The values for the energy thresholds indexed by IM the order numbers the materials are listed in the MATER INP file MTSM RLSTEM 500 Real variables giving the step length for boundry localization applied only to specific materials Any material which does not have a corresponding entry here will have the global step length applied as the default with the value given by the STEPEM variable in the SMIN data card The recommendation for the value of this parameter is the same as described for the STEPEM variable RLSTEM The values for the step lengths indexed by IM the order numbers the mate rials are listed in the MATER INP file 47 MTSH RLSTEH 500 Real variables giving the pilot step length applied only to specific materials Any material which does not have a corresponding entry here will have the global pilot step length applied as the default with the value given by the STEPH variable in the SMIN data card The recommendation for the value of this parameter is the same as described for the S TEPH variable RLSTEM The values for the step lengths indexed by IM the order numbers the mate rials are listed in the MATER INP file MTOG ILAOM 500 Integer variables that allow the choice of the inclusive and exclusive event generators at nuclear inel
168. il 3 1 2 Geometries from other Codes The MARS program can accept geometry descriptions created by a few other programs At present these programs are MCNP FLUKA and the MAD format The MAD format is used by various accelerator design programs as a unified method to describe typical beamline elements For MARS to use a MAD format file the file must first be pre processed through a stand alone parsing program called the MAD MARS Beamline Builder it s use is described in Section 9 FLUKA geometry description files must also be pre processed in this case the parsing program is a script which is distributed with the MARS code and libraries and its use is described in Section 7 Instructions for using MCNP geometry descriptions is in Section 6 1 2 For each of these the processed geometry file from the external code is imported into MARS by appending the file contents onto the end of the main MARS input file MARS INP and then certain flags are set on the INDX card so that MARS knows to examine this file past the STOP card These geometry descriptions function in MARS just as the native geometry descriptions do they describe an array of geometric zones and these zones are treated just as any other defined MARS zones including the volume requirement described above In general the zones created by these imported geometries are treated as non Standard zones and as such must follow the same numbering conventions and limitations on the total numb
169. ilder Users Guide Fermilab FN 738 rev 2004 16 e S I Striganov On the theory and simulation of multiple Coulomb scattering of heavy charged particles Fermilab Conf 04 056 2004 17 The main contributors to this version of the code are N V Mokhov P Aarnio Y I Eidelman K K Gudima C C James M A Kostin S G Mashnik V S Pronskikh I L Rakhno S I Striganov and LS Tropin Abstract This paper is a user s guide to the current version of the MARS15 Monte Carlo code MARS allows inclusive and in many cases exclusive simulations of three dimensional hadronic and electromagnetic cas cades and modeling of heavy ion muon and low energy neutron photon transport in accelerator detector spacecraft and shielding components Particles can have energies from a fraction of an electronvolt up to about 100 TeV The code has undergone substantial improvements since the last documented version MARS13 95 and since previous releases of MARSIS all these as well as other specific features of the MARS code system are explained in detail Descriptions of general input and output with commentary and recommendations are given Examples are given for running the program with distributed sources com plex compounds arbitrary geometries and magnetic fields A built in graphical user interface allows the visualization and detailed analysis of the geometry description Enhanced options are described for the MARS code being coupled with the DP
170. ime per history for example when the neutron cutoff energy is below a few MeV and in presence of magnetic fields It is recommended to conduct a short test to evaluate an efficiency of this option for a given application See Section I3 T for more discussion Note that results for direct energy deposition and related values are not affected by this flag use the default analog method for tabulation of results of transported particles appro priate for geometries which do not model thick shielding switch on forced nuclear interaction point target mode the incident primary hadron or heavy ion interacts with a certain probability with a point like target placed in the system at coordinates xo yo zo The probability is specified by the EFF vari able associated with the VARS data card The material index for this target is defined by user in the BEG1 subroutine If not it is determined automatically at the initial point xo yo Zo see INIT card IM 1 is used if this point belongs to vacuum This switch also forces u decay when the primary is a y variable IO in the IPIB card 7 or 8 without v transport turned on This switch is typically used for models of muon accelerators no point like target and no forced decay for u primaries switch on neutrino beam and transport for both y primary beam and v from 7 and u decays This switch is typically used for models of muon accelerators not for conventional neutrino beams no neutri
171. indow NDX 2 T EVT 1000 50 Z Q 0 02 0 02 Q UH Bl AH f tg wW i 1 0 1 0 ER INP PM Q O1 22 22 5 24 5 44 5 2501 12 34 5 ZNZ C uot Ej N c LTR 3 RSEC 1 5 10 512442 TSM 220 01 0 01 0 01 TSH 220 1 0 1 0 1 STOP C MATR HE HE TI AIR AIR The deck is set up for z sandwich geometry given by INDX 2 T and by the fact that the assignment of materials to zones is given in the ZSEC card There are only three unique materials among the five listed and this is done so that different step sizes can be assigned to the zones of helium and air adjacent to the titanium window The total amount of helium and air on either side is 22cm and is split into large zones 20cm deep and smaller zones 2cm deep adjacent to the window The window itself is 0 5cm thick not a 66 very thin window but the example is for illustrative purposes Each of these five zones is given a unique material ID number Next the global step sizes given by the SMIN card are sized for the 20cm deep zones of helium and air The MTSM and MTSH cards adjust the step sizes downward for materials 2 3 4 with the step sizes in those 3 materials being the same values in this example These smaller step sizes are appropriate for the thickness of the thin window taking similar small steps through the helium and air on either side of the window assures that the window boundary will be acc
172. ing a new factor in the entry field and then clicking on the Draw button Useful to display results without a new Monte Carlo run for another beam intensity or for another units say mrem instead of mSv by increasing the normalization parameter by a factor of 100 An arbitrary histogram value HBK can now be displayed in the PointInfo gt widget It was limited to the 2 x 10 9 lt HBK lt 2 x 10 in the old version 137 10 11 12 13 14 15 16 A histogram data representation uniquely corresponds to a choice of the variable Number Of Decades gt Acceptable values for such a variable are 2 4 8 16 The upper bound is 16 Upon loading a histogram the data are coded into 16 colors and 16 decades The user can improve the resolution of the data representation by reducing the data range hence changing the Number Of Decades gt by entering the appropriate range end points in the relative entry field A lt Reset gt button has conveniently been added to the GUI panel If selected all the current work session data are lost and the GUI is reset to its start up state The MARS15 particle ID JJ has been added to the lt T racks Point gt widget The behavior of the histogram lt ON OFF gt toggle has been forced to be the same as the behavior of the tracks lt ON OFF gt toggle When a histogram is being displayed the aspect ratio text string the ax
173. ing configurations where star density is the main result of interest For such models EM should be set to 0 03 GeV which is the standard star production threshold EPSTAM The star production threshold kinetic energy Default 0 03 GeV which is the standard definition of a star EMCHR The threshold energy applied collectively to muons heavy ions and charged hadrons The smallest possible value in the current version is 107 GeV Default 0 001 GeV EMNEU The threshold energy for neutrons The smallest possible value is 1071 GeV Default 1074 GeV EMIGA The threshold energy for y The smallest possible value is 107 GeV in a de fault non EGS5 mode and 1079 GeV in the EGS5 mode Default 1074 GeV EMIEL The threshold energy for e The smallest possible value is 107 GeV in a default non EGS5 mode and 1079 GeV in the EGS5 mode Default 5 x 1074 GeV EMNU neutrino energy threshold The smallest possible value is 0 01 GeV De fault 0 01 GeV EMEVAP The minimal energy for pre equilibrium and evaporation modeling which is turned off if EMEVAP 70 2 GeV Affects nucleons only Raising this value can substantially reduce CPU time in models with high Z materials For example if one is mainly interested in 7 or u production this value can be safely raised to Default 0 GeV 4 2 4 Materials and Material Dependent Settings MATR MTCH MTNE MTGA MTEL MTSM MTSH MTQG MTEG LEMS BIDC BIPR BIBH BIGV BIAN BIGA BIEA BIAP As
174. ions C3 NXSB NYSB NZSB RP LCS C2 C3 NZSB NRSB RP LCS C2 NRSB RP LCS C2 C3 C4 C5 NZSB NRSB RP LCS Cl1sC3 continued on next page the box length NT gt 0 or half length NT 0 along the LC S z axis the number of subdivisions in x default 1 the number of subdivisions in y default 1 the number of subdivisions in z default 1 defined as the center of the plane perpendicular to the z axis and with the minimum coordinate location the box s z and y LC S axes are parallel to two perpendicular edges of the minimum coordinate location z plane the z axis points from the center of the minimum coordinate location z plane to the center of the maximum coordinate location z plane The z y z axes of the LC S are parallel to those of the GC S the inner radius of the cylinder 0 for a solid cylinder and gt 0 for a cylindrical tube the outer radius of the cylinder the cylinder length NT gt 0 or half length NT 0 along the LC S z axis the number of subdivisions in LC S z default 1 the number of radial subdivisions default 1 defined as the center of the plane perpendicular to the z axis and with the minimum coordinate location the LC S z axis is parallel to the GC S The z axis points from the center of the minimum coordinate location cylinder end to the center of the maximum coordinate location cylinder end The orientation of the LCS x and y axes is arbitrary the inner rad
175. ions for K K and p are derived from PDG data compila tions 54 and PDG parameterizations are used for all particles with energies between 10 GeV and 100 TeV Elastic cross sections Cej for p n v and 77 from 10 MeV to 10 GeV are calculated from CEM algoritms while elastic cross sections for K K and p are interpolated from data by PDG Parameterizations from PDG are used for elastic cross sections for all these particles with energies between 10 and 200 GeV For all particle types with energies between 200 GeV and 100 TeV the optical theorem with universal slope is applied As a sample comparison between data and MARS Figure 3 shows comparisons for Otot and Ce for 1 p collisions 2 2 2 Add on heavy ion cross sections here 2 2 5 Hadron nucleus cross sections Total inelastic and elastic op 4 cross sections from 1 MeV to 5 GeV are described using new compilations and improved interpolation algorithms 56 57 At higher energies 5 GeV E 100 TeV Otot Cin EO prod and c are calculated in the framework of the Glauber multiple scattering theory with the above o as an input The nucleon density distribution in nuclei is represented as the symmetrized Fermi function with the parameters of for medium and heavy nuclei Z gt 10 and the ones of for Z 10 An example is shown in Fig 4lfor neutron nucleus oy as calculated with this algorithm solid line and with the improved algorithm dashed line 2 2 4 Photon nucleus
176. is own special ized purpose then certain user subroutines can be used to create a custom output file see Section 5 for more information AII the filenames used here are the MARS default names These file names can be changed in the main calling routine nar smain f see Section 5 1 11 1 Data Table Output Files The files VOLMC NON MARS OUT MTUPLE MTUPLE NON MTUPLE EXG and MTUPLE MCNP are described in this Section These files report results for different zone types The MARS OUT file Sec tion L12 lists all the tables of results for Standard zones If the user requests expanded output by setting the MARS INP card INDX with flag 1 T then the MTUPLE file is also produced no suffix on this default filename The MTUPLE file Section 1 1 3 contains results for Standard zones and duplicates some of the information in the MARS OUT file but the results are arranged in a single large table rather than several separate ones When non Standard zones are present their results are printed to the MTUP LE NON output file Section L L A these include zones from imported geometry files If Extended Geometry zones are used their output appears in the MTUPLE EXG file Section 11 1 5 If using the MARS MCNP mode and also using MCNP geometry cards to create some of the geometric zones then the results for these zones is reported in the MTUPLE MCNP file Section 11 1 6 Keep in mind that if the users model description uses more than o
177. ius of the sphere 0 for a solid sphere and gt 0 for a spherical shell outer radius of the sphere the number of radial subdivisions default 1 defined as the sphere center the orientation of the axes is arbitrary the inner radius at the lowest LC S z the cone base 0 for a solid and gt 0 for a hollowed cone the outer radius at the lowest LC S z the cone base the inner radius at the highest LC S z the cone top 0 for a solid or closed shape and gt 0 for a tubular cone the outer radius at the highest LCS z the cone top the cone length NT gt 0 or half length NT 0 along the LC S z axis the number of subdivisions in LC S z default 1 the number of radial subdivisions default 1 defined as the center of the minimum coordinate location LC S z plane which is the cone base The z axis points from center of the cone base to the center of the cone top the LC S z axis is parallel to the GC S z axis The orientation of the DC S x and y axes is arbitrary Defined by a set of 4 verticies The user selects one vertex to be the shape s Reference Point RP and enters those coordintes as XR YR ZR in the Shape specification data line coordinates of the second of 4 verticies 12 y2 22 69 Table 7 table continued Shape abs NT Parameter List RP and LC S definitions C4 C6 coordinates of the third of 4 verticies 13 y3 23 C7 C9 coordinates of the fourth of 4 verticies x4 y4 z4 RP
178. l beam 0 a diffused track the beam is distributed uniformly in a box 1075 cm around variables XINI YINI ZINI inthe INIT card default 1 the beam is distributed uniformly in a rectangular area of half size as specified by variables SIXX SIYY in the BEAM card 2 the beam has a simple Gaussian distribution with c and c specified by SIXX SIYY in the BEAM card 3 the beam has a Gaussian spatial distribution as for IBEAM 2 and also has a Gaussian angular spread with c 0z and o in radians specified by variables SITX SITY in the BEAM card This angular spread will always be diverging however Focused beam trajectories must be modeled via the user subroutine BEG1 42 IZPRJ IAPRJ Integer electric charge of the projectile if it is heavier than H e Default 1 Integer mass baryon number of the projectile if it is heavier than H e De fault 1 BEAM SIXX SIYY SITX SITY DLBNCH Real variables used to specify the x y z beam shape around initial values from the INIT card The first four variables are active only for non zero values of IBEAM in the IPIB card default for each is 0 0 SIXX SIYY SITX SITY DLBNCH For IBEAM 1 the half size in x of a uniform retangular beam for IBEAM 2 3 the o of a Gaussian beam Both in cm For IBEAM 1 the half size in y of a uniform retangular beam for IBEAM 2 3 the 0 of a Gaussian beam Both in cm The gaussian ang
179. lated 2 D histograms can be loaded and overlaped with the geometry view on the GDP A HBOOK file is loaded in the Load Hist window and a desirable histogram is selected there from the IDF list by its ID or name The geometry histogram view is now handled as 136 12 2 a whole The Point Info window allows now for a detailed examination of the histogram values even within the same decade color The view can be inverted both vertically and horizontally One can add arbitrary texts all over the GDP with a Text window activated by the mouse right button Variety of fonts can be chosen there Fonts subscripts and superscripts are handled as in the XMGR plotting tool 107 Text can be modified moved around the GDP or deleted Up to 20 of the GDP views can be stored and restored back and then viewed by clicking lt lt or gt gt buttons The GDP can be saved as an Encapsulated Postscript file by clicking the Print button The entire window or its arbitrary fraction can be XV grabbed by clicking the Grab button A version exists for a 3 D solid body representation 108 New Advanced Features Substantial improvements have recently been made to the MARS GUI SLICE package All the following features apply to the MARS15 graphics mode selected through CTRL 1 in MARS INP Selection of four GUI window sizes respectively Extra Large Large Medium Small XL 1000x840 L 700x700 M 580x640 S 480x540 The GUI pops up by clicking
