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A User Guide to the PROCESS Systems Code

1. 3 8 1 Neutronicg 0 ee eee 66 3 8 2 Activation and inventory information 208 67 3 9 Cost Models 2 24642 K4 045240 yb e ed eee eee be thee ba bbe eee ad 67 3 9 1 Cost Options gc 6 dba a ea eA ek ee ape we a ee eed ae 67 3 10 Other Switches and Models e 68 3 10 1 Diagnostic output 2 ee 68 3 10 2 Code parameters affecting other models 0 0 0 00004 68 4 Execution of the Code 69 4 1 The Input Pile a s aara puc dara eb e eee a a A a 69 4 1 1 Tokamak stellarator RFP or IFE e 69 AAD Pile structure s s sul a e ee ek a AR A a 69 41 3 Format rules usina a Rae REE a a eee 70 4 2 The Output File es 71 4 3 Running the Code 2 2 ee 71 4 3 1 Environment setup 72 4 3 2 Non optimisation Mode 72 4 3 3 Optimisation Made 74 4 4 Problem Solving 0 2 0 0 ee 75 4 4 1 Error handling bth Rs E A AA RR a 75 4 4 2 General problems 76 4 43 Optimisation problems e 76 4 44 Unfeasible results ee 76 A AL HINTI A we ee ee a ee a ok Sr Ge eae ee we ee ee e 78 5 Inclusion of New Models Additional Variables and Equations 79 5 1 Input Parameters 205 eres rio Rok oe A Rd BO ee Ste eee a ee 79 5 2 Iteration Variables 2 ee 79 5 3 Other Global Variables ee 80 5 4 Constraint Equati0ons ee 80 5 5 Figur
2. 2 1 Flow diagram of PROCESS in non optimisation mode 12 2 2 Flow diagram of PROCESS in optimisation mode 204 14 3 1 Machine build for D shaped major components o 26 3 2 Machine build for elliptical shaped major components 27 3 3 Machine build for a single null device e a ee RS 28 3 4 Power balance within the core plasma 0 0000 02 eee eee 36 3 5 Schematic diagram of the cross section of a superconducting TF coil inner leg e 44 3 6 Coil and plasma current waveforms ao a s e e e e e a 47 3 7 Schematic diagram of the neutral beam access geometry nooo o a 50 3 8 Power flow within the fusion power plant SA ptm oro Fae hha be ed Ed 52 3 9 Power flow outside the fusion power plant core e e 54 3 10 HELIAS 5 B Stellarator Power Plant Designl 20 59 3 11 Stellarator island divertor configuration 0 o 62 A 1 Illustration of Lagrange multiplier method 107 A 2 Flowchart of the VMCON optimisation solver o o e 110 List of Tables 2 1 List of constraint equations 17 2 2 List of iteration variables 1 to 50 2 0 2 0 00 0002 eee eee 19 2 3 List of iteration variables 51 to102 0 0 0200 000052 2s 20 2 4 List of
3. Among the TF coil parameters calculated by the code are the maximum allowable current density the stresses on the structure the energy stored and the magnetic field produced by the coils The following options are available within the superconducting TF coil model itfsup 1 3 1 7 1 Superconducting materials Switch isumattf specifies which superconducting material is to be used isumattf 1 Nb3Sn superconductor ITER critical surface parameterization 28 standard critical values isumattf 2 Bi 2212 high temperature superconductor isumattf 3 NbTi superconductor isumattf 4 Nb3Sn superconductor ITER critical surface parameterization 28 user defined critical parameters Chapter 3 Physics Engineering and Other Models 44 View from above wwp1 wwp2 Winding Pack thkcas thkwp Single turn half thickness of radial zp plates and steel caps thicndut er assigned to each turn 2 trp Figure 3 5 Schematic diagram of the cross section of the inboard leg of a superconducting TF coil showing the CICC Conductor In Cable Conduit construction The winding pack contains many turns of cable conduit The cable space contains the superconducting filaments and circulating liquid helium coolant The variables shown in red may be changed by the user and those in italics may be chosen as iteration variables Chapter 3 Physics Engineering and Other Models 45
4. 4 Add the constraint equation to routine CONSTRAINTS in source file constraint _equations f90 ensuring that all the variables used in the formula are contained in the modules specified via use statements present at the start of this routine Use a similar formulation to that used for the existing constraint equations remembering that the code will try to force cc i to be zero Don t forget to add suitable correctly formatted comment lines to numerics f90 to document the above changes Remember that if a limit equation is being added a new f value iteration variable may also need to be added to the code 5 5 Figures of Merit New figures of merit see Section 2 6 are added to PROCESS in the following way 1 Increment the parameter ipnfoms in module numerics in source file numerics f90 to accommodate the new figure of merit 2 Assign a description of the new figure of merit to the relevant element of array lablmm in module numerics in source file numerics f90 3 Add the new figure of merit equation to routine FUNFOM in source file evaluators 90 following the method used in the existing examples The value of fc should be of order unity so select a reasonable scaling factor if necessary Ensure that all the variables used in the new equation are contained in the modules specified via use statements present at the start of this file 4 Modify process_dicts py accordingly Don t forget to add suitable correc
5. Table 3 3 Summary of the materials comprising the blanket in the various scenarios available blktmodel 0 only The fractions given are all available to be modified and should of course add up to 1 0 for any given model The type of coolant used is given by the value of switch costr 3 1 6 Shield The stainless steel shield reduces the neutron flux reaching the TF coils and beyond This minimises the radiological impact of the neutrons and their heating of the TF coils which if superconducting Chapter 3 Physics Engineering and Other Models 43 need to remain at liquid helium temperatures The shield is cooled either by gaseous helium or by pressurised water but see Section 3 1 5 1 as chosen using switch costr see Section 3 1 5 2 and as with the blanket the energy deposited in the coolant is used to produce electricity The shield coolant fraction is stored in input parameter vfshld The inboard and outboard shield thicknesses shldith and shldoth respectively may be used as iteration variables 3 1 7 Toroidal field coils The toroidal field TF coils can be either resistive or superconducting Switch itfsup should be set to 1 for superconducting coils or 0 for purely copper coils In the superconductor model the CICC Conductor In Cable Conduit structure shown in Figure 3 5 is assumed and the coils are cooled using a liquid helium cryogenic system The steel radial plates shown in the Fig
6. The fraction of copper present in the superconducting filaments is given by the value of variable fcutfsu iteration variable no 59 For isumattf 2 a technology adjustment factor fhts may be used to modify the critical current density fit for the Bi 2212 superconductor to describe the level of technology assumed i e to account for stress fatigue radiation AC losses joints or manufacturing variations The default value for fhts is 0 5 while a value of 1 0 would be very optimistic For isumattf 4 important superconductor properties may be input by the user as follows the upper critical field at zero temperature and strain is set using input parameter bcritsc and the critical temperature at zero field and strain is set using input parameter tcritsc 3 1 7 2 Stress model Switch tfc_model controls whether a simple stress model tfc_model 0 suitable for solid copper TF coils or a more complex stress model tfc_model 1 should be used If tfc_model 1 a two layer stress model 30 developed by CCFE is used To enforce the stress limits calculated using either of these models constraint equation no 31 case stress and or constraint equation no 32 conduit stress should be turned on with iteration variables no 48 fstrcase and or no 49 fstrcond respectively The stress limit can be adjusted using input parameters csutf and csytf 3 1 7 3 Current density limits The current in the TF coils must be sufficient to
7. fauxmn f value for minimum auxiliary power limit equation 40 0 001DO 1 000DO 65 tohs central solenoid current ramp up time 0 100D0 1 000D3 66 ftohs f value for central solenoid current ramp up time limit equation 41 0 001D0 1 000DO 67 ftcycl f value for minimum cycle time limit equation 42 0 001D0 1 000DO 68 fptemp f value for maximum centrepost temperature limit equation 44 0 001DO 1 000DO 69 rcool average radius of centrepost coolant channel 0 001D0 0 010D0 70 vcool maximum centrepost coolant flow speed at midplane 1 000D0 1 000D2 71 fq f value for minimum edge safety factor limit equation 45 0 001D0 1 000DO 72 fipir f value for maximum Ip I oa limit equation 46 0 001DO 1 000DO 73 scrapli inboard gap between plasma and first wall 0 001D0 10 00D0 74 scraplo outboard gap between plasma and first wall 0 001D0 10 00D0 75 tfootfi ratio of TF coil outboard inboard leg thickness 0 200D0 5 000D0 76 frfptf f value for TF coil toroidal thickness limit equation 47 0 001D0 1 000DO 77 t tort TF coil toroidal thickness use for RFPs only 0 050D0 4 000D0 78 rfpth RFP pinch parameter O 0 010D0 1 800DO 79 fbetap f value for poloidal beta limit equation 48 0 001DO 1 000DO 80 frfpf f value for RFP reversal parameter limit equation 49 0 001D0 1 000DO 81 edrive IFE driver energy 1 000D5 5 000D7 82 drveff IFE driver wall plug to target efficiency 0 010D0 1 000D0 83 tgain IFE target
8. 0 to 11 rows and n 12 to 12 columns 3 Set vmec_zmn_file in the input file to the name of a VMEC output file containing the calculated plasma boundary Z m n Fourier coefficients where m 0 to 11 rows and n 12 to 12 columns This method enables a wide range of potential plasma geometries to be modelled if required The plasma volume surface area and mean cross sectional area are the outputs from the plasma geometry model 3 5 1 2 Absense of plasma current Stellarators try to achieve zero plasma current in order to allow safe divertor operation so no current scalings are required 3 5 1 3 Beta limit The beta limit is assumed to be 5 based on 3 D MHD calculations 40 To apply the beta limit constraint equation no 24 should be turned on with iteration variable no 36 fbetatry 3 5 1 4 Density limit The density limit relevant to stellarators has been proposed to be 41 Nie Nmax 0 25 PBo Ro az 3 22 where n is the line averaged electron density in units of 10 m P is the absorbed heating power MW Bo is the on axis field T Ro is the major radius m and ap is the plasma minor radius m To enforce the density limit turn on constraint equation no 5 with iteration variable no 9 fdene Chapter 3 Physics Engineering and Other Models 61 3 5 1 5 Tz scaling laws Five confinement time scaling laws relevant to stellarators are present within PROCESS The value
9. Chapter 3 Physics Engineering and Other Models There are a great number of individual models within PROCESS characterising many different aspects of a fusion power plant Several of these will always be used by the code and so require no input by the user to activate them However in many cases there is a choice of model available and each of these has its own user controlled switches or flags This chapter summarises these models and indicates their location and interaction within the code together with the relevant switch settings and required parameter values The concepts used iteration variables constraint equations etc and instructions on how to set switches etc are explained fully in Chapter 2 Disclaimer Users are discouraged from using non default or older models as they are likely to be less well tested than the default models and should therefore be treated with caution 3 1 Tokamak Power Plant The default and most detailed power plant model in PROCESS is based on the tokamak magnetic confinement fusion concept This section describes the models relevant to such a plant in some detail starting with the plasma at the centre of the fusion power core and moving outwards to the external components power subsystems and buildings However many of these models are also partly or wholly relevant for the other available machine types especially outside the fusion power core The specific details for these alternative
10. Output proc_plot_out pdf or as specified by user Configuration Options Optional arguments are change the input file name python plot_proc py f MFILE DAT change the output file name python plot_proc py o out pdf show the plot as well as saving the figure python plot_proc py s 6 1 7 plot_sweep py This utility plots normalised values from PLOT DAT and allows comparisons of changes in values from a sweep compared to the first point in the sweep It is now somewhat deprecated due to the existence of more flexible sweep generating and output handling utilities Input PLOT DAT Output PLOT DAT eps default or as specified by user Configuration Options Optional arguments are creates PLOT DAT eps with RO IP beta python plot_sweep py g 11 13 18 Chapter 6 Utility Programs 88 creates demol png with Te n python plot_sweep py o demol png 21 22 6 1 8 plot_mfile_sweep py This utility plots normalised values from MFILE DAT and allows comparisons of changes in values from a sweep compared to the first point in the sweep Input MFILE DAT Output sweep_fig pdf default or as specified by user Optional arguments are creates sweep_fig pdf with RO te aspect same variable names as in MFILE DAT python plot_mfile_sweep py p rmajor te aspect creates demol png with Te n python plot_mfile_sweep py o demol png p te dene creates a sweep_fig pdf with RO aspect with a different MFILE DAT p
11. PF coils ipfloc 3 PF coils ipfloc 3 divertor y Qe es 5 PF coil ipfloc 2 Figure 3 3 Schematic diagram of the fusion power core of a typical tokamak power plant modelled by PROCESS showing the relative positions of the components A single null plasma is assumed snull 1 compare Figure 3 2 the vertical axis are the code variables used to define the vertical thicknesses of the components The arrowed labels adjacent to the axis are the total builds distance from the midplane Z 0 to that point The precise locations and sizes of the PF coils are calculated within the code see Section 3 1 8 The radial build is the same as for a double null configuration shown along Chapter 3 Physics Engineering and Other Models 29 3 1 2 Plasma physics models Arguably the most important component of the machine is the plasma itself By default this is assumed to have an up down asymmetric single null configuration although this can be changed if desired see Section 3 1 4 A great number of physics models are coded within PROCESS to describe the behaviour of the plasma parameters such as its current temperature density pressure confinement etc and also the various limits that define the stable operating domain 3 1 2 1 Plasma geometry The plasma geometric major radius Ry rmajor and aspect ratio A aspect define the size of the plasma torus
12. The script also creates blank upper and lower bound equations these need to be completed manually or deleted All files used need to be in the working directory The original IN DAT is renamed OLD IN DAT Input IN DAT write_constraints conf Output IN DAT OLD IN DAT Configuration Options The configuration file write_constraints conf has the following style Constraints and associated iteration variables y ICC 1 plasma beta consistency ixc 5 beta plasma beta 0 001d0 1 0d0 y ICC 2 global power balance ixc 10 hfact confinement time h factor 0 1d0 3 0d0 ICC 3 ion power balance ICC 4 electron power balance Remaining iteration variables IXC 1 aspect plasma aspect ratio 1 100D0 10 00DO y IXC 2 bt toroidal field on axis 0 010DO 100 0DO IXC 3 rmajor plasma major radius 0 100D0 10 00DO An example version that can be modified is available in the utilities directory 6 1 3 run _process py This program runs PROCESS if necessary with varying iteration variable start parameters until a feasible solution is found Input run_process conf an IN DAT file as specified in the config file Output in the specified work directory All the standard PROCESS output process log log file README txt contains comments from config file Configuration Options The configuration file run_process conf has the following style Chapter 6 Utility Programs 85 This is a comment in the config file Path to working directo
13. get_solution_from_mfile neqns nvars wdir Returns e ifail error value of PROCESS e the objective functions e the square root of the sum of the squares of the constraints a list of the final iteration variable values a list of the final constraint residue values e If the run was a scan the values of the last scan point will be returned get_solution_from_outdat neqns nvars Returns e ifail error value of PROCESS e the objective functions e the square root of the sum of the squares of the constraints a list of the final iteration variable values a list of the final constraint residue values e If the run was a scan the values of the last scan point will be returned 6 2 4 process_config py A collection of Python classes for configuration files used by various PROCESS utilities e g run_process py or test_process py It contains a base class ProcessConfig and two derived classes RunProcessConfig and TestProcessConfig ProcessConfig Object that contains the configuration parameters for PROCESS runs filename Configuration file name wdir Working directory or_in_dat Original IN DAT file process PROCESS binary niter Maximum number of iterations u_seed User specified seed value for the random number generator factor Multiplication factor adjusting the range in which the original iteration variables should be varied comment Additional comment to be written into README txt Chapter 6 Utility
14. htpmw_bikt etahtpbikt Neutron absorption pnucshid Coolant pumping etahtpshid htpmw_shld Neutron absorption ptfnuc Y Cryogenic plant Figure 3 8 Schematic diagram of the flow of power from the plasma to the thermal power deposited within the divertor first wall blanket and shield Variable names are given in The three red bordered contributions are passed from Figure 3 4 while the blue box comes from Figure 3 9 Chapter 3 Physics Engineering and Other Models 53 3 1 13 1 Divertor All of the charged particle transport power leaving the plasma is assumed to be absorbed in the divertor along with a proportion fdiv of the radiation power and the neutron power The power necessary to drive the divertor coolant pumps P htpmw_div in Figure 3 8 is assumed to be a fraction f input parameter fpumpdiv of the total thermal power absorbed by the divertor which includes the coolant pump power itself P f pdivt praddiv pnucdiv P P pais praddiv pnucdiv The efficiency of the divertor coolant pump is given by input parameter etahtpdiv Switch iprimdiv may be used to specify whether the thermal power deposited in the divertor becomes primary high grade thermal power iprimdiv 1 or secondary low grade thermal power see Figure 3 9 3 1 13 2 First wall All of the remaining radiation power i e the fraction not incident upon the
15. t 5 l parameters 1 2 3 2 2 1 1 85e7 0 9 1 5 2 5 71 system parameters 1 35 O Use old blanket model Steel density N B active iteration variable 12 Use superconducting TF coils Maximum TF ripple Three groups of PF coils Locations for each group Number of coils in each group central solenoid current at End Of Flat top central solenoid current at Begin Of Pulse COHEOF Radial position for group 3 Z position for group 3 Height ratio central solenoid TF coil Use cryopump Thermal to electric conversion efficiency Power to MGF units Appendix C Optimisation Input File 120 BASEEL 5 e6 Base plant electric load ISCENR 2 Energy store option Buildings FNDT 2 Foundation thickness EFLOOR 1 d5 Effective total floor space Costs IREACTOR 1 Calculate cost of electricity IFUELTYP 0 Treat blanket first wall etc as capital cost UCHRS 87 9 Unit cost of heat rejection system UCCPCL1 250 Unit cost of high strength tapered copper UCCPCLB 150 Unit cost of TF outer leg plate coils Appendix D Source Code Documentation The development of the PROCESS code since its shipment from Oak Ridge National Laboratory in April 1992 has been fully documented in the Project Work File 31 Presented here is a list of Project Work File Notes as of September 30 2014 that address various issues related to the source code e D
16. widen the boundaries of quadratic the iteration variables subproblem or restriction by artificial bounds ia ie has ADD SOME STUFF HERE CHECK WITH MDK Table A 1 Summary of the description and meaning of the VMCON return parameters ifail Appendix A The Optimisation Solver Explained 112 variable vector but describes the direction of the line search in which a 1d function is minimised using a Newtonian method c f section A 6 Being a second order approximation to the original problem it typically has a faster convergence that sequential linear programming SLP methods 71 chap 10 4 To allow the applicability of the solver to more general problems Powell 6 substituted the Hessian Vz L x 72 with a positive definite approximation B This means that both the objective function f a and the constraint equations c a only have to be continuously differentiable instead of twice continuously differentiable with respect to the iteration variable vector x This makes the method a Quasi Newtonian method as opposed to true Newtonian methods How this approximation is initialised and updated is described in more detail in the section about the Broyden Fletcher Goldfarb Shanno update A 7 To solve the QSP VMCON uses harwqp a modification of the the Harwell library routine VEO2AD which in itself uses the subroutine harwfp LAO2AD to find a feasible point within the variable bounds and linearised constraint
17. 1 000D0 31 gapomin minimum gap between outboard vacuum vessel and TF coil 0 001D0 10 00D0 32 frminor f value for minor radius limit equation 21 0 001DO 1 000DO 33 fportsz f value for beam tangency radius limit equation 20 0 001D0 1 000D0 34 fdivcol f value for divertor collisionality limit equation 22 0 001D0 1 000DO 35 fpeakb f value for peak toroidal field limit equation 25 0 001DO 1 000DO 36 fbetatry f value for beta limit equation 24 0 001D0 1 000D0 37 coheof central solenoid current density at end of flat top 1 000D5 1 000D8 38 fjohc f value for central solenoid current at EOF limit equation 26 0 010D0 1 000D0 39 fjohcO f value for central solenoid current at BOP limit equation 27 0 001D0 1 000D0 40 fgamcd f value for current drive gamma limit equation 37 0 001D0 1 000D0 41 fcohbop central solenoid current density ratio BOP EOF 0 001D0 1 000D0 42 gapoh gap between central solenoid and TF coil 0 001D0 10 00D0 43 cfe0 seeded high Z impurity fraction 1 00D 6 3 00D 3 44 fvsbrnni fraction of plasma current produced by non inductive means 0 001DO 1 000DO 45 fqval f value for fusion gain limit equation 28 0 001D0 1 000DO 46 fpinj f value for injection power limit equation 30 0 001D0 1 000D0 47 feffcd current drive efficiency multiplier 0 001D0 1 000D0 48 fstrcase f value for TF coil case stress limit equation 31 0 001DO 1 000DO 49 fstrcond f value for TF coil cond
18. 10 hfact BOUNDU 60 4 d4 Bound on iteration variable 60 cpttf NEQNS 15 Number of active constraint equations NVAR 25 Number of active iteration variables ICC 1 2 10 11 7 16 8 24 31 32 33 34 35 36 14 Constraint eqns ixc 5 10 12 3 7 36 48 49 50 51 53 54 19 Corresponding 1 2 4 6 13 16 29 56 57 58 59 60 iteration variables IOPTIMZ 1 Turn on optimisation MINMAX 6 Minimise cost of electricity ISWEEP 7 Seven point scan NSWEEP 6 Use WALALW as scanning variable SWEEP 6 0 5 5 4 5 4 0 3 5 3 0 2 5 Values of WALALW for each scan point F values and limits FBETATRY 1 0 N B active iteration variable 36 Physics parameters ASPECT 3 5 N B active iteration variable 1 BETA 0 042 N B active iteration variable 5 BT 6 N B active iteration variable 2 DENE 1 5e20 N B active iteration variable 6 FVSBRNNI 1 0 Non inductive volt seconds fraction DNBETA 3 5 Beta g coefficient HFACT 2 N B active iteration variable 10 ICURR 4 Use ITER current scaling ISC 6 Use ITER 89 P confinement time scaling law IINVQD 1 Use inverse quadrature IITER 1 Use ITER fusion power calculations ISHAPE 0 Use input values for KAPPA and TRIANG KAPPA 2 218 Plasma elongation Q 3 0 Edge safety factor RMAJOR 7 0 N B active iteration variable 3 RNBEAM 0 0002 N B active iteration variable 7 TBU
19. 2 The former case is the default e Coolant type The value of switch costr determines the type of coolant used in the first wall blanket and shield If costr 1 the coolant is assumed to be gaseous helium If costr 2 the coolant is assumed to be pressurised water steam which is the default This switch is used whether or not the full blanket model is used i e is independent of the setting of switch 1b1nkt e Boundary condition The value of switch bstr determines whether the coolant output temperature is to be fixed bstr 1 or whether the maximum blanket temperature is to be fixed bstr 2 The former case is the default The desired coolant output temperature for bstr 1 is set using input parameter xtfo and the required maximum blanket temperature is set using input parameter xtb 3 1 5 3 Blanket materials Table 3 3 summarises the possible options for the blanket materials Switch smstr determines whether a solid blanket of LigO Be smstr 1 or a liquid blanket of LiPb Li smstr 2 is used The former is the default and is the type assumed if lblnkt 1 material lblnkt 1 lblnkt 1 full thermodynamic model simple model smstr 1 solid blanket smstr 2 liquid blanket stainless steel fblss fblss fblss vanadium fblvd fblvd fblvd LigO fblli2o fblli2o beryllium fblbe fblbe LiPb fbllipb lithium fb11i coolant v blkt v blkt v blkt
20. 59 60 24 32 TF coil conduit stress upper limit SCTF L 49 56 57 58 59 60 24 33 TF coil Joperational Lcritical upper limit SCTF L 50 56 57 58 59 60 24 34 TF coil dump voltage upper limit SCTF L 51 52 56 57 58 59 60 24 35 TF coil Jwinding pack J protection upper limit SCTF L 53 56 57 58 59 60 24 36 TF coil temperature margin lower limit SCTF L 54 55 56 57 58 59 60 24 37 current drive gamma upper limit L 40 47 38 first wall coolant temperature rise upper limit PULSE L 62 39 first wall peak temperature upper limit PULSE L 63 40 injection power lower limit PULSE L 64 41 central solenoid current ramp up time lower limit PULSE L 66 65 42 cycle time lower limit PULSE L 67 65 17 43 average centrepost temperature ST C 69 70 13 44 peak centrepost temperature upper limit ST L 68 69 70 45 edge safety factor lower limit ST L 71 1 2 3 46 Ip Irod upper limit ST L 72 2 60 47 TF coil toroidal thickness upper limit RFP L 76 77 13 3 48 poloidal beta upper limit L 79 2 3 18 49 reversal parameter lt 0 RFP L 80 78 3 1 50 IFE repetition rate upper limit IFE L 86 51 startup volt seconds consistency PULSE C 16 29 3 1 52 tritium breeding ratio lower limit L 89 90 91 53 peak neutron fluence on TF coil upper limit L 92 93 94 54 peak TF coil nuclear heating upper limit L 95 93 94 55 final He concentration in vacuum vessel upper limit L 96 93 94 56 Pseparatrix Rmajor upper limit L 97 1 3 57
21. 9 Of these the cryogenic plant power includes the power required to cool the TF coils from the neutron power absorbed by the coils the PF coils as defined by the ratio of the total PF coil stored energy to the fusion power pulse time tpulse and other cold components 3 1 14 Buildings The volume and ground area of all the various buildings on a power plant site are included in the PROCESS calculations for the benefit of the costing algorithms Chapter 3 Physics Engineering and Other Models 55 3 2 Spherical Tokamak Model PROCESS has the ability to perform studies on tokamaks in the low aspect ratio regime major radius lt 2x minor radius The physics and engineering issues 32 associated with these machines are somewhat different from those of conventional aspect ratio and this is reflected by the following special models 2 in PROCESS 1 The inboard build of a spherical tokamak ST is very different from that in a conventional tokamak There is no inboard blanket and possibly no inboard shield and the inboard TF coil legs are replaced by a single centrepost The radial build is altered so that starting from the centreline R 0 the component order is TF coil gap central solenoid vacuum vessel and then continuing as in Figure 3 1 a D shaped cross section is assumed for the first wall blanket shield and vacuum vessel 2 Spherical tokamaks have resistive TF coils t
22. H mode J G Cordey et al EPS Berchtesgaden 1997 27 ITER H 97P ELMy H mode J G Cordey et al EPS Berchtesgaden 1997 28 ITER 96P ITER97 L L mode Nuclear Fusion 37 1997 p 1303 29 Valovic modified ELMy H mode 30 Kaye PPPL April 98 L mode 31 ITERH PB98P y H mode 32 IPB98 y H mode Nuclear Fusion 39 1999 p 2175 33 IPB98 y 1 H mode Nuclear Fusion 39 1999 p 2175 34 IPB98 y 2 H mode Nuclear Fusion 39 1999 p 2175 35 IPB98 y 3 H mode Nuclear Fusion 39 1999 p 2175 36 IPB98 y 4 H mode Nuclear Fusion 39 1999 p 2175 37 ISS95 stellarator Nuclear Fusion 36 1996 p 1063 38 ISS04 stellarator Nuclear Fusion 45 2005 p 1684 39 DS03 H mode Plasma Phys Control Fusion 50 2008 043001 equation 4 13 Table 3 1 Summary of the energy confinement time scaling laws in PROCESS Chapter 3 Physics Engineering and Other Models 36 EDGE PLASMA CORE PLASMA Charged particle power reaching divertor pdivt Alpha power 1 falpha bulk plasma T Electron transport power ptremw Total alpha power palpmw Alpha power lon transport power ptrimw plasma beam interactions Core radiation power palpnb falpha pcoreradmw Neutron power bulk plasma Total neutron power pneutmw Neutron power plasma beam interactions FUSION Non alpha charged particle power pchargem
23. ITER scaling icurr 4 Revised ITER scaling 20 icurr 5 Todd empirical scaling I icurr 6 Todd empirical scaling II icurr 7 Connor Hastie model 3 1 2 8 Plasma current profile consistency Self consistency between the plasma current profile parameters 10 can be enforced by setting switch iprofile to 1 This ensures that the current profile peaking factor alphaj is consistent with the input values for the safety factor on axis and at the plasma edge q0 and q respectively the plasma internal inductance l is consistent with this alphaj and the beta g coefficient dnbeta scales with l It is recommended that current scaling law icurr 4 is used if iprofile 1 Switch gtscale is over ridden if iprofile 1 3 1 2 9 Confinement time scaling laws The particle transport loss power in Watts m from the plasma is defined as W Poss 3 19 TE where the plasma stored energy per unit volume W is given by 3 W neT 2 with particle number density n in m and particle temperature T in eV PROCESS assumes that the electron and ion energy confinement times Tg are equal Many energy confinement time scaling laws are present within PROCESS for tokamaks RFPs or stellarators These are calculated in routine PCOND The value of isc determines which of the scalings is used in the plasma energy balance calculation Section 3 1 2 10 Table 3 1 summarises the available scaling laws Cha
