! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! module numerics !! Module containing callers to the main equation solvers !! HYBRD and VMCON !! author: P J Knight, CCFE, Culham Science Centre !! This module contains the primary numerics variables and the !! calling routines for the two equation solvers in the code. ! ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! #ifndef dp use, intrinsic :: iso_fortran_env, only: dp=>real64 #endif implicit none public integer, parameter :: ipnvars = 175 !! ipnvars FIX : total number of variables available for iteration integer, parameter :: ipeqns = 91 !! ipeqns FIX : number of constraint equations available integer, parameter :: ipnfoms = 19 !! ipnfoms FIX : number of available figures of merit integer, parameter :: ipvlam = ipeqns+2*ipnvars+1 integer, parameter :: iptnt = (ipeqns*(3*ipeqns+13))/2 integer, parameter :: ipvp1 = ipnvars+1 integer :: ioptimz !! ioptimz /1/ : code operation switch:<UL> !! <LI> = -2 for no optimisation, no VMCOM or HYBRD; !! <LI> = -1 for no optimisation, HYBRD only; !! <LI> = 0 for HYBRD and VMCON (not recommended); !! <LI> = 1 for optimisation, VMCON only</UL> !! minmax /7/ : switch for figure-of-merit (see lablmm for descriptions) !! negative => maximise, positive => minimise integer :: minmax character(len=22), dimension(ipnfoms) :: lablmm !! lablmm(ipnfoms) : labels describing figures of merit:<UL> !! <LI> ( 1) major radius !! <LI> ( 2) not used !! <LI> ( 3) neutron wall load !! <LI> ( 4) P_tf + P_pf !! <LI> ( 5) fusion gain Q !! <LI> ( 6) cost of electricity !! <LI> ( 7) capital cost (direct cost if ireactor=0, !! constructed cost otherwise) !! <LI> ( 8) aspect ratio !! <LI> ( 9) divertor heat load !! <LI> (10) toroidal field !! <LI> (11) total injected power !! <LI> (12) hydrogen plant capital cost OBSOLETE !! <LI> (13) hydrogen production rate OBSOLETE !! <LI> (14) pulse length !! <LI> (15) plant availability factor (N.B. requires !! iavail=1 to be set) !! <LI> (16) linear combination of major radius (minimised) and pulse length (maximised) !! note: FoM should be minimised only! !! <LI> (17) net electrical output !! <LI> (18) Null Figure of Merit !! <LI> (19) linear combination of big Q and pulse length (maximised) !! note: FoM should be minimised only!</UL> integer :: ncalls !! ncalls : number of function calls during solution integer :: neqns !! neqns /0/ : number of equality constraints to be satisfied integer :: nfev1 !! nfev1 : number of calls to FCNHYB (HYBRD function caller) made integer :: nfev2 !! nfev2 : number of calls to FCNVMC1 (VMCON function caller) made integer :: nineqns !! nineqns /0/ : number of inequality constraints VMCON must satisfy !! (leave at zero for now) integer :: nvar !! nvar /16/ : number of iteration variables to use integer :: nviter !! nviter : number of VMCON iterations performed !! icc(ipeqns) /0/ : !! array defining which constraint equations to activate !! (see lablcc for descriptions) ! TODO Check the dictionaries are created correctly. ! Issue #491 Default constraints removed. integer, dimension(ipeqns) :: icc logical, dimension(ipeqns) :: active_constraints !! active_constraints(ipeqns) : Logical array showing which constraints are active ! #TODO Do not change the comments for lablcc: they are used to create the ! Python-Fortran dictionaries. This must be improved on. character(len=33), dimension(ipeqns) :: lablcc !! lablcc(ipeqns) : labels describing constraint equations (corresponding itvs)<UL> !! <LI> ( 1) Beta (consistency equation) (itv 5) !! <LI> ( 2) Global power balance (consistency equation) (itv 10,1,2,3,4,6,11) !! <LI> ( 3) Ion power balance DEPRECATED (itv 10,1,2,3,4,6,11) !! <LI> ( 4) Electron power balance DEPRECATED (itv 10,1,2,3,4,6,11) !! <LI> ( 5) Density upper limit (itv 9,1,2,3,4,5,6) !! <LI> ( 6) (Epsilon x beta poloidal) upper limit (itv 8,1,2,3,4,6) !! <LI> ( 7) Beam ion density (NBI) (consistency equation) (itv 7) !! <LI> ( 8) Neutron wall load upper limit (itv 14,1,2,3,4,6) !! <LI> ( 9) Fusion power upper limit (itv 26,1,2,3,4,6) !! <LI> (10) Toroidal field 1/R (consistency equation) (itv 12,1,2,3,13 ) !! <LI> (11) Radial build (consistency equation) (itv 3,1,13,16,29,42,61) !! <LI> (12) Volt second lower limit (STEADY STATE) (itv 15,1,2,3) !! <LI> (13) Burn time lower limit (PULSE) (itv 21,1,16,17,29,42,44,61) !! (itv 19,1,2,3,6) !! <LI> (14) Neutral beam decay lengths to plasma centre (NBI) (consistency equation) !! <LI> (15) LH power threshold limit (itv 103) !! <LI> (16) Net electric power lower limit (itv 25,1,2,3) !! <LI> (17) Radiation fraction upper limit (itv 28) !! <LI> (18) Divertor heat load upper limit (itv 27) !! <LI> (19) MVA upper limit (itv 30) !! <LI> (20) Neutral beam tangency radius upper limit (NBI) (itv 33,31,3,13) !! <LI> (21) Plasma minor radius lower limit (itv 32) !! <LI> (22) Divertor collisionality upper limit (itv 34,43) !! <LI> (23) Conducting shell to plasma minor radius ratio upper limit !! (itv 104,1,74) !! <LI> (24) Beta upper limit (itv 36,1,2,3,4,6,18) !! <LI> (25) Peak toroidal field upper limit (itv 35,3,13,29) !! <LI> (26) Central solenoid EOF current density upper limit (ipfres=0) !! (itv 38,37,41,12) !! <LI> (27) Central solenoid BOP current density upper limit (ipfres=0) !! (itv 39,37,41,12) !! <LI> (28) Fusion gain Q lower limit (itv 45,47,40) !! <LI> (29) Inboard radial build consistency (itv 3,1,13,16,29,42,61) !! <LI> (30) Injection power upper limit (itv 46,47,11) !! <LI> (31) TF coil case stress upper limit (SCTF) (itv 48,56,57,58,59,60,24) !! <LI> (32) TF coil conduit stress upper limit (SCTF) (itv 49,56,57,58,59,60,24) !! <LI> (33) I_op / I_critical (TF coil) (SCTF) (itv 50,56,57,58,59,60,24) !! <LI> (34) Dump voltage upper limit (SCTF) (itv 51,52,56,57,58,59,60,24) !! <LI> (35) J_winding pack/J_protection upper limit (SCTF) (itv 53,56,57,58,59,60,24) !! <LI> (36) TF coil temperature margin lower limit (SCTF) (itv 54,55,56,57,58,59,60,24) !! <LI> (37) Current drive gamma upper limit (itv 40,47) !! <LI> (38) First wall coolant temperature rise upper limit (itv 62) !! <LI> (39) First wall peak temperature upper limit (itv 63) !! <LI> (40) Start-up injection power lower limit (PULSE) (itv 64) !! <LI> (41) Plasma current ramp-up time lower limit (PULSE) (itv 66,65) !! <LI> (42) Cycle time lower limit (PULSE) (itv 17,67,65) !! <LI> (43) Average centrepost temperature !! (TART) (consistency equation) (itv 13,20,69,70) !! <LI> (44) Peak centrepost temperature upper limit (TART) (itv 68,69,70) !! <LI> (45) Edge safety factor lower limit (TART) (itv 71,1,2,3) !! <LI> (46) Equation for Ip/Irod upper limit (TART) (itv 72,2,60) !! <LI> (47) NOT USED !! <LI> (48) Poloidal beta upper limit (itv 79,2,3,18) !! <LI> (49) NOT USED !! <LI> (50) IFE repetition rate upper limit (IFE) !! <LI> (51) Startup volt-seconds consistency (PULSE) (itv 16,29,3,1) !! <LI> (52) Tritium breeding ratio lower limit (itv 89,90,91) !! <LI> (53) Neutron fluence on TF coil upper limit (itv 92,93,94) !! <LI> (54) Peak TF coil nuclear heating upper limit (itv 95,93,94) !! <LI> (55) Vacuum vessel helium concentration upper limit iblanket =2 (itv 96,93,94) !! <LI> (56) Pseparatrix/Rmajor upper limit (itv 97,1,3) !! <LI> (57) NOT USED !! <LI> (58) NOT USED !! <LI> (59) Neutral beam shine-through fraction upper limit (NBI) (itv 105,6,19,4 ) !! <LI> (60) Central solenoid temperature margin lower limit (SCTF) (itv 106) !! <LI> (61) Minimum availability value (itv 107) !! <LI> (62) taup/taueff the ratio of particle to energy confinement times (itv 110) !! <LI> (63) The number of ITER-like vacuum pumps niterpump < tfno (itv 111) !! <LI> (64) Zeff less than or equal to zeffmax (itv 112) !! <LI> (65) Dump time set by VV loads (itv 56, 113) !! <LI> (66) Limit on rate of change of energy in poloidal field !! (Use iteration variable 65(t_current_ramp_up), 115) !! <LI> (67) Simple Radiation Wall load limit (itv 116, 4,6) !! <LI> (68) Psep * Bt / qAR upper limit (itv 117) !! <LI> (69) ensure separatrix power = the value from Kallenbach divertor (itv 118) !! <LI> (70) ensure that teomp = separatrix temperature in the pedestal profile, !! (itv 119 (tesep)) !! <LI> (71) ensure that neomp = separatrix density (nesep) x neratio !! <LI> (72) central solenoid shear stress limit (Tresca yield criterion) (itv 123 foh_stress) !! <LI> (73) Psep >= Plh + Paux (itv 137 (fplhsep)) !! <LI> (74) TFC quench < tmax_croco (itv 141 (fcqt)) !! <LI> (75) TFC current/copper area < Maximum (itv 143 f_coppera_m2) !! <LI> (76) Eich critical separatrix density !! <LI> (77) TF coil current per turn upper limit !! <LI> (78) Reinke criterion impurity fraction lower limit (itv 147 freinke) !! <LI> (79) Peak CS field upper limit (itv 149 fbmaxcs) !! <LI> (80) Divertor power lower limit pdivt (itv 153 fpdivlim) !! <LI> (81) Ne(0) > ne(ped) constraint (itv 154 fne0) !! <LI> (82) toroidalgap > tftort constraint (itv 171 ftoroidalgap) !! <LI> (83) Radial build consistency for stellarators (itv 172 f_avspace) !! <LI> (84) Lower limit for beta (itv 173 fbetatry_lower) !! <LI> (85) Constraint for CP lifetime !! <LI> (86) Constraint for TF coil turn dimension !! <LI> (87) Constraint for cryogenic power !! <LI> (88) Constraint for TF coil strain absolute value !! <LI> (89) Constraint for CS coil quench protection !! <LI> (90) Lower Limit on number of stress load cycles for CS (itr 167 fncycle) !! <LI> (91) Checking if the design point is ECRH ignitable (itv 168 fecrh_ignition) </UL> integer, dimension(ipnvars) :: ixc !! ixc(ipnvars) /0/ : !! array defining which iteration variables to activate !! (see lablxc for descriptions) character*30, dimension(ipnvars) :: lablxc !! lablxc(ipnvars) : labels describing iteration variables<UL> !! <LI> ( 1) aspect !! <LI> ( 2) bt !! <LI> ( 3) rmajor !! <LI> ( 4) te !! <LI> ( 5) beta !! <LI> ( 6) dene !! <LI> ( 7) rnbeam !! <LI> ( 8) fbeta (f-value for equation 6) !! <LI> ( 9) fdene (f-value for equation 5) !! <LI> (10) hfact !! <LI> (11) pheat !! <LI> (12) oacdcp !! <LI> (13) tfcth (NOT RECOMMENDED) !! <LI> (14) fwalld (f-value for equation 8) !! <LI> (15) fvs (f-value for equation 12) !! <LI> (16) ohcth !! <LI> (17) t_between_pulse !! <LI> (18) q !! <LI> (19) beam_energy !! <LI> (20) tcpav !! <LI> (21) ft_burn (f-value for equation 13) !! <LI> (22) NOT USED !! <LI> (23) fcoolcp !! <LI> (24) NOT USED !! <LI> (25) fpnetel (f-value for equation 16) !! <LI> (26) ffuspow (f-value for equation 9) !! <LI> (27) fhldiv (f-value for equation 18) !! <LI> (28) fradpwr (f-value for equation 17), total radiation fraction !! <LI> (29) bore !! <LI> (30) fmva (f-value for equation 19) !! <LI> (31) gapomin !! <LI> (32) frminor (f-value for equation 21) !! <LI> (33) fportsz (f-value for equation 20) !! <LI> (34) fdivcol (f-value for equation 22) !! <LI> (35) fpeakb (f-value for equation 25) !! <LI> (36) fbetatry (f-value for equation 24) !! <LI> (37) coheof !! <LI> (38) fjohc (f-value for equation 26) !! <LI> (39) fjohc0 (f-value for