180. le list into step 2 which describes the geometry downstream of the target In this way one can compare different production models at the target separately from the rest of the geometry 5 4 Subroutines REGI non Standard Zone Description REGI is the interface between MARS and the users s encoding of a complex geometry MARS hands to the routine via the subroutine arguments the current location X Y Z of some particle the user s job is to determine in REG what particular volume that X Y Z belongs to and what the corresponding user assigned non Standard zone number N and material index IM for that volume are and return those numbers to MARS Subroutine VFAN is used to assign a volume to each of the user assigned zones at program start up Recall from Section B I that for MARS to determine the flux of particles through any particular zone it must have a value for the volume of the zone REG can also be used in the extended geometry mode to define subregion numbers NIM inside a given zone with zone numbers and material indecies are determined automatically These NIM can be in particular used in subroutines RFCAVT and ALIGN as a control switch The user can encode as complex a geometry as necessary and can do so in his own set of subroutines which get called from REGI The user has as many as 100 000 non Standard zones at his disposal each declared zone gets the full complement of results accumulated and these are tabulated in the MTUPLE NO
181. led by the left most column note the energy bins are in MeV The columns of data are arranged to be easily cut and pasted into an external graphics or spreadsheet program GRAPH PHOTON ELECTRON SPECIAL REGION SPECTRA 129 This table is similar to the one described above being data accumulated in the volumes specified by the NOBL and RZOB cards This table gives data for y and e in two sub columns for each special region The data here is dN dE in units per GeV cm plotted in energy bins as labeled by the left most column The columns of data are arranged to be easily cut and pasted into an external graphics or spreadsheet program At the end of the table are three additional results summed or accumulated from the spectrum data The first result labeled TOTAL 1 CM 2 the integral of the dN dE spectra the second result is the mean energy E GEV from each spectrum the third result is the dose equivalent DEQ mSv due to the particles passing through each volume region GRAPH TOTAL DOSE EQUIVALENT This table presents data values versus location in the model volume ignoring zone and region bound aries The data is instead mapped into 5 r bins and 10 z bins The maximum r and z bin values describe the maximum extent of the model the Standard zone mother volume the bins are cre ated by equal divisions between zero and the maximums The left most column gives the mean z coordinate in each bin the top two rows give the lower
182. les The numerical values for real variables must contain a decimal point for example 700 is not correct for a real variable while 700 is A message will be generated to the screen if a real number value is missing the decimal point The card is ignored and treated as a comment if it starts with C separated by a space from the rest of the card 4 2 List of Data Cards in MARS INP The listing of Data Cards is organized in functional groups cards used in the overall control of the program cards used to describe the materials and material dependent parameters cards used to describe the Stan dard Zone geometry cards which control histograms and tabulation and cards to control specific physics interactions Cards are generally listed alphabetically within these functional groups 4 2 1 IND Switches for Default non Default Options INDX IND 19 Logical variables which act as on off switches to control various options described by the list below Default 9 F 10 T 9 F IND 1 T The MARS OUT file will contain an extended format such as tables of the time dependent residual dose in all materials See Section TT T 2 for details IND 1 F Standard format MARS OUT file See Section TL 1 2 for details T sets Z sandwich geometry as a basis for the Standard Geometry zones See the ZSEC and RSEC cards IND 2 F sets R sandwich geometry as a basis for the Standard Geometry zones See the ZSEC and RSEC cards
183. leted Ability to zoom in part of the picture using mouse Just hold Crt1 key while marking the opposite corner of zooming box and then redraw the geometry Possibility to view the inverted image You can use the following buttons to set either horizontal or vertical inversion and then redraw the geometry esa va s cbe The ability to draw the geometry with filled or transparence colors or even in colorless black amp white mode using next radiobuttons panel 148 Color x BEW w Fill e The possibility to overlap the geometry view and histogram view User could open histogram after MARS batch runs and draw the result of calculations on top of geometry Load Hist ON 99 99 e Note that it is user responsibility to make picture and histogram coherent One can open hbook file check the histogram list and choose what histogram to load F g 1 em 2 lppp vs 414 E e m 1cm 2 lppp 415 Power density mW qj at A 416 Dose equivalent FTD mwv 1411 F n l cocm zZ lppp vs 14l F ch h 1 cm 2 1ppp 1413 F g i1 ecm Z 1ppp v 1414 F e m 1cm 2 ippp 1415 Power density mW g at 1416 Dose equivalent FTD msv e The possibility to store and restore back number of previous geometry views and then move between them using one mouse click That can be done using next buttons m 149 13 Additional Code Topics 13 1 Rules Of Thumb It is obvious that the quality of
184. lls MARSON is the normal running mode For normal and GUI modes the user does not need to customize anything in routine MARS1514 The only items which might be modified as needed are the declared size of the PAWC common block and the names of the input output and histogram files Some of the settings for the stand alone generator mode are customized from this routine 5 2 1 Stand alone event generator The stand alone generator as mentioned above is useful for To make use of this mode the user must first set the card CTRL 2 IM in the input deck where IM is the material index of the target nucleus the event generator will use The primary particle type and energy are specified in the usual way using the ENRG and IPIB cards in the input deck For example if the user wants to investigate the details of protons striking a graphite carbon nucleus then the pertinent cards in the input deck might be CTRL 2 4 NEVT 100 ENRG 250 IPIB 1 3 ATR MATER INP C MATR AIR AL FE C CONC where CTRL 2 4 indicates that the target nucleus is the 4th material listed in the MATR card which is C for carbon The primary particle is a 250 GeV proton and 100 events have been requested The user next sets variables in routine MARS1514 to control the generator details and the results which will be reported The choices are given by comments within the routine Here the differentials DY DMT X and E are for rapidity tra
185. lopment ELSYN EMISYN EEGHM ISYNHMU ISYNEMS ISYWRT NOSTPMV KEMINCL Real number specifying the synchrotron emission for charge particle i of energy E ECUT ELSYNxm me where Mme is electron mass De fault 0 05 GeV Real number specifying a synchrotron photon energy threshold For E gt EMISYN induced EMS are treated at photon energy otherwise that en ergy is deposited locally Can be as low as 1079 GeV Default 2x 1074 GeV Real number specifying an energy threshold For E gt EEGHM full simulation of muon electron and e production and their showers along hardon tracks local deposition otherwise Default 0 001 GeV Flag for synchrotron radiation generation by hadrons muons and heavy ions ISYNEMU 0 provides analog exclusive generation I SYNHMU 1 provides inclusive generation Default 0 Flag for synchrotron radiation generation in electromagnetic showers ISYNEMS 0 provides analog exclusive generation ISYNEMS 1 provides inclusive generation Default 1 Flag which activates when ISYWRT 1 writing of parameters of first 30000 generated synchrotron photons into a fort 79 file Default 0 Maximum number of steps for a particle in vacuum Default 100000 The value for the electromagnetic shower vertex as well as n y and other neutron interaction verticies while in the MCNP mode modelling switch For KEMINCL 0 the inclusive mode is used For KEMINCL 1 exclusive mod eling is done for all elect
186. low beam energies De fault 0 0002 0 001 0 01 0 03 0 1 0 003 BIAS PPIKDEC PMUPRMT PMUBEHE PMUGVM PMUANN PPHNUC PELNUC PPBAR Variables which provide a global control of biasing in several important processes Fine tun ing of all the biasing schemes is done in user subroutine BLOCK DATA BLPROCESS work in 57 progress Unstable particle decays are controlled by the PP IKDEC parameter and can be mod elled either analogously or as forced events with a Russian roulette The processes controlled by the remaining parameters on this card are modelled as forced events with a Russian roulette The biasing parameters can be applied only to specific materials via the values on the group of cards BIPR through BIAP as described above Such material dependent parameters will overwrite the global values of the BIAS card for the specific material PPIKDEC Real number to control unstable particle decays hadrons except 7 muons and heavy ions It specifies decay modeling in the pure analog way at PPIKDEC 1 and forced at PPIKDEC gt 0 001 For decays of charged pi ons kaons and heavy ions on a path to an inelastic nuclear interaction leakage or ionization absorption the value of 0 001 lt PPIKDEC lt 1 is used as a parameter of the Russian roulette All decays are suppressed if PPIKDEC lt 0 001 For muons any value PPIKDEC gt 0 001 including PPIKDEC 1 results in the pure analog decay modeling otherwise muon decays are suppressed at
187. lt RLCTNE IM 0 0145 GeV at their origin in material with index IM for further transport with a standalone code such as MCNP These neutrons are not tracked in MARS then just dumped to the file instead Default O NWNEUN When set 3 write NEUTRINO file of generated neutrinos at their origin Default 0 Similar actually arbitrary control can be done in the user routine MFILL via IDPRC 53 with neutrino origin info via KORIG 1 16 and 22 A corresponding example is given at the end of the MFILL routine HTIR TIRH TICH 56 Two real variables which specify the irradiation and cooling times for residual dose rate distribu tions scored in histograms and regions of the MARS OUT and MTUPLE files Active only when IND 1 T TIRH The irradiation time days Default 30 TICH The cooling time days Default 1 RTIR TIR 7 Real variables which specify the irradiation times for 2 D residual dose rate distributions scored in materials of the MARS OUT file Active only when IND 1 T TIR i The i irradiation time days Default 0 5 1 5 30 100 365 7300 CFTD IFTD Integer variable which specifies the sets for fluence to dose conversion and radiation weighting factors wg The default provides the effective dose and wg according to ICRP103 10 CFR Part 835 as decribed by J D Cossairt and K Vaziri Fermilab PUB 08 244 ESH REV Dec 2008 for neutrons The effective dose and wp for other particles are calculated according to
188. lts are presented in tables histograms and other specialized formats MARS allows the user extensive control over the simu lated physics processes over the tabulation criteria and over runtime optimizations via a variety of options and switches implemented from an input file and via customizable user subroutines The basic model for the original MARS program introduced in 1974 18 19 came from Feynman s ideas concerning an inclusive approach to multiparticle reactions and from the use of certain weighting techniques At each interaction vertex a particle cascade tree is constructed using only a fixed number of representative particles the precise number and type depending on the specifics of the interaction and each particle carries a statistical weight which is equal in the simplest case to the partial mean multiplicity of the particular event Energy and momentum are conserved on the average over a number of collisions A similar scheme is the basis of the program CASIM introduced in 1975 21 22 Other codes have also adopted this approach the EGS simulation of high energy electromagnetic showers 23 and hadronic showers simulated by the FLUKA program 24 The details of this inclusive scheme are described in several references 25 26 27 28 The practical reasons for using this approach are e the CPU time per incident particle grows logarithmically with incident energy compared to the linear increase in CPU time when perf
189. ment is done in MARS of processes near and below the Coulomb barrier in hadron and muon transport ionization absorption vs nuclear interaction vs decay 16 2 9 1 Pions A stopping 7 decays into u of 4 1 MeV plus a neutrino while a 77 attaches to a nucleus via the modified Fermi Teller law While cascading down the atomic energy levels the pion is captured from a high orbit thus emitting only a few low energy photons which are neglected here The hadronic interaction of the stopped Tr is treated using the Cascade Exciton Model with a few modifications When hydrogen is the target it is assumed there is a 60 probability to for charge exchange Tp rn whereupon the n decays into two photons of 68 9 MeV each and the neutron acquires a small 0 4 MeV kinetic energy The remaining 40 of stopped m in hydrogen interact via radiative capture Tp ny Here the photon acquires 129 4 MeV and the neutron 8 9 MeV kinetic energy Other nuclides have a much smaller probability for radiative capture 1 2 which is taken into account in competition with CEM95 The photon energy is chosen from an empirical fit to experiment while the remainder is deposited as excitation energy 2 9 2 Muons A stopping u always decays into ev while a yu attaches itself to a nucleus When a yu stops in a com pound or mixture one first decides to which nucleus the u attaches modified Fermi Teller law Following attachment the muon may still decay as d
190. mentioned in the previous section the user declares what materials are present in his simulation in the input file for example MATER INP whose name is defined in the input file MARS INP on the MATR card MATR MATER INP A character string up to 32 characters which specifies the name of the materials file An example of such a file is given below First line is a task name Next numbered cards or blocks describe materials for the given task For built in materials each line includes their name and density if different from that of Tables 3 and 4 For other arbitrary materials the numbered card contains the material name density and the number of elements NEL The initial temperature temp in Kelvin can be specified for any material if different from the global one TEM PO of the VARS card Just add for example temp 4 2 at the very end of the corresponding material numbered card see example below The allowed range currently is 1 8 to 1800K Default TEMPO 300 The numbered material card with NEL is followed by NEL cards with atomic mass charge and weight fraction for each element The last functional card is STOP cards after it are ignored The number of numbered cards defines the total number of materials NREMA in the model 45 m1514 materials example 12 18 13 1 AL temp 4 2 2 VAC 3 WATR 4 QUAR 2 64 temp 70 5 BCH2 6 Aluminium honeycomb 0 05114 5 temp 293 26 98000 13 00000 0 97670 14 00
191. meters or cutoff energies to different vacuum regions The first 100 elements in the periodic table and many common compounds used in particle and nuclear physics are built in to the MARS code These are listed in Tables 3 and 4 The user can also define his own compounds or mixtures All compounds are defined through the weight or atomic fractions of the individual elements they consist of At program startup MARS calculates the cross sections and other physics interaction parameters for the list of compounds declared for use in the simulation The precise effect of individual elements in compounds is taken into account for all the electromagnetic and nuclear elastic and inelastic processes modeled by MARS material averaging by using an effective overall Z and A is no longer performed It is recommended that the user replaces air and other gases with vacuum if a thickness of gaseous regions is less than about 10 30 cm A CPU performance and even transport accuracy would be 25 Table 3 Built in elements The first 100 elements in the periodic table are built in and listed in order of atomic number in the table below Their MARS abbreviation is the same as their standard abbreviation H HE LI BE B G N O E NE NA MG AL SI P S CL AR K CA SC TI V CR MN FE CO NI CU ZN GA GE AS SE BR KR RB SR X ZR NB MO TC RU RH PD AG CD IN SN SB TE I XE CS BA LA CE PR ND PM SM EU GD TB DY HO ER TM YB LU HF TA W RE OS IR PT AU HG TL PB BI PO AT