24. If ipfres 1 they are assumed to be resistive with their resistivity given by the value of variable pfclres 3 1 8 4 Superconducting materials If ipfres 0 switch isumatpf specifies which superconducting material is to be used for the PF coils and the central solenoid isumatpf 1 binary Nb3Sn superconductor isumatpf 2 ternary Nb3Sn superconductor isumatpf 3 NbTi superconductor 3 1 9 Ohmic heating coil The ohmic heating OH coil is a PF coil used primarily during start up but also during the burn phase to create and maintain the plasma current by inductive means Swinging changing the current through the central solenoid causes a change in the flux linked to the plasma region inducing a current in it PROCESS calculates the amount of flux required to produce the plasma current and also the Chapter 3 Physics Engineering and Other Models current ramp lp ramp up heat beginning of pulse j eS eh time dwell Figure 3 6 Plot showing schematically the current waveforms for the plasma a typical PF coil and the central solenoid AT Chapter 3 Physics Engineering and Other Models 48 amount actually available The code measures the magnetic flux in units of Volt seconds Webers The central solenoid can be either resistive or superconducting controlled via switches ipfres and isumatpf as for the other PF coils Switch iohcl controls whether a central solenoid is pre
25. OBSOLETE TF coil outer leg toroidal thickness lower limit SCTF L 99 29 13 58 OBSOLETE TF coil outer leg radial thickness limit lower SCTF L 100 13 Table 2 1 Summary of the constraint equations present in PROCESS Consistency equations are marked C limit equations are marked L Some non exhaustive iteration variable numbers see Tables and 2 3 2 2 that directly affect the associated constraint equations are given the one listed first being the most relevant Chapter 2 Program Overview The Fundamental Concepts 18 to the input see Figures 2 1 and 2 2 The nvar iteration variables that the user chooses for a given run are activated by including the variable numbers in the first nvar elements of array ixc Tables 2 2 and 2 3 list the iteration variables available in PROCESS Clearly the equation solvers need at least as many variables to iterate as there are equations to solve i e nvar gt negns If the run is a non optimising case then neqns variables are iterated the values of the remaining nvar neqns variables are left alone If the run is an optimising case then all the active iteration variables are adjusted so as to find the minimum or maximum value of a parameter the figure of merit in the nvar dimensional space of the problem All the iteration variables are constrained to lie between lower and upper bounds stored in arra
26. Programs 95 ProcessConfig echo_base Echos the attributes of the base class to standard output ProcessConfig echo Echos the values of the current class to standard output ProcessConfig prepare_wdir Prepares the work directory for the run ProcessConfig create_readme directory Creates a file called README txt containing ProcessConfig comment ProcessConfig modify_in_dat Modifies the original IN DAT file ProcessConfig setup Sets up the program for running ProcessConfig run_process Runs PROCESS binary ProcessConfig get_comment Gets the comment line from the configuration file ProcessConfig get_attribute attributename Gets a class attribute from the configuration file ProcessConfig set_base_attributes Sets the attributes of the base class TestProcessConfig filename test_process conf Object that contains the configuration parameter of the test_process py program ioptimz sets ioptimz optimisation solver in IN DAT epsvmc sets epsvmc VMCON error tolerance in IN DAT epsfcn sets epsfcn finite diff steplength in IN DAT minmax sets minmax figure of merit switch in IN DAT TestProcessConfig echo Echos the values of the current class to std out TestProcessConfig modify_in_dat Modifies IN DAT using the configuration parameters RunProcessConfig filename run_process conf Configuration parameters of the run_process py program no_allowed_unfeasible The number of al
27. The plasma minor radius a rminor is calculated from these values The shape of the plasma cross section is given by its last closed flux surface LCFS elongation k kappa and triangularity 6 triang which can be scaled automatically with the aspect ratio if required using switch ishape e If ishape 0 the input values for kappa and triang are used directly e If ishape 1 the following scaling is used which is suitable for low aspect ratio machines 1 A 2 2 05 1 0 44 e 3 1 0 53 1 0 77 amp 3 2 e If ishape 2 the Zohm ITER scaling 9 is used to calculate the elongation E 0 5 k minimum 2 0 1 5 A 1 3 3 while the input value of the triangularity is used unchanged The values for the plasma shaping parameters at the 95 flux surface are calculated as follows 10 Ros 1 12 3 4 095 0 1 5 3 5 The plasma surface area cross sectional area and volume are calculated using formulations that approximate the LCFS as a revolution of two arcs which intersect the plasma X points and the plasma midplane outer and inner radii This is a reasonable assumption for double null diverted plasmas but will be inaccurate for single null plasmas snull 1 Switch igeom determines whether an old method is used igeom 0 or calculations based on a more recent derivation igeom 1 11 3 1 2 2 Fusion reactions The most likely fusion reaction to be utilised in a power plant is th
28. a new IN DAT with modular structure INDATNew read_in_dat Reads an IN DAT file without modular structure INDATNew write_in_dat filename new_IN DAT Writes a new IN DAT without modular structure INDATNew add_variable var Adds an INVariable object to the INDATNew class INDATNew remove_variable var_name Removes an INVariable object from the INDATNew class INDATNew add_constraint_eqn eqn_number Adds constraint equation eqn_number to the list of constraint equations InVariable class if the equation is not already in the list INDATNew remove_constraint_eqn eqn_number Removes constraint equation eqn_number from the list of constraint equations InVariable class if the equation is already in the list INDATNew add_iteration_variable var_number Adds iteration variable var_number to the list of iteration variables InVariable class if the variable is not already in the list INDATNew remove_iteration_variable var_number Removes iteration variable var_number to the list of iteration variables InVariable class if the variable is already in the list clear_lines lines Removes comment only lines and replaces multiple empty lines with a single empty line variable_type var_name var_value Checks the type of an IN DAT variable using DICT_VAR_TYPE fortran_python_scientific var_value Changes from FORTRAN double precision notation D to Python s e notation 6 2 2 mfile py A set of Python classes to read and extract data f
29. ad e Ea eo i a 2 8 5 Other modules ssri grant w honans aie d a i a a ee 3_ Physics Engineering and Other Models 3 1 Tokamak Power Planti oe s s e d e ee al EA Mo are e he a a Gee A 3 1 1 Radial and vertical build a a a a 10 10 11 11 11 11 13 13 15 15 15 15 16 18 18 18 21 21 21 23 23 3 1 2 Plasma physics Models e 29 31 3 First Wall seecae k a Ra ee Oe MERA e EAS A 38 3 1 4 Divert eee eG Re ee oe ee ek ee 39 3 1 0 Blanket cacas is wee eee ee eRe Se ee Dee bee Ga ae 39 LO Shield i 44 eae A ee a add e Bae oe ee a a e e 42 3 1 7 Toroidal field coil oaa ee 43 3 1 8 Poloidal field coils s e a soma a as a a aa e a a aE aae 2 a a e eee 45 3 1 9 Ohmic heating coil a 46 3 1 10 Auxiliary power systems heating and current drive 48 3 1 11 Structural components 51 3 1 12 Cryostat and vacuum system 2 ee 51 3 1 13 Power conversion and heat dissipation systems 51 3 1 14 gt Buildings s s ea sa keke ee ss ser a a a e ee Se 54 3 2 Spherical Tokamak Model
30. and helium fractions fblhebpi fblhebpo the rest being steel Together the BZ BM and BP make up the blanket with total radial thicknesses blnkith inboard and blnkoth outboard and void coolant fraction vfblkt Note that these quantities are calculated from the sub assembly values if blktmodel gt 0 rather than being input parameters e Low Temperature Shield and Vacuum Vessel lumped together for these calculations with radial thicknesses inboard and outboard respectively sh1dith ddwi shldothtddwi and water coolant fraction vfshld the rest being assumed to be steel for its mass calculation the neutronics model assumes that the shield contains 2 boron as a neutron absorber but this material is not explicitly mentioned elsewhere in the code so its cost is not calculated for example N B The fact that water is assumed to be the coolant in the shield whereas helium is the coolant in the blanket leads to an inconsistency when specifying the coolant type via switch costr see Section 3 1 5 2 At present we mitigate this by forcing costr 2 making water the coolant as in this case the coolant mass and pumping costs are higher giving the more pessimistic solution with regards to costs A few other input parameters are useful for tuning purposes as follows e fhole is the hole area fraction of the first wall and blanket that neutrons leaving the plasma see due to the presence of the divertor fo
31. and shield calculations machine build calculations PF coil calculations heat transport and power balance calculations pulsed power plant calculations steady state temperatures after a LOCA event superconducting TF coil calculations support structure calculations resistive TF coil calculations vacuum system calculations Table 2 8 Summary of the engineering modules in PROCESS 2 8 4 Costing module The costing module costs f90 performs all the cost calculations including values in M for each machine system and the cost of electricity in m kWh 2 8 5 Other modules These modules perform miscellaneous tasks such as initialisation of variables and file input output File process f90 contains the main program and includes the overall controlling loop Table 2 9 summarises these modules Chapter 2 Program Overview The Fundamental Concepts 24 source file description error_handling f90 fson_library f90 global_variables f90 initial f90 input f90 output f90 process f90 centralised error handling module library used to read in data from JSON format files defines and initialises most shared variables checks self consistency of input variables and switches reads in user defined settings from input file utility routines to format output to file main program and top level calling routines Table 2 9 Summary of the remaining modules in PROCESS
32. at producing a useful result It can be a somewhat laborious process to arrive at a working case and unfortunately perhaps experience is often of great value in this situation It should be remembered that sufficient iteration variables should be used to solve each constraint equation For instance a particular limit equation may be A lt B i e A fB where the f value f must lie between zero and one for the relation to be satisfied However if none of the iteration variables have any effect on the values of A and B and A happens to be greater than B then PROCESS will clearly not be able to solve the constraint The lower and upper bounds of the iteration variables are all available to be changed in the input file Constraints can be relaxed in a controlled manner by moving these bounds although in some cases care should be taken to ensure that unphysical values cannot occur The code indicates which iteration variables lie at the edge of their range It is suggested that constraint equations should be added one at a time with sufficient new iteration variables activated at each step If the situation becomes unfeasible it can be helpful to reset the initial iteration variable values to those shown in the output from a previous feasible case and rerun the code Finally it should be borne in mind that the machine that is envisaged may not be a valid solution to the constraints being imposed no matter how many degrees of freedom i e
33. cost of electricity is the net electric power calculation performed in routine POWER It is possible that the net electric power can become negative due to a high recirculating power Switch ipnet determines whether the net electric power is scaled to always remain positive ipnet 0 or whether it is allowed to become negative ipnet 1 in which case no cost of electricity calculation is performed 3 10 Other Switches and Models 3 10 1 Diagnostic output Switch verbose can be set to 1 in the input file to allow the code to write some additional diagnostic output to the screen Currently extra information about the progress of the optimiser is produced This setting is likely to be of interest only to expert users 3 10 2 Code parameters affecting other models This chapter has summarised the methods by which several of the models in the code can be activated There are many others present however and it is suggested that the user refers to the variable descriptor file vardes html As stated earlier in Section 2 2 this contains details of all the parameters within the code that can be changed by the user in order to customise the machine modelled by PROCESS Chapter 4 Execution of the Code The intention of this chapter is to provide a comprehensive prescription for setting up and performing runs with the code Firstly the input file s structure and format is described The user is then taken through the procedure for s
34. cpttf no 60 and tftort no 77 should not be turned on in the input file as they are calculated self consistently the code will stop with an error message if this is attempted 3 6 Reversed Field Pinch Model In addition to the tokamak and stellarator magnetic confinement devices the code has the ability to perform calculations based on the physics and engineering of a reversed field pinch RFP device This third type of toroidal magnetic device is superficially similar in design to a tokamak so therefore shares many of the same components but the magnetic field configuration differs The model used in PROCESS is largely based on the TITAN fusion power plant 47 48 The following sections summarise its main features where they differ from those for tokamaks To activate the RFP coding it is necessary to create a file device dat containing the single character 2 in the first row in the working directory see Section 4 1 This has the effect of setting the internally used switch irfp 1 If the file is absent or its first character is set to something other than 2 the RFP model is not used and irfp is set to 0 3 6 1 RFP physics The plasma in RFPs is circular in cross section and is axisymmetric 3 6 1 1 Beta limit The poloidal beta is limited to a maximum value given by input parameter betpmx default 0 19 using constraint equation 48 and iteration variable 79 fbetap Chapter 3 Phys
35. maximum value vvhealw by turning on constraint equation no 55 with iteration variable no 96 fvvhe e The blanket lifetime is calculated assuming a maximum allowable level of neutron damage to its steel of 60 dpa currently not adjustable For the blktmodel 0 model the allowable blanket fluence abktflnc in MW years m may be input 3 1 5 2 Full thermodynamic blanket model Remove asap N B it is recommended that this model is not used in conjunction with the advanced blanket neutronics model blktmodel gt 0 Chapter 3 Physics Engineering and Other Models 42 Switch 1blnkt determines whether the blanket is to be simulated using a full thermodynamic model 27 lblnkt 1 or simply assumed to be made up of relevant materials see Section 3 1 5 3 in user defined proportions The former model also performs a self consistent calculation of the thermal to electric conversion efficiency whereas the latter simply uses the input value etath The following switches control the details of the full thermodynamic model of the blanket e Cooling channel geometry The value of switch astr determines whether the cooling channels have a circular cross section astr 1 or an annular cross section astr 2 The latter case is the default e Cooling channel orientation The value of switch estr determines whether the cooling channels lie in the radial direction estr 1 or in the poloidal direction estr
36. mode Sometimes one wants to find an optimal machine that is both consistent with the physics and engineering constraints but also minimises or maximises a certain figure of merit This requires running PROCESS in optimisation mode For these applications PROCESS uses the routine VMCON 5 based on a variable metric method for constrained optimisation by Powell 6 It finds a stationary point of an objective function figure of merit consistent with a set of equality and inequality constraints 11 Chapter 2 Program Overview The Fundamental Concepts 12 initialise variables input from file define free parameters define rules to be obeyed evaluate physics engineering and cost functions apply consistency equations iterate free parameters self consistent yes write output Figure 2 1 Flow diagram of PROCESS in non optimisation mode Chapter 2 Program Overview The Fundamental Concepts 13 c f section A 1 It is designed to solve the necessary but not sufficient conditions of a constrained optimum hence the solution does not have to be a global optimum c f A 2 The detailed algorithm is explained in Appendix A and is based on the Lagrange method c f section A 2 that combines both the objective function and the constraints using Lagrange multipliers It applies a sequential quadratic programming approach c f
37. models are introduced later in the Chapter 3 1 1 Radial and vertical build Figure 3 1 shows schematically the layout of a typical tokamak as modelled by PROCESS This is the so called build of the machine the relative locations of the major components Their positions are referenced to the R Z coordinate system where R is the radial distance from the vertical centreline axis of the torus and Z is the vertical distance from the equatorial midplane about which the machine is assumed to be up down symmetrical by default the vertical build is slightly different for single null plasma devices see Figure 3 3 Components are often referred to as being inboard or outboard which simply means that they lie at a radius R less than or greater than Ro respectively where Ro is the plasma major radius rmajor For the sake of clarity the thicknesses are not drawn to scale and the space labelled as the divertor does not indicate in any way the actual shape of that component The first wall blanket shield and vacuum vessel may be either D shaped in cross section or each may 25 Chapter 3 Physics Engineering and Other Models 26 be defined by two half ellipses compare their shapes in Figures two possibilities is set using input parameter fwbsshape ellipses ddwex PF coil clht ipfloc 1 tfcth hmax 7 vgap2 hmax x Boe EA ohhghf ddwi y shldtth divfix E vgap rminor
38. number of constraints and c A and p i 1 m are their respective components B and I are n x n dimensional matrices while Vc is an n x m dimensional matrix Appendix B Non optimisation Input File The following is a typical input file used to run PROCESS in non optimisation mode Comments in have been added to the right of each line Numerics information Comment NEQNS 14 Number of active constraint equations NVAR 14 Number of active iteration variables ICC 1 2 10 11 7 16 24 5 31 32 33 34 35 36 Constraint eqns ixc 5 10 12 3 7 6 36 9 48 49 50 51 53 54 Iteration variables IOPTIMZ 1 Turn off optimisation ISWEEP 0 No scans non optimisation mode F values and limits FBETATRY 1 0 Physics parameters ASPECT 3 5 BETA 0 042 BT 6 DENE 1 5e20 FVSBRNNI 1 0 DNBETA 3 5 HFACT 2 ICURR 4 ISC 6 TINVQD 1 TITER 1 ISHAPE 0 KAPPA 2 218 Q 3 0 RMAJOR 7 0 RNBEAM 0 0002 TBURN 227 9 TE 15 TRIANG 0 6 Current drive parameters IRFCD IEFRF FEFFCD 3 1 N B active iteration variable 36 Machine aspect ratio N B active iteration variable 5 Toroidal field on axis N B active iteration variable 6 Non inductive volt seconds fraction Beta g coefficient N B active iteration variable 10 Use ITER current scaling Use ITER 89 P confinement time scaling law Use inv
39. of a theoretical first wall with 100 coverage which may be set as input parameters fdiv divertor area fraction fhcd heating current drive diagnostics apparatus and fhole any other gaps The remaining fraction 1 fdiv fhcd fhole is the area fraction of the actual first wall Chapter 3 Physics Engineering and Other Models 52 1 etahtpdiv Divertor coolant pump electrical power htpmwe_div 1 etahtpfw First wall coolant pump electrical power htpmwe_fw Heat Transport Pumps electrical power htomw Blanket coolant pump electrical power htpmwe_bikt 1 etahtpbikt Shield coolant pump electrical power htpmwe_shld 1 etahtpshid Heat Transport Pumps waste heat htpsecmw Gaps through heating current drive ata apparatus diagnostics psechcd psechole fhole mm fhole thea Charged particle power reaching divertor pdivt Total neutron power pneutmw Total radiation power pradmw fdiv fdiv t fdiv fhcd fhole t fdiv fhcd fhole pnuctwbs Charged particles Radiation Neutrons pdivi praddiv pnuediv Coolant pumping htpmw_div etahtpdiv Incident radiation Neutron absorption pradiw pnuctw etahtpfw Coolant pumping htpmw_fw Neutron absorption pnucblkt Coolant pumping
40. operations to outline the difference between non optimisation and optimisation modes For a more detailed and correct VMCON flow diagram please see Figure A 2 Chapter 2 Program Overview The Fundamental Concepts 15 In addition global code parameters are labelled FIX These can only be changed by editing the relevant source file but this should not be carried out unless it is absolutely necessary All the variables that are shown with a default value are available to be changed by the user using the input file Section 4 1 except for those which are labelled FIX Variables not shown with a default value are calculated by the code from a combination of other parameters and so it would be meaningless to initialise them Obviously these variables cannot be changed using the input file The file is generated from specially formatted comment lines within the source code see Section 7 2 for more details Therefore it is exceedingly important to keep these comment lines relevant and in sync with the variables they describe 2 3 Input Parameters Input parameters make up a large proportion of the variables listed in the variable descriptor file They comprise all those variables that once set in the initialisation routine or redefined in the input file do not change throughout a PROCESS run In fact only those variables defined as iteration variables Section 2 5 can change during the cour
41. relative to the electron density are set using input array fimp 1 to nimp where nimp 14 is the number of impurity species in the radiation model The available impurities are as follows Chapter 3 Physics Engineering and Other Models 33 1 Hydrogen fraction calculated by code 2 Helium fraction calculated by code 3 Beryllium 4 Carbon 5 Nitrogen 6 Oxygen 7 Neon 8 Silicon 9 Argon 10 Iron 11 Nickel 12 Krypton 13 Xenon 14 Tungsten As stated above the number density fractions for hydrogen all isotopes and helium need not be set as they are calculated by the code to ensure that plasma quasi neutrality is maintained and taking into account the fuel ratios fdeut ftrit and fhe3 see Section 3 1 2 2 and the alpha particle fraction ralpne which may be input by the user The impurity fraction of one of the elements listed in array fimp may be used as an iteration variable although it will only have any effect if imprad_model 1 The element to use is specified using input parameter impvar which may be set to a value between 3 and nimp and the initial estimate to use for the element s impurity fraction must be set using iteration variable no 102 fimpvar The synchrotron radiation power 18 19 is assumed to originate from the plasma core The wall reflection factor ssync may be set by the user By changing the input parameter coreradius the user may set the normalis
42. s ssa donaca a adia adea era a e o a a a i aea 6 3 1 Launching itt dod id a a A PO SS e e RA 6 3 2 Editing variables e 6 3 3 Opening and saving files e e 6 3 4 Searching O A ta ene 7 Code Management Tools 7 1 The Makefile 7 1 1 Compilation 7 1 2 Archiving utilities 7 1 3 Code documentation 7 2 Automatic Documentation 8 Acknowledgements amp Bibliography A The Optimisation Solver Explained A 1 The General Nonlinear Programming Problem 99 99 99 100 100 100 101 106 A 2 The Lagrange Method 0 0 0 00 ee ee 108 A 3 Sequential Quadratic Programming SQP o 4 4 4 486400 eee 048 109 PAA NMCOND Cia ce at Rok dads Soe OR OR a we a Go ce de ees ke Be we a 109 A 5 The Quadratic Subproblem QSP ya 0 04 a4 2a ede ds Oe Ree ed ee 109 A 6 The Line Search se eu ca coi ea naaa ca ee ee Re ER ee be a 112 A 7 The Broyden Fletcher Goldfarb Shanno BFGS quasi Newton update 113 AS SVMDOIS e e sa gh he te e Bw na e oe eo ae A A Sgr ow Ge awe BE 114 B Non optimisation Input File 115 C Optimisation Input File 118 D Source Code Documentation 121 List of Figures
43. self consistently with the blanket Chapter 3 Physics Engineering and Other Models 40 and shielding materials and sub assembly thicknesses and for constraints to be applied to satisfy the engineering requirements The rest of this section describes this model in more detail The model is based on the Helium Cooled Pebble Bed HCPB blanket concept developed by KIT a second advanced model Helium Cooled Lithium Lead HCLL will be implemented in due course The blanket shield and vacuum vessel are segmented radially into a number of sub assemblies Moving in the direction away from the plasma first wall these are e Breeding Zone BZ which includes the first wall with radial thicknesses inboard and outboard respectively fwith blbuith fwoth blbuoth This consists of beryllium with fraction by volume fblbe breeder material fblbreed steel fblss and helium coolant Three forms of breeder material are available lithium orthosilicate Li SiO chosen by setting breedmat 1 lithium metatitanate LigTiO3 breedmat 2 or lithium zirconate LigZrO3 breedmat 3 The Li enrichment percentage may be modified from the default 30 using input parameter 1i6enrich e Box Manifold BM with radial thicknesses inboard and outboard respectively blbmith blbmoth and helium fractions fblhebmi fblhebmo the rest being steel e Back Plate BP with radial thicknesses inboard and outboard respectively blbpith blbpoth
44. subscripts in which case the following element order is assumed B 1 1 B 2 1 B 3 1 The use of the input file to specify multiple dimension array elements is prone to error 9 Unscripted array elements must be separated by commas 10 Blank lines are allowed anywhere in the input file 11 Lines starting with a are assumed to be comments 12 Comment lines starting with five or more asterisks i e x are reproduced verbatim in the output file These should be used copiously to give a great deal of information about the run being performed and should be updated before every single run of the code as it is very easy to lose track of what is being attempted 13 In line comments are usually ignored but there can be problems if one contains a comma If this is the case there must also be a comma after the variable s value and before the comment It is useful to divide the input file into sections using suitable comment lines to help the user keep related variables together The following is a valid fragment of an input file the vertical lines are simply to help show the column alignment Chapter 4 Execution of the Code 71 This line is a comment that will not appear in the output x xxkk This line is a comment that will appear in the output bound1 1 2 5 BOUNDU 10 3 BOUNDU 45 1 Another comment Note that real values can be entered as if they were integers and vice versa but it s not recom
45. to enforce the fusion gain Q to be at least bigqmin Chapter 3 Physics Engineering and Other Models 50 r tanmax 7 lt _ b Figure 3 7 Top down schematic view of the neutral beam access geometry The beam with the maximum possible tangency radius is shown here Chapter 3 Physics Engineering and Other Models 51 3 1 11 Structural components Structural components are required to provide support for the fusion power core systems against gravity and the magnetic forces that will be encountered during operation The required structural masses and their costs are calculated 3 1 12 Cryostat and vacuum system The internal vacuum vessel provides a toroidal evacuated chamber containing the plasma first wall blanket and shield and the space between this item and the external cylindrical cryostat encloses those components that need to operate at liquid helium temperatures These include any superconducting TF or PF coils and the inter coil structure PROCESS calculates the cryogenic power load and the resulting heat exchanger requirements The vertical distance h between the uppermost PF coil and the external cryostat lid may be adjusted by changing the value of input parameter clhsf a scaling based on ITER is used 3 20 2 x rdewex h clhsf 28 440 The vacuum system is used for four different processes Firstly before plasma operations the chamber must be evac