equation 27) !! <LI> (40) fgamcd (f-value for equation 37) !! <LI> (41) fcohbop !! <LI> (42) gapoh !! <LI> (43) NOT USED !! <LI> (44) fvsbrnni !! <LI> (45) fqval (f-value for equation 28) !! <LI> (46) fpinj (f-value for equation 30) !! <LI> (47) feffcd !! <LI> (48) fstrcase (f-value for equation 31) !! <LI> (49) fstrcond (f-value for equation 32) !! <LI> (50) fiooic (f-value for equation 33) !! <LI> (51) fvdump (f-value for equation 34) !! <LI> (52) NOT USED !! <LI> (53) fjprot (f-value for equation 35) !! <LI> (54) ftmargtf (f-value for equation 36) !! <LI> (55) NOT USED !! <LI> (56) tdmptf !! <LI> (57) thkcas !! <LI> (58) thwcndut !! <LI> (59) fcutfsu !! <LI> (60) cpttf !! <LI> (61) gapds !! <LI> (62) fdtmp (f-value for equation 38) !! <LI> (63) ftpeak (f-value for equation 39) !! <LI> (64) fauxmn (f-value for equation 40) !! <LI> (65) t_current_ramp_up !! <LI> (66) ft_current_ramp_up (f-value for equation 41) !! <LI> (67) ftcycl (f-value for equation 42) !! <LI> (68) fptemp (f-value for equation 44) !! <LI> (69) rcool !! <LI> (70) vcool !! <LI> (71) fq (f-value for equation 45) !! <LI> (72) fipir (f-value for equation 46) !! <LI> (73) scrapli !! <LI> (74) scraplo !! <LI> (75) tfootfi !! <LI> (76) NOT USED !! <LI> (77) NOT USED !! <LI> (78) NOT USED !! <LI> (79) fbetap (f-value for equation 48) !! <LI> (80) NOT USED !! <LI> (81) edrive !! <LI> (82) drveff !! <LI> (83) tgain !! <LI> (84) chrad !! <LI> (85) pdrive !! <LI> (86) frrmax (f-value for equation 50) !! <LI> (87) NOT USED !! <LI> (88) NOT USED !! <LI> (89) ftbr (f-value for equation 52) !! <LI> (90) blbuith !! <LI> (91) blbuoth !! <LI> (92) fflutf (f-value for equation 53) !! <LI> (93) shldith !! <LI> (94) shldoth !! <LI> (95) fptfnuc (f-value for equation 54) !! <LI> (96) fvvhe (f-value for equation 55) !! <LI> (97) fpsepr (f-value for equation 56) !! <LI> (98) li6enrich !! <LI> (99) NOT USED !! <LI> (100) NOT USED !! <LI> (101) NOT USED !! <LI> (102) fimpvar # OBSOLETE !! <LI> (103) flhthresh (f-value for equation 15) !! <LI> (104) fcwr (f-value for equation 23) !! <LI> (105) fnbshinef (f-value for equation 59) !! <LI> (106) ftmargoh (f-value for equation 60) !! <LI> (107) favail (f-value for equation 61) !! <LI> (108) breeder_f: Volume of Li4SiO4 / (Volume of Be12Ti + Li4SiO4) !! <LI> (109) ralpne: thermal alpha density / electron density !! <LI> (110) ftaulimit: Lower limit on taup/taueff the ratio of alpha !! <LI> (111) fniterpump: f-value for constraint that number !! <LI> (112) fzeffmax: f-value for max Zeff (f-value for equation 64) !! <LI> (113) ftaucq: f-value for minimum quench time (f-value for equation 65) !! <LI> (114) fw_channel_length: Length of a single first wall channel !! <LI> (115) fpoloidalpower: f-value for max rate of change of !! <LI> (116) fradwall: f-value for radiation wall load limit (eq. 67) !! <LI> (117) fpsepbqar: f-value for Psep*Bt/qar upper limit (eq. 68) !! <LI> (118) fpsep: f-value to ensure separatrix power is less than !! <LI> (119) tesep: separatrix temperature calculated by the Kallenbach divertor model !! <LI> (120) ttarget: Plasma temperature adjacent to divertor sheath [eV] !! <LI> (121) neratio: ratio of mean SOL density at OMP to separatrix density at OMP !! <LI> (122) oh_steel_frac : streel fraction of Central Solenoid !! <LI> (123) foh_stress : f-value for CS coil Tresca yield criterion (f-value for eq. 72) !! <LI> (124) qtargettotal : Power density on target including surface recombination [W/m2] !! <LI> (125) fimp(3) : Beryllium density fraction relative to electron density !! <LI> (126) fimp(4) : Carbon density fraction relative to electron density !! <LI> (127) fimp(5) : Nitrogen