192. modeling of elec tromagnetic showers EMS in the 1 keV to 20 MeV energy range applied only to specific mate rials Any material which does not have a corresponding entry here will have the global switch LEMSGL applied as the default see the EMST data card If the EGS5 mode enabled and anything was changed in the MATER INP file be sure that all egs5job and pgs5job files were deleted from this directory before running a job with the modified MATER INP file For LEMS 1 0 the native MARS module is used for EMS at all energies For LEMS 1 1 the EGS5 module is used below EGS5PH and EGS5EL For LEMS i 2 the EGS5 module is used below the material dependent photon neutron production thresholds for example 0 018 GeV in beryllium and 0 006 GeV in uranium For LEMS i 3 the use of EGS5 module is forced at all energies up to the beam energy LEMS The values for the model switch indexed by IM the order numbers the materials are listed in the MATER INP file BIDC RLDEC 500 Real variables for unstable particle decays applied only to specific materials Any material which does not have a corresponding entry here will have the global parameter applied as the default with the value given by the PPIKDEC variable in the BIAS data card Currently the global parameter PPIKDEC overwrites any values given on this card and is applied to all materials RLDEC The values for the unstable particle decay control indexed by IM the orde
193. mplex primary beam trajectories must be modeled via the user subroutine BEG1 XINI YINI ZINI These are initial zo yo zo coordinates of the beam spot center Default 0 0 0 0 0 0 in cm DXIN DYIN DZIN These are initial direction cosines of the beam centroid De WINIT fault 0 0 0 0 1 0 The initial weight of each incident particle which the results are normalized to Beware of interference between this value and AINT in the VARS card which also affects normalization An often used example put WINIT d Ain when the point like target efficiency EFF 1 on the VARS card here d is the target thickness and A n is an nuclear inelastic mean free path of the beam hadrons in the thin target material Beware of interference between this value and AINT in the VARS card which also affects normalization Default 1 0 ENRG E0 EM EPSTAM EMCHR EMNEU EMIGA EMIEL EMNU EMEVAP 43 Real variables which specify the incident particle energy and the thresholds in matter for subse quent generated particles In most cases generated particles will not be tracked once their energy is below the threshold and their contribution to flux and energy distributions will no longer be counted exceptions to this are noted below These thresholds are global applied to all zones material zone specific thresholds can be specified using variables assigned to the MTCH MTNE MTGA and MTEL data cards The minimal threshold energy is 1071 GeV for neutrons 1
194. mulated and reported in the output results 2 3 3 Deuteron nucleus collisions Deuteron interactions have little in common with the general picture of the interaction between complex nuclei because of the deuteron s relatively large size and small binding energy Therefore a special model has been developed and implemented into MARS Deuteron nucleus interactions are classified as elas tic dissociation stripping and full inelastic In elastic interactions the deuteron emerges intact in the final state while the nucleus may be unchanged coherent elastic or have lost one nucleon incoherent Coher ent elastic uses Glauber s treatment with some adjustments of the parameters to fit experiment Incoherent elastic scattering assumes a differential cross section to be twice that of the proton using the prescription of and the nuclear parameters as for the coherent case This is then multiplied by a deuteron and a nucleon form factor as well as a Pauli suppression factor which hinders low momentum transfers Exchange of a long range virtual photon may result in Coulomb dissociation whereby the deuteron splits into a proton 13 Tp 1 total i Sol 2t mun ed o tal cro To Cross section mb 3 E m T I s T s a j EN yn CU etm ua m m sinp 10 i i i nici Ep iai rou rii 10 10 10 10 10 M TN M GeV c Ekin MeV Figure 7 missi
195. n MeV Figure 5 missing figure from CEM section Figure 6 missing figure from CEM section energy proton nucleus interactions 64 Special attention is paid to high p events 1 and kaon production and low momentum pions p lt 2 GeV c from intermediate incident proton momenta 5 pg 30 GeV c The following form is used for the double differential cross section of the pA 7 X reaction d g X i dgr gt X Lib MN React X A A 1 where p and p are total and transverse momenta of 7 and A is the atomic mass of the target nucleus The function R 4 7 X measurable with much higher precision than the absolute yields is almost independent of p and its dependence on po and p is much weaker than for the differential cross section itself Rather so phisticated algorithms have been developed to treat this function for pion production on nuclei in the forward xp gt 0 and backward xp lt 0 hemispheres separately It is demonstrated in that model predictions are in a good agreement with data in the entire kinematic region Typical examples of comparison with data are shown in Figs 7 and 8 Calculations with the MARS13 98 code of the pion double differential spectra from a thick lead target at pp 8 GeV c agree reasonably well with data 65 in the difficult momentum region 0 5 p 5 GeV c Fig 0 whereas GEANT seems to have a problem Information on the nuclides generated in nuclear collisions is now scored or accu
196. n geometry modules including REGI when propagating particles If the user s non Standard zones fit within larger Standard zones then the user should test the input X Y Z on entry to REGI and if the current location is outside the overall non Standard volume RETURN to MARS with the input zone number N unchanged This is far more efficient than letting all possible X Y Z locations fall through the user s code If one wants to study cascades in a very complex geometry not embraced by the above options user subroutines REGI and REG2 must be provided MARS version 13 95 allows the user to place geometri cal objects of almost any complexity inside the pre defined standard r z or extended geometry By convention the total number of standard regions NF ZP must be NF ZP 71 With the help of his her own sub routines REG1 X Y Z N NIM and REG2 N IM MAG the user can describe arbitrary physical regions numbered from the NMIN lt N lt NMAX interval Here NMAX 10000 NMIN NFZP 1 for the Standard ge ometry sector and NMIN NEXGM NVOLUM for the extended geometry sector Each region can be divided into any number of arbitrary subregions with index NIM with a default value NIM 0 This feature provides the possibility of distinguishing geometrical zones without scoring results there The user can successfuly substitute this with the HBOOK histogramming see MAIN For each call a subroutine REG1 X Y Z N NIM finds the position of the given point
197. n is included in the model 2 4 Elastic Scattering Modern evaluated nuclear data as well as fitting formulae are used to simulate hadron nucleus elastic scat tering For protons nuclear Coulomb elastic scattering and their interference is taken into account At E gt 5 GeV a simple analytical description used in the code for both coherent and incoherent components of do dt is quite consistent with experiment 2 5 Muon Production Simulation algorithms for 7 p v V7 and K u v 1 decays and for prompt muon production single muons in charmed meson decays pairs in vector muon decays and the dimuon continuum with forced generation of weighted muons have been improved Prompt muons produced in electromagnetic showers are described in detail e Bethe Heitler pairs yZ Zt are produced at E gt 0 25 GeV at arate of m_ m times that for e e with the appropriate statistical weights and a complete simulation of electromagnetic showers It was shown that this approach produces remarkable results that agree with those based on the numerical integration in the Tsai formalism i e muon production with forced decays of mesons and short lived resonances 26 28 74 75 e very efficient algorithms for muon interactions ionization bremsstrahlung direct ee pair and deep inelastic and transport well advanced compared to previous versions 37 28 741 75 e optional forced jjL ev decays and synchr
198. n will be shown 146 Tracks 2 point Track Into e User can add texts all over the picture One can do it by holding Shift key and pressing mouse right button simultaneously Text will be drawn where the mouse pointer is positioned at this moment Dialog window will appear where text can be entered Text Ol x Enter the text ASMA e NNUmSsSNO XN collider OK The same convention as in well known XMGR drawing tool 107 is used Namely n will switch you to font number n S will switch text to superscript mode s will switch text to subscript mode and N will return text back to normal position Example above will produce the next text a uo collider e You also can choose fonts interactively by pressing Fonts button Dialog will occur which will show you what fonts are available Font numeration in the dialog is exactly the same used in text entry field 147 Fonts Courier AaBbCeDd ma Courier Italic AaBbCoDd w Courier Bold BaBbCeDd y Helvetica AaBbCcDd Helvetica Italic AaBbCcDa ww Helvetica Bold AaBbCeDd Ww Times AaBbicDd v Times Italic AabaCcid v Times Bold AabbCcDd Greek AaBBXxA6 T i Ww Symbol Ok All fonts Beset Texts can be moved around the picture by grabbing them with third mouse button and dragging them around User can delete texts by holding Ctrl key and pressing third mouse button on text fragment to be de
199. nd location of each detector is specified by the accompanying FLOC data card Active only when IND 5 F NDE1 The number of detectors 0 lt NDE1 lt 10 Default 0 FLOC RD XD 10 YD 10 ZD 10 Real variables which specify the size and location of each of the declared point like low energy neutron detectors Active only when IND 5 F and NDE1 gt 1 RD The radius of all declared detectors Default 0 5 XD i YD i ZD i The coordinates of the 1 detector Default 30 0 0 TAPE NWEGH NWANS NWMJL NWPSI NWNEUN Integer flags which control the creation of various output files NWEGH Only one of the following files is generated in any single job depending on the value Default O 17 Write a MUON EGH file with muon generated EMS for post run process ing and analysis 18 Write TRACK PLOT file with particle tracks for NSTOP events or for the event NHIPR only if it is present on the NEVT card 19 Write VERTEX PLOT file with particle interaction vertices 20 Write MUON PLOT file with particles generated at muon interaction ver tices Those particles are not transported while muons are NWANS When set 2 write ANSYS ED file of energy deposition density to be used by the ANSYS system Default 0 NWMJL When set 12 write EDMJL GRA graphics oriented file of energy deposition density Default O NWPSI When set 13 write PSINEU GRA graphics oriented file of neutron spectra When set 14 write LENEUTRONS file of neutrons with E
200. nd results The full MCNP code contains very detailed material handling taking into account the nuclear physics details that occur in interactions with different nuclei and this affects residual rate calculations MCNP also includes the n y reactions critical to predicting prompt dose calculations in labyrinth type geometries where slow neutrons are dominant Using MARS with the full MCNP code requires that the user obtain and install the MCNP code library The code is obtained from RSICC 86 the Radiation Safety Information Computational Center at the Oak Ridge National Laboratory on the web at www rsicc ornl gov or from the NEA Databank in Europe 87 The code package is proprietary and a license must be purchased For further details on using MARS in the MARS MCNP mode see Section 6 19 3 Using the MARS Package MARS uses it s physics models to generate particles and track them through a described geometry applying appropriate physics interactions and tabulating the particle flux energy deposition and other parameters in the various portions of the geometry This Section describes how the MARS package functions by giving overviews of MARS geometric zones the particle types used in the simulation and how MARS tracks these particles through a modeled geometry how materials are defined how results are tabulated and what histogram options are available variance reduction techniques and interfaces to other codes Each overview
201. ne and this Standard zone must be sized to surround the maximum geometrical extent of the encoded non Standard zones The total number of all zones Standard non Standard Extended and imported has a maximum value of 200 001 and this limitation is set by the maximum size of the arrays used to store and accumulate the results of the simulation The number of Extended zones must be between 0 and 200 000 but there is no similar limit on the number of other zone types except the upper limit on the sum of all the types It is up to the user to keep track of the numbers of the zone types declared and to be certain they remain within the stated limits A single model description can use all zone types simultaneously and these can even overlap in space but doing so will cause MARS to use it s own priority system to determine the final zone number for the overlapped area The priority to zone assignment is based on the order in which MARS calls the different geometry modules When MARS has a coordinate position and needs to know what zone that coordinate is located in it first calls the non Standard geometry module via user subroutine REG1 Imported geometries are grouped with the non Standard zones If no zone is defined for the coordinate position there then next the Extended Geometry module is called If no zone is assigned there then the Standard geometry module is called If no zone is assigned to a coordinate position after all these modules are
202. ne on going developments 152 15 Acknowledgements We express our gratitude to P Aarnio Y I Eidelman K K Gudima M A Kostin O E Krivosheev S G Mashnik LL Rakhno A J Sierk S I Striganov and I D Tropin for their contribution to this ver sion of the MARS code References 1 2 3 4 5 6 7 r 8 9 10 11 12 13 14 15 N V Mokhov P Aarnio Yu I Eidelman K K Gudima A Yu Konobeev V S Pronskikh I L Rakhno S I Striganov I S Tropin MARS15 code developments driven by the intensity frontier needs Technical Report Fermilab Conf 12 635 APC 2012 V S Pronskikh A F Leveling N V Mokhov I L Rakhno Calculation of residual dose around small objects using Mu2e target as an example Technical Report Fermilab FN 0930 APC 2011 N V Mokhov Mars15 overview Recent Mars15 developments nuclide inventory DPA and gas production Technical Report Fermilab Conf 10 518 APC 2010 P Aarnio Decay and transmutation of nuclides Technical Report CMS NOTE 1998 086 CERN 1998 A Isotalo Modifications to DeTra Technical Report September 18 2008 N V Mokhov I L Rakhno and S I Striganov Simulation and verification of DPA in materials in Applications of High Intensity Proton Accelerators World Scientific Proc pp 128 131 2010 I L Rakhno Modeling heavy ion ionization energy loss at low and intermediate energies Technical Repo
203. ne type of zone Standard and non Standard Standard and Extended or any other combination then the results will be spread around among the different files If the results in an area of interest are split between files because of the use of different zone types then the user may wish to rethink his model s geometry description in order to more efficiently organize the results The format of data tables in these files is defined within non user code and cannot be changed by the user The tabular format of these files is intended to make it easy to look up the results for certain key zones of interest The rows and columns can also be cut and pasted into other software plotting packages such as GNUPLOT XMGR KALEIDAGRAPH and EXCEL Copied data can also be read into PAW although in most cases if PAW is being used it is simpler to use the histogram options to create such a file directly Each of the output files has it s own sub Section with each table of data defined 123 11 1 1 The VOLMC NON File The VOLMC NON file is a pre run output file The file is created only when MARS is run in volume MC mode see Section 42 2 for the switch settings to use this mode The file lists Zones by their MARS zone number and gives the volume for each of these zones as measured by the program These volume values are cut and pasted into the user subroutine VFAN see Section 5 5 for a more detailed discussion of the process The contents of a
204. ng figure from hadron production Figure 8 missing figure from hadron production section section and neutron This is calculated using a Weiszacker Williams approach for virtual photon emission Disso ciation may also result from nuclear elastic processes at relatively high momentum transfers In stripping one nucleon undergoes an inelastic nuclear event while its partner continues without interaction The total stripping probability is calculated based on the projected n p separation as predicted by the deuteron wave function and geometrical arguments Deuterons dissociate as in with full relativistic kinematics Interaction with the nucleus by one of the partners proceeds within the standard MARS scheme In full in elastic events both nucleons interact with the nucleus The stripping routine provides the angular deflection and momentum of each nucleon after which both are allowed to interact as other MARS nucleons As an example a calculated 7 K meson yield out of a 3 cm radius gallium target 36 cm long in a 7 5 cm radius solenoid B 20 T is presented in Fig IO for proton and deuteron beams of equal momentum per nucleon 2 3 4 Quark Gluon String Model code LAQGSM2012 Exclusive particle event generator for hadron and heavy ion nuclear interactions from 1 MeV to 1000 GeV Comes here 2 3 5 Exclusive hadron production from 5 GeV to 100 TeV The DPMJET 3 3 code is implemented into MARS to sample the initial hN hA AA and vA interaction