46. understanding and maintaining the code The use of Fortran 90 95 modules provides a natural and convenient way for this to be done The following sections describe briefly the modules into which PROCESS is divided 2 8 1 Numerics modules These modules contain the equation solvers their calling routines and other relevant procedures Various mathematical routines from a number of standard libraries are also incorporated into these files Table 2 6 summarises the numerics source file contents 2 8 2 Physics modules These modules contain the main physics routines that evaluate the plasma and fusion parameters Also included here are the routines describing the current drive and divertor systems Table 2 7 summarises the physics source file contents 2 8 3 Engineering modules These modules contain the description of the machine geometry and its major systems including the PF and TF coil sets the first wall blanket and shield and other items such as the buildings vacuum system power conversion and the structural components Table 2 8 summarises the engineering source Chapter 2 Program Overview The Fundamental Concepts 22 nsweep scan variable description Roa 125002000 0N gt 0 NNNDNDN yN DNyN DNNNONDER FR RAR SO ONODOTKBRWNFOCOUW AN DTK W wn aspect hidivlim pnetelin hfact oacdcp walalw beamfus0 fqval te boundu 15 dnbeta bscfmax boundu 10 fi
47. will also be included as the need arises 3 9 Cost Models The cost accounting used by PROCESS combines methods 61 used in the TETRA code 1 and the Generomak 62 scheme The costs are split into the standard accounting categories 63 generally used in the reporting of power plant costs The best references for the algorithms used are 2 and source file costs 90 in the code itself The majority of the costed items have a unit cost associated with them These values scale with for example power output volume component mass etc and many are available to be changed via the input file All costs and their algorithms correspond to 1990 dollars 3 9 1 Cost options 3 9 1 1 N of a kind costs The unit costs of the components of the fusion power core are relevant to first of a kind items That is to say the items are assumed to be relatively expensive to build as they are effectively prototypes and specialised tools and machines have perhaps been made specially to create them However if a production line has been set up and R amp D progress has allowed more experience to be gained in constructing the power core components the costs will be reduced as a result Variable fkind may be used to multiply the raw unit costs of the fusion power core items by a factor less than one to simulate this cost reduction for an N of a kind device In other systems studies of fusion power plants
48. x kappa L a amp Ssssss O 5 2 o 233 g 2 5 8g is romax rsldi divertor rminor PF coil ipfloc 2 rmajor 3 1 and 3 2 The choice between these 8 which should be 1 for D shaped or 2 for vacuum vessel shield blanket first wall external cryostat PF coils ipfloc 3 TT z i of 30 o 5 E E 2383 35 3 Se R E PEE Boe 2 os ors e D gt 3 a 3 0 0 x rsido rtot rdewex Figure 3 1 Schematic diagram of the fusion power core of a typical tokamak power plant modelled by PROCESS showing the relative positions of the components A double null plasma is assumed snul1 0 3 3 compare Figure and the first wall blanket shield and vacuum vessel are D shaped in cross section chosen by setting switch fwbsshape 1 compare Figure 3 2 Also shown are the code variables used to define the thicknesses of the components The arrowed labels adjacent to the azes are the total builds to that point The precise locations and sizes of the PF coils are calculated within the 9 1 8 code see Section Most of the thicknesses shown in Figures 3 1 and 3 2 are input parameters so are not changed during the course of the simulation The rest are calculated by the code during execution In addition some of the component sizes can be used as iteration variables see Sec
49. 2 5 OHHGHF 71 Vacuum system parameters NTYPE 1 Heat transport parameters ETATH 0 35 FMGDMW 0 BASEEL 5 e6 ISCENR 2 Buildings FNDT 2 EFLOOR 1 d5 Use old blanket model Steel density N B active iteration variable 12 Use superconducting TF coils Maximum TF ripple Three groups of PF coils Locations for each group Number of coils in each group central solenoid current at End Of Flat top central solenoid current at Begin Of Pulse COHEOF Radial position for group 3 Z position for group 3 Height ratio central solenoid TF coil Use cryopump Thermal to electric conversion efficiency Power to MGF units Base plant electric load Energy store option Foundation thickness Effective total floor space Appendix B Non optimisation Input File 117 Costs IREACTOR 1 IFUELTYP 0 UCHRS 87 9 UCCPCL1 250 UCCPCLB 150 Calculate cost of electricity Treat blanket first wall etc as capital cost Unit cost of heat rejection system Unit cost of high strength tapered copper Unit cost of TF outer leg plate coils Appendix C Optimisation Input File The following is a typical input file used to run PROCESS in optimisation mode Comments in have been added to the right of each line Numerics information Comment bound1l 1 2 5 Bound on iteration variable 1 aspect BOUNDU 10 3 Bound on iteration variable
50. 20000000 2 pee ee ee 55 3 2 1 Spherical tokamak switches 2 a 55 3 3 Pulsed Plant Operation a ee 56 3 3 1 Thermal cycling package 2 ee 56 3 3 2 First wall coolant temperature rise limit 20 56 3 3 3 First wall peak temperature limit a a e 56 3 3 4 Start up power requirements 1 ee 56 3 3 5 Plasma current ramp up te 57 3 3 6 Burn time science Ge 57 3 3 7 Thermal storage ee 57 3 4 Hydrogen Production Facility 2 ee 57 3 5 Stellarator Model 3s sos sa Asie Bw k Soe a eR OS ee See Ee Pa E a 58 3 5 1 Stellarator physics ea 58 3 5 2 Machine configuration o oo oaa ee 62 3 6 Reversed Field Pinch Model 2 02 0 200 0000 02 eee eee 63 36A REP physics os ac 4g Ree a Se BORA Dek eS a es Ro dw hl 63 362 TE Coll o Gg anced Be we Se Ha Sere TE Ge ed oe Ee de 64 3 6 3 Ohmic heating COLS ee 65 3 0 4 EFE Coils ea Els ae eck Be Re Se Bgl ee BDA Ace A ee i 65 3 020 DIVERTOR ae a aros ke whe Gow Go Sw we A ee me Bee ee awe be ee 65 3 6 6 Code modifications oa eo a ee 65 3 7 Inertial Fusion Energy Model 2 2 e 65 3 8 Safety and Environment Models 66
51. 3 Running the Code This section will attempt to guide the user through the actual running of the code in its various modes In most cases only minor changes to the input file are necessary to change the code s mode Chapter 4 Execution of the Code 72 of operation usually the physics and engineering variables etc remain unchanged with the major differences occurring in the numerical input only 4 3 1 Environment set up Under normal circumstances the code is only available for execution from the CCFE Fusion Unix Network on which you must have an account To set up your environment to be able to run the code and the associated Python utilities see Chapter 6 add the following lines to your bashrc file module use home pknight modules module swap python module load process master If you want to use with care the latest draft version of the code instead of the latest verified release version replace module load process master with module load process develop above After re logging in execute PROCESS by simply typing process on the command line 4 3 2 Non optimisation mode Non optimisation mode is used to perform benchmark comparisons whereby the machine size output power etc are known and one only wishes to find the calculated stresses beta values and fusion powers for example When starting to model a new machine PROCESS should always be run first in non optimisation mode before any attempt
52. 33 34 35 36 37 M Kovari et al PROCESS a systems code for fusion power plants Part 1 Physics in preparation 2014 H Lux et al Impurity radiation in DEMO in preparation 2014 Albajar Nuclear Fusion 41 2001 665 Fidone Giruzzi and Granata Nuclear Fusion 41 2001 1755 N A Uckan Fusion Technology 14 1988 299 W M Nevins et al Summary Report ITER Specialists Meeting on Heating and Current Drive ITER TN PH 8 4 13 17 June 1988 Garching FRG H R Wilson Nuclear Fusion 32 1992 257 O Sauter C Angioni and Y R Lin Liu Physics of Plasmas 6 1999 2834 O Sauter C Angioni and Y R Lin Liu Physics of Plasmas 9 2002 5140 N A Uckan et al Fusion Technology 13 1988 411 A Li Puma F Franza and L V Boccaccini WP12 SYS01 T02 Model Improvements Blanket Model EFDA_D_2LKMCT v1 0 EFDA Power Plant Physics amp Technology February 2013 P J Karditsas PROCESS Code Development simple blanket model neutron heat input Work File Note F RS CIRE5523 PWF 0142 November 1992 L Bottura J B T Parameterizations for the ITER Nb3Sn Production ITER Document 2MMF7J 2008 https user iter org uid 2MMF7 J amp action get document J Myall ORNL internal note 28th August 1987 scanned copy available in Mya11_1987_TF_stress_calc pdf J Morris PROCESS Superconducting Toroidal Field Coil Model CCFE internal note 1st May 2014 P J
53. 64 values for this multiplier have ranged from 0 5 to 0 8 3 9 1 2 Level of safety assurance Many of the unit costs have four possible choices relating to the level of safety assurance 65 flag 1sa A value lsa 1 corresponds to a plant with a full safety credit i e is truly passively safe Levels 2 and 3 lie between the two extremes and level 4 corresponds to a present day fission reactor with no safety credit 3 9 1 3 Replaceable components The first wall blanket divertor centrepost if present and current drive system have relatively short lifetimes because of their hostile environment after which they must be replaced Because of this frequent renewal they can be regarded as though they are fuel items and can be costed accordingly Switch ifueltyp is used to control whether this option is used in the code If ifueltyp 1 the costs of the first wall blanket divertor and a fraction fcdfuel of the cost of the current drive system are treated as fuel costs If ifueltyp 0 these are treated as capital costs Chapter 3 Physics Engineering and Other Models 68 3 9 1 4 Cost of electricity calculations Switch ireactor determines the type of cost of electricity calculation that is performed If ireactor 0 no cost of electricity calculation is performed If ireactor 1 then the cost of electricity is evaluated with the value quoted in units of m kWh 3 9 1 5 Net electric power calculation Related to the
54. CESS error code of a successful run PARAMETER_DEFAULTS Default values for making a PLOT DAT file from MFILE DAT DICT_VAR_TYPE Maps the PROCESS variable name to its value type The value type can be one of int_array int_variable real_array or real_variable DICT_IXC_SIMPLE Maps the string number of the iteration variable to its variable name DICT_IXC_FULL Maps the string number of the iteration variable to a dictionary that contains the variable name under name the default lower variable bound float under Ib and the default upper variable bound float under ub DICT_IXC_BOUNDS Maps each iteration variable name to a dictionary that contains the default lower variable bound float under lb and the default upper variable bound float under ub NON_F_VALUES List of iteration variable names that start with an f but are not f values DICT_NSWEEP2IXC Maps the sweep variable number nsweep to the respective iteration variable number if applicable DICT_IX2NSWEEPC Maps the iteration variable number to the respective sweep variable number nsweep if applicable DICT_TF_TYPE Maps the PROCESS TF coil type number to its type DICT_OPTIMISATION_VARS Maps each figure of merit number to its description DICT_IXC_DEFAULT Maps each iteration variable name to its default value Add new stuff used by GUI etc 6 2 6 a_to_b_config py To do Chapter 6 Utility Programs 97 6 2 7 proc plot func py A coll
55. During the line search VMCON struggles to find calls VMCON has reached the a solution Retry with maximum different start number of total function parameters calls maxfev 100 3 Line The results produced by The developer needs to search required 10 input objective check the consistency functions calls function constraints and numerical robust and their gradients are ness of the objective inconsistent This can function constraints be due and their derivatives to numerical noise inthe Perhaps the accurracy input functions in numerical integra tions differentiations needs to be higher As a user try changing the iteration bounds or adding other iteration variables 4 Uphill search The quadratic This happens if an direction was subproblem inconsistency between calculated has suggested a search the objective function direction in which the the constraints and objective function only their respective increases derivatives occurs c f ifail 3 5 qpsub No Either no optimum lies As a user add a new feasible solution or within the space allowed iteration variable as bad approximation by the constraints and developer try using a of Hessian variable bounds or the multiple of the identity identity matrix is not a matrix as initial Hessian good instead first approximation of the Hessian 6 qpsub This is fairly If this is meaningful Singular matrix in self explanatory
56. EL 1 0 PNETELIN 1200 0 Consistency equations 1 2 10 11 and 7 are activated together with limit equations 16 5 and 24 refer to Table 2 1 This example assumes that neutral beam current drive is present equation 7 with variable 7 and that the net electric power is to be fixed at 1200 MW Note the optional but beneficial practice of vertically aligning corresponding equations and variables constraint equation 16 has no corresponding iteration variable which would normally be no 25 fpnetel as we want the net electric power to be fixed at the value given by pnetelin Since in non optimisation mode the number of variables must be equal to the number of equations we have scope to add a free iteration variable refer to Tables 2 2 and 2 3 in this case no 4 electron temperature to help raise the fusion power sufficiently to obtain the required net electric power Finally note the use of the density and beta limit equations 5 and 24 respectively the final values of the corresponding f values will indicate if the limits are exceeded and by how much On running PROCESS and hopefully achieving a feasible result examination of the output may well show up discrepancies between some of the parameter values produced and their known values if available Remember that of all the variables shown in the variable descriptor file with a default value only those declared as active iteration vari
57. Knight PROCESS Reactor Systems Code AEA Fusion Project Work File F RS CIRE5523 PWF 1992 Y K M Peng and J B Hicks Engineering Feasibility of Tight Aspect Ratio Tokamak Spherical Torus Reactors AEA Fusion Report AEA FUS 64 1990 Pulsed Fusion Reactor Study AEA Fusion Report AEA FUS 205 1992 F Schauer K Egorov and V Bykov HELIAS 5 B magnet system structure and maintenance concept Fusion Engineering and Design 88 2013 1619 1622 F Warmer Stellarator Plasma Geometry model for the systems code PROCESS IPP Greifswald Germany internal note 19 06 2013 F Warmer Stellarator Divertor model for the systems code PROCESS IPP Greifswald Germany internal note 21 06 2013 F Warmer and F Schauer Stellarator Coil model for the systems code PROCESS IPP Greifswald Germany internal note 07 10 2013 Chapter 8 Acknowledgements amp Bibliography 104 38 39 40 41 42 43 44 45 46 47 48 49 50 5l 52 53 54 55 56 57 58 VMEC MHD force balance code for toroidal domains http vmecwiki pppl wikispaces net VMEC J Geiger Darstellung von ineinandergeschachtelten toroidal geschlossenen Fl chen mit Fourierkoeffizienten Representation of nested closed surfaces with Fourier coefficients IPP Greifswald Germany internal document 06 07 2010 J N hrenberg et al Plasma Physics and Controlled Fusion 35 1993 B115
58. Options The configuration file 2D_scan conf has the following style x This is a comment No evaluations of the first variable Ni 10 lower bound of first variable LBi 1 upper bound of first variable UBi 3 name of first variable NAME1 abktflnc No evaluations of the second variable N2 15 lower bound of the second variable LB2 3 upper bound of the second variable UB2 8 name of the second variable NAME2 bktlife Qutput variables as given by their variable description OUT_VARS Major Radius Pdivt OUT_VARS Directory path to IN DAT PATH DIR2INDAT Boolean flag to store OUT DAT and PLOT DAT for each run in the Data subdir DATA 0 Chapter 6 Utility Programs 90 6 1 11 ato b py Takes an initial IN DAT and a target IN DAT and runs PROCESS repeatedly with the aim of walking the solution to the initial input file to a solution using the values of the variables in the target input file After each step the output values of the iteration variables are used as the input values for the next step Input a_to_b conf Output When the program finishes the DAT files from the last run of PROCESS can be found in the specified working directory If option keep_output True IN DAT OUT DAT MFILE DAT and logged process output of each step are stored Files are prefaced with their step number eg 003 IN DAT and copied to the specified output directory Configuration Option
59. RN 227 9 Burn time 118 Appendix C Optimisation Input File 119 TE 15 TRIANG gt 0 6 Current drive parameters IRFCD IEFRF FEFFCD Divert ANGINC 0 PRN1 0 2 t 32 or parameters 262 85 Machine build BORE 0 OHCTH GAPOH TFCTH DDWI 0 SHLDITH BLNKITH FWITH SCRAPLI SCRAPLO FWOTH BLNKOTH SHLDOTH GAPOMIN VGAPTF 12 0 1 0 08 0 9 07 0 69 0 115 0 035 0 14 0 15 0 035 0 235 1 05 0 21 0 N B active iteration variable 4 Plasma triangularity Use current drive Use ITER neutral beam current drive Artificially enhance efficiency Angle of incidence of field lines on plate Density ratio N B active iteration variable 29 N B active iteration variable 16 Inboard gap N B active iteration variable 13 Vacuum vessel thickness Inboard shield thickness Inboard blanket thickness Inboard first wall thickness Inboard scrape off layer thickness Outboard scrape off layer thickness Outboard first wall thickness Outboard blanket thickness Outboard shield thickness Outboard gap Vertical gap First wall blanket shield parameters LBLNKT 0 DENSTL 7 TF coi DACDCP ITFSUP RIPMAX PF coi NGRP IPFLOC NCLS 2 COHEOF FCOHBOP ROUTR ZREF 3 OHHGHF 3 Vacuum NTYPE Heat transport parameters ETATH 0 FMGDMW 800 1 parameters 1 4e7
60. S Sudo Y Takeiri H Zushi et al Nuclear Fusion 30 1990 11 R J Goldston H Biglari G W Hammett et al Bull Am Phys Society 34 1989 1964 K Lackner and N A O Gottardi Nuclear Fusion 30 1990 767 U Stroth et al Nuclear Fusion 36 1996 1063 H Yamada et al Nuclear Fusion 45 2005 1684 F Warmer Stellarator Modular Coil model for the systems code PROCESS IPP Greifswald Germany internal note 31 07 2013 The TITAN Reversed Field Pinch Fusion Reactor Study Scoping Phase Report UCLA Report UCLA PPG 1100 January 1987 The TITAN Reversed Field Pinch Fusion Reactor Study Final Report UCLA Report UCLA PPG 1200 1990 P J Knight PROCESS 3009 Incorporation of Inertial Fusion Energy Model Work File Note F MI PJK PROCESS CODE 032 Bourque et al Overview of the OSIRIS IFE Reactor Conceptual Design Fusion Technology 21 1992 1465 Meier and Bieri Economic Modeling and Parametric Studies for OSIRIS a HIB Driven IFE Power Plant Fusion Technology 21 1992 1547 Ghose et al BOP Designs for OSIRIS and SOMBRERO IFE Reactor Plants Fusion Technology 21 1992 1501 Sviatoslavsky et al A KrF Laser Driven Inertial Fusion Reactor SOMBRERO Fusion Technology 21 1992 1470 Meier and Bieri Economic Modeling and Parametric Studies for SOMBRERO a Laser Driven IFE Power Plant Fusion Technology 21 1992 1552 Moir et al HYLIFE II A Molten
61. Salt Inertial Fusion Energy Power Plant Design Final Report Fusion Technology 25 1994 5 Moir HYLIFE II Inertial Fusion Energy Power Plant Design Fusion Technology 21 1992 1475 Hoffman and Lee Performance and Cost of the HYLIFE II Balance of Plant Fusion Technology 21 1992 1475 P J Knight PROCESS IFE Build Details F MI PJK LOGBOOKI12 pp 52 53 56 57 Chapter 8 Acknowledgements amp Bibliography 105 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 Bieri and Meier Heavy lon Driver Parametric Studies and Choice of a Base 5 MJ Driver Design Fusion Technology 21 1992 1557 N P Taylor R A Forrest P J Knight and L J Baker Safety and Environmental Modelling in the PROCESS Code Strategic Studies Note 94 14 1994 R L Reid and Y K M Peng Potential Minimum Cost of Electricity of Superconducting Coil Tokamak Power Reactors Proceedings of 13th IEEE Symposium on Fusion Engineering Knoxville Tennessee October 1989 p 258 J Sheffield et al Cost Assessment of a Generic Magnetic Fusion Reactor Fusion Technology 9 1986 199 S Thompson Systems Code Cost Accounting memo FEDC M 88 SE 004 1988 J D Galambos L J Perkins S W Haney and J Mandrekas Nuclear Fusion 35 1995 551 J P Holdren et al Report of the Senior Committee on Environmental Safety and Economic Aspects of Mag
62. T amp M PKNIGHT PROCESS MANUAL A User Guide to the PROCESS Systems Code P J Knight Culham Centre for Fusion Energy Culham Science Centre Abingdon Oxon OX14 3DB UK 2014 09 29 Revision 340 Contents 1 Introduction 1 1 Rationale 1 2 History 1 3 Layout of the User Guide 2 2 ee 2 Program Overview The Fundamental Concepts 2 1 Equation Solvers s e se sa caca RE RE Oe ee a 2 1 1 Non optimisation mode 0 0 00 2b ee ee 2 1 2 Optimisation made 2 1 3 Sang ecards a Se Be Ree ee 2 2 The Variable Descriptor File 0 2 a 2 3 Input Parameters s ge eek baa RP RS RS PR a Pe wa a 2 4 Constraint Equations ee 2 4 1 Consistency equations 24 2 Limit equations skeis a a a Se a a Ee a ee 2 5 Treration Variables oa a ak i e ok Ee eR Se Oe ed he EE 26 Figures ol Merit e ms sraide bok Aw cum SR ane rl aria Gob ewe doe eo a 2 7 Scanning Variables s sa e se aroa a senera dsa do Ea aaa a a a 2 8 Code Structure a s sae raud ei gbk Ra cm SR Ae rl aria Boh ee Ge wo a 2 8 1 Numerics modules aoaaa ee ee 2 8 2 Physics modules s s s a s s boi eo aoe a h e E DOB a i a 2 8 3 Engineering moduleg a ao aa 02 ee ee 2 8 4 Costing module s sa s s hoa sos emd
63. Tped Ppea r I 3 1 Ppea T LU 2Ppca 1 Tred 2 Ppea r Tsep 3 16 T 1 ar 2 Pr Pear T ar T 2 Br Gr T ar sin ra r 1 ar 2 Pr T Peed D Q 8r br where T is the gamma function for integer ar 3 17 for non integer ar Note that both density and temperature can have different pedestal positions Pped n rhopedn and Pped T rhopedt in agreement with simulations 3 1 2 4 Beta limits The plasma beta limit 14 15 is given by I MA lt a 3 18 lt 9 Gn Bo T where Bo is the axial vacuum toroidal field and 8 is defined with respect to the total equilibrium B field 15 The beta coefficient g is set using input parameter dnbeta but see Section 3 1 2 8 To Chapter 3 Physics Engineering and Other Models 32 apply the beta limit constraint equation no 24 should be turned on with iteration variable no 36 fbetatry The limit can be applied to either the total plasma beta in which case switch iculbl should be set to 0 to only the thermal component of the plasma beta in which case iculb1 should be set to 1 or to the thermal plus neutral beam components in which case iculbl should be set to 2 Aspect ratio scaling of beta y coefficient Switch gtscale determines whether the beta g coefficient dnbeta should scale with aspect ratio gtscale 0 or be fixed at the input value gtscale 0 Note that gtscale is over ridden if iprof
64. a first wall gap The region directly outside the last closed flux surface of the core plasma is known as the scrape off layer and contains no structural material Plasma entering this region is not confined and is removed by the divertor PROCESS treats the scrape off layer merely as a gap Switch iscrp determines whether the inboard and outboard gaps should be calculated as 10 of the plasma minor radius iscrp 0 or set equal to the input values scrapli and scraplo iscrp 1 3 1 3 First wall The first wall acts as a physical barrier protecting the rest of the machine from the hot plasma Due to its hostile environment the first wall has only a short lifetime and therefore needs to be replaced regularly Its stainless steel structure is cooled either by gaseous helium or by pressurised water as chosen using switch costr see Section 3 1 5 2 The first wall coolant fraction is given by the value of fwclfr which is calculated if a pulsed power plant is being modelled lpulse 1 see Section 3 3 and assumed to be the input value otherwise Chapter 3 Physics Engineering and Other Models 39 Wall load calculation Switch iwalld determines whether the neutron wall load power per unit area should be calculated using the plasma surface area iwalld 1 or the first wall area iwalld 2 as the denominator In the former case input parameter ffwal default value 0 92 can be used to scale the neutron power rea
65. able to use is defined by the value of nsweep and the chosen variable s values during the scan are set in array sweep Runs involving scans of this kind can only be performed in optimisation mode The results from the previous scan point are used as the input to the next scan point Routine SCAN in source file scan 90 stores many of the output quantities in a separate output file called PLOT DAT which can be read by the utility program plot_sweep to produce graphical output see Chapter 6 Scanning of derived quantities requires use of the appropriate constraint equations For instance if the net electric power is scanned constraint equation 16 should be employed For obvious reasons the active scanning variable must not also be an active iteration variable 2 8 Code Structure The structure of the majority of the code reflects to a certain extent the layout of the machine being modelled As stated above a large proportion of the code is simply a description of the underlying Chapter 2 Program Overview The Fundamental Concepts 19 ixc icc lower upper no variable name description eqn bound bound 1 aspect plasma aspect ratio 1 100D0 10 00DO 2 bt toroidal field on axis 0 010D0 100 0DO 3 rmajor plasma major radius 0 100D0 10 00DO 4 te electron temperature 5 000DO 500 0DO 5 beta plasma beta 0 001DO 1 000DO 6 dene electron density 1 00D19 1 00D21 7 rnbeam hot beam density electron d
66. ables can change from their initial values whether they are set in the input file or in the relevant module However some of the calculated parameters may be wrong the most common of which are as follows e Plasma current this can be adjusted using the edge safety factor q Ip x 1 q e Fusion power this scales roughly with the density profile factor alphan e Build parameters it may be necessary to change non critical thicknesses to achieve the correct machine build It may still be difficult if not impossible to reconcile the fusion power and the net electric power with the required values This may well be due to the power conversion efficiency values being used refer to Figure 3 91 With luck a few iterations of this process will produce an adequate benchmark case A typical input file for use with PROCESS in non optimisation mode is contained in Appendix B Chapter 4 Execution of the Code 74 4 3 3 Optimisation mode Running PROCESS in optimisation mode requires few changes to be made to the input file from the non optimisation case The main differences between optimisation mode and non optimisation mode are 1 Optimisation mode applies lower and upper bounds to all active iteration variables 2 There is no upper limit to the number of active iteration variables in optimisation mode ew A figure of merit must be specified in optimisation mode 4 Scans can be performed in optimisation mode Switch iop
67. ables neqns and nvar are automatically calculated 6 3 4 Searching There is currently no search feature but searching for a particular variable can be done using the browser s in built search Use the button in the top right of the screen to expand every module heading and use Ctrl f to search through the page Chapter 7 Code Management Tools This chapter will be of interest to people involved in the continuing maintenance of the PROCESS source code As stated elsewhere the source code is maintained by CCFE and resides in a Git repository on the CCFE servers 7 1 The Makefile In addition to its normal role for compilation the makefile named Makefile includes a number of utility functions that perform tasks such as automatic generation of the code documentation and the creation of a tar file containing the entire source code its documentation files and the input and output files This has proved to be of great benefit in keeping all of the data from a given run together for archival purposes 7 1 1 Compilation Compilation is trivially performed using the makefile Currently the available options are type the following on the command line make ARCH FUN CCFE Fusion Unix Network Intel Fortran ifort compiler make ARCH GFORT GNU Fortran compiler gfortran N B only versions 4 6 3 or above make ARCH JAC JET Analysis Cluster pgf95 compiler The Intel Fortran compiler is the default option so typing simply make will have t
68. achine configuration There are a large number of possible stellarator configurations As stated earlier the one chosen for the PROCESS model is based on the HELIcal Advanced Stellarator HELIAS concept in which all the coils resemble distorted non planar TF coils no helical coils or tokamak like PF coils are present The coil geometry is scaled from the HELIAS 5 B power plant design which is based on a five field period HELIAS configuration 3 5 2 1 Machine build Since a stellarator is inherently non axisymmetric the build of the PROCESS stellarator is defined in terms of the mean thicknesses of components The surface areas for the first wall blanket and shield components are scaled linearly with their effective minor radius from the plasma surface area calculation the area of a simple torus of circular cross section is 41 Ra hence the linear scaling with a The input parameter fhole may be used to specify the hole fraction to adjust the surface area to take account of ports and divertors for instance The volumes of the first wall etc are simply given by the product of their surface area and their mean thickness In contrast to tokamaks which in PROCESS are assumed to have a cylindrical external cryostat completely surrounding the fusion power core the stellarator model assumes that the external cryostat labelled as the outer vessel in Figure 3 10 is toroidal with a circular cross section Its cross section is assumed to be