fraction relative to electron density !! <LI> (128) fimp(6) : Oxygen density fraction relative to electron density !! <LI> (129) fimp(7) : Neon density fraction relative to electron density !! <LI> (130) fimp(8) : Silicon density fraction relative to electron density !! <LI> (131) fimp(9) : Argon density fraction relative to electron density !! <LI> (132) fimp(10) : Iron density fraction relative to electron density !! <LI> (133) fimp(11) : Nickel density fraction relative to electron density !! <LI> (134) fimp(12) : Krypton density fraction relative to electron density !! <LI> (135) fimp(13) : Xenon density fraction relative to electron density !! <LI> (136) fimp(14) : Tungsten density fraction relative to electron density !! <LI> (137) fplhsep (f-value for equation 73) !! <LI> (138) rebco_thickness : thickness of REBCO layer in tape (m) !! <LI> (139) copper_thick : thickness of copper layer in tape (m) !! <LI> (140) dr_tf_wp : radial thickness of TFC winding pack (m) !! <LI> (141) fcqt : TF coil quench temperature < tmax_croco (f-value for equation 74) !! <LI> (142) nesep : electron density at separatrix [m-3] !! <LI> (143) f_copperA_m2 : TF coil current / copper area < Maximum value !! <LI> (144) fnesep : Eich critical electron density at separatrix !! <LI> (145) fgwped : fraction of Greenwald density to set as pedestal-top density !! <LI> (146) fcpttf : F-value for TF coil current per turn limit (constraint equation 77) !! <LI> (147) freinke : F-value for Reinke detachment criterion (constraint equation 78) !! <LI> (148) fzactual : fraction of impurity at SOL with Reinke detachment criterion !! <LI> (149) fbmaxcs : F-value for max peak CS field (con. 79, itvar 149) !! <LI> (150) REMOVED !! <LI> (151) REMOVED !! <LI> (152) fgwsep : Ratio of separatrix density to Greenwald density !! <LI> (153) fpdivlim : F-value for minimum pdivt (con. 80) !! <LI> (154) fne0 : F-value for ne(0) > ne(ped) (con. 81) !! <LI> (155) pfusife : IFE input fusion power (MW) (ifedrv=3 only) !! <LI> (156) rrin : Input IFE repetition rate (Hz) (ifedrv=3 only) !! <LI> (157) fvssu : F-value for available to required start up flux (con. 51) !! <LI> (158) croco_thick : Thickness of CroCo copper tube (m) !! <LI> (159) ftoroidalgap : F-value for toroidalgap > tftort constraint (con. 82) !! <LI> (160) f_avspace (f-value for equation 83) !! <LI> (161) fbetatry_lower (f-value for equation 84) !! <LI> (162) r_cp_top : Top outer radius of the centropost (ST only) (m) !! <LI> (163) f_t_turn_tf : f-value for TF coils WP trurn squared dimension constraint !! <LI> (164) f_crypmw : f-value for cryogenic plant power !! <LI> (165) fstr_wp : f-value for TF coil strain absolute value !! <LI> (166) f_copperaoh_m2 : CS coil current /copper area < Maximum value !! <LI> (167) fncycle : f-value for minimum CS coil stress load cycles !! <LI> (168) fecrh_ignition: f-value for equation 91 !! <LI> (169) te0_ecrh_achievable: Max. achievable electron temperature at ignition point !! <LI> (170) beta_div : field line angle wrt divertor target plate (degrees) !! <LI> (171) casths_fraction : TF side case thickness as fraction of toridal case thickness !! <LI> (172) casths : TF side case thickness [m] !! <LI> (173) EMPTY : Description !! <LI> (174) EMPTY : Description !! <LI> (175) EMPTY : Description ! Issue 287 iteration variables are now defined in module define_iteration_variables in iteration variables.f90 character(len=14), dimension(:), allocatable :: name_xc real(dp) :: sqsumsq !! sqsumsq : sqrt of the sum of the square of the constraint residuals character(len=40) :: objf_name !! Description of the objective function real(dp) :: norm_objf !! Normalised objective function (figure of merit) real(dp) :: epsfcn !! epsfcn /1.0e-3/ : finite difference step length for HYBRD/VMCON derivatives real(dp) :: epsvmc !! epsvmc /1.0e-6/ : error tolerance for VMCON real(dp) :: factor !! factor /0.1/ : used in HYBRD for first step size real(dp) :: ftol !! ftol /1.0e-4/ : error tolerance for HYBRD real(dp), dimension(ipnvars) :: boundl !! boundl(ipnvars) /../ : lower bounds used on ixc variables during !! VMCON optimisation runs ! Issue #287 These bounds now defined in initial.f90 real(dp), dimension(ipnvars) :: boundu ! !! boundu(ipnvars) /../ : upper bounds used on ixc variables real(dp), dimension(ipnvars) :: bondl real(dp), dimension(ipnvars) :: bondu real(dp), dimension(ipnvars) :: rcm real(dp), dimension(ipnvars) :: resdl real(dp), dimension(ipnvars) :: scafc real(dp), dimension(ipnvars) :: scale real(dp), dimension(ipnvars) :: xcm real(dp), dimension(ipnvars) :: xcs real(dp), dimension(ipvlam) :: vlam contains ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! subroutine init_numerics() ! Initialise module variables ioptimz = 1 minmax = 7 lablmm = (/ & 'major radius ', & 'not used ', & 'neutron wall load ', & 'P_tf + P_pf ', & 'fusion gain ', & 'cost of electricity ', & 'capital cost ', & 'aspect ratio ', & 'divertor heat load ', & 'toroidal field ', & 'total injected power ', & 'H plant capital cost ', & 'H production rate ', & 'pulse length ', & 'plant availability ', & 'min R0, max tau_burn ', & 'net electrical output ', & 'Null figure of merit ', & 'max Q, max t_burn ' & /) ncalls = 0 neqns = 0 nfev1 = 0 nfev2 = 0 nineqns = 0 nvar = 16 nviter = 0 icc = 0 active_constraints = .false. lablcc = (/ & 'Beta consistency ', & 'Global power balance consistency ', & 'Ion power balance ', & 'Electron power balance ', & 'Density upper limit ', & '(Epsilon x beta-pol) upper limit ', & 'Beam ion density consistency ', & 'Neutron wall load upper limit ', & 'Fusion power upper limit ', & 'Toroidal field 1/R consistency ', & 'Radial build consistency ', & 'Volt second lower limit ', & 'Burn time lower limit ', & 'NBI decay lengths consistency ', & 'L-H power threshold limit ', & 'Net electric power lower limit ', & 'Radiation fraction upper limit ', & 'Divertor heat load upper limit ', & 'MVA upper limit ', & 'Beam tangency radius upper limit ', & 'Plasma minor radius lower limit ', & 'Divertor collisionality upper lim', & 'Conducting shell radius upper lim', & 'Beta upper limit ', & 'Peak toroidal field upper limit ', & 'CS coil EOF current density limit', & 'CS coil BOP current density limit', & 'Fusion gain Q lower limit ', & 'Inboard radial build consistency ', & 'Injection power upper limit ', & 'TF coil case stress upper limit ', & 'TF coil conduit stress upper lim ', & 'I_op / I_critical (TF coil) ', & 'Dump voltage upper limit ', & 'J_winding pack/J_protection limit', & 'TF coil temp. margin lower limit ', & 'Current drive gamma limit ', & '1st wall coolant temp rise limit ', & 'First wall peak temperature limit', & 'Start-up inj. power lower limit ', & 'Plasma curr. ramp time lower lim ', & 'Cycle time lower limit ', & 'Average centrepost temperature ', & 'Peak centrepost temp. upper limit', & 'Edge safety factor lower limit ', & 'Ip/Irod upper limit ', & 'TF coil tor. thickness upper lim ', & 'Poloidal beta upper limit ', & 'RFP reversal parameter < 0 ', & 'IFE repetition rate upper limit ', & 'Startup volt-seconds consistency ', & 'Tritium breeding ratio lower lim ', & 'Neutron fluence on TF coil limit ', & 'Peak TF coil nucl. heating limit ', & 'Vessel helium concentration limit', & 'Psep / R upper limit ', & 'TF coil leg rad width lower