205. no beam and transport initiates the use of special algorithms as referenced in 100 to construct ex tremely accurately the particle trajectories prior to the first two inelastic nuclear in teractions The current default algorithm now provides the same level of accuracy therefore this option is obsolete switch off the above algorithms Default The flag activates muon transport with all possible interaction processes included see Section I3 2 for details turns off muon transport 37 IND 11 2T adds the p dimension to the Standard r z Geometry zones giving an azimuthal structure to the accumulation of the results The user must specify the number and size of the azimuthal zones via the NAZM and AZIM data cards IND 11 F no azimuthal divisions in the Standard Geometry zones IND 12 reserved for the point kernel option to calculate residual radioactivity with routine MARACT not implemented in this version IND 13 T switch on the use of the MAD MARS beam line builder MMBLB interfaced with the MAD lattice description and define histograms using user subroutines MARS2BML and BML2MARS IND 13 F MMBLB is not activated IND 14 T User subroutines ALIGN SAGIT and RFCAVT are called by the MARS geometry description software modules IND 14 F The above subroutines are not called IND 15 T Enables a global parameter set for thick shielding The set consists of various physics options energy thresholds and tabul
206. ns listed on the IMNC card as low as 1 e 6 GeV It is OK to keep corresponding hadron heavy ion cutoff energies as default 2 e 4 GeV for materials in centimeter scale and larger regions In latter case production yields NUCLIDES PROD IM and stopped nuclides NUCLIDES STOP IM should be very similar Nuclide inventory is calculated correctly with ICEM 4 1 default for energies below 8 GeV If one specifically needs its accurate calculation at higher energies one should run MARS with ICEM 4 3 It is also recommended to use the MCNP x section mode with neutron cutoff energy low 1 e 12 GeV NCLD The number of materials on the IMNC card for nuclide production calcula tions 1XNCLD lt 40 Default 1 IMNC IMNC 40 55 Integer variables which specify the material indicies where detailed 2 D mass charge nuclide distributions are calculated and nuclide production rate files for DETRA generated Exam ple IMNC 1 5 14 to calculate and print nuclide production and stopping in first fifth and fourteenth materials with a NCLD card as NCLD 3 six input files generated for DETRA have names NUCLIDES PROD IM 1 NUCLIDES PROD IM 5 NUCLIDES PROD IM 14 NUCLIDES STOP IM 1 NUCLIDES STOP IM 5 and NUCLIDES STOP IM 14 respec tively IMNC i The index of the i material Default 1 39 0 NDET NDE1 Integer variable which sets the number of point like detectors for the spectrum flux and energy deposition of low energy neutrons The size a
207. ns of muons charged hadrons andheavyiong 2 6 2 Multiple Coulomb scattering 2 a e esci II eroski a dd led da E PIER SIUS RP AR rr A Pe Renae ee ee oe ee saw A Rs oe NM ee E oe ee ee ee 211 Low Enersy Neuttong 236m aa Re a aoe Oe ge ewe BAe EL RUPEE E wh 3 Using the MARS Package 3 1 Describing a Geometry by Zone ee AA AA pea TENER E 3 2 Particles usedin MARS 22er Meee he ku kbS eh RED EGG Sk oes Shoe eee SSE EE E 5 4 Materials vii us be p bre ROS a deu Se whee e He ae Be Bo 3 5 Tabulation amp Results ee 11 11 11 11 11 12 12 12 13 14 14 15 15 16 16 16 16 16 16 17 17 18 18 18 3 6 Histogram Opa 29 Lia ns inicia as lo eee ee ee eee 29 o e a a sa dio 29 A e ee 29 A Oe eee eee ee hrs ee oe 30 ee fud eT ee ee ee ee ee ee ee 30 34 4 1 Structure of the MARS INP Input Deck 2 2 ee 35 4 2 List of Data Cards in MARS INPE Res 36 4 2 1 IND Switches for Default non DefaultOptiond llle 36 4 2 6 Importance Sampling IMPT IMPZ IMPRI bm eine OS 4 20 Termination STOB 5 SoG eS EER SRG BER ERO EAMUS x 62 TULIT 62 4 31 Z Sandwich Geometry ee 62 Sue Soe Ae CARES RE A Sa 64 hee ade UR Td dtd eo Oh E ree Od oe 65 4 4 Extended Geometry GEOM INP Input Filg aaa ee 67 4 4 1 E
208. nsities for each compound is also listed The user can modify this density using the MTDN card in the MARS INP file as described in Section 4 2 4 Table 4 Built in compounds with their default density values Abbr p g cm Compound Name Formula VAC 0 Vacuum CH2 0 950 Polyethylene C H BCH2 0 950 Borated Polyethylene CH 1 032 Polystyrene continued on next page 26 Table 4 table continued Abbr p g cm Compound Name Formula TEFL 2 200 Teflon C F gt NAI 3 670 Sodium Iodide crystal ELEC 1 034 Electronics N Si Pb mixture BGO 7 100 Bismuth germanate Bi203 Ge02 3 PBWO 8 280 PbWO 4 G10 1 700 NEMA G10 6096541054096 epoxy QUAR 2 640 Quartz 705 TISS 1 000 Tissue H4004 NO17 WATR 1 000 Water H2O PARA 0 930 Parafin wax C H3 C H5 54C Hs AIR 0 0012 Air at 18 C and 58 humidity SOIL 1 900 Soil Hi705 Al Sig CONC 2 350 Concrete steel reinforcing O2Si CaNaF eAl BART 3 200 Boron Barite Concrete BMCN 3 637 Borated Magnetite Concrete STST 7 920 Stainless Steel 304 SCON 7 000 Super Conductor 90 60 Cu 40 NbT 10 Kapton YOKE 7 870 Steel magnet yoke COIL 5 108 Water cooled copper coil INSU 1 690 Insulation CABL 2 896 Cables CH4 0 4224 Methane C H4 MYLR 1 390 C5 H402 MYAL 1 783 Aluminized Mylar KAPT 1 420 Kapton C22H10N205 CRMC 3 970 Ceramic A1203 TIAL 4 30 Ti alloy 0 97 0 0641 0 04V by weight INCO 8 190 Inconel alloy 718 FECO 8 000 0 64 Fe 0 36Co by weight NBSN 6 80
209. nsverse mass Feynman x and energy respectively Selecting one of these determines the contents of the tables of data which are the result of the calculation 5 3 Subroutine BEG1 Primary Beam Description Routine BEGI is used to customize the primary particle beam The subroutine arguments are the variables used to fully describe the trajectory and properties of a given primary particle JJ is the particle type index given in Table 2 w is the relative weight given to the particle E is the energy of the particle X Y Z is the particle s starting location DX DY DZ are the direction cosines TOFF is INTA is a flag to impose a point like interaction NREG1 is a Zone number where the source term is located When the primary beam is described using Input Deck IPIB and BEAM cards MARS uses those input deck parameters on beam spot size and shape to generate a particle trajectory within that specified envelope The trajectory is described by the starting position X Y Z and the direction cosines DX DY DZ These variables are passed to BEGI and can be further modified to describe beam envelopes more complex than what can be specified only by the Input Deck cards For example consider a beam which has a gaussian distribution of particles but has been clipped in one view The input deck cards are used to describe the gaussian properties In routine BEGI the user examines the X Y position If the X or Y are beyond the clipped edge then the traj
210. o statistical errors are given The table presents arranged by Standard zone number No statistical errors are given The table presents arranged by Standard zone number No statistical errors are given The table presents arranged by Standard zone number No statistical errors are given Crude estimation of three dimensional distribution of residual dose rate in Rad hr after 30 day irra diation at the mean beam intensity AINT particles per sec and 1 day cooling These are valid only for sufficiently thick systems beyond a lateral thickness of gt Ain 2 Three dimensional distribution of the relative statistical errors of star densities fluxes and energy deposition densities 3 Leakage data number and energy of albedo hadrons of punchthrough had rons and of hadrons that escaped the sides of the system leakage energy of low energy neutrons and of electromagnetic showers total leakage energy energy balance 4 Leakage energy spectra of different particles for the upstream plane downstream plane and for the rest of the system 5 If NOB 1 energy spectra of different particles in the pre determined special regions 6 Tables of particle spectra of star density of hadron muon and low energy fluence of total energy deposition density and of temperature rise ready for use with graphics packages The same tables are saved in separate GRA files if activated in MAIN 11 1 3 The MTUPLE File IND 1 T ALWAYS
211. of KDLE 0 can save a fare amount of CPU time spent tracking high energy muons if the details of the produced muons are not important to the user s results KMCS An integer whose value turns on or off the elastic and Coulomb scattering For KMCS 1 scattering is turned off For KMCS 0 only hadron elas tic scattering is turned on For KMCS gt 0 both hadron elastic scattering and Coulomb scattering are turned on and in this case the value k of KMCS gives the number of levels of the particle cascade tree to which the scattering applies Default KMCS 1 5 KDLE Integer number controlling the ionization energy loss modeling For KDLE 0 a simple continuous dE dx process is applied For KDLE gt 0 a more sophis ticated algorithm is applied which includes delta electron production and di rect e e pair production and the simulation of the resulting induced electro magnetic showers for the first k lt KDLE levels of the hadron cascade tree and for all muons For KDLE 1 there is no transported charged particle energy loss at all used for special studies only Default KDLE 1 5 MCSDLE Integer number controlling the correlation in ionization energy and Coulomb scattering ForMCSDLE 1 correlated energy loss straggling and Coulomb scattering are modeled for all charged particles For MCSDLE 0 these two processes are modeled independently Default 1 INEXDL Integer number controlling the modelling mode of delta electron production Fo
212. of radial subdivisions default 1 RP defined as the center of the minimum coordinate location LC S z plane which is the cone base LCS The z axis points from center of the cone base to the center of the cone top the LC S z axis is parallel to the GC S z axis Conical sector 9 C1 the inner radius at the lowest LC S z the cone base C2 the outer radius at the lowest LC S z the cone base C3 the inner radius at the highest LC S z the cone top C4 the outer radius at the highest LC S z the cone top C5 the cone length NT gt 0 or half length NT 0 along the LC S z axis NZSB the number of subdivisions in LC S z default 1 NRSB the number of radial subdivisions default 1 NASB the number of azimuthal subdivisions default 1 PHI1 first angle degrees defining the sector default 0 PHI2 second angle degrees defining the sector default 360 if PHI1 PH12 a clockwise sector is defined otherwise a counterclockwise sector is defined RP defined as the center of the minimum coordinate location LC S z plane which is the cone base LCS The z axis points from center of the cone base to the center of the cone top the LC S z axis is parallel to the GC S z axis Important note Currently December 2013 the Conical Sector shape no 9 can t overlap the adjacent zones while the opposite is allowed Also some issues with scoring in the conical sector regions can exist without at 70 Figure 21 The diagrams demonstrate shape overlapping b
213. of the r sandwich Example Figure 17 A cross section view of the same r The grid lines outline the declared Zones sandwich geometry 64 ARS15 Example R sandwich geometry INDX 6 T NEVT 1000 ENRG 100 0 05 0 05 IPIB 3 3 B S EAM 5 0 5 0 0 1 0 1 IN 052 5 The input deck for this example is ATR MATER INP NLNG 1 ZSEC 350 1251 27 NLTR 3 RSEC 30 80 100 51 22 101 132 NOBL 1 RZOB 0 100 0 350 At the top of the deck INDX 2 F declares this to be a r sandwich type geometry and this means the zone materials are declared in the RSEC card The NL TR and RSEC cards declare 3 major r sections with the 1 and 2 sections each sub divided into 2 sub sections 51 2 2 The 1 major section is composed of steel the 2 concrete and the 3 air 101 1 3 2 The materials are listed in the same order as for example 1 where the 2 1 3 refer to the order those materials are listed in the MATR card The NLNG and ZSEC cards declare only 1 major z section which is in turn divided into 7 sub sections 1251 7 These sections and sub sections are delineated by the grid lines seen in Figures I6 and I7 The sections are always defined from minimum to maximum r or from the center r 0 to the outermost r value The inner steel section is 30cm in radius the surrounding concrete section is 50cm thick and there is a 20cm thick layer or air surrounding the concrete the 30 80 100 values listed reflect the loca
214. om used for definition of flux to dose conversion coefficients is placed there Contrary the absorbed dose DAB and power density type histograms PDT through PDE are calculated in the course of Monte Carlo directly from energy deposited on a step in a non vacuum region 119 Table 12 Histogram types in XY Z histograming DLT is currently not activated STA star density cms total flux of hadrons flux of protons flux of neutrons flux of charged pions kaons flux of muons flux of photons flux of e and e absorbed dose Gy yr at 2x10 s yr DPA total DPA yr at 2x 10 s yr DPA by NIEL hadrons and muons DPA yr at 2x 107 s yr DPA by neutrons at E lt 14 MeV DPA yr at 2x 107 s yr DPA by electrons and photons DPA yr at 2x 107 s yr Hydrogen gas capture cm s71 Helium gas capture em 3s Tritium gas capture cm isa prompt dose equivalent total prompt dose equivalent protons prompt dose equivalent neutrons prompt dose equivalent ch pion K prompt dose equivalent muons prompt dose equivalent photon prompt dose equivalent e and e power density total mW g or Gy s power density protons mW g or Gy s power density neutrons mW g or Gy s power density ch pion kaons mW g or Gy s power density muons mW g or Gy s power density photons mW g or Gy s power density e and e mW g or Gy s neutron energy spectrum z proton energy spectrum pion kaon energy spectrum muon energy spectrum photon energy spectrum e e energy spectrum 120
215. on of Standard Non Standard Extended or imported geometric zones there can be no holes left undefined and yet surrounded by defined spaces If such holes exist then MARS will take care of defining them for you by assigning it s own zone number to them and if no other material is defined for that location filling the areas with the material called black hole The material functions as named any simulated particle which enters the volume of the hole will disappear be dropped from the tracking list and not propagated into the surrounding zones In the GUI visualization of the model these undefined spaces show up as black filled For most applications if such holes exist the simulation results will not be correct There are however certain applications where the user might desire to kill off particles which cross into a certain zone the user subroutine LEAK Section 5 11 gives an example The outermost extent of the user s entire model is a Standard zone cylinder whose extent is given by the values in the ZSEC and RSEC cards in the MARS INP input file This fact implies that there must be at least one Standard zone a sort of container zone All other zones Standard Extended and non Standard including imported must fit within the Standard zone container or have outer boundaries aligned with it For example if the users model is defined entirely using software encoded non Standard zones he must still have at least one Standard zo
216. on sequence is y around z axis then 8 around y axis and then a around x axis A STOP card one it s own line and with no parameters terminates the GEOM INP data card list Remember that there must be at least one Standard zone defined in the MARS INP file and this one zone or the largest of the defined Standard zones must contain all other defined volumes including the Extended Geometry zones The user must determine the extent of his Extended zones and define an appro priate Standard zone to surround all of them If Non Standard zones also exist in the users model then these have priority over the Extended zones When MARS has a particle location x y z the user routine REGI is checked first if code within that routine describes a zone which contains the x y z location then MARS is given this Non Standard zone number and the Extended Geometry module is not called If instead the program exits from the REG1 subroutine with no zone number assigned then the Extended Geometry module will be called The reverse does not occur if upon exiting the Extended Geometry module a zone number still has not been assign to the input z y z location MARS will not return to the REGI subroutine it will likely assign that location a negative zone number which becomes a blackhole material and any particle at that location will be dropped from the tracking list By default there is no optimization in Extended Geometry meaning that