69. ake a relatively long time to evaluate and the results are only used for diagnostic purposes no constraints are imposed at present to minimise doses for instance N B These models are currently not available in the present version of the code 3 8 1 Neutronics The neutronics module predicts the neutron flux spectra in the inboard and outboard first wall and blanket components The spectra are based on a simplified tokamak device that has a fixed ratio 1 5825 between the outboard blanket thickness and the inboard blanket thickness and are scaled according to the actual thickness of the outboard blanket This relatively limited single parameter approach is expected to be replaced by a more general method which should allow a more accurate portrayal of the device being modelled by PROCESS Chapter 3 Physics Engineering and Other Models 67 3 8 2 Activation and inventory information The code evaluates the consequences of exposing the power plant s materials to the calculated neutron fluxes subject to the limitations imposed by the neutronics module A library of neutron cross sections and decay data is used to calculate the total activity gamma ray dose rate and decay heat output due to the materials exposure to neutrons both at the end of the plant s life and at a time 100 years later These values are relevant to decommissioning and disposal studies and additional parameters that can be obtained from the nuclide inventory
70. allows for poloidally continuous single or double divertor configurations the periodicity of helical advanced stellarators leads to multiple X points with a corresponding chain of magnetic islands This island structure may be exploited by carefully placing divertor plates along the stochastic field lines naturally leading to a discontinuous divertor with the individual plates being placed in a complex 3 D geometry see Figure 3 11 Rather than trying to describe the complex physics with a two point scrape off layer model as is used for tokamaks the stellarator divertor model 36 is based on fundamental principles which relate the power crossing the separatrix with an effective wetted area on the divertor plates allowing the code to estimate the heat load delivered to the divertor A basic island divertor model is used which assumes diffusive cross field transport and high radiation at the X point The radiated power fraction in the scrape off layer is given by the input parameter f_rad This is in contrast to the method used for tokamaks in which the radiated power fraction is a calculated quantity A number of other input parameters may be used to modify the divertor model see the variable descriptor file for more details Chapter 3 Physics Engineering and Other Models 62 ANN MATA E Ari ANG Dom PAN i Figure 3 11 A five period HELIAS plasma specifically W7 X with island divertor plates shown in red 3 5 2 M
71. are based on the TITAN I EF coils which are two superconducting NbTi coils that provide the correct vertical field at the plasma centre The coil locations scale with the plasma major radius and TF coil radius along with the ohmic heating coils 3 6 5 Divertor The TITAN divertor concept uses three poloidal divertors which bear little resemblance to the typical tokamak toroidal divertor systems The code uses the TITAN divertor lifetime of one year to enable the divertor costs to be reasonable although the divertor surface area and therefore the cost per divertor is likely to be inaccurate 3 6 6 Code modifications As with the stellarator model the RFP model has been incorporated in such a way as to allow its simple removal again if required in the future All new routines are confined to the dedicated source file rfp f90 The tokamak relevant consistency equations in PROCESS see Section 2 4 are used without modification to ensure that the coil currents and the fields they produce are consistent with the plasma parameters 3 7 Inertial Fusion Energy Model As well as magnetic confinement devices PROCESS has the ability to model inertial fusion plants in which a laser or ion beam is used to ignite a target pellet containing the fusion fuel To activate the inertial fusion energy IFE coding it is necessary to create a file device dat containing the single character 3 in the first row in the working directory see Secti
72. at Culham on the code s arrival from ORNL in the early 1990s to improve this situation with the code being given a complete but careful upgrade routine by routine For many years this Fortran 77 code was used for systems code studies of various power plant scenarios and was modified from time to time by the addition of new and or improved models including machines based on the stellerator reversed field pinch and inertial confinement concepts In 2012 the code structure was revised again to allow it to benefit from modern software practices and the whole program was upgraded to Fortran 90 95 At the same time a number of useful code management utilities were added As with all active research codes PROCESS will continue to be developed into the future This User Guide is updated in parallel with the Fortran source code itself to ensure that the documentation remains consistent with the latest version of the code It is to be hoped that it will be of assistance to all users of PROCESS whether they are planning to modify or run the code or are simply trying to understand what the code aims to achieve 1 3 Layout of the User Guide The User Guide is divided into a small number of logically separate chapters each one of which provides specific information on a given topic It depends on the user s motive for referring to the manual as to which chapter will be the most useful although hopefully the style and structure adopted will allow one to b
73. at transport pumps Wall plug electrical power injection power htpmw pinjwp Figure 3 9 Schematic diagram of the flow of power beyond the fusion power core showing the origin of the primary and secondary thermal power and the electrical power balance within the plant Variable names are given in The input power contributions in green boxes originate in Figure 3 8 The primary high grade i e useable thermal power comprises the thermal power contributions from the first wall and blanket and possibly also those from the divertor and shield depending on the values of the switches iprimdiv and iprimshld as described in the previous sections The primary thermal power less any thermal power required to produce hydrogen in a hydrogen production plant see Section 3 4 is used to produce steam to turn the turbines thus generating the plant s gross electrical power with an efficiency given by input parameter etath The power lost via the turbines inefficiency escapes from the plant to the environment The electrical power required to operate the power plant itself is the so called recirculating electric power Any surplus is exported to the electricity grid as net electric power The recirculating power comprises the electrical power required to run all of the associated electrical systems surrounding the fusion power core plus the on site building services offices etc as shown in Figure 3
74. be no more than the value of variable tpkmax by turning on constraint equation no 39 with iteration variable no 63 ftpeak 3 3 4 Start up power requirements The minimum auxiliary power required during the start up ignition phase is calculated on the basis of a POPCON analysis Ignition is accessed via the so called Cordey Pass the path in plasma Chapter 3 Physics Engineering and Other Models 57 density temperature space which minimises the power requirement and the code ensures that there is sufficient auxiliary power to accommodate this In fact this calculation is very CPU intensive so the relevant routine is not called at present In practice the auxiliary power tends to exceed the minimum allowable value anyway without any need to constrain it to do so The auxiliary power reaching the plasma can be forced to be more than the minimum allowable value auxmin by turning on constraint equation no 40 with iteration variable no 64 fauxmn The value of auxmin is determined by the code if the start up model is activated otherwise it may be initialised via the input file 3 3 5 Plasma current ramp up time This calculation ensures that the plasma current ramp rate during start up is prevented from being too high as governed by the requirement to maintain plasma stability in l qy space see Section 3 1 9 1 3 3 6 Burn time The length of the burn time is calculated from the surplus volt seconds available from t
75. c machines so one should not believe the output values from these runs Unfortunately the stationary scan method sometimes though not always fails to help these cases since it will tend to keep starting the run at the same point Ill defined problems sometimes produce arithmetic errors for obscure reasons Though a great deal of work has been performed on the code to improve its standard there can be no guarantee that PROCESS is entirely bug free simply because of its large size Rarely then it may be that an unfeasible result indicates that the code has encountered a programming error although its precise location will be almost impossible to find by simply examining the output file It may be the case that the act of satisfying all the required constraints is impossible No machine can exist if the allowed operating regime is too restrictive or if two constraint equations require conflicting The constraint residues are the final values of c in the constraint equations see Section 2 4 The value sqsumsq is the square root of the sum of the squares of these residuals Chapter 4 Execution of the Code 78 parameter spaces In this case some relaxation of the requirements is needed for the code to produce a successful machine design 4 4 5 Hints The above sections should indicate that it is the complex interplay between the constraint equations and the iteration variables that determines whether the code will be successful
76. centred at the mean plasma major radius Chapter 3 Physics Engineering and Other Models 63 All items external to the fusion power core buildings turbines power conversion systems etc remain unchanged 3 5 2 2 Stellarator coils The stellarator coil model 37 46 combines scaling aspects based on the HELIAS 5 B design in combination with analytic inductance and field calculations The fully three dimensional shape of the coils is assumed to be fixed but the sizes of the coils are scaled from the HELIAS 5 B values to the geometrical values for the machine being modelled using fundamental physics and engineering principles The stellarator coils are assumed to be superconducting no resistive coil calculations are performed The critical field at the superconductor is calculated using circular approximations for the coils in the inductance and field calculations and the limit is enforced automatically Available superconductors are Nb3Sn isumattf 1 and NbTi isumattf 3 The winding pack cross section is rectangular for the stellarator coils rather than the complicated two step cross section assumed for tokamaks The coil thicknesses and most of the dimensions of the materials within the coil cross section are outputs from the model instead of being inputs as is the case for tokamaks see the variable descriptor file for details In addition certain iteration variables tfcth no 13 thkcas no 57
77. ching the first wall 3 1 4 Divertor The divertor provides a means of removing plasma reaching the scrape off layer and heavy ions that are ejected from the first wall By default two divertors are assumed in the PROCESS tokamak placed symmetrically above and below the plasma The principal outputs from the code are the divertor heat load used to determine its lifetime and its peak temperature The divertor is cooled either by gaseous helium or by pressurised water Switch snull controls the overall plasma configuration Setting snull 0 corresponds to an up down symmetric double null configuration the default while snul1 1 assumes a single null plasma with the divertor at the bottom of the machine The vertical build see Figure 3 3 and PF coil current scaling algorithms take the value of this switch into account although not the plasma geometry at present The Harrison Kukushkin Hotston divertor model 14 developed for ITER is used except for the case of spherical tokamaks or stellarators see later This is appropriate for conventional aspect ratio machines but care should be taken in inputting the divertor magnetics for this model and projections far from the ITER CDA machine parameters are likely to be unreliable 3 1 5 Blanket The blanket performs a number of tasks An incoming neutron from a deuterium tritium D T fusion reaction in the plasma loses energy in the blanket This energy is removed by the b
78. convergence 70 Note that in this method locally inactive inequality constraints c f 2 4 2 are not having any effect It should always be possible to find a solution that fulfills a 0 gt at A 9 if m Ta lt 0 A 10 a 0 Appendix A The Optimisation Solver Explained 113 In case the derivative is positive dflsa gt 0 an uphill search direction has been determined and the code stops with ifail 4 This typically only happens if the objective function or constraints are inconsistent with their own derivatives As the line search tries to determine the optimum of a one dimensional but fully non linear function a it creates a series of a values At each iteration l a quadratic local function q fullfilling the boundary conditions 0 P 0 0 0 A and aj_1 aj_1 is minimised where typically A 0 This leads to am 0 Ao 12 a amp 0 Aa z A 11 1 1 and minimising this gives ai A 12 Imin S a 9 0 Aaa i Powell then sets a7 min a amp min 0 1011 On each iteration the convergence of the line search is tested It is reached if a 0 lt 0 1A A 13 which assures that the change in the function is small in comparison to its derivative and 0 1 is a factor determined by experience If this criterion is successful the code exits the line search and updates all function evaluations As a modification to the original cod
79. d from the plasma Pure D He tokamak power plants do not include blankets because of the near absence of neutrons leaving the plasma and the fact that no tritium needs to be produced for fuel The contributions from all four of the above fusion reactions are included in the total fusion power production calculation The fusion reaction rates are calculated using the parametrizations in 12 integrated over the plasma profiles correctly with or without pedestals The fractional composition of the fuel ions D T and He is controlled using the three variables fdeut ftrit and fhe3 respectively M uel Np NT M3He particles m3 np fdeut fuel np ftrit nfe N3He fhe3 Nfuel PROCESS checks that fdeut ftrit fhe3 1 0 and stops with an error message otherwise 3 1 2 3 Plasma profiles By default NOT ANY MORE switch ipedestal 0 the plasma profiles are assumed to be parabolic i e they are of the form Density n p ny 1 py 3 10 Temperature T p To 1 pra 3 11 Current J r Jo 1 p 3 12 where p r a and a is the plasma minor radius This gives volume averaged values n no 1 an and line averaged values 7 ny y 1 an etc These volume and line averages are used throughout the code along with the profile indices a in the various physics models many of which are fits to Chapter 3 Physics Engineering and Other Models 31 theory based or empirical scalings Thus t
80. divertor or lost through holes or the heating current drive apparatus is assumed to be absorbed by the first wall The same fraction of the neutron power is assumed to pass into the first wall Of this neutron power a fraction 1 e2 4 is assumed to be absorbed in the first wall of thickness d given by the neutron decay length A in the first wall input parameter declfw As for the divertor the first wall coolant pump power is a fraction fpumpfw of the total thermal power absorbed by the first wall and the efficiency of the first wall coolant pump is etahtpfw 3 1 13 3 Blanket A fraction 1 exp dec1b1kt blnkoth of the neutron power incident on the blanket is assumed to be absorbed in the blanket where input parameter declblkt is the neutron decay length in the blanket This absorbed neutron power is multiplied by the energy multiplication factor emult to calculate its contribution to the thermal power within the blanket As for the other components the blanket coolant pump power is a fraction fpumpblkt of the total thermal power absorbed by the blanket and the efficiency of the blanket coolant pump is etahtpbl1kt 3 1 13 4 Shield A fraction 1 exp declshld shldoth of the neutron power incident on the shield is assumed to be absorbed in the shield where input parameter declshld is the neutron decay length in the shield As for the other components the shield coolant pump power is a fraction fpumpshld of the total ther
81. e we have added an adhoc fix that exits the line search in the case of a 0 gt 0 A 14 This has been added as experience have shown that VMCON typically does not converge in these situations but if it is forced to caculate a new search direction in this way it sometimes successfully finishes Note that this cannot force VMCON to converge on any false solutions as it only exits positively when the convergence criterion A 5 is fulfilled Typically the line search already converges after one iteration and therefore a 1 Hence the VMCON line search has an upper limit of maximally 10 iterations before it terminating with ifail 3 c f Table A 1 This is higher than Powell s original limit of 5 to avoid a few cases of early termination without a major effect on efficiency Within the line search VMCON also checks that the total number of function calls has not exceeded maxfev 100 If this is the case it exits with error code ifail 2 Both checks assure that the routine stops if it does not seem to be able to find a solution A 7 The Broyden Fletcher Goldfarb Shanno BFGS quasi Newton update VMCON uses a quasi Newtonian update the Broyden Fletcher Goldfarb Shanno update in the approximation of the Hessian of the Lagrange function This means it is applicable to all continously differentialbe objective and constraint functions Note that due to the constraints it is not actually necessary for the H
82. e CONVXC where the iteration process itself is performed Otherwise the numerical procedure cannot adjust the value as it requires and the program will fail 5 3 Other Global Variables This type of variable embraces all those present in the modules in global_variables f90 and some others elsewhere which do not need to be given initial values or to be input as they are calculated within the code These should be added to the code in the following way 1 Choose the most relevant module usually one of those in source file global_variables f90 Keeping everything in alphabetical order add a declaration statement for the new variable specifying the initial value 0 0DO and a correctly formatted comment line to describe the variable copying the examples already present 2 Ensure that all the modules that use the new variable reference the relevant module via the Fortran use statement 5 4 Constraint Equations Constraint equations see Section 2 4 are added to PROCESS in the following way 1 Increment the parameter ipeqns in module numerics in source file numerics f90 to accommodate the new constraint 2 Add an additional line to the initialisation of the array icc in module numerics in source file numerics f90 3 Assign a description of the new constraint to the relevant element of array lablcc in module numerics in source file numerics f90 Chapter 5 Inclusion of New Models Additional Variables and Equations 81
83. e deuterium tritium reaction D T tHe n 17 6 MeV 3 6 Chapter 3 Physics Engineering and Other Models 30 20 of the energy produced is given to the alpha particles He which remain but c f falpha within the plasma and thermalise slow down due to collisions thus heating the plasma The remaining 80 is carried away by the neutrons which deposit their energy within the blanket and shield PROCESS can also model D He power plants which utilise the following primary fusion reaction D He gt tHe p 18 3 MeV 3 7 The fusion reaction rate is significantly different to that for D T fusion and the power flow from the plasma is modified since charged particles are produced rather than neutrons Because only charged particles which remain in the plasma are produced by this reaction the whole of the fusion power is used to heat the plasma Useful energy is extracted from the plasma since the radiation power produced is very high and this can be converted to electricity in a number of ways Since the temperature required to ignite the D He reaction is considerably higher than that for D T it is necessary to take into account the following D D reactions which have significant reaction rates at such temperatures D D gt He n 3 27MeV 3 8 D D T p 4 03MeV 3 9 Also as tritium is produced by the latter reaction D T fusion is also possible As a result there is still a small amount of neutron power extracte
84. e f c Vef Vee e j 0 nfev 1 Solve QSP ipa Y calculate AY Vel h l i test convergence O MA a Evaluate f c e test convergence e calculate a ile calculate A set a 1 update x evaluate f c nfev il il 1 evaluate f c Vef Vac calculate VgL BFGS update Figure A 2 described in Table This is the flow interpretation of the successful ifail 4 1 chart of the VMCON optimisation solver HA ifail 0 l ifail 5 Rl ifail 6 l ifail 1 gt O ifail 4 ifail 3 The criteria for and the 1 and unsuccessful fail 1 return parameters are Appendix A The Optimisation Solver Explained 111 ifail Description Meaning Recommendation 0 VMCON Improper The input parameters to This needs to be fixed input parameters the solver are wrong on the developer side e g negative number of and should only occur iteration variables in the test phase of new modules 1 VMCON Normal VMCON has found Test return a solution that fulfills whether the solution is the necessary conditions a global solution by within the specified using different starting error tolerances c f eq parameters A 5 2 Too many function
85. ection of functions and lists used by plot_proc py RADIAL_BUILD A list of radial build variables VERTICAL_BUILD A list of vertical build variables FILL_COLS A list of plotting colours For all of the functions below the arguments are axis Matplotlib axis object to plot to mfile_data MFILE data object MFile scan Scan number to plot plot_plasma axis mfile_data scan Function to plot plasma plot_machine_pic axis mfile_data scan Function to plot machine build plot_tf_coils axis mfile_data scan Function to plot the TF coils plot_pf_coils axis mfile_data scan Function to plot the PF coils plot_geometry_info axis mfile_data scan Function to plot the geometry info block plot_physics_info axis mfile_data scan Function to plot the physics info block plot_magnetics_info axis mfile_data scan Function to plot the magnetics info block plot_power_info axis mfile_data scan Function to plot the power info block plot_current_drive_info axis mfile_data scan Function to plot the current drive info block plot_geometry_info axis mfile_data scan Function to plot the geometry info block 6 3 User Interface The user interface is still being developed but currently allows for viewing and editing of IN DAT files in a web browser It can be found in the utilities gui directory 6 3 1 Launching The interface uses Django for its web framework Currently it can only be launched by running the Django development server locall
86. ed radius defining the core region imprad_model 1 only Only the impurity and synchrotron radiation from the core region affects the confinement scaling but see iradloss below while the power flowing into the divertor is assumed to exclude all radiation power Add radiation power flow diagram as on p 26 logbook24 New overall power flow diagram should elucidate this Constraint equation no 17 with iteration variable no 28 fradpwr ensures that the calculated total radiation power does not exceed the total power available that can be converted to radiation i e the sum of the fusion alpha power other charged particle fusion power auxiliary injected power and the ohmic power This constraint should always be turned on Switch iradloss may be used to exclude iradloss 1 default or include iradloss 0 the core radiation power in the transport power used in the confinement time and power balance calculations see Section 3 1 2 10 Chapter 3 Physics Engineering and Other Models 34 3 1 2 7 Plasma current scaling laws A number of plasma current scaling laws exploiting the inverse relationship between plasma current and edge safety factor qy 15 are available in PROCESS These are calculated in routine CULCUR which is called by PHYSICS Flag icurr must be set to the relevant value as follows icurr 1 Peng analytic fit icurr 2 Peng double null divertor scaling ST 2 icurr 3 Simple
87. ehensive description of the model please provide a full list of references A list of all inputs and outputs descriptions default input values allowed ranges units If possible please cross reference any input output variables to existing global variables listed in the variable descriptor file see Section 2 2 A description of any new numerics requirements input parameters iteration variables constraint equations figures of merit etc e A definition of any pre requisites A description of any side effects Any available test data code examples or test programs in Fortran or other language would be useful Chapter 6 Utility Programs A number of Python utilities for PROCESS are available which allow the user to perform a number of useful actions for instance to modify the input file IN DAT run PROCESS until a feasible solution is found or to extract and plot data from the PROCESS output All utilities are available from pknight process bin utilities For PROCESS users only the Python executables described in Section 6 1 are relevant For anyone interested in modifying the existing code or developing new Python utilities the PROCESS Python libraries are described in Section 6 2 All executables are using Python library functions either from the publicly available numpy scipy and matplotlib libraries or the PROCESS Python libraries documented in Section 6 2 To use the PROCESS Python
88. ement ipfloc j assigned to it Input parameter ngrp should be set to the number of groups and ncls j should be assigned the number of coils in each group which should be 2 in each case Chapter 3 Physics Engineering and Other Models 46 In the following all variables are defined in the variable descriptor file vardes htm1 The values for rpf1 rpf2 zref j and routr should be adjusted by the user to locate the PF coils accurately The three possible values of ipfloc j correspond to the following PF coil positions Redo taking into account snull and other recent changes e g rclsnorm ipfloc j 1 PF coils are placed above the central solenoid one group only R rohc rpfi Z hmax ohhghf 0 1 0 5 hmax x 1 0D0 ohhghf tfcth 0 1 ipfloc j 2 PF coils are placed above the TF coils one group only R rmajor rpf2 triang rminor Z hmax tfcth 0 86 ipfloc j 3 PF coils are placed radially outside the TF coils any number of groups R Z rminor zref j rtot tfthko 2 0D0 routr 3 1 8 2 PF coil currents The PF coil currents are calculated in routine EFC and vary as a function of time during the tokamak operation as indicated in Figure 3 6 3 1 8 3 PF coil resistance The PF coils can be either resistive or superconducting This is determined from the value of ipfres If ipfres 0 the PF coils and the central solenoid are assumed to be superconducting
89. ensity 1 00D 6 1 000DO 8 fbeta f value for 3 limit equation 6 0 001DO 1 000DO 9 fdene f value for density limit equation 5 0 001D0 1 000D0 10 hfact confinement time H factor 0 100D0 3 000D0 11 pheat heating power not used for current drive 0 001D0 1 000D3 12 oacdcp overall current density in TF coil inboard leg 1 000D5 1 500D8 13 tfcth TF coil inboard leg thickness 1 000D0 5 000D0 14 fwalld f value for wall load limit equation 8 0 001DO 1 000DO 15 fvs f value for volt second limit equation 12 0 001D0 1 000DO 16 ohcth central solenoid thickness 0 001D0 1 000D2 17 tdwell dwell time 0 100D0 1 000D8 18 la edge safety factor 2 000D0 100 0DO 19 enbeam neutral beam energy 1 000D0 1 000D6 20 tcpav average resistive TF coil temperature 40 00DO 1 000D3 21 ftburn f value for burn time limit equation 13 0 001D0 1 000D0 22 tbrnmn minimum burn time 0 001DO 1 000D6 23 fcoolcp coolant fraction of resistive T F coil 0 100D0 0 500D0 24 cdtfleg TF coil leg overall current density 1 000D4 1 000D8 25 fpnetel f value for net electric power limit equation 16 0 001D0 1 000DO 26 ffuspow f value for fusion power limit equation 9 0 001DO 1 000DO 27 fhldiv f value for divertor heat load limit equation 18 0 001D0 1 000D0 28 fradpwr f value for radiation power limit equation 17 0 001D0 1 000D0 29 bore machine bore 0 100D0 10 00D0 30 fmva f value for MVA limit equation 19 0 010D0
90. erse quadrature Use ITER fusion power calculations Use input values for KAPPA and TRIANG Plasma elongation Edge safety factor N B active iteration variable 3 N B active iteration variable 7 Burn time Electron temperature Plasma triangularity Use current drive Use ITER neutral beam current drive Artificially enhance efficiency 115 Appendix B Non optimisation Input File 116 Divertor parameters ANGINC 0 262 PRN1 0 285 Machine build BORE 0 12 DHCTH 0 1 GAPOH 0 08 TFCTH 0 9 DDWI 0 07 SHLDITH 0 69 BLNKITH 0 115 FWITH 0 035 SCRAPLI 0 14 SCRAPLO 0 15 FWOTH 0 035 BLNKOTH 0 235 SHLDOTH 1 05 GAPOMIN 0 21 VGAPTF 0 Angle of incidence of field lines on plate Density ratio Machine bore central solenoid thickness Inboard gap Inboard TF coil leg thickness Vacuum vessel thickness Inboard shield thickness Inboard blanket thickness Inboard first wall thickness Inboard scrape off layer thickness Outboard scrape off layer thickness Outboard first wall thickness Outboard blanket thickness Outboard shield thickness Outboard gap Vertical gap First wall blanket shield parameters LBLNKT 0 DENSTL 7800 TF coil parameters DACDCP 1 4e7 ITFSUP 1 RIPMAX 5 PF coil parameters NGRP 3 IPFLOC 1 2 3 NCLS 2 2 2 1 COHEOF 1 85e7 FCOHBOP 0 9 ROUTR 1 5 ZREF 3