limit', & 'TF coil leg rad width lower limit', & 'NB shine-through frac upper limit', & 'CS temperature margin lower limit', & 'Minimum availability value ', & 'taup/taueff ', & 'number of ITER-like vacuum pumps ', & 'Zeff limit ', & 'Dump time set by VV stress ', & 'Rate of change of energy in field', & 'Upper Lim. on Radiation Wall load', & 'Upper Lim. on Psep * Bt / q A R ', & 'pdivt < psep_kallenbach divertor ', & 'Separatrix temp consistency ', & 'Separatrix density consistency ', & 'CS Tresca yield criterion ', & 'Psep >= Plh + Paux ', & 'TFC quench < tmax_croco ', & 'TFC current/copper area < Max ', & 'Eich critical separatrix density ', & 'TFC current per turn upper limit ', & 'Reinke criterion fZ lower limit ', & 'Peak CS field upper limit ', & 'pdivt lower limit ', & 'ne0 > neped ', & 'toroidalgap > tftort ', & 'available_space > required_space ', & 'beta > betalim_lower ', & 'CP lifetime ', & 'TFC turn dimension ', & 'Cryogenic plant power ', & 'TF coil strain absolute value ', & 'CS current/copper area < Max ', & 'CS stress load cycles ', & 'ECRH ignitability ' & /) ! Please note: All strings between '...' above must be exactly 33 chars long ! Each line of code has a comma before the ampersand, except the last one. ! The last ad_varc line ends with the html tag "</UL>". ! Issue #495. Remove default iteration variables ixc = 0 ! WARNING These labels are used as variable names by write_new_in_dat.py, and possibly ! other python utilities, so they cannot easily be changed. lablxc = '' ! Issue 287 iteration variables are now defined in module define_iteration_variables in iteration variables.f90 sqsumsq = 0.0D0 objf_name = "" norm_objf = 0.0D0 epsfcn = 1.0D-3 epsvmc = 1.0D-6 factor = 0.1D0 ftol = 1.0D-4 boundl = 9.d-99 ! Issue #287 These bounds now defined in initial.f90 boundu = 9.d99 bondl = 0.0D0 bondu = 0.0D0 rcm = 0.0D0 resdl = 0.0D0 scafc = 0.0D0 scale = 0.0D0 xcm = 0.0D0 xcs = 0.0D0 vlam = 0.0D0 if (allocated(name_xc)) deallocate(name_xc) allocate(name_xc(1)) name_xc = "" end subroutine init_numerics ! eqsolv() has been temporarily commented out. Please see the comment in ! function_evaluator.fcnhyb() for an explanation. ! subroutine eqsolv(fcnhyb,n,x,fvec,tol,epsfcn,factor,nprint,info, & ! wa,lwa,resdl,nfev) ! !! Find the non-optimising HYBRD solution to the problem ! !! author: Argonne National Laboratory. Minpack Project. March 1980. ! !! author: Burton S. Garbow, Kenneth E. Hillstrom, Jorge J. More ! !! author: P J Knight, CCFE, Culham Science Centre ! !! fcnhyb : external routine name : see below ! !! n : input integer : number of functions and variables ! !! x(n) : input/output real array : On input X must contain ! !! an initial estimate of the solution vector. On output X ! !! contains the final estimate of the solution vector. ! !! fvec(n) : output real array : Functions evaluated at output X ! !! tol : input real : Termination occurs when the algorithm ! !! estimates that the relative error between X and the solution ! !! is at most TOL. ! !! epsfcn : input real : Used in determining a suitable ! !! step length for the forward-difference approximation ! !! (see <A HREF="hybrd.html">hybrd</A>) ! !! factor : input real : Used in determining the initial step bound ! !! (see <A HREF="hybrd.html">hybrd</A>) ! !! nprint : input integer : Number of iterations between print-outs ! !! info : output integer : If the user has terminated execution, ! !! INFO is set to the (negative) value of IFLAG, see description below. ! !! Otherwise, INFO is set as follows: ! !! <PRE> ! !! INFO = 0 Improper input parameters. ! !! INFO = 1 Algorithm estimates that the relative error ! !! between X and the solution is at most TOL. ! !! INFO = 2 Number of calls to FCNHYB has reached or exceeded ! !! 