217. one mode The user can also set parameters to gen erate exclusive EM interactions but continue using the default inclusive method for hadronic interactions or visa versa these parameters are controlled by the iput cards BIAS ICEM and PHOT and discussed in Section 4 The list of particle types employed by MARS is given in Table 2 located in Section 3 2 2 4 Basic Monte Carlo Method As stated in the Introduction Feynman s inclusive approach is used for multiparticle reactions At an interaction vertex a particle cascade tree is constructed using a fixed number of representative particles and each particle carries a statistical weight which is equal in the simplest case to the partial mean multi plicity for the particular interaction Energy and momentum are conserved on the average over a number of collisions but not precisely conserved at any single vertex An example of this simplest case is shown in Figure J for an electromagnetic shower showing a diagram of a full shower the exclusive approach compared to the inclusively modeled version While the exclusive picture looks more satisfying as an event 9 slow cascade Exclusive Inclusive nucleon W 1 W 2 W 4 hyperons W 8 evaporation pou ime netic W 16 products Figure 1 The left diagram is a full EM shower Figure 2 An hA vertex as modeled by the MARS each particle with a weight 1 The right diagram 5 particles exit the vertex representing the labeled is the
218. orming a full exclusive simulation This allows for easier simulation of multi TeV particle cascades e in many applications one considers effects due to the simultaneous interactions of a huge number of particles so to describe the cascades it is sufficient to obtain the first moment of the distribution function using the inclusive cross sections in the same manner as with Boltzman s equation e experimental data on inclusive interaction spectra are more readily available than for exclusive ones e the use of statistical adjustments to the assigned weights allows for the enhanced production of se lected particles within a phase space region of interest especially for rarely produced particles The main disadvantage of this approach is the impossibility of directly studying a single interaction or examining fluctuations from cascade to cascade or of studying production correlations Such studies require the simulation of the full exclusive interaction So MARS offers the alternative of using exclusive also called analogous simulations of hadronic and electromagnetic cascades but using these alternatives will result in greatly increased CPU time per generated event The MARS code has been developed over the past 3 decades and is now widely used in the high energy physics accelerator and radiation shielding communities The code is under continuous development and benchmarked against new data as it becomes available to maintain the simul
219. otron radiation generation 177 15 e At E gt 45GeV direct positron annihilation e e up is simulated according to with c 86 8 s nb where s is in GeV and with 1 cos 0 as the angular distribution e For j evv decays the vector momenta of the emitted electrons and neutrinos are sampled according to the differential decay probability of the Vector Axial model of four fermion interactions 78 2 6 Electromagnetic Interactions of Heavy Particles 2 6 Electromagnetic interactions of muons charged hadrons and heavy ions in arbitrary composite materials are simulated down to several tens of keV Radiative processes and atomic excitation and ionization with energy transfer e greater than a cutoff e are considered as discrete events involving production of electrons e e pairs and bremsstrahlung photons which are followed explic itly 79 Energy losses with e lt c so called restricted losses are considered as continuous Their distri bution is described by Vavilov function with redefined parameters which approaches a Gaussian with decreasing c Independent of energy material or thickness traversed the quality of the Gaussian approxi mation is governed by the average number of events xn one chooses to evaluate individually and becomes acceptable for most purposes when gt 10 Bremsstrahlung and direct et e production differential cross sections used in the code are as given in Ref 80 2 6 2 Multiple C
220. oulomb scattering is modeled from the Moliere distribution with nuclear form factors included 81 A very careful treatment is done in MARS of processes near and below the Coulomb barrier in hadron muon and heavy ion transport ionization absorption vs nuclear interaction vs decay as is further described in Ref The scattering is applied as a continuous process while the particle passes through material rather than being applied at discrete locations 2 7 Electromagnetic Showers New modules for simulating electromagnetic showers based on current knowledge of physics of electro magnetic interactions were recently developed and have been implemented into the code 82 The main focus is given to electron and photon interactions in arbitrary composite solid liquid and gaseous materials at low energies 1 keV to a few MeV The entire shower and such processes as emission of synchrotron photons photohadron production yZ pu and e e ut pu can be treated in the spirit of the MARS framework either analogously or inclusively with corresponding statistical weights The choice of method is left for the user to decide via the input settings following statement needs more detail Generation and transport of de excitation photons is improved Undesirable fluctuations in the inclusive description of electromagnetic showers are reduced 2 8 Synchrotron Radiation text to be added 2 9 Stopped Hadrons and Muons A very careful treat
221. ow to process a FLUKA geometry file for use as input to MARS The more advanced user can create his own input files as required by a specific problem special source terms e g DPM EVE for event generators or BLOSS for beam loss distributions in a beam line or ac celerator lattice magnetic field maps in detectors and accelerator elements e g QUAD1 MAP particle distributions produced by MARS in a previous job for multi stage runs and many various optics and lattice element files used by the MAD MARS Beam Line Builder In many cases the user will have to customize a user subroutine to open and read these customized files and then also ensure the data is placed into appro priate variables and made accessible to MARS 34 4 1 Structure of the MARS INP Input Deck The MARS INP file sometimes called the input deck is always required to run a MARS executable At the very least the MARS INP file describes the geometry s Standard Zone s there must be at least one and the list of materials used by the model The input deck consists of what are called cards following ancient FORTRAN conventions a card is a line or series of lines in the MARS INP file The name of the file is by default MARS INP but if the user wishes to change the file name he must edit the corresponding line in the main program mar smain f see Section 5 1 The units used by the input deck parameters and indeed used throughout MARS are energy in GeV
222. particles those with a small weight below the weight window the method of Russian 10 Roulette is applied When such a particle is generated it is simply dropped most of the time but once in a while it is kept and it s weight is adjusted upward to compensate For example a p impacts a target and the cross section probability for producing a p is say 10 Instead of keeping a particle with such a small weight it is simply dropped 99 of the time In 1 of the events which produce it however the p is kept and given a larger weight to make up for all the events in which it was generated but dropped This method gives more statistically stable contributions to the simulation results from rarely produced particle types For cases where the user is interested in interactions which involve rarely produced particles their generation and interactions can be forced see Section 4 2 6 2 2 Nuclear Cross Sections There are several models used for these discrete interactions depending on the type of incoming particle and the energy range of the incoming particle 2 2 1 Hadron nucleon cross sections Updates now cover elastic and inelastic o y interactions for hadrons with kinetic energies from 1 MeV to 100 TeV Total cross sections Ctot for p n 1 and m with energies from 1 MeV to 10 GeV are calculated by the Cascade Exciton Model CEM algorithm used by the code package CEM95 53 This package has recently been updated Cross sect
223. precision This means that all real value assignments must be of the form XVar 0 24D0 or Parameter YLimit 435 76D0 The exception to this is when user defined histograms are employed real variables loaded into HBOOK must be single precision 75 Subroutine name MARSMAIN MARSI5NN MIXTUR BEGl REG REG3 FIELD SUFI LEAK ALIGN SAGIT RFCAVT EDGEUS VFAN MHSETU MFILL HISTO DB WRTSUR TAGPR TAGGING KILLPTCL BLPROCESS HISTDUMP MARS2BML BML2MARS BLINIT BLGEOINIT TUNNELGEO Table 8 User subroutines Description Main program contains names of the main I O files initialize run write output steering subroutine nn release define a compound material redefine the primary particle distribution define user encoded non Standard zones redefine the material content of Standard zones define magnetic fields read in magnetic field data tag score particles which reach selected blackhole zones discrete fictitious scattering between selected zones fictitious scattering within a zone RF Kick at the boundary of selected zones edge scattering define the volumes of all non Standard or ovelapped zones booking of user defined histograms filling of user defined histograms a Block Data for parameters of user defined histograms tag score particles which cross selected user defined surfaces particle origin tagging place holder for user defined tagging kill particle under certain user defined conditions Block Data of swit
224. r numbers the materials are listed in the MATER INP file BIPR RLPRM 500 Real variables specifying the parameters of the inclusive forced prompt muon production in the inelastic nuclear interaction vertex applied only to specific materials Any material which does not have a corresponding entry here will have the global parameter applied as the default with the value given by the PMUPRMT variable in the BIAS data card Values of the RLPRM array specify prompt muon production modelling It is forced with the appropriate statistical weight at RLPRM i 1 forced with the Russian roulette at 0 001 lt RLPRM i lt 1 or suppressed at RLPRM i 0 Default 0 05 RLPRM The values for the prompt muon production control indexed by IM the order numbers the materials are listed in the MATER INP file BIBH RLBEH 500 Real variables specifying the parameters of the inclusive forced Bethe Heitler muon production applied only to specific materials Any material which does not have a corresponding entry here will have the global parameter applied as the default with the value given by the PMUBEHE variable in the BIAS data card Values of the RLBEH array specify Bethe Heitler muon production modelling It is forced with the appropriate statistical weight at RLBEH i 1 forced with the Russian roulette at 0 001 lt RLBEH i lt 1 modelled exclusively at RLBEH i 1 or suppressed at RLBEH i 0 Alternatively the Bethe Heitle
225. r INEXDL 1 exclusive modelling is used For INEXDL 0 inclu sive modelling is used Default 0 60 MUON EFLU IPAR KPHA ISOURCE Variables which control the modeling of bremsstrahlung and direct pair production by muons extend of hadron cascades and muon and neutrino beams EFLU IPAR KPHA ISOURCE The energy above which full modeling of bremsstrahlung and direct pair pro duction by muons is done at lower energies a continuous energy loss approx imation for these two processes is used Default 5 GeV A parameter which if equals zero can be used to turn off the default model ing of direct pair production by muons and use instead the continuous energy loss approximation for this process at all energies Default IPAR 1 The number of hadron generations to follow i e the number of levels in the hA vertex tree Default 55 A parameter which defines the beam type original at ISOURCE 0 and ISOURCE 1 broad at ISOURCE 2 y decays in a straight section z lt 0 at ZMIN 0 at ISOURCE 3 and y decays in a ring at ISOURCE 4 Default 0 NUFR ZLNUFR ZUNUFR RUNUFR Real variables which define a cylindrical region where v interactions are forced ZLNUFR PHOT ELSYN EMISYN EEGHM ISYNHMU ISYNEMS ISYWRT NOSTPMV KEMINCL ZUNUFR RUNUFR The cylindrical region where neutrinos are forced to interact with matter when IND 8 T Default 0 0 0 Variables which control features of electro magnetic shower deve
226. r muon production cross section can be increased 1 to 500 times with 500 lt RLBEH i lt 1 an appropriate correction to a statistical weight assures correct results It is automatically set to 1 for KEMIN i 1 For example RLBEH i 0 03 is recommended for most of the high energy muon collider and LHC applications Default 1 RLBEH The values for the Bethe Heitler muon production control indexed by IM the order numbers the materials are listed in the MATER INP file 49 BIGV RLGVM 500 Real variables specifying the parameters of the inclusive forced muon production via vector mesons generated in photo nuclear reactions at E gt 1 5 GeV when IND 10 T applied only to specific materials Any material which does not have a corresponding entry here will have the global parameter applied as the default with the value given by the PMUGVM variable in the BIAS data card Values of the RLGVM array specify muon production via vector mesons modelling It is forced with the appropriate statistical weight at RLGVM i 1 forced with the Russian roulette at 0 001 lt RLGVM i lt 1 modelled exclusively at RLGVM i 1 or suppressed at RLGVM i 0 It is automatically set to 1 for KEMIN i 1 Default 0 02 when the primary beam particle is photon electron or positron 10 9 10 or 11 on the IPIB card otherwise it is 0 005 at E gt 20 GeV or 0 at E lt 20 GeV RLGVM The values for the control of muon production via
227. rced antiproton production It is forced with the appropriate statistical weight at PPBAR 1 forced with the Russian roulette at 0 001 lt PPBAR lt 1 or suppressed at PPBAR 0 Default 0 05 EMST RELEMS EGSSPH EGSSEL LEMSGL Variables which control for electromagnetic showers electron positron stepsize and transition to EGSS RELEMS Real number specifying the fraction of electron positron energy to be lost on average on a step Default 0 1 EGS5PH EGS5EL Real numbers specifying the photon and electron positron energies at which a transition to the EGS5 module occurs Default 0 001 0 001 LEMSGL The integer value that controls the use of the EGSS module for precise exclu sive modeling of electromagnetic showers EMS above 1 keV If the EGS5 mode enabled and anything was changed in the MATER INP file be sure that all egs5job and pgs5job files were deleted from this directory before running a job with the modified MATER INP file For LEMSGL 0 the native MARS module is used for EMS at all energies For LEMSGL 1 the EGS5 module is used below EGS5PH and EGS5EL For LEMSGL 2 the EGS5 module is used below the material dependent photon neutron production thresholds for example 0 018 GeV in beryllium and 0 006 GeV in uranium For LEMSGL 3 the use EGS5 module is forced at all ener gies up to the beam energy Default 0 ICEM C1CEM C2CEM EMODEL IQGSM NEVTYPE Variables which control hadron event generator and u
228. ributing particles The units are GeV per g per primary Statistical errors are given DOSE EQUIVALENT mSv per 1 inc particle The table only has meaning if the standard zones listed in it are made of a tissue equivalent TE ma terial It represents the prompt dose equivalent calculated directly in the course of Monte Carlo from energy deposited in the TE regions multiplied by a corresponding quality factor The values of this Table can be similar to those in the Table TOTAL DOSE EQUIVALENT ICRP103 gt MAXIMUM OR 1 CM only in the TE material regions and are certainly different otherwise the table is mean ingless in the latter case The units are mSv per primary No statistical errors are given TEMPERATURE RISE K AT TO 3 000E 02 PER 1 000E 12 PPP The table presents arranged by Standard zone number the instantaeous temperature rise the material in this zone would experience in Kelvin due to the impact of beam It is assumed that the material is initially at standard room temperature but this can be changed by setting the TEMPO value in the VARS card The temperature rise is calculated on a per pulse basis rather than per primary where a pulse contains by default 1012 primaries this pulse size value can be changed by setting the AINT value in the VARS card No statistical errors are given LEAKAGE BACKWARD FORWARD SIDE This table and the values following it present information on particles which have passed out of the model s
229. ript in the installation directory uses compiler options appropriate for the code and for the operating system and compiler version on the machine where the code is installed The GNUmakefile contains pointers to all the required external libraries including those for graphics and for CERNLIB The directory sample above is located on a hypothetical cluster which contains various types of computer platforms The directories named by platform type linux sun irix hold the MARS object libraries compiled for that platform within a 1ib subdirectory and also hold a subdirectory of include files include which contain MARS common blocks and variable declarations On a single node or on a cluster of identical machines there will be just one platform directory listed instead of the multiple platforms shown in this example Some geometric models which have a simple cylindrical structure can be described completely via the main MARS INP input deck using MARS Standard zones an example of such a geometry is given in Section The sample MARS INP file contained in the MARS installation directory is fairly simple and lists the items which most users will typically customize It also lists on the 2nd line of the file the full path on the user s local system to the dat files in the installation directory which the MARS executable will need to load at run time Other geometric models can be adequately described using groups of boxes spheres and other