91. es of Merit evo soes eee ras Pa ee Re Ba eee ee we a es 81 5 6 Scanning Variables ee 81 5 7 Submission of New Models e 82 6_ Utility Programs 83 6 1 Executables i ls is a da ee eM a a Pe PS eee ee 83 6 1 1 write newindat _py 2 2 0 ee 6 1 2 write_constraints py 2 te khi ta i a Eaa 6 1 3 TUD process pP lt ete rriar Re ee ee a 6 1 4 bulld indet py ses 4 is pa a ea e e ee a Aa 6 1 5 make plot d t PY sa aoma a a a e hae be a E a a ee 6 1 6 Pl t PrO Psae e 244s a ee OA aa Swe he Ea Pe e A ar 6r pl t sSWE PPY ws eek a e a a ae i a ps ee Ro e a ee a we 6 1 8 plot mfile sweep py eoo a 6 1 9 diagnose_process py o oo oo ee 6 1 10 2D aanp oo e a A A eRe e a A SE OL Ato Dy a a a E E a a Ee a eee E 6 1 12 create dicts py 2 ee 6 2 Libraries socos s esaa sos s eca Re ea Rae RE DADE eek ee eH 6 2 1 in dat py 2544 ra bebe ee be ba aS ERED ORES SES Oh ae a eS 6 2 2 mfilevpy oe na 4 sb beck e SPE Raa i ERA YARED Se eee Rea ees 6 2 3 process funcs py eee ka ea RR aE ee ee 6 2 4 process_config py o ooa a 6 2 5 process_dicts py gt sa car o ocara sa ee 6 2 6 a_to_b_config py sooo ee 6 2 7 proc_plot_func _py ooa a a 6 3 User Interface s ss
92. escription type ixc variables 1 plasma beta consistency C 5 2 global power balance C 10 1 2 3 4 6 11 3 ion power balance C 10 1 2 3 4 6 11 4 electron power balance C 10 1 2 3 4 6 11 5 density upper limit L 9 1 2 3 4 5 6 6 epsilon beta poloidal upper limit L 8 1 2 3 4 6 7 beam ion density NBI C 7 8 neutron wall load upper limit L 14 1 2 3 4 6 9 fusion power upper limit L 26 1 2 3 4 6 10 toroidal field 1 R consistency C 12 1 2 3 13 11 radial build consistency C 3 1 13 16 29 42 61 12 volt second capability lower limit L 15 1 2 3 13 burn time lower limit PULSE L 21 1 16 17 22 29 42 44 61 14 beam energy NBI C 19 1 2 3 6 15 UNUSED 16 net electric power lower limit L 25 1 2 3 17 radiation power upper limit L 28 18 divertor heat load upper limit L 27 19 MVA upper limit L 30 20 neutral beam tangency radius upper limit NBI L 33 31 3 13 21 minor radius lower limit L 32 22 divertor collisionality upper limit L 34 43 23 UNUSED 24 Beta upper limit also beta limit in stellarators L 36 1 2 3 4 6 18 25 peak toroidal field upper limit L 35 3 13 29 26 central solenoid current density at End of Flat top upper limit L 38 37 41 12 27 central solenoid current density at Beginning of Pulse upper limit L 39 37 41 12 28 fusion gain Q lower limit L 45 47 40 29 inboard radial build specified value C 3 1 13 16 29 42 61 30 injection power upper limit L 46 47 11 31 TF coil case stress upper limit SCTF L 48 56 57 58
93. essian of the solution to be positive definite even though this is essential for the convergence of the algorithm In quasi Newtonian methods the identity matrix I is often chosen as an initial estimate of the Hessian because of its positive definiteness In some cases it can be helpful to chose a constant multiple of the 6In the actual code a calpha and a alphaxQ1 1 Appendix A The Optimisation Solver Explained 114 identity matrix instead The BGFS update 7 is one way of revising the initial Hessian approximation using the update of the iteration variable vector E x gri A 15 and the update of the Jacobian of the Lagrange function y VaL X Ve L x A A 16 Note that unless a 1 in the line search 4 6 To assure the positive definiteness of B Powell 6 suggested a variation of the standard formalism that uses y instead of y n 07 1 0 BE A 17 with E a 1 Ely gt 0 2 BE ms Ty lt 0 2 B to calculate a new approximation of the Hessian B TB T dB ee A 19 EBE En Using the modified version of the BFGS update as suggested by Powell furthermore assures superlinear convergence even if the true Hessian is indefinite 75 A 8 Symbols In the previous sections the following conventions have been assumed 2 6 y and 7 are n dimensional vectors where n is the number of iteration variables c A 4 are m dimensional vectors where m is the total
94. etting up the code to model a new machine and finally an attempt is made to indicate and solve the problems that the user will face whilst trying to achieve a feasible solution Please note There is now a prototype Graphical User Interface GUI for people to use to run PROCESS see Section 6 3 for details 4 1 The Input File The input file IN DAT is used to change the values of the physics engineering and other code parameters from their default values and to set up the numerics constraint equations iteration variables etc required to define the problem to be solved 4 1 1 Tokamak stellarator RFP or IFE In addition to the main input file IN DAT a second input file device dat is used to signal to the code whether a tokamak stellarator reversed field pinch or inertial fusion enery plant is to be modelled If the file does not exist in the working directory the standard tokamak model is used File device dat should contain a single character in the first line which is interpreted as follows use tokamak model use stellarator model use reversed field pinch model use inertial fusion energy model Nro 4 1 2 File structure The input file comprises a number of lines reminiscent of the Fortran NAMELIST format used by some programs to read in data Except for comment lines that start with a character each line is of the form variable value 69 Chapter 4 Execution of the Code 70 where
95. ever incompatible with the code s iterative approach to solving the optimisation problem since this requires repeated evaluation of the same large number of expressions This is not to say that the models employed by the code are oversimplified in general they represent good numerical estimates of present theoretical understanding or are fits to experimental data PROCESS provides a useful overall description of how a conceptual and feasible power plant may look Chapter 1 Introduction 10 1 2 History PROCESS is derived from several earlier systems codes but is largely based on the TETRA Tokamak Engineering Test Reactor Analysis code 1 and its descendant STORAC Spherical TOrus Reactor Analysis Code 2 which includes routines relevant to the spherical tokamak class of machines These codes and much of the original version of PROCESS itself were written by personnel at Oak Ridge National Laboratory in Tennessee USA with contributions from a number of other laboratories in the USA In addition many of the mathematical routines have been taken from a number of different well established source libraries Since the code is descended from such a wide range of sources its structure was initially not ideal from the programmer s viewpoint Non standard practices and inconsistent layout within the code led to difficulties in modifying interpreting and indeed running the code A great deal of effort was therefore expended
96. f all iteration variables update_ixc_bounds wdir Updates the lower and upper bounds in DICT_IXC_BOUNDS from IN DAT get_variable_range itervars factor wdir Returns the lower and upper bounds of the variable range for each iteration variable itervars string list of all iteration variable names factor defines the variation range for non f values by setting them to value factor and value factor respectively while taking their PROCESS bounds into account For f values the allowed range is equal to their PROCESS bounds check_logfile logfile process log Checks the log file of the PROCESS output Stops if an error occurred that needs to be fixed before rerunning process_stopped logfile process log Checks the PROCESS logfile whether it has prematurely stopped process_warnings logfile process log Checks the PROCESS logfile whether any warnings have occurred mfile_exists Checks whether MFILE DAT exists Chapter 6 Utility Programs 94 no_unfeasible_mfile wdir Returns the number of unfeasible points in a scan in MFILE DAT no_unfeasible_outdat wdir Returns the number of unfeasible points in a scan in OUT DAT vary_iteration_variables itervars lbs ubs Changes the iteration variables in IN DAT within given bounds itervars string list of all iteration variable names lbs float list of lower bounds for variables ubs float list of upper bounds for variables
97. f 0 8 Amps per Watt of power injected into the plasma the coding for this model is therefore trivial The wall plug to injector efficiency is set using input parameter etaof which has a default value of 0 5 and the unit cost is set using input parameter ucof The default value for ucof is 3 3 per Watt of injected power The bootstrap fraction is assumed to be zero Plasma ignition and additional plasma heating using auxiliary power are treated as for tokamaks 3 6 2 TF coils The TF coils for the RFP option are derived from the TITAN II coil set which uses circular copper coils The radial thickness is set using tfcth as usual but the toroidal thickness may also be set using iteration variable no 77 tftort This is constrained to be no larger than is geometrically possible using constraint equation no 47 with iteration variable no 76 frfptf Chapter 3 Physics Engineering and Other Models 65 3 6 3 Ohmic heating coils The TITAN I ohmic heating coil locations currents etc are assumed These comprise 14 copper coils with currents swinging from positive to negative during the plasma start up period and then decaying back to zero To account for different plasma geometries and currents the ohmic heating coil locations relative to the plasma centre scale with the TF coil radius and with the plasma major radius and the current per turn scales linearly with the plasma current 3 6 4 EF coils The Equilibrium Field coils
98. f the return parameter if ail are described and interpreted in Table A 1 A 5 The Quadratic Subproblem QSP Within sequential quadratic programming the complex nonlinear problem is broken down into solving a sequence of local quadratic subproblems with linear constraints This is based on the assumption that locally the problem is well approximated by a second order Taylor expansion of the Lagrange function Hence the local quadratic subproblem is described by l 1 E minimise Q 6 f a771 9 Vz f x Va La AIH A 6a subject to T Vpci f7 e 771 0 i 1 k A 6b and T Visca c t gt 0 i k4 1 m A 6c where 6 x xf the index j 1 indicates the parameter values of the previous iteration and VirLl a J is the Hessian of the Lagrange function The solution of the QSP 6 describes the change of the current iteration variable vector that minimises the local approximation of the problem To assure convergence even from bad starting points it is not directly used to update the iteration 2 www hsl rl ac uk 3This should not be confused with Powell s algorithm 69 which solves a multidimensional unconstrained minimisation problem without derivatives Note within the VMCON routine ifail is called info 5Note j is called ngp in the VMCON routine Appendix A The Optimisation Solver Explained 110 adhoc fix Setup e initialise B e evaluat
99. figures of merito 21 2 5 List of scanning variables ooo ee 22 2 6 Summary of numerics modules 000 ee ee 22 2 7 Summary of physics modules oo a 23 2 8 Summary of engineering modules 2 0 0000 ee ee 23 2 9 Summary of other modules 0 000000 eee ee 24 3 1 List of available energy confinement scaling A 35 3 2 List of available L H power threshold scalings o e 38 3 3 Summary of blanket material scenarios e ee 42 3 4 PROCESS switches for spherical tokamaks 1 2 0 02 22 o 56 3 5 Variables used in the hydrogen plant model 0 e 58 A l Summary of the description and meaning of the VMCON return parameters ifail 111 Chapter 1 Introduction 1 1 Rationale During the course of studies into a proposed fusion power plant there may be times when questions of the following type arise Are the machine s physics and engineering parameters consistent with one another Which machine of a given size and shape produces the cheapest electricity What is the effect of a more optimistic limit on the maximum plasma density on the amount of auxiliary power required Questions such as these are extremely difficult to answer since the large number of parameters involved are highly dependent on one another Fortunately computer programs have been written to address these issues and PROCESS is one of them Suppose that an outline po
100. filling the KKT conditions are describing the derivative of the objective function with respect to the constraint equation k and are therefore a measure of how much the objective function changes with respect to each constraint In the special case of a continuously differentiable convex objective function f x and equality constraints as well as affine inequality constraints these KKT conditions are also sufficient for a global optimum The PROCESS optimisation solver has been designed to converge on the KKT conditions but does not test whether these are sufficient for a global optimum It is therefore crucial that the user verifies that a global optimum has been found Furthermore these conditions and therefore the solver assume that both the objective function and constraints are at least first order continuously partially differential i e that their first order partial derivatives are all continuous functions This might not always be the case in PROCESS and is a potential source of errors Please note that what is called figure of merit in PROCESS is called objective function in the mathematical optimisation context Hence both names are used equivalently in this document Appendix A The Optimisation Solver Explained 109 A 3 Sequential Quadratic Programming SQP Based on the Lagrange method sequential also successive or recursive quadratic programming is the most efficient method to numerically solve constrained nonlinear optim
101. find a self consistent set of device parameters that satisfy all of the system s constraint equations see Section 2 4 PROCESS is organised in a standard equation solver format to enable this task to be performed efficiently The physics and engineering routines together serve as a function evaluator providing the information used in the solution of the constraints The numerical modules present in PROCESS perform the iteration required and also incorporate the option to maximise or minimise a given figure of merit see Section 2 6 2 1 Equation Solvers PROCESS contains two non linear equation solver packages which reflect the two major modes of operation available Each of these has its own uses as is now discussed 2 1 1 Non optimisation mode The first of the two equation solvers present in PROCESS is the non optimisation package HYBRD 3 4 Formally HYBRD finds a zero of a system of N non linear functions in N variables This means simply that N variables power plant parameters are iterated by PROCESS in such a way as to solve a set of N equations physics or engineering laws i e a set of self consistent power plant parameters is found This is useful for performing benchmark comparisons when the device size is kept fixed and one only wishes to find calculated stresses beta values fusion powers etc A flow diagram of PROCESS in non optimisation mode is shown in Figure 2 1 2 1 2 Optimisation
102. g Berlin 1978 M Avriel Nonlinear Programming Analysis and Methods Dover Publications Inc Mineola NY 2003 P J Knight Surface Area and Volume Calculations for Toroidal Shells CCFE internal note T amp M PKNIGHT PROCESS 009 May 2013 H Zohm et al On the Physics Guidelines for a Tokamak DEMO FTP 3 3 Proc IAEA Fusion Energy Conference October 2012 San Diego T Hartmann and H Zohm Towards a Physics Design Guidelines for a DEMO Tokamak Document EFDA Report March 2012 Activity_3_Physics_Design_Guidelines_2L8QVN_v1_0 1 pdf P J Knight CCFE Logbook F MI PJK LOGBOOK14 pp 41 43 H S Bosch and G M Hale Improved Formulas for Fusion Cross sections and Thermal Reactivities Nuclear Fusion 32 1992 611 J Johner Helios A Zero Dimensional Tool for Next Step and Reactor Studies Fusion Science and Technology 59 2011 308 349 N A Uckan and ITER Physics Group ITER Physics Design Guidelines 1989 ITER Documentation Series No 10 IAEA ITER DS 10 1990 T C Hender M K Bevir M Cox R J Hastie P J Knight C N Lashmore Davies B Lloyd G P Maddison A W Morris M R O Brien M F Turner and H R Wilson Physics Assessment for the European Reactor Study AEA Fusion Report AEA FUS 172 1992 102 Chapter 8 Acknowledgements amp Bibliography 103 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
103. gain 1 000D0 500 0DO 84 chrad radius of IFE chamber 0 100D0 20 00D0 85 pdrive IFE driver power reaching target 1 000D6 2 000D8 86 frrmax f value for maximum IFE repetition rate equation 50 0 001DO 1 000DO 87 helecmw electrical power required for hydrogen production 1 000D0 4 000D3 88 hthermmw thermal power required for hydrogen production 1 000D0 4 000D3 89 ftbr f value for tritium breeding ratio limit equation 52 0 001DO 1 000D0 90 blbuith inboard blanket breeding unit thickness 0 001D0 2 000D0 91 blbuoth outboard blanket breeding unit thickness 0 001D0 2 000D0 92 fflutf f value for fast neutron fluence on TF coil equation 53 0 001D0 1 000DO 93 shldith inboard shield thickness 0 001D0 10 00D0 94 shldoth outboard shield thickness 0 001D0 10 00D0 95 fptfnuc f value for TF coil nuclear heating limit equation 54 0 001DO 1 000D0 96 fvvhe f value for vessel He concentration limit equation 55 0 001D0 1 000D0 97 fpsepr f value for Pseparatrix major limit equation 56 0 001D0 1 000DO 98 1i6enrich lithium 6 enrichment percentage blktmodel 1 0 001DO 100 0DO 99 ftftort OBSOLETE f value for TF coil toroidal thickness lower limit eqn 57 0 001D0 1 000DO 100 tfthko OBSOLETE f value for TF coil radial thickness lower limit eqn 58 0 001DO 1 000D0 101 prp ratio of TF coil radial plate area to winding pack area 1 00D 6 0 010D0 102 fimpvar impurity fraction of element impva
104. h the objective function f x and the constraints ci x are nonlinear functions of the n dimensional vector of variables with bounds Q In this context all a Q that fulfill the constraints c x are called feasible They describe the allowed space in which we are trying to optimise the objective function f x Note that any maximisation problem can be written as a minimisation by using f x f a and that any equality constraint c a a can be rewritten as c a c w a 0 Any inequality constraint can therefore be rearranged analogously to fit the form described in eq A 1cl 106 Appendix A The Optimisation Solver Explained Figure A 1 Illustration of Lagrange Multiplier Method credit Wikipedia showing two contour lines of the objective function f x y d dark blue dashed lines and the nonlinear constraint g x y c red solid line as well as their gradients blue and red arrows at various positions including the constrained optimum light blue and orange arrows 107 Appendix A The Optimisation Solver Explained 108 A 2 The Lagrange Method The general nonlinear programming problem can be solved mathematically using Lagrange s method It assumes that the constraints cannot be used to explicitly reduce the parameter space of the iteration variables as it is typically the case for non linear constraints and objective functions and is therefore a powerful method applicable to a general clas
105. hat combine into a single centrepost at the centre of the machine The centrepost is constructed from copper as are the outboard TF coil sections and is tapered lengthways so that it is narrowest at the midplane of the device Routine CNTRPST calculates various parameters relevant to the centrepost including the pump pressure maximum temperature and pipe radius and these may be limited using constraint equations 43 to 46 if required Equation 43 is a consistency equation for the average centrepost temperature Equation 44 can be used to limit the peak centrepost temperature to a maximum value ptempalw using iteration variable no 68 fptemp Equation 45 can be used to force a lower limit to the edge safety factor qlim see below using iteration variable no 71 fq Equation 46 can be used to apply an upper limit to the ratio of plasma current to TF coil rod current using iteration variable no 72 fipir 3 A gaseous divertor model is used and a simple divertor heat load calculation is employed rather than the more complex divertor model assumed for conventional aspect ratio tokamaks 4 A simple PF coil current scaling algorithm is available for use with the ST option 5 The plasma shaping terms elongation and triangularity can be calculated directly given the aspect ratio using ishape 1 see Section 3 1 2 1 This setting also scales the lower limit 2 for the edge safety factor for use with constraint equatio
106. he OH PF coil system during the plasma burn phase after the flux required during the plasma start up is taken into account A minimum burn time can be enforced via constraint equation no 13 and iteration variable no 21 ftburn 3 3 7 Thermal storage During every cycle there is a period when no fusion power is produced The net electric output from the plant must however be maintained and this is achieved using thermal storage There are three types of thermal storage available within PROCESS and the value of switch istore determines which is to be used If istore 1 the default option 1 of Ref 33 is assumed which utilises the thermal storage inherent in the machine s steam cycle equipment This should be used if the machine down time is less than 100 seconds If istore 2 option 2 of Ref 33 is assumed which uses the same method as before but augments it with an additional boiler This may be used for machine down times of up to 300 seconds Finally if istore 3 a large stainless steel block acts as the thermal storage medium 3 4 Hydrogen Production Facility Fusion power plants have been mooted as a means of producing hydrogen for use in fuel cells for cars for instance PROCESS includes options to enable the plant to produce hydrogen using a number of different processes To include the production of hydrogen by the power plant it is necessary to set the switch ihplant as follows ihplant 0 No
107. he plasma model in PROCESS may be described as 5 D The relevant profile index variables are alphan alphat and alphaj respectively see Section 3 1 2 8 If ipedestal is set to 1 however the density and temperature profiles may include a pedestal using the forms specified in 13 5 yan Nped no Nped p r 0 lt pP lt Pped n density np Ppedn 3 13 Nsep Nped sen E Pped n lt p lt 1 Pped n per oe Ted To Tred Ul Br 0 lt p lt Pped T temperature T p Pped T 3 14 1 Tsep Tred Tsep Pped T lt P lt 1 Pped T Subscripts 0 ped and sep denote values at the centre p 0 the pedestal p Ppea and the separatrix p 1 respectively The density and temperature peaking parameters a and ar as well as the second exponent Gr input parameter tbeta not to be confused with the plasma beta in the temperature profile can be chosen by the user as can the pedestal heights and the values at the separatrix neped nesep for the electron density and teped tesep for the electron temperature the ion equivalents are scaled from the electron values by the ratio of the volume averaged values The density at the centre is given by 1 no 3077 3 n 1 An sep l On 2 Pped n Poed Pped n Nped a EN Qn 1 T Pped n an 3 15 where n is the volume averaged density The temperature at the centre is given by 1 To Tped Y
108. he same effect as typing make ARCH FUN The code is almost trivial to port to new architectures by adding extra stanzas to the makefile as required To force a full recompilation type make clean N B This will remove without prompting all backup files as well as certain other files from the working directory Extra run time diagnostics array bound checking etc is turned on by default at present the code is sufficiently quick to run that the performance penalty is barely noticeable However this can be turned off beware results can change by adding DEBUG NO to the relevant command above i e type make ARCH DEBUG N0 N B there must be no spaces either side of the characters in any of the above commands 99 Chapter 7 Code Management Tools 100 7 1 2 Archiving utilities The makefile can be used in a number of ways to pack the various file sets together into a single compressed tar file for ease of portability and archiving e make tar Typing this command produces a file process tar gz that contains all of the source files utility programs and documentation files necessary to run the program from scratch on a new machine or in a new directory Note that the input files IN DAT and device dat are not included This is useful for transferring new copies of source files etc into an existing directory already containing a previous PROCESS run as the pre existing customised input files will not be over
109. hydrogen production default ihplant 1 Hydrogen production by low temperature electrolysis ihplant 2 Hydrogen production by endothermic high temperature electrolysis Il w ihplant Hydrogen production by exothermic high temperature electrolysis Chapter 3 Physics Engineering and Other Models 58 ihplant 4 Hydrogen production by thermo chemical processes Table 3 5 describes the additional options available for each of the types of hydrogen production given above The different processes use either electrical power or thermal power directly so the required inputs differ Variable helecmw iteration variable no 87 is the electrical power in MW required for hydrogen production while hthermmw iteration variable no 88 is the thermal power required Note that hthermmw must not be used as an iteration variable if ihplant 4 as it will be calculated from the required electrical power instead Similarly helecmw must not be used as an iteration variable if ihplant 4 The efficiency variables given in Table 3 5 are all input parameters and are the factors hydrogen plant option helecmw hthermmw efficiency variable ihplant 1 input Zero etahlte ihplant 2 input calculated etahten ihplant 3 input calculated etahtex ihplant 4 Zero input etahth Table 3 5 Summary of the variables in PROCESS that relate to the different hydrogen plant processes to be used to conver
110. ics Engineering and Other Models 64 3 6 1 2 Density limit No density limit is explicitly coded for RFPs other than by simply constraining the upper bound of the electron density variable dene iteration variable 6 3 6 1 3 Tz scaling law One confinement time scaling law relevant to RFPs is present within PROCESS The value of switch isc determines the scaling to be used in the plasma energy balance calculation Tr TITAN RFP 47 isc 25 0 05 a I MA 3 6 1 4 F plot Much of the RFP physics is derived from the characteristic F 0 plot where F Bg a Bg O Bo a Bg and Bg is the average value of the toroidal field over the plasma cross section Given a value of the pinch parameter O the corresponding value of the reversal parameter F may be read from the F 0 plot and from these the plasma current and the current in the TF coils may be obtained using Hol Bola Ho lTEFC Bg a a the second of these assumes that By a is approximately equal to the vacuum toroidal field at the plasma centre The pinch parameter O is set using iteration variable no 78 rfpth The corresponding value of the reversal parameter F rfpf is calculated using routine FTHETA F is constrained to be negative using constraint equation no 49 with f value frfpf iteration variable no 80 3 6 1 5 Current drive The RFP oscillating field current drive option is turned on by setting iefrf 9 with a fixed efficiency o
111. ile 1 see Section 3 1 2 8 Limiting e p To apply a limit to the value of 3 where e a R is the inverse aspect ratio constraint equation no 6 should be turned on with iteration variable no 8 fbeta The limiting value of 3 should be set using input parameter epbetmax 3 1 2 5 Density limits Several density limit models 15 are available in PROCESS These are calculated in routine CULDLM which is called by PHYSICS To enforce any of these limits turn on constraint equation no 5 with iteration variable no 9 fdene In addition switch idensl must be set to the relevant value as follows idensl 1 ASDEX model idensl 2 Borrass model for ITER I idensl 3 Borrass model for ITER II idensl 4 JET edge radiation model idensl 5 JET simplified model idensl 6 Hugill Murakami M q model idensl 7 Greenwald model 3 1 2 6 Impurities and radiation The impurity radiation model in PROCESS can be chosen using the switch imprad_model where imprad model 0 gives the original ITER 1989 model 16 and imprad_model 1 uses a multi impurity model which integrates the radiation contributions over an arbitrary choice of density and temperature profiles 17 If imprad model 0 the impurity species and fractions are chosen using input parameters impc impo fbfe cfe0 and zfear see the variable descriptor file for more details If imprad_model 1 the impurity number density fractions
112. is made to optimise the machine s parameters The first thing to do is to add to the input file all the known details about the machine to be modelled This may include some or all of the following e machine build e plasma aspect ratio e PF coil locations e type of current drive to be used e net electric power e various physics parameters e g toroidal field on axis electron density electron temperature elongation triangularity beta g coefficient edge safety factor Chapter 4 Execution of the Code 73 In addition some of the switch values summarised in Chapter 3 may have to be altered from their default values Next the relevant numerics information must be entered Switch ioptimz must be set to 1 for non optimisation mode Then the user must decide which constraint equations and iteration variables to activate this choice is dictated partly by the information required by the user and partly by the machine being modelled itself As stated earlier all the relevant consistency equations must be activated together with the corresponding iteration variables A number of limit equations can also be activated to investigate how the calculated values compare with the physics or engineering limits The following is part of an example non optimisation input file IOPTIMZ 1 NEQNS 8 NVAR 8 Icc 1 2 10 11 7 16 5 24 IXC 5 10 12 29 7 9 36 4 FPNET