200*(N+1). ! !! INFO = 3 TOL is too small. No further improvement in ! !! the approximate solution X is possible. ! !! INFO = 4 Iteration is not making good progress. ! !! </PRE> ! !! wa(lwa) : input/output real array : work array ! !! lwa : input integer : work array size, not less than (N*(3*N+13))/2 ! !! resdl(n) : output real array : residuals ! !! nfev : output integer : number of iterations performed ! !! Routine EQSOLV is the Argonne Minpack subroutine HYBRD1 ! !! which has been modified by D.T. Blackfield FEDC/TRW. ! !! The routine is the same except some of the arguments are ! !! user supplied rather than 'hardwired'. ! !! <P>The purpose of EQSOLV is to find a zero of a system of ! !! N nonlinear functions in N variables by a modification ! !! of the Powell hybrid method. This is done by using the ! !! more general nonlinear equation solver <A HREF="hybrd.html">HYBRD</A>. ! !! The user must provide a subroutine which calculates the functions. ! !! The Jacobian is then calculated by a forward-difference ! !! approximation. ! !! <P>FCNHYB is the name of a user-supplied subroutine which ! !! calculates the functions. FCNHYB must be declared ! !! in an external statement in the user calling ! !! program, and should be written as follows: ! !! <PRE> ! !! subroutine fcnhyb(n,x,fvec,iflag) ! !! integer n,iflag ! !! double precision x(n),fvec(n) ! !! ---------- ! !! calculate the functions at x and ! !! return this vector in fvec. ! !! --------- ! !! return ! !! end ! !! </PRE> ! !! The value of iflag should not be changed by FCNHYB unless ! !! the user wants to terminate execution of EQSOLV. ! !! In this case set IFLAG to a negative integer. ! !! None ! ! ! ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! use global_variables, only: icase, verbose, vlabel ! use constants, only: mfile, nout ! use maths_library, only: HYBRD ! implicit none ! ! Interface for the external fcnhyb subroutine argument ! ! This interface is necessary when wrapping with f2py ! interface ! subroutine fcnhyb(n, x, fvec, iflag) ! use, intrinsic :: iso_fortran_env, only: dp=>real64 ! integer, intent(in) :: n ! real(dp), dimension(n), intent(inout) :: x ! real(dp), dimension(n), intent(out) :: fvec ! integer, intent(inout) :: iflag ! end subroutine fcnhyb ! end interface ! ! Arguments ! external :: fcnhyb ! integer, intent(in) :: n, nprint, lwa ! real(dp), dimension(n), intent(inout) :: x ! real(dp), dimension(n), intent(out) :: fvec, resdl ! real(dp), dimension(lwa), intent(out) :: wa ! real(dp), intent(in) :: tol, epsfcn, factor ! integer, intent(out) :: info, nfev ! ! Local variables ! integer :: n1,indx,lr,maxfev,ml,mode,mu ! real(dp), parameter :: one = 1.0D0 ! real(dp), parameter :: zero = 0.0D0 ! real(dp) :: xtol ! ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! info = 0 ! ! Check the input parameters for errors ! if ( (n == 0).or.(tol < zero).or.(lwa < ((n*(3*n + 13))/2) ) ) return ! ! Call HYBRD ! maxfev = 200*(n + 1) ! xtol = tol ! ml = n - 1 ! mu = n - 1 ! mode = 2 ! wa(:) = one ! lr = (n*(n + 1))/2 ! indx = 6*n + lr ! n1 = n ! !+**PJK 23/10/92 Warning produced by QA Fortran : ! !+**PJK 23/10/92 Arg 16 in call to HYBRD has wrong dimensions. ! !+**PJK 23/10/92 Code works at present, but beware of future ! !+**PJK 23/10/92 modifications. ! call hybrd(fcnhyb,n,x,fvec,xtol,maxfev,ml,mu,epsfcn,wa(1),mode, & ! factor,nprint,info,nfev,wa(indx+1),n1,wa(6*n+1),lr, & ! wa(n+1),wa(2*n+1),wa(3*n+1),wa(4*n+1),wa(5*n+1), & ! resdl) ! if (info == 5) info = 4 ! end subroutine eqsolv end module numerics