230. romagnetic shower and n y verticies five EMS bias keys see the BIAS data card are automatically converted to 1 i e to the exclusive mode For KEMINCL N gt 1 exclusive modeling is used for the first N generations and inclisive one for remaining higher generation levels of the electromagnetic shower Default 10 61 IIFLUG IIFLUG The integer value that controls ionization energy loss fluctuations in modeling of electromagnetic showers EMS in the 100 keV to 100 TeV energy range For I IFLUG 1 these are modelled with the energy angle correlations taken into account along with detailed modeling of large angle Coulomb scattering Currently this is a rather CPU time consuming option For I IF LUG 0 the continuous slowing down approximation modeling of ionization energy loss in EMS with no correlations to the Coulomb scattering modelled in a small angle approximation Substantially faster option Default 0 RZMN RMI514 RMA514 ZMI514 ZMA514 RMINTR RMAXTR ZMINTR ZMAXTR Real variables which define two cylindrical volumes each volume is defined by minimum and maximum radii and minimum and maximum z coordinates The first four variables define a volume where the IND 5 T condition applies The second four variables define a volume where the particles entering are recorded in TRACK PLOT and VERTEX PLOT files if those files have been requested via the TAPE data card RMI514 RMA514 ZMI514 ZMA514 The cylindrical region where IN
231. rt Fermilab FN 0835 APC 2009 N V Mokhov and S I Striganov Mars15 overview Technical Report Fermilab Conf 07 008 AD 2007 N V Mokhov et al Physics models in the mars15 code for accelerator and space applications in Int Conf on Nuclear Data for Science and Technology AIP Conf Proc 769 pp 1618 1623 2004 S G Mashnik K K Gudima A J Sierk M I Baznat and N V Mokhov Cem03 01 user manual Technical Report LANL LA UR 05 7321 2005 N V Mokhov E I Rakhno and I L Rakhno Residual activation of thin accelerator components Technical Report Fermilab FN 0788 AD 2006 I L Rakhno N V Mokhov and S I Striganov Modeling heavy ion ionization loss in the mars15 code Technical Report Fermilab Conf 05 019 AD 2005 N V Mokhov et al Recent enhancements to the mars15 code Technical Report Fermilab Conf 04 053 2004 N V Mokhov K K Gudima S G Mashnik I L Rakhno and S I Striganov Towards a heavy ion transport capability in the mars15 code Technical Report Fermilab Conf 04 052 2004 M A Kostin and N V Mokhov Parallelizing the mars15 code with mpi for shielding applications Technical Report Fermilab Conf 04 054 2004 153 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 M A Kostin O E Krivosheev N V Mokhov and I S Tropin An improved mad mars beam line builder
232. rtance in terms of their contribution to the result By default the values of importance are set equal to unity For a card describing a blackhole zone both the material number and importance must be zero and the material density value must be omitted See the MCNP manual for more details These MCNP zones are treated by MARs as Non Standard zones They are numbered by MARS in the order in which they appear in the MCNP section of the MARS INP file Non Standard zones are numbered starting from N FZP 1 where NFZP is the number of Standard zones Recall that there must be at least one Standard Zone defined in the MARS INP file a container zone which surrounds all other defined zones Also keep in mind that the MCNP geometry cards can be used in conjunction with all other methods which MARS uses to define zones If the model contains encoded Non Standard zones in addition to the MCNP geometry zones then the user must check for conflicts between the zone numbers assigned by the users code and the zone numbers MARS assigns to the MCNP zones Also recall that MARS must have the volumes of all defined zones in order to calculate various quan tities For any MCNP zones having a cylindrical symmetry MCNP itself calculates volumes and hands this information to Mars Otherwise the user must provide the zone volumes Volumes can be calculated by hand or by running Mars in volume MC mode once all the zones are defined see Section 3 T T Once the MC
233. s a series of seven tables Each of the seven tables is labeled by J 1 J 2 etc where the value of the index identifies the produced particle type these are the same seven listed at the top of the output file Each table has the structure DEGR 0 0 5 00 10 00 15 00 20 00 30 00 60 00 90 00 135 00 180 00 EE GEV D2N DEDO qDN DE 5 000 7 49E 02 8 06E 02 9 04E 02 8 61E 02 1 77E 01 4 30E 01 3 31E 01 2 03E 01 9 10E 02 3 13E 01 10 000 3 64E 02 2 47E 02 4 10E 03 0 00E 00 0 00E 00 0 00E 00 0 00E 00 0 00E 00 0 00E 00 1 30E 02 The tables hold the production cross section d N dEdQ for the given particle type as used by the generator with the columns being bins in degrees and the rows being bins in energy The last column is dN d E The number of rows which appears is determined by the value of NEVBIN set in routine MARS1514 If instead the user set IDNDX 3 in routine MARS1514 then the TMA file contains a different series of seven tables where the columns are Ed N d P in bins of P and the rows are bins in X f The last column is dN dX 114 9 MAD MARS Beam Line Builder The MAD lattice description language has become the ingua franca of computational accelerator physics Any new developments in accelerator physics computational codes and libraries should have the re quirements to read and understand lattice descriptions written in MAD The ideas and modules of Ref are used in a new interface which is able to read parse and store in memory MAD
234. s are exactly those which are the BEG1 subroutine arguments The first step process ends resulting in this file of particles which reached that particular Zone A second MARS process is started consisting of the geometry downstream of the first process s LEAK zone the file of particles from step 1 is the input for routine BEGI in step 2 This two or multi step process is useful when modeling labyrinths or shielding penetrations step 1 generates many particles a few of which reach the entrance of a labyrinth the LEAK zone and are written to output step 2 works only with the particles which enter the labyrinth and models only the labyrinth portion of the geometry In this case different energy thresholds can be applied in steps 1 and 2 in order to optimize execution time for example to concentrate only on thermal neutrons in the labyrinth The multi step process is also useful when investigating the effects of beam loss distributions step 1 models the actual beam loss and records the particles which are created in that interaction shower step 2 tracks only the shower to investigate it s effects on the surrounding area Another example if the LEAK BEG1 multi step process is to separate the primary event generator from the processes which occur in the rest of the geometry model a primary beam hitting a target use DPMJET or ISAJET to model what happens in the target and record via LEAK everything which exits the target input the resulting partic
235. satisfied the code falls through to the end of this list of statements If the conditional statements are coded correctly then the code should never reach the fall through point One can use this fact to catch errors While this tactic may seem unnecessary for a simple example the logic to encode more intricate geometries can rapidly become very complex and difficult to debug Now that the encoding and zone assignment of the simple beam dump is defined return to the zone initialization process Every non Standard zone where the user wants results to be tabulated must have it s volume declared to MARS The default method for handing volume values to MARS is to use subroutine VFAN As shown in the above code section the default version of REGI is set up to call VFAN in it s initialization section and similarly VF AN contains an initialization section of it s own executed this first time the routine is called For the simple beam dump example subroutine VFAN is as follows SUBROUTINE VFAN N V IMPLICIT DOUBLE PRECISION A H O Z INTEGER I N INCLUD INCLUD blregl inc tallyl inc E pd DATA NENTER 0 SAVE NENTER 82 Parameter ZConc 400 0D0 Parameter ZSteel 150 0D0 Parameter ZSteel middle 75 0D0 Parameter XSteel 30 0D0 Parameter YSteel 35 0D0 Parameter XConc 100 0D0 Parameter YConc 120 0D0
236. se of cascade exciton and quark gluon string models and evaporation scheme C1CEM C2CEM Real numbers specifying the energy ECEM below which the CEM code is called on a nucleus with atomic mass A gt 3 where ECEM C1CEM C2CEMxZ Default 5 0 0 EMODEL Real number specifying the transition energy between the use of high energy and low energy event generator algorithms Default 5 GeV IQGSM An integer that allows a global choice of the inclusive and exclusive event generators at nuclear inelastic interactions similarly to that with the MTQG card for specific materials For TOGSM 0 exclusive modeling with the CEM code is done at E lt 3 GeV the MARS inclusive model is used at E gt 5 GeV and mix and match between these two models is used at 3 E 5 GeV If A lt 3 or E 0 02 GeV the LAQGSM code instead of the CEM code is used above LAQGSM instead of CEM is always used if a projectile particle is p K d t He He m hyperon or heavy ion This mode is most suitable for shielding type simulations For TOGSM 1 exclusive modeling with the CEM code is done at E lt 59 0 3 GeV mix and match between CEM and LAQGSM is used at 0 3 E 0 5 GeV exclusive modeling with LAQGSM is done at 0 5 E 8 GeV mix and match between LAQGSM and the MARS inclusive model is used at 8 E 10 GeV and the MARS inclusive model is used at E 10 GeV LAQGSM instead of CEM is used under the same conditions as in the pre vious mode
237. se particles with a kinetic energy greater than the value of the threshold EMCHR set in the ENRG card default value 0 0002 GeV OR with a kinetic energy greater than EM if EM has been set to greater than it s 0 0145 GeV default value The statistical errors are also given TOTAL STAR NUMBER Not a table of values but a single value summed over all Standard zones LATERAL INTEGRATED A table of several values all of which are summed across all Standard zone r values for the given z range The first two columns give the lower and upper z boundaries for each z range The third column S CM is the integrated stars Note the units stars cm for each zone in the z range have been integrated over r so that the units are now stars cm The fourth column FTOT is the total hadron flux which includes neutrons above the threshold EM default value 0 0145 GeV here the flux values from each zone have been summed so the units are cm The fifth column F1 is charged hadron flux for hadrons with energy greater than 0 0001 GeV The sixth column F2 is charged hadron flux for hadrons with energy greater than 0 02 GeV The seventh column F 3 is the e flux for e with energy greater than 0 00010 GeV The eighth column F4 is the e flux for e with energy greater than 0 02 GeV The ninth column F5 is the muon flux for muons with energy greater than 0 00010 GeV The tenth column F 6 is the muon flux for muons with energy greater than
238. son of mars and fluka simulation codes Technical Report FN 697 Fermilab 2000 156 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 I S Baishev M A Maslov and N V Mokhov in Proc VIII All Union Conference on Charged Particle Accelerators volume 2 page 167 Dubna 1983 M A Maslov and N V Mokhov Technical Report IHEP 85 8 Serpukhov 1985 N V Mokhov Nucl Phys B Proc Suppl 51A 210 1996 C Johnstone and N Mokhov Optimization of a muon collider interaction region with respect to detector backgrounds and the heat load to the cryogenic systems Technical Report Conf 96 366 Fermilab 1996 A Drozhdin M Huhtinen and N Mokhov Nucl Instruments and Methods A381 531 1996 A I Drozhdin M Harrison and N V Mokhov Study of beam losses during fast extraction of 800 gev protons from the tevatron Technical Report FN 418 Fermilab 1985 I S Baishev A I Drozhdin and N V Mokhov Beam loss and radiation effects in the ssc lattice elements Technical Report SSCL 306 SSC Laboratory 1990 A Drozhdin N Mokhov R Soundranayagam and J Tompkins Toward design of the collider beam collimation system Technical Report SSCL Preprint 555 SSC Laboratory 1994 A Drozhdin N Mokhov and B Parker Accidental beam loss in superconducting accelerators Simulations consequences of accidents
239. standard shapes and these models can be created using MARS Extended Geometry zones via the GEOM INP deck an example of such a geometry is given in Section ref ingeom The sample GEOM INP and MARS INP exgeom files are set up to illustrate the use of Extended zones one must put INDX 3 T 31 to MARS INP to execute the example Both these simple geometric models using only the MARS INP file or the MARS INP and GEOM INP files together do not require customization of the user subroutines In these cases however the user must still compile a local copy of the user subroutines to obtain an executable even if the routines have not been modified from their initial dummy state For some problems involving the production and interactions of low energy neutrons the user might consider using MARS coupled with the MCNP code library See the discussion in Section for the relevant conditions Details on running in MARS MCNP mode are in Section 6 The MARS executable can be run interactively in the background or submitted to a batch system By default the executable and the input MARS INP and GEOM INP files must all reside in the same directory For batch running when the executable and input files might not be located in the same directory the paths to the input files can be modified via customization of the user routine MARS1514 see Section 5 2 for more information The running time per event can vary widely depending on the complexit
240. start b12 theta bl12 phi b12 psi InitZone call setebl BeamKineticE BeamMass 5 6780d 03 call blmaxmat nblnzmax if nblnzmax gt M_MAX then write beamline 1 nblnzmax as read from blmatmax nblnzmax write is greater then M MAX M MAX stop STOP else if nblnzmax 1t M MAX then write beamline 1 nblnzmax as read from blmatmax nblnzmax write is less then M MAX M MAX endif 101 if nblnzmax gt 0 then X call blmat IMUN m else D write Number of zones for NuMI beamline lt 0 Stop a endif do i 1 st nof zones call simple tunnel mat i IMUN i st first zone 1 D end do C volume names call set current beamline 1 call blname VOLNM NFZPEX 1 call set current beamline 2 Cs call blname VOLNM NFZPEX 1 RETURN END 5 19 4 Subroutine BLGEOINIT SUBROUTINE BLGEOINIT BEAMLINE_ID Cr Ak A at Le A eke st Ra MM A GAs Des ed Era eue te ca EUR ER Eug C MMBLB ELEMENT REGISTRATION C CALLED IF IND 13 T C E JN ll ut amp CREATED 2001 BY KRIOL C MODIFIED 17 OCT 2003 BY MAK C LAST CHANGE 04 DEC 2003 BY NVM E AN A a e a Relates eee IMPLICIT NONE INTEGER BEAMLINE ID C EXAMPLE OF REAL WORK uncomment and modify whereever needed m INCLUDE DRIFT INC INCLUDE RBENDEPB INC d EXTERNAL amp DRIFT NAME FUNC amp DRIFT INIT FUNC x amp DRIFT_MAT_FUNC
241. t rio Recommended Ar z Aj Default 10 0 0 WRIMPT Importance factors at the above radii which define the factors for hadron weight splitting and Russian roulette If Ar Ain then recommended WRIMPT i e 22 7 Default 2 0 4 2 7 Histograms and Tabulation NOBL RZOB NSUR RZTS TOFF NHBK HBKE NCLD IMNC NDET FLOC TAPE HTIR RTIR CFTD DPAC NOBL NOB MHIRFL NHSPE NR1 NZ1 NR2 NZ2 NR3 NZ3 Integer variables which give the number of special rz regions in which RZ volume type histograms will be accumulated the flag which controls creation of z histograms and the type of scale for spectral histograms See Section IO T for the list of the histograms and their IDs The size of the volume of each region is given in the accompanying RZOB data card NOB The number of special regions OXNOB x3 Default 0 MHIRFL Currently not used 53 NHSPE The type of scale for the particle energy spectra histograms for special regions and surface detectors dN dE if NHSPE 0 and dN dlog y E if NHSPE 1 Default 0 NR1 NZ1 The numbers of bins in r and z directions for the first special region De fault 120 200 NR2 NZ2 The numbers of bins in r and z directions for the second special region Default 120 200 NR3 NZ3 The numbers of bins in r and z directions for the third special region De fault 120 200 RZOB RZO 4 3 Real values which specify the location and size of each special region It is currently required that thes