113. is situation A typical input file for use with PROCESS in optimisation mode is contained in Appendix C 4 4 Problem Solving Experience has shown that the first few attempts at running PROCESS with a new input file tends to produce unfeasible results that is the code will not find a consistent set of machine parameters The highly non linear nature of the numerics of PROCESS is the reason for this difficulty and it often requires a great deal of painstaking adjustment of the input file to overcome 4 4 1 Error handling In general errors detected during a run are handled in a consistent manner with the code producing hopefully useful diagnostic messages to help the user understand what has happened There are three levels of error that may occur Level 1 An informational message is produced under certain conditions for example if the code has modified the user s input choice for some reason Level 2 A warning message is produced if a non fatal situation has occurred that may result in an output case that is inaccurate or unreliable in some way Level 3 An error message will occur if a severe or fatal error has occurred and the program cannot continue These messages are printed on the screen during the course of a run and those still active at the final feasible or unfeasible solution point are also written to the end of the output file messages encountered during the iteration process are not copied
114. isation problems 67 It combines a simple solver for a quadratic optimisation problem with linear constraints that determines a search direction with a line search to find an optimum along that search direction It is a type of the more general feasible direction methods which is itself a type of primal method that solve nonlinear programming problems in the n m dimensional feasible subspace 68 A 4 VMCON The optimisation solver implemented in PROCESS is the Fortran routine VMCON 5 It is a modified version of the vf02ad routine from the Harwell Software Library and implements a SQP method originally suggested by Powell 6 based on work by Han 70 As stated before VMCON is designed to converge on a solution of the necessary KKT conditions A 4 but does not check the sufficient conditions Its convergence criterion is therefore given by Vaf 17 64 gt sei w lt epsvmc A 5 i 1 where epsvmc is a user specified error tolerance 6 is the vector in direction of the next line search c f section A 6 and j is the counter of the sequential quadratic programming iteration Hence the first part estimates the predicted improvement due to the next line search and the second part measures the error in the complimentary condition A 4b of the KKT conditions Figure A 2 describes the flow chart of the VMCON routine while the various values o
115. iteration variables are available In this case and many others the user has to relax the constraints slowly until a feasible result is found Chapter 5 Inclusion of New Models Additional Variables and Equations It is often useful to add extra features to the code in order to model new situations This chapter provides instructions on how to add various numerics related items to PROCESS Please remember to modify the relevant Table s in this User Guide if changes are made to the source code 5 1 Input Parameters Input parameters see Section 2 3 are added to the code in the following way 1 Choose the most relevant module usually one of those in source file global_variables f90 Keeping everything in alphabetical order add a declaration statement for the new variable specifying a sensible default value and a correctly formatted comment line to describe the variable copying the examples already present 2 Ensure that all the modules that use the new variable reference the relevant module via the Fortran use statement 3 Add the parameter to routine PARSE_INPUT FILE in source file input 90 in a suitable place keep to alphabetical order The existing examples provide guidance on how to do this Note that real i e double precision and integer variables are treated differently as are scalar quantities and arrays 4 Modify process dicts py and write _constraints conf accordingly 5 2 I
116. lanket coolant and used to produce electricity The neutron may also react with a lithium nucleus present in the blanket to produce breed a tritium nucleus which can be re used as fuel The competing requirements of heating and tritium synthesis mean that a neutron multiplier must be present to ensure balance between tritium destruction and creation The blanket therefore contains beryllium to fulfil this purpose As with the first wall the blanket has a relatively short lifetime because of the high neutron fluence 3 1 5 1 Blanket neutronics model Switch blktmodel determines whether a simple blanket neutronics model or a more comprehensive treatment based on recent full neutronics analyses for EFDA 26 is used In the simple model blktmodel 0 the overall radial thicknesses of the inboard and outboard blanket sections are specified via input parameters blnkith and blnkoth respectively The energy multiplication in the blanket emult is also an input parameter Steel and vanadium may be used as structural materials within the blanket which is cooled either by gaseous helium or by pressurised water The nuclear heating of the TF coil superconductor is calculated assuming an exponential neutron attenuation through the blanket and shield materials based on 1990 ITER data The more advanced model blktmodel 1 allows the energy multiplication factor emult the shielding requirements and tritium breeding ratio to be calculated
117. libraries you need to make sure their directory is in your Python path Use the commands given in Section 4 3 1 to do this All Python code has been written for Python 3 and adheres to the PEP8 standard 6 1 Executables All executables can be run by using any of the following commands python executable_name py python3 executable_name py executable_name py and they typically have a short description of their usage when putting h or help as arguments python executable_name py h Some executables come with a configuration file that typically follows the naming convention executable_name conf To run the executable please copy the config file into your own work directory Do NOT try to edit the config file in the PROCESS directory 6 1 1 write_new_in_dat py This program modifies a given IN DAT file such that all iteration variables are given by their values in OUT DAT The final values of the iteration variables in OUT DAT are set in a block at the end of IN DAT Any other definitions of these variables are commented out 83 Chapter 6 Utility Programs 84 Input IN DAT OUT DAT Output new_IN DAT 6 1 2 write constraints py This Python script modifies the PROCESS input file IN DAT to include the constraints marked Y or y in a configuration file called write constraints conf It automatically adds the required iteration variable for each constraint and any additional iteration variables selected
118. lowed unfeasible points in a sweep create_itervar_diff Boolean to indicate the creation of a summary file of the iteration variable values at each stage add_ixc List of iteration variables to be added to IN DAT del_ixc List of iteration variables to be deleted from IN DAT add_icc List of constrained equations to be added to IN DAT del_icc List of constrained equations to be deleted from IN DAT dictvar Dictionary mapping variable name to new value replaces old or gets appended del_var List of variables to be deleted from IN DAT RunProcessConfig get_attribute_csv_list attributename Get a class attribute list from the configuration file expects comma separated values Chapter 6 Utility Programs 96 RunProcessConfig set_del_var Sets the RunProcessConfig del_var attribute from the config file RunProcessConfig set_dictvar Sets the RunProcessConfig dictvar attribute from config file RunProcessConfig echo Echos the values of the current class RunProcessConfig modify_in_dat Modifies IN DAT using the configuration parameters RunProcessConfig modify_vars Modifies IN DAT by adding deleting and modifiying variables RunProcessConfig modify_ixc Modifies the array of iteration variables in IN DAT RunProcessConfig modify_icc Modifies the array of constraint equations in IN DAT 6 2 5 process_dicts py A collection of dictionaries and lists used by various PROCESS utilities IFAIL_SUCCESS This is the PRO
119. mal power absorbed by the shield and the efficiency of the shield coolant pump is etahtpshld Switch iprimshld may be used to specify whether the thermal power deposited in the shield becomes primary high grade thermal power iprimshld 1 or secondary low grade thermal power see Figure 3 9 The remaining neutron power after passing through the shield is assumed to be absorbed in the TF coils as quantity ptfnuc This power contributes to the total cryogenic power requirements of the machine Chapter 3 Physics Engineering and Other Models 54 3 1 13 5 Power conversion outside of the fusion power core Figure 3 9 summarises the power conversion mechanisms outside of the fusion power core 1 iprimaiv t iprimshld iprimaiv iprimshla psecdiv Primary psecshld pthermmw Environment Hydrogen production plant thermal power hthermmw A Hydrogen production plant electrical power helecmw Tritium processing plant trithtmw Cryogenic plant crypmw Vacuum system vachtmw er cal LA re systems A electric power e r Facilities fachtmw oil resistive power t crnw Balance of plant power offices labs etc forosbop pgrossmw Net electric power fonts L 3 Electricity grid TF c He
120. mended epsfcn 10 e 4 Ftol 1 D 4 The next line sets the first five elements of array icc ICC 2 10 11 24 31 The next line sets the first ten elements of array ixc ixc 10 12 3 36 48 1 2 6 13 16 IOPTIMZ 1 maxcal 200 nsweep 7 NEQNS 5 This is an in line comment NVAR 10 Another but successfully containing a comma The following are invalid entries in the input file Q Why boundl 1 1 2 5 BOUNDU N 3 A line of random characters like this will clearly wreak havoc eps fcn 10 e 4 ftol 1 D 4 epsvmc 1 0 e 4 ICC 2 10 11 24 31 IOPTIMZ 1 0 This will in fact be okay but is not recommended NEQNS 5 An in line comment on a line with only one comma character If the code encounters a problem reading the input file it will stop immediately with a hopefully useful error message It may be worth looking at the contents of the output file as well to help narrow down on which line of the input file the problem might lie 4 2 The Output File The main output from the code is sent to file OUT DAT in the working directory A second file MFILE DAT is also produced in the working directory This file contains most of the same data as OUT DAT but in a different format and has been designed to be machine readable by some of the utility programs described in Chapter 6 to allow simple post processing and graphical output to be produced easily 4
121. minimum makes it difficult for the code to escape to the global minimum Again a helpful technique is to either change the list of iteration variables in use or to simply modify their initial values to try to help the code avoid such regions A technique that occasionally removes problems due to unfeasible results particularly if an error code ifail 3 is encountered during an optimisation run is to adjust slightly one of the limits imposed on the iteration variables even if the limit in question has not been reached This subtly alters the gradients computed by the code during the iteration process and may tip the balance so that the code decides that the device produced is feasible after all For instance a certain component s temperature might be 400 K and its maximum allowable temperature is 1000 K Adjusting this limit to 900 K which will make no difference to the actual temperature may be enough to persuade the code that it has found a feasible solution Similarly the order in which the constraint equations and iteration variables are stored in the icc and ixc arrays can make the difference between a feasible and unfeasible result This seemingly illogical behaviour is sadly typical of the way in which the code works Another technique in such situations may be to change the finite difference step length epsfcn as this might subtly change the path taken in the approach towards a solution Unfeasible cases often produce unrealisti
122. modules separated with lines with S MODULE_NAME and SEND INModule add_variable var Adds an INVariable object to the INModule class INModule remove_variable variable_name Removes an INVariable object from the INModule class INModule add_line line Adds a line from the IN DAT that isn t a variable line e g a comment to the INModule class INModule get_var var_name Returns an INVariable object from the INModule class INModule add_constraint_eqn eqn_number Adds constraint equation eqn_number to the list of constraint equations InVariable class if the equation is not already in the list INModule remove_constraint_eqn eqn_number Removes constraint equation eqn_number from the list of constraint equations InVariable class if the equation is already in the list INModule add_iteration_variable var_number Adds iteration variable var_number to the list of iteration variables InVariable class if the variable is not already in the list INModule remove_iteration_variable var_number Removes iteration variable var_number to the list of iteration variables InVariable class if the variable is already in the list Chapter 6 Utility Programs 92 INDATClassic filename IN DAT Initialises an IN DAT class which can be given a different filename This class is used for an IN DAT with a module structure INDATClassic read_in_dat Reads an IN DAT file with modular structure INDATClassic write_in_dat filename new_IN DAT Writes
123. n no 45 qrim 3 1 2 6 e 3 21 where e a R 6 Among the physics models that differ from those relevant to conventional aspect ratio machines are i the plasma poloidal field B ii the bootstrap current fraction iii the beta limit and iv the neutron heating of the centrepost 2 3 2 1 Spherical tokamak switches Switch itart provides overall control of the ST switches within the code and subroutine CHECK ensures that no conflicting values are inadvertently set by the user in the input file Table 3 4 summarises the switch values relevant to each aspect ratio regime Chapter 3 Physics Engineering and Other Models 56 conventional aspect ratio low aspect ratio switch itart 0 itart 1 ishape 0 2 0 1 ibss Section 3 1 2 11 1 2 3 2 3 icurr Section 3 1 2 7 1 3 4 5 6 7 2 itfsup Section 3 1 7 0 1 0 Table 3 4 Summary of the switch values in PROCESS that relate to conventional aspect ratio and low aspect ratio machines 3 3 Pulsed Plant Operation If the plasma current is not to be driven by purely non inductive means it is necessary to operate the plant in a pulsed manner as the current swing in the OH PF coils cannot be continued indefinitely PROCESS can perform a number of calculations relevant to a pulsed power plant as detailed below Switch 1pulse determines whether the power plant is a
124. n the middle of a range of values to try to keep the scan within the same family of machines The optimum machine found may otherwise suddenly jump to a new region of parameter space causing the output variables to seem to vary unpredictably with the scanning variable It should be noted that in general the machine produced by PROCESS will always sit against one or more operation limits If during a scan the limit being leant upon changes i e if the machine jumps from leaning on the beta limit to leaning on the density limit the output parameters may well become discontinuous in gradient and trends may suddenly change direction 4 4 4 Unfeasible results In the numerics section of the output file the code indicates whether the run produced a feasible or unfeasible result The former implies a successful outcome although it is always worth checking that the estimate of the constraints sqsumsq is small 107 or less the code will issue a warning if the run seems feasible but the value of sqsumsq exceeds 107 If this occurs reducing the value of the HYBRD tolerance Chapter 4 Execution of the Code 77 ftol or VMCON tolerance epsvmc as appropriate should indicate whether the result is valid or not the output can usually be trusted if 1 the constraint residues fall as the tolerance is reduced to about 1078 and 2 the code indicates that a feasible solution is still found An unfeasible result occurs if PROCESS cannot fi
125. nd a set of values for the iteration variables which satisfies all the given constraints In this case the values of the constraint residues shown in the output give some indication of which constraint equations are not being satisfied those with the highest residues should be examined further In optimisation mode the code also indicates which iteration variables lie at the edge of their allowed range Unfeasible runs are caused either by ill defining the problem to be solved or by starting the problem in an unfavourable region of parameter space The latter can be checked simply by changing the initial values of the active iteration variables in the input file but the former requires some extra work This situation arises if there are insufficient iteration variables for the given constraint equations It is important to choose the right number of useful iteration variables for the problem to be solved it is possible to activate too many iteration variables as well as too few some of which may be redundant Both optimisation and non optimisation runs can fail with an error message suggesting that the iteration process is not making good progress This is likely to be due to the code finding itself unable to escape a region of the parameter space where the minimum in the residuals is significantly above zero In this situation there is either no solution possible the residuals can therefore never approach zero or the topology of the local
126. netic Fusion Energy Fusion Technology 13 1988 7 Git version control system http git scm com K Schittkowski Nonlinear Programming Codes Springer Berlin 1980 D G Luenberger and Yinyu Ye Linear and Nonlinear Programming International Series in Operations Research and Management Science 3rd Edition Springer Science and Business Media LCC 2008 M J D Powell An efficient method for finding the minimum of a function of several variables without calculating derivatives Computer Journal 7 No 2 1964 155 162 S P Han A Globally Convergent Method for Nonlinear Programming Department for Computer Science Cornell University Report 75 257 1975 M S Bazaraa H D Sherali and C M Shetty Nonlinear Programming Theory and Algorithms John Wiley amp Sons Inc New York 1993 R Fletcher A General Quadratic Programming Algorithm Atomic Energy Research Establishment Report T P 401 March 1970 R Fletcher The calculation of feasible points for linearly constrained optimisation problems Atomic Energy Research Establishment Report R 6354 April 1970 R Fletcher A FORTRAN subroutine for general quadratic programming Atomic Energy Research Establishment Report R 6370 June 1970 M J D Powell The convergence of variable metric methods for nonlinearly constrained optimisation calculations presented at Nonlinear Programming Symposi
127. nt equation no 52 with iteration variable no 89 ftbr The inboard and outboard blanket BZ thicknesses blbuith and blbuoth can also be used as iteration variables 90 and 91 respectively to help the constraint to be met e The tritium production rate in grammes day is calculated e The fast neutron fluence neutrons m on the TF coils is calculated The peak value of this quantity may be constrained to be no more than a maximum value nflutfmax by turning on constraint equation no 53 with iteration variable no 92 fflutf The inboard and outboard shield thicknesses shldith and shldoth can also be used as iteration variables 93 and 94 respectively to help the constraint to be met Note that in this calculation the TF coil case surrounding the superconductor winding pack is ignored e The nuclear heating power MW m on the inboard and outboard TF coils is calculated Again this can be limited to be no more than a maximum value ptfnucmax by turning on constraint equation no 54 with iteration variable no 95 fptfnuc The inboard and outboard shield thicknesses also help this constraint to be met Note that in this calculation the TF coil case surrounding the superconductor winding pack is ignored This constraint equation may also be used with blktmodel 0 e The helium concentration in the vacuum vessel at the end of the plant lifetime is calculated This needs to be constrained for re weldability purposes and can be kept below a
128. ocumentation of each individual source routine is an ongoing task A Work File Note will be produced as each routine is processed with the eventual aim of bringing all these together into a single document i e a future edition of this manual e Summary of work performed since April 1992 Note 0160 e Code status routine SCCS version numbers Note 0165 e SCCS Source Code Control System implementation for PROCESS Note 0003 e Present code standard Note 0160 e Future code standard to be adhered to Note 0167 e Directory structure and location of all relevant files Note 0168 e Proposed future work Note 0160 e Pulsed power plant coding Note 0189 e Nuclide inventory and activation FISPACT module Notes 0195 and 0231 e New cost algorithms Note 0224 e Stellarator model Note 0246 e D He tokamak model Note 0265 Reference 31 has recently been superseded by a new Project Work File F MI PJK PROCESS e Spherical Tokamak model Note 001 e Reversed Field Pinch model Note 009 e Test cases Note 019 121
129. of switch isc determines which of these is used in the plasma energy balance calculation TE Large Helical Device 41 isc 21 0 17 R8 a A no Be Tp Gyro reduced Bohm 42 isc 22 0 25 B88 n mf M Pia S a En p Lackner Gottardi 43 isc 23 0 17 Ro as aie By s p06 ne re 1SS95 44 isc 37 0 079 R a221 n951 p083 p 0 59 704 T ISS04 45 isc 38 0 134 Ry a Ma By pr0 61 Al 3 27 Here T is the rotational transform which is equivalent to the reciprocal of the tokamak safety factor q 3 5 1 6 Heating power options Stellarators require no current drive although provision for auxiliary heating does need to be present The method by which auxiliary heating power is supplied is determined by the switch isthtr isthtr 1 electron cyclotron resonance heating isthtr 2 lower hybrid heating isthtr 3 neutral beam injection The value of variable pheat determines the actual amount of auxiliary heating power in Watts to be applied to the plasma This variable may be used as an iteration variable no 11 Switch ignite may be used if necessary see Section 3 1 10 4 3 5 1 7 Divertor Although the divertor has the same function in both stellarators and tokamaks the envisaged concepts differ quite substantially This is not only related to the different geometry and symmetries but also specifically to the magnetic configuration While the inherent axisymmetry of a tokamak
130. ollowing files are used autodoc f90 adheader src adfooter src To create the 380 html files from the source code type make html Then point your favourite web browser to the file process html or calling tree html in the working directory The variable descriptor file vardes html see Section 2 2 is also produced at the same time though it is best to modify the file manually afterwards to remove empty sections from it In addition a full ATX User Guide process tex this document is rigorously maintained to ensure its continuing strict agreement with the evolving source code To create an Adobe PDF file process pdf from process tex and the associated PostScript figures type make manual Finally to produce both the html files and the User Guide in one go simply type make doc Chapter 8 Acknowledgements z Bibliography The author would like to thank the following people for many useful and revealing discussions during his work on PROCESS John D Galambos Paul C Shipe and Y K Martin Peng of Oak Ridge National Laboratory USA lan Cook Robin Forrest Winston Han Roger Hancox and Panos Karditsas all formerly of Fusion Physics Department UKAEA Fusion John Hicks formerly of Engineering Department UKAEA Fusion Chris Gardner formerly of Microwave and Interpretation Department UKAEA Fusion Tim Hender of CCFE and all the co authors of reference 15 Da
131. on 4 1 This has the effect of setting the internally used switch ife 1 If the file is absent or its first character is set to something other than 3 the IFE model is not used and ife is set to 0 The IFE model 49 is controlled using two additional switches ifetyp 0 Generic device build 1 OSIRIS type device build 50 51 52 ifetyp ifetyp 2 SOMBRERO type device build 53 54 ifetyp 3 HYLIFE IEtype device build 55 56 57 Chapter 3 Physics Engineering and Other Models 66 Switch ifetyp defines the type of device that is assumed this varies widely between different conceptual designs The generic type assumes a cylindrically symmetric device while the other types are approximations to the builds of the given conceptual machines 58 In general the build from the centre of the device at the target ignition location is in the order chamber first wall gap blanket gap shield gap building wall The user specifies the thicknesses of these regions and also the materials that are present and in what proportions expand ifedrv 1 Driver efficiency and target gain are input as functions of driver energy ifedrv 0 Driver efficiency and target gain are input ifedrv 1 SOMBRERO laser drive efficiency and target gain assumed ifedrv 2 OSIRIS heavy ion beam driver efficiency and target gain are assumed Switch ifedrv defines ho
132. on variables than constraint equations to aid the minimisation process Finally note that a three point scan in the beta g coefficient dnbeta scanning variable 11 is to be performed A useful practice in optimisation mode is to perform stationary scans whereby the same value is given to the scanning variable on successive iterations This provides a check as to how well converged Chapter 4 Execution of the Code 75 the solution has become If scans of a given variable are to be made over a large range of values it is often a good idea to start the scan in the middle of the desired range and to split the scan in two one going downwards from the initial value and the other upwards This ensures that the whole range of the scan produces well converged machines assuming a good initial point without sharp changes in gradient in the parameter values It should be remembered that the value of the scan variable is set in the array sweep and this overrules any value set for the variable elsewhere in the input file For instance in the example above the values of dnbeta set in the sweep array would overrule any value for dnbeta set elsewhere in the file The output from an optimisation run contains an indication as to which iteration variables lie at their limiting values On the whole there is a greater chance of unfeasible solutions being found whilst in optimisation mode and Section 4 4 will hopefully be of some use in th
133. ooic fjprot rmajor bmxlim gammax bound 16 tbrnmn sigpfalw cfactr boundu 72 powfmax kappa triang tbrmin bt coreradius fimpvar plasma aspect ratio maximum divertor heat load required net electric power confinement time H factor overall current density in TF coil inboard leg allowable wall load beam background fusion multiplier f value for fusion gain limit eqn electron temperature upper bound on f value fvs beta g coefficient bootstrap current fraction use negative values upper bound on confinement time H factor hfact f value for TF coil operational current limit eqn f value for TF coil current protection limit eqn plasma major radius maximum toroidal field maximum current drive gamma lower bound on central solenoid thickness ohcth minimum burn time pulsed operation machine allowable stress in the PF coils plant availability factor N B requires iavail 0 upper bound on f value fipir maximum fusion power plasma elongation plasma triangularity minimum tritium breeding ratio blktmodel 1 toroidal field on axis normalised radius defining the core region impurity fraction of element impvar Table 2 5 Summary of the scanning variables available in PROCESS source file description caller f90 evaluators f90 maths_library f90 numerics f90 scan f90 constraint_equations f90 iteration_variables f90 calls physics and engineering routines defines the cons
134. ower balance The sum of this core alpha power any power carried by non alpha charged particles the ohmic power and any injected power is converted into charged particle transport power Pjoss in Equation 3 19 plus core radiation power see Section 3 1 2 6 as shown in Figure 3 41 Note that if switch iradloss is set to zero the above summed input power is converted into charged particle transport power only and the core radiation power may be assumed to originate from the transport power i e the core radiation power is treated the same as the edge radiation power in Figure 3 4 instead of having an arrow leading directly to it from the core plasma power balance The core power balance calculation is turned on using constraint equation no 2 which should therefore always be used 3 1 2 11 Bootstrap current scalings The fraction of the plasma current provided by the so called bootstrap effect can be either input into the code directly or calculated using one of four methods as summarised here Note that methods ibss 1 to 3 use fits to parabolic density and temperature profiles and do not take into account the existence of pedestals ipedestal 1 whereas the Sauter et al scaling ibss 4 allows general profiles to be used e Direct input To input the bootstrap current fraction directly set bscfmax to 1 times the required value e ITER scaling 14 To use
135. produce the required toroidal field at the centre of the plasma The field falls off at a rate 1 R with the peak value occurring at the outer edge of the inboard portion of the TF coil winding pack Rmax Tr rbmax The maximum TF coil current depends on the field it produces and the allowable current density Two limits can be applied to the current density J in the superconducting TF coils To ensure that J does not exceed the critical value constraint equation no 33 should be turned on with iteration variable no 50 fiooic To ensure that J does not exceed the current density protection limit constraint equation no 35 should be turned on with iteration variable no 53 fjprot 3 1 8 Poloidal field coils The poloidal field PF coils are used initially to cancel the vertical field produced at the centre of the plasma by the central solenoid Section 3 1 9 during start up and then to maintain the plasma position and shape during the flat top period 3 1 8 1 PF coil positions The positions and sizes of the PF coils are partly input and partly calculated after consideration of the required currents and allowable current density The PF coil locations are controlled using a set of switches stored in array ipfloc see Figure 3 1 and are calculated in routine PFCOIL The coils are usually organised into groups containing two PF coils placed symmetrically above and below the midplane and each group j has an el