242. t is assumed to produce only pi ons neglecting some of the rarer modes involving strange particles Charges of produced pions are slightly skewed towards 7 in view of the brought in negative charge Pion momenta are chosen from an inclu sive distribution loosely based on experiment The energy weighted distribution is normalized to twice the nucleon mass which predicts a multiplicity of 4 3 close to observation In a complex nucleus the anni hilation is treated as though it occurs on free nucleon except that each pion produced by the annihilation process is given a 50 probability to interact within the nucleus This shortcut attempts to include at least qualitatively participation by the constituents nucleons For antiprotons in flight the annihilation cross section results in a larger cross section for pA vis a vis pA especially for light nuclei at lower energies Total cross sections for both pA and pA are estimated on the basis of simple geometrical considerations and pp pn and pp pn cross sections The ratio 054 054 is then applied to the more accurate opa used in MARS Annihilation in flight uses the same inclusive pion distribution as at rest in the p nucleon rest frame after which the pions are Lorentz transformed back to the lab Above about 0 1 GeV c a small pp Tn component is included For both mechanisms nuclear target effects are again approximated by allowing emerging particles to interact in the same nucleus or esc
243. t sample code as reminders for their use but the user should consult this manual for details on the full usage of the subroutines Table 8 lists the names of the user subroutines and a brief description of their purpose The user is free to split file m1514 f up into other files for example combining all his customized subroutines into a single file and storing all the unused dummy user subroutines in another file The user can also create his own subroutines which are called from the user subroutines The user can create his own set of common blocks to carry information among his own subroutines none of his values or variables will be carried back into the main MARS code however With a few exceptions the communication between MARS and the user subroutines is via subroutine arguments If the user rearranges subroutines into files other than m1514 f then he must remember to also modify the default GNUmakefile appropriately so the compiler linker knows to pick up the local user files This manual assumes the user knows how to compile and link code using gmake or make on unix or linux systems It is important to remember that MARS uses double precision in all calculations and all real variables are declared double precision The user will utilize MARS real variables delivered via subroutine arguments and rather than copy them to local single precision variables it is highly recommended that all user real variables be likewise declared double
244. the location and size of each surface and a real giving an optional unit number for recording the particles crossing each surface It is currently required that these values or at least some of them coincide with boundaries of geometry zones This card is valid only if NSURF in the NSUR card is 71 See Section T0 2 for an example RZTSUR 1 i The minimum radius of the i surface 0 0 minimum radiusc RMAX Default 0 0 RZTSUR 2 i The maximum radius of the i surface minimum radius lt maximum radius X RMAX Default 0 0 RZTSUR 3 i The minimum z coordinate of the it coordinate X ZMAX Default 0 0 RZTSUR 4 i The maximum z coordinate of the it surface minimum coordinate maximum coordinate lt ZMAX Default 0 0 54 surface ZMIN lt minimum UNIT i A real number not integer i to open a file named FORT I which holds a list of all particles crossing the i surface 81 i lt 90 If 1 0 then no file will be created Default 0 TOFF TOFMIN TOFMAX TOFSHF Real variables which define the time interval in seconds for the time of flight spectra accumu lated for the surfaces declared by the NSUR and RZTS data cards when NTOFF 1 TOFMIN The begining of the time interval Default 0 0 TOFMAX The end ofthe time interval Default 1000 0 TOFSHF Atime shift applied to the time spectra Default 0 0 NHBK NHBK Integer variable which defines the number of materials for the global energy deposition his togr
245. the typical output of any code for given physics model depends on how the user built the calculational model and how he she handled the code The geometry description is of primary importance Then as stated above the most essential parameters to control the calculational accuracy for given physics model are the number of incidents primary events NEVT and the inclusive exclusive switches Some other parameters also affect the computing efficiency the accuracy of boundary localization in iterative transport algorithm STEPEM IND 6 option cutoff energies geometry details histogramming etc Naturally the higher NEVT the better the result will be But here we come to a contradiction with both CPU time t and time ta alotted for the whole problem The strategy would be to keep both t and t as small as possible There are a few rules for a user to get the best from the MARS code These rules are 1 Required NEVT is determined by a statistical error in a phase space or geometrical region of inter est The calculated results in a given region N are statistically valid only if a R M S statistical error 2096 So run until this condition is satisfied Do short runs first to estimate required NEVT and play with DUMP output 2 Before a long run try to understand what a combination of inclusive exclusive options provides high est computing efficiency 3 Use as few as possible geometrical regions described in all the standard extended an
246. tions of the outer boundary of each major r section The input beam is described identically to the z sandwich example This example could also be a model of a secondary pion beam striking a beam dump only the emphasis is on mapping the radial deposition outward through the different layers of materials The same energy cutoffs and global step sizes are used as for the z sandwich example Also the identical NOBL and RZOB cards are used encompassing the entire declared geometry However since the materials are arranged in a different geometry the hadronic flux map Figure I8 appears slightly different from that for the z sandwich example Since the color maps display only from r 0 to r Rmax the frame of the view has been modified to show just the upper half of the geometry 4 3 3 Thin Window The example of a thin window shows the usage of material dependent parameter settings such as step lengths The model is of a small proton beam traveling through helium The beam encounters a thin titanium window and then a region of air There are no interactions of significance in the helium or the air and allowing large step sizes in those areas can reduce the overall running time However one must be careful of the combination of small size zones and large step sizes It is fairly obvious that if the step size is of the same order as a thin zone size then some generated particles may jump over the thin zone and some results for the the thin zone s
247. tor based on a FLUKA input geometry description overall view left and a central fragment right 113 8 LAQGSM and DPMJET Modes 8 1 LAQGSM The 2013 version of the Los Alamos Quark Gluon String Model code LAQGSM was implemented into MARS15 for particle and heavy ion projectiles 13 Such processes as 77 capture and p annihilation on nu clei are treated down to essentially zero enrgy Details of this event generators can be found elsewhere This implementation provides the capability of full theoretically consistent modeling of exclusive distributions of secondary particles spallation fission and fragmentation products 8 2 DPMJET 8 3 Event Generator Output Section 5 2 explained the use of the MARS stand alone event generator Here the output produced by that running mode is described in more detail The output files produced are TMA OUT TDNDX OUT The TMA file always contains a table with the heading AVERAGE MULTIPLICITY AND ENERGY with columns labeled by produced particle type and several rows The rows are defined as BLACK I haven t a clue GREY likewise SHOWER enter appropriate descriptions here FORW CS gt 0 X gt 0 BT gt 0 2 X lt 0 BT0 2 TOTAL E X gt 0 BT gt 0 2 E X lt 0 BT gt 0 2 ETOT SUBCUT NO SUBCUT E ELAE EBIND YIELD pit YIELD pi SU EG EXGAM EXWGA If the user set IDNDX 2 in routine MARS1514 then the TMA file also contain
248. ts supported by MAD An arbitrary number of beam lines arbitrary positioned and oriented can be put in a MARSIS model More sophis ticated algorithms and new data structures enable more efficient searches through the beam line geometry Tunnel geometry can now follow the beam line or be described independently of it For more details and use of MMBLB the user must read Ref 16 115 10 Histogram Input and Output Files In many cases it is worthwhile to initialize the HBOOK package to use the output file MARS HBOOK for interactive analysis with the MARS GUI or PAW systems All the powerful features of MARS GUI are described in Section I2 while those of PAW are described in 105 Both can be used for comprehensive physics analysis of the run session Histograms can be requested by the appropriate cards in mars inp and xyzhis inp At least one of the non zero cards NOBL NSUR or NHBK must be presented in mars inp for that Then there will be an output file mars hbook The MARS code is linked to the CERN library and uses the hbook package to produce the mars hbook file There are several methods to use which each generate different histogram sets Some histogram sets are built in MARS defines and fills the set of histograms and the user cannot change the bin specifications or contents only specify the geometric area the histograms cover Other sets of histograms or ntuples are completely under the users control and require the use o
249. ts to keep in mind First the MARS zone number will be assigned according to the order in which the lines appear in the file Second overlapping shapes are layered according to the order the lines appear in the file with the top layer shapes being listed at the top of the file and so on down see Fig 21 as an example The user needs to keep these points in mind and order shapes appropriately so as to obtain the desired result It is strongly advised to add at the very end of GEOM INP a region coinciding with the mother volume defined in MARS INP It is generated automatically if there is no other standard geometry regions besides the mother volume In this case a message is streaming to the screen for example Just one standard region mother volume NFZP 1 is defined in MARS INP The extended geometry region coinciding with it is automatically generated as MOTHER 2 0 2 0 0 10 0 35 70 Table 7 Shape types listed by the shape ID number which are imple mented in Extended Geometry and used in the GEOM INP file with their descriptors their Reference Point RP location and definition of their Local Coordinate System LC S Shape abs NT Parameter List RP and LC S definitions Box 1 C1 the box half size along the DC S x axis C2 the box half size along the LC S y axis continued on next page 68 Shape Cylinder Sphere Cone Tetrahedron Table 7 table continued abs NT Parameter List RP and LCS definit
250. ty of processes taking into account all interactions of hadrons leptons photons and heavy ions during their passage through matter The modeled energy range is large up to 100 TeV for all particles and down to 100 keV for muons charged hadrons and heavy ions down to 1 keV for electrons and photons and to 0 00215 eV for neutrons All processes introduced in older versions of the code and described in prior versions of this manual are for the most part still present Processes updated for the current version include a new nuclear cross section library a model for soft pion production a cascade exciton model a quark gluon string model a dual parton model deuteron nucleus and neutrino nucleus interaction models a detailed description of negative hadron and muon absorption and a unified treatment of muon charged hadron and heavy ion electromagnetic interactions with matter This Section summarizes the simulated physics interactions and gives brief descriptions of the Monte Carlo techniques and the modeling algorithms used to implement them References to sources and to more detailed descriptions are given for the interested reader All algorithms are benchmarked against available experimental data and some of these comparisons are shown here Physics interactions are classified into two types discrete and continuous A discrete interaction would be when a particle collides with a nucleus a variety of things can happen at this particular
251. uced by the Mars GUI interface Figure I4 is a color filled diagram of the Standard zones with each color being a distinct material light blue is air orange is steel and tan is concrete Figure I5 is the same zone diagram with no color fill and with a 2 D histogram of the charged hadronic flux density super imposed over it 62 The input deck for this example is ARS15 Example Z sandwich geometry INDX 2 T 6 T NEVT 1000 ENRG 100 0 05 0 05 IPIB 3 3 B S EAM 5 0 5 0 0 1 0 1 MIN 0 2 5 ATR MATER INP NLNG 3 ZSEC 50 150 350 1252 4 4 2501 2 1 3 NLTR 1 RSEC 100 51 4 NOBL 1 RZOB 0 100 0 350 100 50 50 100 em 5 1e 01 0 0e 00 100 i103 310 10 10 10 10 107 10 ta L Figure 14 Plan View of the z sandwich Example Figure 15 The same z sandwich geometry with a The grid lines outline the declared Zones histogram of the hadronic flux density overlaid At the top of the deck INDX 2 T declares this to be a z sandwich type geometry and this means the zone materials are declared in the ZSEC card The NLNG and ZSEC cards declare 3 major z sections with the 2 and 3 sections each sub divided into 4 sub sections 1252 4 4 The 1 major section is composed of air the 2 steel and the 3 concrete 2501 2 1 3 where the 2 1 3 refer to the order those materials are listed in the MATR card The NLTR and RSEC cards declare only 1 major r section which is in turn di
252. uch as energy deposition will be incorrect What is less obvious is controlling the accuracy with which the zone boundary is located MARS uses a zig zag approach to locate a boundary The pilot step the global STEPH or the material dependent RLSTEH is first applied if within that step the zone number changes then MARS will iterate back and forth in smaller and smaller steps to locate the boundary between the zones The minimum size of these iterative steps is given by the global STEPEM or the material dependent RLSTEM Therefore the 65 85 170 255 340 1 20 00 NER NN a O 0 00 T z a er emi 10 10 10 10 10 10 10 10 10 the Figure 18 Plan View of the r sandwich Example with a map of the hadronic flux overlaid zone boundary will be located to the accuracy of the size of STEPEM or RLSTEM Moreover one does not want to have a large value of STEPEM on one side of a boundary and a smaller value of RLSTEM on the other side of a boundary A better strategy is to make big steps until within a certain distance from the thin zone and then reduce the step size on approach step through the thin zone continue taking small steps for a certain distance past it and then increase the step size again This requires dividing the material in front of and behind the thin material into sections where the step size can be adjusted The following deck sets up this sort of controlled boundary localization ARS15 Example Thin W
253. ugh Second MARS calculates the step size Deont allowed by the algorithm which models the main continuous process the effect of magnetic fields The step size for tracking through magnetic fields varies with the particle energy as it is determined by limits on the bend angle the MARS defaults for these limits are adequate for most situations and can be modified by the user using the ALMX card in the input deck described in Section 4 2 8 Third MARS sets the overall interaction distance Dj by choosing the minimum of Dj and Deont i 23 The fourth part of the line segment size determination compares Dj to the step size allowed by the geometry description Dg The geometry portion of the tracking steps through the users model using a pilot step size and after each such step MARS queries the geometry description routines to determine what material or zone number is present at the end point of the step If the material or zone number has not changed from the previous step then Dg is set to the pilot step size If however the material or zone number has changed then there are two possibilities In the extended geometry mode see Section 4 4 the code takes as the next step the distance to the nearest surface boundary by solving corresponding equations In all other geometry modes the code jumps back to near the start of the pilot step checks to see that the initial material is located there jumps forward again with a reduced step si
254. ugh ionization losses from charged hadrons and muons ETOT is the total energy deposition combined from all these sources in the given r ranges DIRECT ENERGY DEPOSITION GEV This table is not arranged by zone number but has combined the results across r bins Each row lists various energy deposition results for all r between the z values given in the first two columns The third column LEN is energy deposited by low energy neutrons those below the hadron energy threshold as given by EM on the ENRG card the next column LCH is energy deposited by low energy charged hadrons also below energy EM from nuclear de excitation processes EMS is energy deposited by electro magnetic showers DEX is the energy deposited through ionization losses from all charged hadrons and muons The TOTAL IN SLAB adds all the contributions for that z row TOTAL IN BLOCK sums each z row with the one before making a cumulative sum A last row below the table gives the sums for all z of the values in each column TOTAL DOSE EQUIVALENT ICRP103 gt MAXIMUM OR 1 CM mSv PER 1 INC PAR TICLE This is the first of many tables arranged by Standard zone number called Region Number in the file The table presents the prompt dose equivalent based on the ICRP103 flux to dose conversion 125 coefficients for energy and particle dependent fluxes in the given region of an arbitrary material even vacuum to the maximum dose in a tissue equivalent TE material as
255. ular spread c 0 in radians used only when IBEAM 3 The gaussian angular spread o 0y in radians used only when IBEAM 3 The RMS bunch length c of a Gaussian beam in cm 30 cm 1 ns If pos itive it specifies a Gaussian longitudinal distribution around ZI NT sam ple z position and clock start around ty 0 Be sure that ZMIN lt ZINI 6 x DLBNCH If DLBNCH lt 0 then the code generates the initial particle time distribution from a Gaussian distribution with lt t gt 0 and c derived from abs DLBNCH sample clock start only The z coordinate of the initial particle is unchanged z ZINI Corresponding time of flight distributions in all detectors are naturally affected in both cases Note that all the MARS versions before July 27 2005 had just a positive DLBNCH as a beam RMS bunch length cm to generate a Gaussian time distribution with lt t gt 0 with the unchanged initial z coordinate The cur rent version prints on screen parameters of several first projectiles so one can always control the initial conditions INIT XINI YINI ZINI DXIN DYIN DZIN WINIT The Real variables used to specify the initial starting point and direction cosines of the incident beam In particular if the starting point of the users model is not zero as given by variable ZLEFT in the ZMIN card then the starting point of the primary should be adjusted appropriately Use these variables for simple beam descriptions More co
256. umed to be in octal therefore no digit should be greater than 7 Default 54217137 shift example 64217136 NTOTIN Default 0 NTOT2N Default O SMIN STEPEM STEPH Real variables specifying global boundary localization precision and pilot step lengths The pro gram tracks particles in line segment steps see discussion in SectionB 3 The pilot step STEPH is used initially if it is smaller than that defined from physics and magnetic field criteria if within that step the zone number changes then the program will iterate back and forth in smaller and smaller steps to locate the boundary between the zones the boundary is located exactly without iterations in the Extended Geometry mode The minimum size of these iterative steps is given by STEPEM The larger the step lengths the faster the code will run but accuracy is affected if the step lengths are so large that smaller size zones become invisible One can however specify fairly large or small step lengths here and then apply smaller or larger step lengths to particular materials via variables assigned to the MTSM and MTSH cards See the example in Section 4 3 3 STEPEM The global parameter in cm for the accuracy of boundary localization in the particle transport algorithm It is strongly recommended to define STEPEM to be no larger than 0 1 x tmin where tmin is the smallest dimension of the smallest zone in the model Default 0 01 STEPH The global pilot step length in cm
257. urately located and data like energy deposition correctly tabulated In keeping with a desire for accurate energy deposition data the deck allows all the default energy thresholds specifying only the energy of the incoming pion beam the beam is described as a simple di verging gaussian Radial zones are defined in the RSEC card so that the data can used to show how the energy deposition changes versus radial distance an example of extracting and plotting this data is given in the output examples in Section 11 1 2 Y x t tu Figure 19 Plan View of the Thin Window exam Figure 20 A cross section view of the Thin Win ple dow example Figures 19 and 20 show the plan and cross section views of the Thin Window described by the input deck The helium zones are a light purple and the air zones a light blue with the lighter tones being the 2cm deep zones just in front of and behind the thin window where the step lengths are reduced The thin window itself is a gold color The cross section view shows the radial zones in the thin window where data on parameters like energy deposition are accumulated 4 4 Extended Geometry GEOM INP Input File Extended Geometry zones are another way to describe the user s model when the Standard zones described by the ZSEC and RSEC cards in the MARS INP file are insufficient The term extended refers to an extension beyond the r z symmetric Standard zones Exten
258. utines The files described in this Section are the mandatory MARS Input file MARS INP and the optional Extended Geometry input file GEOM INP The MARS INP file is used to define the main operating parameters for running the simulation there are many switches and selections that can be set The number and size of the Standard Zones are defined within the MARS INP file The file might also contain an optional section for importing geometry descriptions from other programs Section 3 1 2 contains a brief description of these options and refers to the manual sections which contain further details for each The optional GEOM INP file is used to define Extended Geometry Zones Note that all the various geometry descriptions which MARS can utilize Standard Non Standard Extended MCNP imported can be used simultaneously and can co exist and overlap in the same setup in a single problem However it is the users job to number the defined zones appropriately and uniquely and to be certain that the correct volumes for each zone have been defined For more information see the introductory Section B T and references therein The main MARS INP deck controls many features in MARS such as the primary beam parameters ma terials energy thresholds termination conditions hA vertices parameters scoring parameters and regions where the standard histograms are accumulated Nearly all these features have default values built into the code i
259. vertex as given by cross section probabilities A continuous interaction would be Coulomb scattering the particle experiences the effect everywhere along it s path through a material In general MARS first examines the likelihood of a discrete interaction occurring and then applies continuous interactions to the list of surviving or newly produced particles The methods for modeling most continuous interactions like Coulomb scattering or a magnetic field are fairly standard and their discussion below is brief Of more interest to users of a simulation program like MARS is how the discrete interactions are handled and how well the simulation compares to data The basic inclusive modeling method used for most discrete interactions is briefly discussed here Sub sections fill in the details sources of algorithms and applicable energy ranges for specific interaction types The inclusive approach to discrete interactions also called biased interaction method is the MARS de fault Exclusive production models also called analogous or unbiased are also available in MARS In certain situations MARS applies an exclusive approach by default as that is the only means to accurately reproduce data such cases are noted where applicable in the physics model descriptions But in most cases the use of exclusive interactions in MARS must be explicitly activated by the user For example Section 5 2 T describes how to use the DPMJET generator in a stand al
260. vided into 4 sub sections 51 4 These sections and sub sections are delineated by the grid lines seen in Figures 4 and I5 The sections are always defined from minimum to maximum z or from left to right in the MARS coordinate system The air section is 50cm deep the steel 100cm deep and the concrete 200cm deep the 50 150 350 values listed reflect the locations of the right hand boundary of each major section The input beam is composed of 100 GeV 7 and the IPIB and BEAM cards define a fairly large spreading beam the example could be a model of a secondary pion beam striking a beam dump Energy cutoffs of 0 05 GeV are given for both the EM and EPSTAM parameters in the ENRG card This setting in 63 conjunction with IND 6 T means that the user is interested primarily in star density and in overall flux density patterns and not in a detailed analysis of energy deposition The zone sizes are relatively large and the global step sizes in the SMIN card are set correspondingly No special energy cutoffs or step sizes are specified beyond the global values The NOBL and RZOB cards declare one volume encompassing all declared zones A standard set of histograms then accumulates various parameters and are written to a mars hbook file This file can be opened from the GUI interface a separate job from the one which produced the hbook file and selected histograms projected onto the geometry as in Figure I5 NOBL histograms are accumulat
261. writes in termediate results to the DUMP file Recommended 10 Default O Use ful to keep track of the session in a standard Monte Carlo run as well as in the event generator EVT gt 1 or volume Monte Carlo IVOL l sessions If NTIME 1 then a file TRACKFIRST is generated which con tains x y z dcx dcy coordinates and direction cosines of the first track use ful for beam line studies an event number which will be written in great detail to file TRACK PLOT if NWEGH 18 on the TAPE card and to file fort 30 If NHIPR is negative then the event number of the current event being generated is printed to the screen starting with event number N abs NHIPR Default O 40 NITRMX the maximum event number for which the TRACK PLOT file is generated Default 1000 IPRINM If IPRINM 1 then detailed tables of hadron and photon nuclear cross sections as well as electromagnetic energy loss dE dx are printed to MARS OUT for each material in the model and as a function of energy De fault O NBEGRND IfNBEGRND gt 1 then the random number generator is called NBEGRND times at the very beginning This is found to be useful in some applications Note that the main control of the random number sequence is done via the SEED card Default 0 SEED IJKLIN NTOTIN NTOT2N Integer variables to initialize the random number generator and to track how many random num bers are used IJKLIN Theinitial 64 bit seed The integer entered is ass
262. xample of Extended Geometry 2 oo a 72 75 A A SNe oe ey ee a 76 A aden es 4 ak eee uas 4 Age 76 CPP 77 esoo cross creas 77 E Ape oe ee pie ee Gt Seba 78 Lola Gow Orie Sasa eA dde SEE PEE 85 CLTC TTC 87 7 s ne 87 T 88 Pv 88 5 10 Edge Scattering EDGEUS llle 89 11 Subroutine LEAK Creating custom source terms llle 90 5 12 Subroutines MHSETU MFILL HISTODB User Histograma lees 91 nd reko le okey eee eee de dea ae 93 93 96 96 he Enid eek pee E eee Eae 96 kop Re Siete de cada 96 ee A re yee ee eee ere ERU RUE RA 97 P329 RR Riek cw dris Shey Ghee e bee NT 97 hp eae eee ae oa 98 rrr 99 Tr 102 5 19 5 Subroutine TUNNELGEO lll ll rns 104 Arras peda eT eee eee 104 Seed Oe eee ee UA aan 104 yak eins ea ee Be a He es Eee 105 6 ode 106 6 1 Setting up MARS INP for use with MCNB ee 106 6 1 1 Mode 1 MCNP with Material description only llle 107 TTC A 108 eee re te er Te eee SM E IE CLR MTM E 111 113 114 8 GSM a see Se ed a A ae aei e a A 114 e Oa Pee ee da Ene 114 ck RG AE Hees HC AACE De ee Pe we eS 114 115 116 Ty bE eer RK ERS Ra ados e aba 116 dd dao de lod ee ee eee eee eee 117 10 3 Other Built in Histograma ee 118 TP 118 10 ser Defined Histograms and Ntupled les 122 Output o es ation 123 11 1 Data Table Output Filed Ress 123
263. y NY 1 nxyztp 3 gt Y Zina Az slice y v z h defined by NX 1 nxyztp 4 gt Energy spectra in the macro box defined by NX NY NZ 1 8 A card following a XY Z card contains a list of histogram types for this macro box any combination of the above 38 types An arbitrary cut off energy can be defined for each 2 D histogram except HY D HEL and TRI as mentioned above using the following syntax FEN gt 0 03 which means that neutron flux in this particular histogram is scored above 0 03 GeV not above the default threshold or that defined in the MARS INP file A list of histograms to be filled in the run is generated at the completion of the initialization stage and shows up in an XYZHIS TAB file which contains all attributes for each histogram Here is the file created with the above XYZHIS INP Here is an example of a XYZHIS INP file XYZ histo test 01 May 2007 xyz 20 20 0 4 0 4 0 50 40 1 50 Xz scan at yl 0 4 STA DRE FLT gt 0 02 DET DEN gt 0 1 DAB PDT xyz 0 4 0 4 10 10 0 50 1 20 50 YZ scan at x 0 4 fluxes STA FLT gt 0 02 DET DEG gt 0 05 DAB gt 0 02 FLP FLE DPA 121 xyz 5 5 2 8 12 13 10 5 1 XY scan in a z 12 13 cm slice FLT DPA xyz 5 5 5 5 12 13 10 5 1 Muon flux profile at shower max FLM xyz 0 5 2 7 10 15 11 1 Spectrum 1 in a 5x5x5 cm cube SPP SPN SPK SPM SPG SPE Ixyz 5 5 5 5 10 20 111 Muon spectrum SPM stop
264. y of the user s model The user is advised to try short trial runs of 100 to 1000 events to make an estimate of the cpu time required The more events which are generated the better the statistical error on the results will be In general any zone of interest should have a relative error of no more than 20 for the results in that zone to have a physical validity More discussion on this subject is in Section I3 T The interactive GUI interface is invoked by setting a flag in the main MARS INP input deck The interface is very useful to visually check the geometry of the model before actually running the executable to generate events The flag must be reset to run MARS in the event generating mode as this mode and the interactive GUI mode cannot be run simultaneously Details on using the GUI interface are given in Section 2 The default output files are MARS OUT MTUPLE MTUPLE EXG MTUPLE MCNP and MTUPLE NON if histograms were requested there will also be a mars hbook file MARS OUT and MTUPLE list the results accumulated in MARS Standard zones with some information on Non Standard zones also contained within MARS OUT MTUPLE EXG lists results accumulated in Extended Geometry zones MTUPLE NON lists results accumulated in Non Standard zones The format of these files is defined within non user code and so cannot be changed by the user Details on the contents of these files and other specialized output files is found in Section I 32
265. y zone number the density of helium gas production within each zone which can be used to assist in estimates of radiation damage to the material located in this zone TRITIUM GAS PRODUCTION 1 cm 3 P P The table presents arranged by zone number the density of tritium gas production within each zone which can be used in a corresponding radiation safety analysis TRACK LENGTH HADRON FLUENCE IN HIGH ENERGY SECTOR 1 CM 2 The table presents arranged by zone number the total hadron flux in each zone as calculated from the total track lengths of these particles passing through this zone The hadrons used for the tabulation have a kinetic energy greater than the value of EM the hadron threshold energy in the ENRG card the default threshold value is 0 0145 GeV The statistical errors are also given CHARGED HADRON FLUENCE AT E gt ETH HADRONS CM2 The table presents arranged by zone number the total hadron flux in each zone for charged hadrons with a kinetic energy greater than the value of the threshold EMCHR set in the ENRG card default value 0 0002 GeV OR with a kinetic energy greater than EM if EM has been set to greater than it s 0 0145 GeV default value The statistical errors are also given NON NEUTRON NEUTRAL HADRON FLUENCE AT E gt ETH HADRONS CM2 The table presents arranged by zone number the neutral hadron flux but not including neutrons in each zone for those particles with a kinetic energy greater than the value of
266. ze checks to see if the material has changed and so back and forth in smaller and smaller steps until the smallest allowed step size bridges across the boundary between the two materials Figure I3 shows a simple schematic of this boundary localization procedure Dg is reset at each iteration to a shortened step length which approaches or crosses the material boundary and is compared to Dj The boundary localization process halts when Dg is smaller than Dj or when Dg has reached an allowed minimum size If this allowed minimum step crosses the boundary into a new material then D must be redefined and the tracking sequence resets back to part one described above The final tracking line segment length is the minimum of Dj and Dg The current algorithm for multiple Coulomb scattering correlated with the ionization energy loss provides accurate modeling on this segment independent of its size Material 1 Material 2 Zone Boundary Localization The initial geometric line segment length De is the Pilot Step Length If the material type changes after taking a pilot Pilot Step step as between points D and C then the code iterates back and forth as in points a through k stopping when the length between two steps is the smallest allowed iterative step size The iterative steps are expanded here for clarity They actually all lie on top of each other along the line connecting B and C Figure 13 A schematic of the

The MARS Code System User`s Guide Version 15(2014)

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