136. pter 3 Physics Engineering and Other Models 35 isc scaling law reference 1 Neo Alcator ohmic 14 2 Mirnov H mode 14 3 Merezhkin Muhkovatov L mode 14 4 Shimomura H mode JAERI M 87 080 1987 5 Kaye Goldston L mode Nuclear Fusion 25 1985 p 65 6 ITER 89 P L mode Nuclear Fusion 30 1990 p 1999 7 ITER 89 O L mode 14 8 Rebut Lallia L mode Plasma Physics and Controlled Nuclear Fusion Research 2 1987 p 187 9 Goldston L mode Plas Phys Controlled Fusion 26 1984 p 87 10 T10 L mode 14 11 JAERI 88 L mode JAERI M 88 068 1988 12 Kaye Big Complex L mode Phys Fluids B 2 1990 p 2926 13 ITER H90 P H mode 14 ITER Mix minimum of 6 and 7 15 Riedel L mode 16 Christiansen et al L mode JET Report JET P 1991 03 17 Lackner Gottardi L mode Nuclear Fusion 30 1990 p 767 18 Neo Kaye L mode 14 19 Riedel H mode 20 ITER H90 P amended Nuclear Fusion 32 1992 p 318 21 Large Helical Device stellarator Nuclear Fusion 30 1990 p 11 22 Gyro reduced Bohm stellarator Bull Am Phys Society 34 1989 p 1964 23 Lackner Gottardi stellarator Nuclear Fusion 30 1990 p 767 24 ITER 93H H mode Plasma Physics and Controlled Nuclear Fusion Research Proc 15th Int Conf Seville 1994 IAEA CN 60 E P 3 25 TITAN RFP TITAN RFP Fusion Reactor Study Scoping Phase Report UCLA PPG 1100 page 5 9 Jan 1987 26 ITER H 97P ELM free
137. r 1 00D 6 0 010D0 Table 2 3 Iteration constraint equations see Table 2 1 variables 51 to 102 present in PROCESS The f values correspond to the given The other iteration variables are shown in Table 2 2 Chapter 2 Program Overview The Fundamental Concepts 21 minmax description 1 plasma major radius 2 ratio of fusion power to input power 3 neutron wall load 4 total TF coil PF coil power 5 ratio of fusion power to injection power 6 cost of electricity 7 direct cost if ireactor 0 i constructed cost otherwise 8 aspect ratio 9 divertor heat load 10 toroidal field on axis 11 injection power 12 hydrogen plant capital cost 13 hydrogen production rate 14 pulse length 15 plant availability factor N B requires iavail 1 Table 2 4 Summary of the available figures of merit in PROCESS If the figure of merit is to be minimised minmaz should be positive and if a maximised figure of merit is desired minmaz should be negative physics and engineering issues in terms of numerous expressions and relationships In effect these define the machine so that the numerical solver within the code can then get to work adjusting the parameters in its search for a self consistent solution It is essential for a program of the size and complexity of PROCESS to be modular to a high degree in order to simplify the tasks of
138. r instance That is 1 fhole is the first wall area coverage factor N B see Section 3 1 13 e fvolsi and fvolso are the area and volume coverage factors for the inboard and outboard shields respectively e fvoldw is a multiplier for the volume of the vacuum vessel used in the item s mass calculation to account for ports etc e npdiv is the number of divertor ports used in the calculation of the tritium breeding ratio blktmodel gt 0 only Chapter 3 Physics Engineering and Other Models 41 e nphcdin and nphcdout are the number of heating current drive ports on the inboard and outboard sides respectively used in the calculation of the tritium breeding ratio bl1ktmodel gt 0 only These may be either small hcdportsize 1 or large hcdportsize 2 e wallpf is the neutron wall load peaking factor maximum mean used in the calculation of the blanket lifetime blktmodel gt 0 only e ucblbreed is the unit cost kg of the breeder material blktmodel gt 0 only Model outputs and available constraints The advanced blanket neutronics model provides the following outputs e The total nuclear power deposited in the blanket and shield pnucblkt and pnucshld respectively and the energy multiplication factor in the blanket emult are calculated e The tritium breeding ratio tbr This can be constrained to be no less than a certain value tbrmin for tritium self sufficiency by turning on constrai
139. ray icc 2 Set fpnetel 1 0DO 3 Ensure that fpnetel iteration variable no 25 DOES NOT appear in array ixc 4 Set pnetelin to the required net electric power Limit equations are not restricted to optimisation mode In non optimisation mode the iteration variables are not bounded but the f values can still be used to provide information about how calculated values compare with limiting values without having to change the characteristics of the device being benchmarked to find a solution It is for this reason that all the constraint equations used in PROCESS are formulated as equalities despite the fact that equation solver VMCON can solve for inequalities as well The use of f values precludes this need and allows the non optimising equation solver HYBRD to use the same constraint equations 2 5 Iteration Variables It is necessary to calculate numerical derivatives during the solution of the constraint equations The iteration variables are the parameters that the equation solvers use for this purpose all the other code variables input parameters see above remain fixed at their initial value Successive calls are made to the physics and engineering routines with slightly different values for the iteration variables on each call and the equation solver determines the effect on the output due to these small changes 17 Chapter 2 Program Overview The Fundamental Concepts icc corresponding no d
140. rned on with iteration variable no 66 ftohs 3 1 9 2 Current density limits The current density in the central solenoid can be limited at the beginning of pulse BOP and at the end of flat top EOF see Figure 3 6 The limiting value is dependent on the maximum allowable stress in the coil as given by the value of sigpfalw To limit the current density at the BOP constraint equation no 27 should be turned on with iteration variable no 39 f fjohc0 To limit the current density at the EOF constraint equation no 26 should be turned on with iteration variable no 38 fjohc 3 1 10 Auxiliary power systems heating and current drive 3 1 10 1 Current Drive The use of purely inductive current drive leads to pulsed plant operation because of the limited flux swing that can be achieved using the central solenoid This poses problems due to the fact that fatigue failures may result and there would also be a need for thermal storage to maintain a level supply between pulses However the plasma current can also be produced and maintained partially or wholly using non inductive means which in principle removes this restriction PROCESS contains a number of auxiliary current drive schemes including various RF methods Lower Hybrid Electron Cyclotron and Ion Cyclotron Fast Wave current drives and also Neutral Beam current drive systems The code calculates the efficiency and the resulting power requirements of the chosen sys
141. rom MFILE DAT MFileVariable var_name var_description Object to contain information for a single MFILE DAT variable MFileVariable set_scan scan_number scan_value Sets the variable value for scan number scan_number MFileVariable get_scan scan_number Returns the variable value for scan number scan_number Chapter 6 Utility Programs 93 MFileVariable get_scans Returns the variable value for all scans MFile filename MFILE DAT Object to contain information for all variables in an MFILE DAT for all scans MFile search_keys variable Search for an MFILE variable in the data dictionary MFile search_des description Search for an MFILE description in the data dictionary MFile make_plot_dat custom_keys filename make_plot_dat out file_format row Create a PLOT DAT equivalent for the variables in custom_keys in either row or column format MFile get_num_scans Returns the number of scans in the MFILE DAT read_mplot_conf filename make_plot_dat conf Reads the config file make_plot_dat conf and fills the list custom_keys with these variables write_mplot_conf filename make_plot_dat conf Writes a new make_plot_dat conf adding any additional variables that the user gave make_plot_dat py at runtime 6 2 3 process_funcs py This library contains a collection of functions used by various PROCESS utilities get_neqns_itervars wdir Returns the number of equations and a list of variable names o
142. rowse through without difficulty Chapter 2 provides an overview of the program and outlines the numerical and programming concepts involved Chapter 3 describes the physics engineering and economic models that are used within the code and lists the switches available allowing the user to customise the models details to achieve the desired simulation Chapter 4 describes how to run the program from scratch and provides a number of hints and suggestions for the user to bear in mind to help the code find a feasible machine Chapter 5 shows how to modify the code in specific ways for example how to add extra constraints and variables to the code A useful set of utility programs is introduced in Chapter 6 and some code management tools are described in Chapter 7 Finally the Appendices give detailed information about the optimisation method example input files for PROCESS in non optimisation and optimisation modes and lists of references that provide information about the code status its location and other details relating to the implementation of PROCESS to date Chapter 2 Program Overview The Fundamental Concepts Fusion power plants are complex systems consisting of many non linear interactions One method that can be used to model this kind of system is to iterate a number of free parameters the so called iteration variables see Section 2 5 in a controlled way so as to
143. ry in which PROCESS is run WDIR Runt original IN DAT name ORIGINAL_IN_DAT demoia_10_sep_13 IN DAT PATH to PROCESS binary PROCESS pknight process bin process ONE line comment to be put into README txt COMMENT This is a test DEMO run Max no iterations NITER 5 integer seed for random number generator use None for random seed SEED 2 factor within which the iteration variables are changed FACTOR 1 5 Number of allowed unfeasible points that do not trigger rerunning NO_ALLOWED_UNFEASIBLE 0 include a summary file with the iteration variables at each stage INCLUDE_ITERVAR_DIFF True add iteration variables comma separated ADD_IXC 99 77 remove iteration variables comma separated DEL_IXC add constraint equations comma separated ADD_ICC 57 remove constraint equations comma separated DEL_ICC set any variable to a new value the variable does not have to exist in IN DAT VAR_TFTORT 1 9 VAR_EPSVMC le 4 remove variables DEL_VAR_IITER A configuration file with an alternative name can be specified using the optional argument run_process py f CONFIGFILE 6 1 4 build index py Creates an index of all PROCESS run comments in a series of subfolders Input None Output Index txt Chapter 6 Utility Programs 86 Configuration Options Optional arguments are change the name of the file containing the folder description build_inde
144. s Both routines go back to a method by Fletcher 72 73 74 The Lagrange multipliers are also determined from results of the harwqp routine If the routine cannot find a feasible point it fails with ifail 5 c f Table A 1 As the routine is only checking the local linear approximation of the constraints rather the full non linear constraints there is a chance that a feasible point exists even though the routine fails with ifail 5 In these cases it is possible that the first approximation of the Hessian has not been good and the algorithm has therefore taken an inappropriately large step Then using a multiple of the identity matrix will improve convergence of the algorithm If a singular matrix is encountered with the QSP solver or the solution is restricted by the artificial bounds VMCON fails with ifail 6 In this case it can be helpful to widen the boundaries of the iteration variables A 6 The Line Search The line search is an essential part of the SQP algorithm As Powell 6 pointed out it is necessary to allow convergence from poor starting conditions It uses the vector 6 from the QSP to update al xi aJ6 where the step length parameter af gt 0 is determined by the line search as the parameter that minimises k m a f 2 rule S mimino c A 7 i 1 i k 1 where the weights are defined as Ai ip A ME maz 111 24 t j gt A to assure maximally efficient
145. s The configuration file a to b conf has the following style xComment line Working directory to store temporary files default wdir wdir wdir Switch to keep DAT files for every step default True keep_output True Directory for output if keep_output True default steps outdir steps IN DAT file for A default A DAT a_filename A DAT IN DAT file for B default B DAT b_filename B DAT Path to process binary path_to_process home pknight process bin process path_to_process home pknight process bin process Number of iterations of vary_iteration_variables to run default 20 vary_niter 20 Number of steps to go from A to B default 10 nsteps 10 Factor to vary iteration variables within default 1 2 factor 1 2 Chapter 6 Utility Programs 91 Gap between upper and lower bounds to narrow to default 1 001 bound_gap 1 001 6 1 12 create _dicts py To do 6 2 Libraries All library modules and functions are documented using docstrings These can be accessed by reading the code directly or via the help function in Python 6 2 1 in _dat py A set of Python classes to read modify and write an IN DAT file INVariable name value comment Initialises an IN DAT variable class which requires a name and a value INModule name Initialises an IN DAT module class which requires a name This class stores information for an IN DAT file which has
146. s of problems If we assume for simplicity that we have a 2D problem with only one equality constraint c x y 0 we know that we only need to search for the optimum along that constraint At the optimum the value of the objective function will then be stationary i e it does not locally increase or decrease along the constraint As the gradient of a function is perpedicular to its contour lines of f x y d this is equivalent to saying that the gradient of the objective function at that point is parallel to the gradient of the constraints Vi z y AVe z y A 2 where the factor A is necessary as only the direction but not the magnitude nor the sign of the gradients need to be equal This is also illustrated in Figure A 1 When expanding the method to several equality and inequality constraints we can make use of the Lagrange function For the nonlinear programming problem described by A 1 it is given by L A f x Y reia A 3 a 1 with the corresponding Lagrangian multipliers A It allows us to formulate the first order necessary conditions for a constrained optimum x with corresponding Lagrange multipliers A the Karush Kuhn Tucker KKT conditions Valla A Vaf a Y A Vaci a 0 A 4a i l Mes a 0 i 1 m A 4b ci 0 i 1 k A 4c AG 0 t k 1 m A 4d ola gt 0 k 1 m A 4e Please note that by construction the Lagrange multipliers Af ful
147. se of a run 2 4 Constraint Equations Any computer program naturally contains myriads of equations The built in equation solvers within PROCESS act on a special class known as constraint equations all of which are formulated in routine CONSTRAINTS in source file constraint_equations f90 Table 2 1 summarises the constraint equations available in PROCESS These can be split into two types 1 consistency equations that enforce consistency between the physics and engineering parameters and 2 limit equations that enforce various parameters to lie within their allowed limits The neqns constraint equations that the user chooses for a given run are activated by including the equation numbers in the first neqns elements of array icc 2 4 1 Consistency equations Consistency equations are usually equalities that ensure that the machine produced by PROCESS is self consistent This means therefore that many of these constraint equations should always be used namely equations 1 2 10 and 11 see Table 2 1 Equation 7 should also be activated if neutral beam injection is used The other consistency equations can be activated if required A typical consistency equation ensures that two functions g and h are equal GEG 200 h z y z g i 1 35 h The equation solvers VMCON and HYBRD need the constraint equations c to be given in the form shown since they adjust the iteration variables so as
148. section A 3 in which a series of subproblems is solved that constitute a local quadratic expansion of the Lagrangian c f section A 5 The solution of the quadratic subproblem is the direction of a line search along which a one dimensional optimisation is performed c f section A 6 This line search was introduced by Powell to assure convergence from bad starting parameters Within PROCESS we have modified the line search of the original VMCON routine to assure convergence even for slightly inconsistent input functions The algorithm uses a quasi Newtonian approach which only requires continuous first derivatives of these functions While the first derivatives are evaluated using a finite difference approximation the second derivatives are estimated using a variant of the Broyden Fletcher Goldfarb Shanno update c f section A 7 The convergence criterium of the solver as well as the detailed interpretation of the various error codes are explained in section A 4 A flow diagram of PROCESS in optimisation mode is shown in Figure 2 2 2 1 3 Scans It is often useful to be able to scan through a range of values of a given parameter to see what effect this has on the machine as a whole Sensitivity studies of this kind can be achieved very easily using PROCESS Scans are carried out in optimisation mode whereby the code performs initially a run using the parameters specified in the input file and
149. sent A value of 1 denotes that this coil is present and should be assigned a non zero thickness ohcth A value of iohcl O denotes that no central solenoid is present in which case the thickness ohcth should be set to zero No PF coils should be located at positions defined by ipfloc j 1 if no central solenoid is present 3 1 9 1 Plasma current ramp up time In the steady state power plant scenario lpulse 4 1 see Section 3 3 the length of time taken for the central solenoid current to reverse which is equal to the plasma current ramp up time see Figure 3 6 is determined from the value of switch tohsin If tohsin 0 0DO then the plasma current ramp up time tohs in seconds is given by tohs 0 5 where J is the plasma current in MA Furthermore the PF coil ramp time tramp and shutdown time tqnch are set equal to tohs If tohsin 0 0DO the plasma current ramp up time tohs tohsin and the PF coil ramp and shutdown times are input parameters If however a pulsed power plant is being modelled lpulse 1 the plasma current ramp up time tohs is either an input parameter or it can be iterated by using iteration variable 65 The ramp and shutdown times in the pulsed case are always set equal to tohs To ensure that the plasma current ramp rate during start up is prevented from being too high as governed by the requirement to maintain plasma stability in q space constraint equation no 41 should be tu
150. ssumed to be based on steady state 1pulse 0 or pulsed 1pulse 1 operation 3 3 1 Thermal cycling package This performs calculations on the first wall of the machine Evaluation of the mechanical and thermal stresses on this component lead to a measure of the maximum number of cycles to which the first wall can be subjected and hence to the minimum allowable length of each reactor cycle for a specified first wall lifetime The cycle time can be constrained to be at least the minimum value by turning on constraint equation no 42 with iteration variable no 67 ftcycl The thickness of the first wall is constrained to lie within lower and upper bounds which ensures that it can withstand the internal coolant pressure and the peak temperature and neutron fluence Switch itcycl activates the desired model for the first wall axial stress calculations If itcycl 1 the default the wall is fully constrained axially and no bending can occur If itcycl 2 there is no constraint on the axial motion but no bending can occur Finally if itcycl 3 again there is no axial constraint and bending is allowed to occur 3 3 2 First wall coolant temperature rise limit The rise in temperature of the first wall coolant can be limited to be no more than the value of dtmpmx by turning on constraint equation no 38 with iteration variable no 62 fdtmp 3 3 3 First wall peak temperature limit The maximum first wall temperature can be limited to
151. t the value of helecmw to the amount of hydrogen produced in MW equivalent these can be greater than unity in all cases except ihplant 4 3 5 Stellarator Model The code has the ability to perform calculations based on the physics and engineering of a stellarator which although being a toroidal device is radically different in a number of ways from a tokamak The model is largely based on W7 X and the HELIAS 5 B stellarator power plant design 34 Figure 3 10 and related modelling that has been performed by IPP Greifswald 35 36 37 To activate the stellarator coding it is necessary to create a file device dat containing the single character 1 in the first row in the working directory see Section 4 1 This has the effect of setting the internally used switch istell 1 If the file is absent or its first character is set to something other than 1 the stellarator model is not used and istell is set to 0 The stellarator model is largely contained within source file stellarator f90 The following consistency equations see Section 2 4 should be used without modification 1 plasma beta consistency 2 global power balance 11 radial build consistency 3 5 1 Stellarator physics Much of the physics is identical to that for tokamaks including the plasma composition and the fusion power calculations However some physics topics do differ between stellara
152. tem The fraction of the required plasma current to be produced by non inductive means fvsbrnni should Chapter 3 Physics Engineering and Other Models 49 be set and flag irfcd should be set to 0 for purely inductive scenarios or 1 otherwise The current drive efficiency model to be used in this latter case is defined by the value of switch iefrf iefrf 1 Fenstermacher Lower Hybrid model iefrf 2 Jon cyclotron model 14 iefrf 3 Fenstermacher electron cyclotron resonance model iefrf 4 Ehst Lower Hybrid model iefrf 5 ITER neutral beam model 14 15 iefrf 6 Culham Lower Hybrid model 15 iefrf 7 Culham electron cyclotron model 15 iefrf 8 Culham neutral beam model 15 iefrf 9 Oscillating Field current drive RFPs only see Section 3 6 1 5 Note that at present the neutral beam models assume parabolic plasma profiles only It is sometimes useful to adjust artificially the current drive efficiency values produced by these routines This can be achieved by setting the scaling coefficient feffcd The wall plug to plasma efficiencies can also be adjusted by changing the relevant variable etaech etalh etanbi or etaof 3 1 10 2 Plasma heating In addition to current drive some auxiliary power can be used purely to heat the plasma The value of input parameter pheat determines the amount of auxiliary heating power in Watts
153. teration Variables New iteration variables see Section 2 5 following additions are added in the same way as input parameters with the 1 Increment the parameter ipnvars in module numerics in source file numerics f90 to accommodate the new iteration variable 79 Chapter 5 Inclusion of New Models Additional Variables and Equations 80 2 Add an additional line to the initialisation of the array ixc in module numerics in source file numerics f90 3 Assign sensible values for the variable s bounds to the relevant elements in arrays boundl and boundu in module numerics in source file numerics f90 4 Assign the relevant element of character array lablxc to the name of the variable in module numerics in source file numerics f90 5 Add the variable to routines LOADXC and CONVXC in source file iteration_variables f90 mimicking the way that the existing iteration variables are coded 6 Modify process_dicts py and write_constraints conf accordingly Don t forget to add suitable correctly formatted comment lines to numerics f90 to document the above changes If an existing input parameter is now required to be an iteration variable then simply carry out the tasks mentioned here It should be noted that iteration variables must not be reset elsewhere in the code That is they may only be assigned new values when originally initialised in the relevant module or in the input file if required and in routin
154. the ITER scaling method for the bootstrap current fraction set ibss 1 and bscfmax to the maximum required bootstrap current fraction lt 1 This method is valid at high aspect ratio only e General scaling 21 To use a more general scaling method set ibss 2 and bscfmax to the maximum required bootstrap current fraction lt 1 e Numerically fitted scaling 22 To use a numerically fitted scaling method valid for all aspect ratios set ibss 3 and bscfmax to the maximum required bootstrap current fraction lt 1 e Sauter Angioni and Lin Liu scaling 23 24 Set ibss 4 and bscfmax to the maximum required bootstrap current fraction lt 1 3 1 2 12 L H power threshold scalings Transitions from a standard confinement mode L mode to an improved confinement regime H mode called L H transitions are observed in most tokamaks A range of scaling laws are available that provide estimates of the auxiliary power required to initiate these transitions via extrapolations from present day devices PROCESS calculates these power threshold values for the scaling laws listed in Table 3 2 in routine PTHRESH Chapter 3 Physics Engineering and Other Models 38 name reference 1 1996 ITER scaling nominal ITER Physics Design Description Document 2 1996 ITER scaling upper bound D Boucher p 2 2 3 1996 ITER scaling lower bound 4 5 1997 ITER scaling e
155. then a series of runs using the parameters produced at the end of the previous iteration The value of the quantity being scanned is specified at every stage see Section 2 7 This method ensures that a smooth variation in the machine parameters is achieved 2 2 The Variable Descriptor File The variable descriptor file vardes html is an invaluable resource for the user of PROCESS It acts as a dictionary reference manual for the code s variables and contains the following information about each e name e dimensions of arrays e default value s of those variables that are not initially derived from a combination of other values The default values are mostly set in the modules contained within source file global variables f90 e description including physical units if relevant e for switches flags the meanings of all allowed values e iteration variable number if relevant e corresponding constraint equation if relevant Chapter 2 Program Overview The Fundamental Concepts 14 define rules define performance requirements define figure of merit evaluate physics engineering and cost functions apply consistency equations and limit equations iterate free parameters self consistent F o M minimised yes write output Figure 2 2 Conceptual flow diagram of PROCESS in optimisation mode Please note that this is a simplistic interpretation of the actual sequence of
156. timz must be set to 0 or 1 for optimisation mode If ioptimz 0 a non optimisation pass is performed first to provide a hopefully feasible set of initial conditions if ioptimz 1 this is skipped and the code runs in optimisation mode from the start However it is recommended to use ioptimz 1 for optimisation runs as using the HYBRD step before a VMCON iteration tends to cause PROCESS to fail to converge more often As before the user must decide which constraint equations and iteration variables to activate Again the choice depends largely on the information required by the user and the extent of the freedom that the code may have with the machine s parameters The following is part of an example optimisation input file IOPTIMZ 1 NEQNS 16 NVAR 19 ICC 1 2 10 11 7 16 5 24 14 8 31 32 33 34 35 36 Ixc 5 10 12 29 7 9 36 19 14 48 49 50 51 53 54 4 6 1 18 BOUNDL 1 2 5 BOUNDU 10 2 0 MINMAX 6 FPNETEL 1 0 PNETELIN 1200 0 WALALW 4 4 ISWEEP 3 NSWEEP 11 SWEEP 3 5 3 7 3 9 The figure of merit in this example is the minimum cost of electricity minmax 6 Note that additional limit equations are now active along with a second consistency equation related to the neutral beam current drive the number of decay lengths to the plasma centre is constrained to be equal to the input value tbeamin which is not shown here Furthermore there are now more iterati
157. tion process 2 5 to help in the optimisation Chapter 3 Physics Engineering and Other Models 27 Z A ddwex PF coil pe clht ipfloc 1 PF coil ipfloc 2 MEE vacuum vessel i EEE shield E blanket 7 DA first wall E tfcth external cryostat hmax 7 vgap2 hmax x 4 ohhghf ddwi y shldtth divfix vgap PF coils ipfloc 3 rminor x kappa TT oO EA f NY 3ZESe t t qe So o 5 x 2 5 6 Uiaz s o fo fe See 635 g 5 E 3 8 S80ss2 ess 338 3 E R o D 5 0 E E 573 5 goo romax rsldi rmajor rsido rtot rdewex Figure 3 2 Schematic diagram of the fusion power core of a typical tokamak power plant modelled by PROCESS The first wall blanket shield and vacuum vessel cross sectional shapes are each assumed to be defined by two ellipses chosen by setting switch fwbsshape 2 compare Figure 3 1 Chapter 3 Physics Engineering and Other Models 28 ddwex clht hpfu gt tfcth vgap2 ddwi 4 shldtth binktth fwith fwoth 2 4 scrapli scraplo 2 7 hmax x ohhghf rminor x kappa rminor x kappa vgap divfix shldtth ddwi J hmax t cth clht ddwex vgap2 PF coil ipfloc 1 PF coil ipfloc 1 vacuum vessel shield blanket first wall external cryostat E PF coil ipfloc 2
158. tly formatted comment lines to numerics f90 to document the above changes 5 6 Scanning Variables Scanning variables see Section 2 7 are added to PROCESS in the following way 1 Increment the parameter ipnscnv in module scan module in source file scan f90 to accommodate the new scanning variable 2 Add a short description of the new scanning variable to the nsweep entry in source file scan 90 3 Add a new assignment to the relevant part of routine SCAN in source file scan f90 following the examples already present including the inclusion of a short description of the new scanning variable in variable xlabel 4 Ensure that the scanning variable used in the assignment is contained in one of the modules specified via use statements present at the start of this routine 5 Modify process dicts py if necessary Chapter 5 Inclusion of New Models Additional Variables and Equations 82 5 7 Submission of New Models The PROCESS source code is maintained by CCFE and resides in a Git 66 repository on the CCFE servers We welcome contributions of alternative or improved models and algorithms The Fortran 90 95 source code has a uniform visual style and structural layout CCFE will transfer any contributed models into PROCESS in order for us to maintain its present coding standard To simplify this task we request that contributors provide the following information for any new models that they provide e A compr
159. to be applied to the plasma This variable may be used as an iteration variable no 11 3 1 10 3 Neutral beam access If present a neutral beam injection system needs sufficient space between the TF coils to be able to intercept the plasma tangentially The major radius rtanbeam at which the centreline of the beam is tangential to the toroidal direction is user defined using input parameter frbeam which is the ratio of rtanbeam to the plasma major radius rmajor The maximum possible tangency radius rtanmax is determined by the geometry of the TF coils see Figure 3 7 and this can be enforced using constraint equation no 20 with iteration variable no 33 fportsz The thickness of the beam duct walls may be set using input parameter nbshield 3 1 10 4 Ignited plasma Switch ignite can be used to denote whether the plasma is ignited i e fully self sustaining without the need for any injected auxiliary power during the burn If ignite 1 the calculated injected power does not contribute to the plasma power balance Section 3 1 2 10 although the cost of the auxiliary power system is taken into account the system is then assumed to be required to provide heating etc during the plasma start up phase only use pheat to indicate the power requirement If ignite 0 the plasma is not ignited and the auxiliary power is taken into account in the plasma power balance during the burn phase Also constraint equation no 28 can be turned on
160. to obtain c 0 thereby ensuring that g h 2 4 2 Limit equations The limit equations are usually nequalities that ensure that various physics or engineering limits are not exceeded Each of these equations has an associated f value which allow them to be coded as Chapter 2 Program Overview The Fundamental Concepts 16 equalities The f values are used as follows In optimisation mode all iteration variables have prescribed lower and upper bounds In general limit equations have the form calculated quantity f x maximum allowable value where f is the f value If f has a lower bound of zero and an upper bound of one then the limit equation does indeed constrain the calculated quantity to lie between zero and its maximum allowable value as required As with the consistency equations the general form of the limit equations is Ci 1 f Pmax where hmax is the maximum allowed value of the quantity h Sometimes the limit equation and f value are used to ensure that quantity his larger than its minimum value Amin In this case 0 lt f lt 1 as before but the equation takes the form h Amin c 1 f By fixing the fvalue i e not including it in the ixc array the limit equations can be used as equality constraints For example to set the net electric power to a certain value the following should be carried out 1 Activate constraint equation 16 by including it in the first neqns elements of ar
161. to the output file as the convergence to a valid solution might resolve some of the warnings produced earlier in the solution process The error_status variable returns the highest severity level that has been encountered or zero if no abnormal conditions have been found if a severe error level 3 is flagged at any point the program is terminated immediately The final message number encountered during a run is returned via output variable error_id In addition with certain messages a number of diagnostic values may also be given these can be used to provide extra diagnostic information if the source code is available Chapter 4 Execution of the Code 76 4 4 2 General problems A code of the size and complexity of PROCESS contains myriads of equations and variables Virtually everything depends indirectly on everything else because of the nature of the code structure so perhaps it is not surprising that it is often difficult to achieve a successful outcome Naturally problems will occur if some of the parameters become unphysical For example if the aspect ratio becomes less than or equal to one then we must expect problems to appear For this reason the default bounds on the iteration variables and the allowed ranges of all the input variables have been selected with great care The code contains a large though probably not exhaustive number of error traps to try and prevent problems from propagating These include tests for unph
162. tors and tokamaks as follows Chapter 3 Physics Engineering and Other Models 59 Vertical ports Outer vessel OV support Coil support structure K Plasma vessel Horizontal ports Figure 3 10 Fusion power core of the HELIAS 5 B conceptual power plant design from 34 Chapter 3 Physics Engineering and Other Models 60 3 5 1 1 Plasma geometry The plasma geometry model uses Fourier coefficients to represent the complex 3 D plasma shape typical of stellarators A VMEC 38 calculation or other equilibrium code that can provide the Fourier coefficients of the LCFS must have been performed prior to running with PROCESS The overall size of the plasma is scaled correctly for the required mean major and minor radii for the machine being modelled 39 It is necessary to provide three input files that define the plasma shape 1 Set vmec_info file in the input file to the name of a file with the following format the numbers given are those for the W7 X high mirror configuration in practice only the effective major and minor radius values R_ eff and a eff respectively and the number of field periods are used R_eff m a_eff ml Aspect ratio Plasma vol m3 LCFS surf area m2 field periods 5 486576 0 4942638 11 10050 26 45749 133 4281 5 0 2 Set vmec_rmn_file in the input file to the name of a VMEC output file containing the calculated plasma boundary R m n Fourier coefficients where m
163. traint equations function evaluators for HYBRD and VMCON packages adjusts values of iteration variables miscellaneous black box maths routines including HYBRD and VMCON numerics array definitions and calling routines for HYBRD and VMCON packages performs a parameter scan Table 2 6 Summary of the numerics modules in PROCESS Chapter 2 Program Overview The Fundamental Concepts 23 source file description current_drive f90 divertor f90 fispact f90 ife f90 impurity_radiation f90 physics f90 plasma_geometry f90 plasma _profiles f90 r p f90 startup f90 stellarator f90 current drive efficiency calculations divertor model calculations nuclide inventory activation calculations inertial fusion energy physics engineering radiation power calculations tokamak plasma and fusion calculations plasma geometry algorithms reversed field pinch physics engineering plasma start up auxiliary power requirements stellarator relevant physics engineering plasma density and temperature profile calculations Table 2 7 Summary of the physics modules in PROCESS file contents source file description availability f90 buildings f90 wbs f90 machine _build f90 p coil f90 plant_power f90 pulse f90 safety f90 sctfcoil f90 structure f90 t coil f90 vacuum f90 plant component lifetimes and overall availability buildings calculations first wall blanket
164. uated to remove outgassed impurities from the structure Secondly the chamber must be re evacuated between burn operations Thirdly helium ash must be removed to prevent it from diluting the fuel Finally deuterium and tritium is removed on a steady state basis PROCESS calculates the parameters of a vacuum system that satisfy all four requirements with the option of either turbo pumps or cryo pumps being used Switch ntype controls whether a turbopump ntype 0 or a cryopump ntype 1 is used in the vacuum system 3 1 13 Power conversion and heat dissipation systems The PROCESS power plant takes into account all the systems required to perform the necessary conversion of fusion power to electricity from the coolant systems in the plant components to the heat exchangers and turbines Figures 3 8 and 13 9 show schematically the overall power transfer mechanisms within the power plant outside of the plasma the power flow within the plasma is shown in Figure 3 4 Note that these figures and the following description assume that switch ipowerflow is set to 1 its default value is currently zero as the new power flow model is in draft form Figure 3 8 shows how the power contributions originating from the plasma are converted to thermal power in the first wall blanket shield and divertor The radiation and neutron power contributions are distributed according to the following area fractions
165. uit stress limit equation 32 0 001DO 1 000DO 50 fiooic f value for TF coil operational current limit equation 33 0 001D0 0 500DO Table 2 2 Iteration variables 1 to 50 present in PROCESS The f values correspond to the given constraint equations see Table 2 1 The other iteration variables are shown in Table 2 3 Chapter 2 Program Overview The Fundamental Concepts 20 ixc icc lower upper no variable name description eqn bound bound 51 fvdump f value for TF coil dump voltage limit equation 34 0 001D0 1 000D0 52 vdalw allowable TF coil dump voltage 0 001D0 1 000D6 53 fjprot f value for TF coil current protection limit equation 35 0 001DO 1 000DO 54 ftmargtf f value for TF coil temperature margin limit equation 36 0 001DO 1 000DO 55 tmargmin minimum allowable TF coil temperature margin 0 001D0 100 0DO 56 tdmptf dump time for TF coil 10 00D0 1 000D6 57 thkcas TF coil external case thickness 0 050DO 1 000DO 58 thwcndut TF coil conduit case thickness 0 001D0 1 000D0 59 fcutfsu copper fraction of cable conductor 0 001DO 1 000DO 60 cpttf current per turn in the TF coils 0 001D0 4 000D4 61 gapds gap between vacuum vessel and inboard TF coil 0 001D0 10 00D0 62 fdtmp f value for 1st wall coolant temperature rise limit equation 38 0 001DO 1 000DO 63 ftpeak f value for 1st wall peak temperature limit equation 39 0 001DO 1 000DO 64
166. um 3 Madison Wisconsin 1977 Appendix A The Optimisation Solver Explained To give the user a better understanding of the optimisation solver implemented in PROCESS and the interpretation of its results we give a short introduction into the mathematical background for solving these type of problems as well as the specific algorithm used In section A 1 we the general nonlinear programming problem is defined which is the mathematical description of our problem This problem is typically formulated using Lagrange multipliers c f A 2 and is solved numerically most efficiently using sequential quadratic programming c f A 3 The Fortran subroutine that is used to implement such an optimisation solver in PROCESS is called VMCON c f A 4 which iterates between solving a local quadratic subproblem c f A 5 and a one dimensional line search c f A 6 As the total method is using a quasi Newtonian approach the Hessian matrix is approximated by a variant of the Broyden Fletcher Goldfarb Shanno update A 7 Section A 8 summarises the symbol convention used in this chapter A 1 The General Nonlinear Programming Problem Mathematically the general nonlinear programming problem or nonlinear constrained optimisation problem is defined as minimise f x A la subject to c a 0 T Lore A 1b and c a gt 0 i k 1 m A 1c where bot
167. ure help in the winding process and also provide extra support against tangential stresses Grooves are machined into the radial plates which act as a guide for the cable Each winding pack turn slots into a radial plate and is covered by a steel cap Each turn is assigned half the thickness along each edge of its surrounding radial plates and steel caps in the calculation of the cross sectional areas Iteration variable no 101 prp is the ratio of the total radial plate plus steel cap cross sectional area within the winding pack to the total winding pack cross sectional area from this the half thickness trp is calculated The outboard leg of the TF coil is assumed to be the same width in the toroidal direction as the outside edge of the inboard leg In the radial direction for resistive TF coils the input parameter tfootfi gives the ratio of the outboard leg thickness to the inboard leg thickness tfcth for superconducting coils the outboard thickness is set equal to the inboard thickness Each TF coil is defined in the R Z plane by four circular arcs of different radius which create a D shaped profile Because of the finite number of TF coils used in a tokamak typically around 16 the toroidal field has a ripple introduced into it the amplitude of which can be limited to a few percent given by input parameter ripmax default value 1 by the code by adjusting the outboard gap thickness labelled gapsto in Figures 3 1 and 33 2
168. variable is the name of one of the input parameters or iteration variables listed in the variable descriptor file and value is the usually numerical initial value required for that variable Arrays as opposed to scalar quantities are treated differently see below Variables can be specified in any order in the input file The routines that read in and parse the data from the input file are in source file input 90 They allow a great deal of error trapping to be carried out at the input stage All input data are screened for non sensible values directly this is a useful feature of the code since without such intervention modern computers are notorious at not terminating programs when an arithmetically impossible or undefined operation NaN error is encountered 4 1 3 Format rules The following rules must be obeyed when writing an input file 1 Each variable must be on a separate line 2 Variable names can be upper case lower case or a mixture of both 3 Spaces may not appear within a variable name or data value 4 Other spaces within a line and trailing spaces are ignored 5 Commas are not necessary between variables but see below 6 Data can extend over more than one line 7 One dimensional arrays can be explicitly subscripted or unscripted in which case the following element order is assumed A 1 A 2 A 3 8 At present multiple dimension arrays can only be handled without reference to explicit
169. vid Ward Richard Kemp Michael Kovari Hanni Lux and James Morris all of CCFE and the members of the PROCESS User Group throughout Europe This work was funded by the RCUK Energy Programme under grant EP 1501045 and the European Communities under the contract of Association between EURATOM and CCFE The views and opinions expressed herein do not necessarily reflect those of the European Commission Part of this work was carried out within the framework of the European Fusion Development Agreement 101 Bibliography 10 11 12 13 14 15 R L Reid et al ETR ITER Systems Code Oak Ridge Report ORNL FEDC 87 7 1988 J D Galambos STAR Code Spherical Tokamak Analysis and Reactor Code Unpublished internal Oak Ridge document A copy exists in the PROCESS Project Work File 31 J J More B S Garbow and E Hillstrom User Guide for MINPAC 1 Argonne National Laboratory Report ANL 80 74 1980 M J D Powell A Hybrid Method for Non linear Algebraic Equations Numerical Methods for Non linear Algebraic Equations ed P Rabinowitz Prentice Hall R L Crane K E Hillstrom and M Minkoff Solution of the General Nonlinear Programming Problem with Subroutine VMCON Argonne National Laboratory Report ANL 80 64 1980 M J D Powell A Fast Algorithm for Nonlinearly Constrained Optimization Calculations Lecture Notes in Mathematics vol 630 pp 144 157 Springer Verla
170. w Ohmic heating power OHMIC pohmmw Auxiliary power to electrons pinjemw Core Plasma Power Balance Edge radiation power pedgeradmw AUXILIARY INJECTION Total injected power pinimw Auxiliary power to ions pinjimw Total radiation power pradmw Wall plug injection power h pinjwp 1 h Secondary heat Figure 3 4 Schematic diagram of the flow of power within the plasma core Variable names are given in Refer to Figure 3 8 for the onward flow of power from the three red bordered boxes while the source of the power in the blue box is indicated in Figure 3 9 Chapter 3 Physics Engineering and Other Models 37 3 1 2 10 Plasma core power balance Figure 3 4 shows schematically the flow of power within the plasma as calculated by the code Figures 3 8 and 3 9 show the power transfer mechanisms for the remainder of the power plant The primary sources of power are the fusion reactions themselves ohmic power due to resistive heating within the plasma and any auxiliary power provided for heating and current drive see Section 3 1 10 The power carried by the fusion generated neutrons is lost from the plasma but is deposited in the surrounding material see Section 3 1 13 A fraction falpha of the alpha particle power is assumed to stay within the plasma core to contribute to the plasma p
171. w the code calculates the driver efficiency and target gain these are the primary outputs required from the physics part of the model For the SOMBRERO and OSIRIS cases ifedrv 1 and ifedrv 2 respectively the driver efficiency and gain are calculated from curves of these parameters as functions of the driver energy For the ifedrv 1 case the user provides the driver efficiency and target gain versus driver energy via the two arrays etave 1 10 and gainve 1 10 respectively the element number corresponds to the driver energy in MJ and outside the range 1 10 MJ the curves are extrapolated linearly Finally for the ifedrv 0 case the user inputs single values for the driver efficiency drveff and target gain tgain Constraint equation no 50 can be turned on to enable the ignition repetition rate to remain below a user specified upper limit rrmax iteration variable no 86 frrmax is the associated f value see Section 2 4 The other iteration variables relevant for the IFE model are nos 81 85 edrive drveff tgain chrad and pdrive see Table 2 3 3 8 Safety and Environment Models At present the neutronics activation and inventory calculations comprise the safety and environment models in the code The models comprising the safety and environmental calculations 60 within the code are all called from routine FISPAC They are only performed once at the end of each run as they t
172. wer plant design calls for a machine with a given size and shape which will produce a certain net electric power There may be a vast number of different conceptual machines that satisfy the problem as stated so far and PROCESS can be used in non optimisation mode to find one of these whose physics and engineering parameters are self consistent However the machine found by PROCESS in this manner may not be possible to build in practice the coils may be overstressed for instance or the plasma pressure may exceed the maximum possible value PROCESS contains a large number of constraints to prevent the code from finding a machine with such problems and running the code in so called optimisation mode forces these constraints to be met The number of possible conceptual machines is thus considerably reduced and optimisation of the parameters with respect to say the cost of electricity will reduce this number to a minimum possibly one Formally then PROCESS is a systems code that calculates in a self consistent manner the parameters of a fusion power plant with a specified performance ensuring that its operating limits are not violated and with the option to optimise a given function of these parameters It would not be fair to call PROCESS a fusion power plant design code as this implies that a great deal of complexity would need to be present in each and every model describing one of the component systems Such complexity is how
173. written To extract the individual files again copy the file to the destination working directory and type tar zxvf process tar gz e make archive Typing this command produces a file process_run tar gz containing the working directory s input and output files IN DAT OUT DAT PLOT DAT MFILE DAT and device dat which must exist to avoid an error message see Section 4 1 1 together with all of the source files utility programs and documentation files These files together comprise the full set that define a given run and so the file produced by this command is suitable for long term storage for archival purposes To extract the contents type tar zxvf process_run tar gz Note that each of the above commands will overwrite the given named tar file if one already exists in the working directory 7 1 3 Code documentation The makefile can also be used to produce source code documentation as described in the next section 7 2 Automatic Documentation The PROCESS source code is self documenting to a degree using an included parser program autodoc to generate html files for each subprogram from specially formatted comment lines within the code It is the responsibility of the programmer to keep the autodoc comments within the source code relevant comprehensive and up to date Use the examples in the code as a starting basis for new routines the output section corresponding to the various autodoc tags should be self explanatory The f
174. x py r README txt append the results to Index txt instead of creating a new file build_index py m a change the name of the subfolder Base default Run build_index py b Base give a list of subfolder suffixes default all build_index py s 1 4 6 8 9 12 increase verbosity build_index py v An example Index txt file might look like this Run1 Original run Run2 Changed the no TF coils 6 1 5 make _plot_dat py Creates a PLOT DAT type file from MFILE DAT Input make_plot_dat conf MFILE DAT Output make_plot_dat out Configuration Options Optional arguments are new variables for output make_plot_dat py p rmajor writes make_plot_dat out in columns make_plot_dat py columns resets make_plot_dat conf to PLOT DAT layout make_plot_dat py reset config file to read as input make_plot_dat py f MFILE DAT run with default parameters make_plot_dat py defaults An example version of make_plot_dat conf might look like this Chapter 6 Utility Programs 87 make_plot_dat out config file rmajor aspect rminor bt powfmw pnetelmw te pdivt strtf1 strt 2 6 1 6 plot_proc py A utility to produce the standard PROCESS summary output covering the major parameters provenance data and a machine cross section It allows a wide range of graphical output formats and can easily be customised using the function gather_info in plot_proc_func py Input MFILE DAT
175. xcluding elongation J A Snipes ITER H mode Threshold Database 1997 ITER scaling including elongation Working Group Controlled Fusion and Plasma Physics 24th EPS Conference Berchtesgaden June 1997 vol 21A part III p 961 6 2008 Martin scaling nominal Martin et al 11th IAEA Tech Meeting on H mode 7 2008 Martin scaling 95 upper bound Physics and Transport Barriers Journal of Physics 8 2008 Martin scaling 95 lower bound Conference Series 123 2008 012033 Table 3 2 Summary of the L H power threshold scalings implemented in PROCESS 3 1 2 13 Other plasma physics options Neo classical correction effects Switch ires controls whether neo classical correction effects 25 are included in the calculation of the plasma resistance and ohmic heating power in routine POHM which is called by routine PHYSICS If ires 1 these effects are included Note that the scaling used is only valid for aspect ratios between 2 5 and 4 and it is possible for the plasma resistance to be wrongly calculated as negative if ires 1 and the aspect ratio is too high Inverse quadrature in Tz scaling laws Switch iinvqd determines whether the energy confinement time scaling laws see Section 3 1 2 9 due to Kaye Goldston isc 5 and Goldston isc 9 should include an inverse quadrature scaling with the Neo Alcator result isc 1 A value iinvqd 1 includes this scaling Plasm
176. y This is performed automatically if you launch the GUI by typing start_gui from the command line For instructions on starting the server manually see the README file in the utilities gui directory Chapter 6 Utility Programs 98 6 3 2 Editing variables Every variable should be listed along with its current value a reference value and a short description Hovering over the short description will provide a longer description All values begin with the default value assigned by PROCESS The reference values are used to compare differences between two files Differences between the reference value and the current input value will be highlighted in red The Meta section allows editing of the run description which will be placed at the top of the created IN DAT Changes to the iteration variables and constraint equations that are enabled can be done using the checkboxes in the relevant section 6 3 3 Opening and saving files An input file and a reference file can be opened using the buttons at the top of the screen The files opened must be compatible with the PROCESS version number shown in the top right of the screen The Save button should produce a IN DAT file with a similar layout to the GUI Variables whose values are set different from the PROCESS default are listed under module headings along with a comment describing the variable For integer variables a description of the value taken may also be included The vari
177. ys boundl and boundu respectively For instance the plasma electron density is by default confined to lie between the values 101 m and 107 m Of course it can also be constrained to lie below the calculated density limit if constraint equation 5 is activated and the f value fdene iteration variable no 9 is bounded by the values 0 and 1 It is important to remember that iteration variables must never be initialised to zero The code will not be able to adjust the variable s value if this is done and it will stop with an error message 2 6 Figures of Merit In optimisation mode PROCESS finds the self consistent set of iteration variable values that maximises or minimises a certain function of them known as the figure of merit Several possible figures of merit are available all of which are formulated in routine FUNFOM in source file evaluators f90 Switch minmax is used to control which figure of merit is to be used as summarised in Table 2 4 If the figure of merit is to be minimised minmax should be positive and if a maximised figure of merit is desired minmax should be negative 2 7 Scanning Variables One of a number of variables can be scanned during the course of a PROCESS run This option provides a method of determining the sensitivity of the results to different input assumptions The user specifies which variable is to be scanned see Table 2 5 and its required value at each point in the scan The scanned vari
178. ysical values and checks to prevent divisions by zero and non sensible arguments for logarithms and square roots etc However occasionally arithmetic NaN errors still occur although their incidence is low They now usually only occur due to unfeasibility problems see later The error messages produced by the code attempt to provide diagnostic information telling the user where the problem occurs and also suggest a possible solution These messages are out of necessity brief and so cannot promise to lead to a more successful outcome For expert users there is the option to turn on extra debugging output to do this set verbose 1 in the input file 4 4 3 Optimisation problems On reflection it is perhaps surprising that PROCESS ever does manage to find the global minimum figure of merit value since if there are nvar iteration variables active the search is over nvar dimensional parameter space in which there may be many shallow minima of approximately equal depth Remember that nvar is usually of the order of twenty The machine found by PROCESS may not therefore be the absolutely optimal device It is quite easy to have two or more solutions with results only a few per cent different but a long way apart in parameter space The technique of stationary scans described in Section 4 3 3 above can often help in this situation which is why this method is recommended at all times Scans should be started i
179. ython plot_mfile_sweep py f diff_mfile dat p rmajor aspect Show plot to screen instead of saving with RO and aspect python plot_mfile_sweep py p rmajor aspect show Use h or help for help 6 1 9 diagnose_process py This utility aids the user to interpret unsuccessful PROCESS runs unless PROCESS has terminated prematurely It takes an existing MFILE DAT and plots the normalised iteration variables i e the iteration variable values normalised to their bounds such that 0 indicates an iteration variable at its lower bound and 1 an iteration variable at its upper bound Furthermore it shows the normalised constraint residuals Input MFILE DAT Output Displays plots on screen still need to be saved by the user Remember to use Y or X if sshing into a remote machine Optional arguments are allows to specify another location name for the MFILE python diagnose_process py f MFILE DAT Use h or help for help Chapter 6 Utility Programs 89 6 1 10 2D scan py N B This utility is currently not working please do not try to use it Runs a two dimensional scan of PROCESS variables This code does not yet use the new PROCESS Python libraries Input 2D_scan conf IN DAT Output All the standard PROCESS output files ERROR DAT Error matrix for all iterations EDGETABLE DAT Marks if variables at bounds MATRICES DAT Solution for each variable EDGEVARS DAT Names of variables at bounds Configuration

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