! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! module constraints !! author: J Morris !! !! Module defining the constraint equations and the routine that evaluates the !! constraint equations. ! Import modules #ifndef dp use, intrinsic :: iso_fortran_env, only: dp=>real64 #endif use error_handling, only: report_error, idiags, fdiags implicit none public :: constraint_eqns ! type constraint_args_type ! real(dp) :: cc ! !! Residual error in constraint equation ! real(dp) :: con ! !! constraint value for constraint equation in physical units ! real(dp) :: err ! !! residual error in constraint equation in physical units ! character(len=1) :: symbol ! !! `=<`, `>`, `<` symbol for constraint equation denoting its type ! character(len=10) :: units ! !! constraint units in constraint equation ! end type contains subroutine constraint_eqns(m,ieqn,cc,con,err,symbol,units) !! Routine that formulates the constraint equations !! !! **author: P J Knight** (UKAEA) !! !! **author: J Morris** (UKAEA) !! !! if `ieqn` is zero or negative, evaluate all the constraint equations, otherwise !! evaluate only the `ieqn`th equation. The code attempts to make \( cc(i) = 0 \) for all !! \( i \in \{1,\cdots,m\} \) equations. All relevant consistency equations should be active in !! order to make a self-consistent machine. !! !! **References** !! !! 1. use numerics, only: icc use maths_library, only: variable_error implicit none integer, intent(in) :: m !! Number of constraint equations to solve integer, intent(in) :: ieqn !! Switch for constraint equations to evaluate; real(dp), dimension(m), intent(out) :: cc !! Residual error in equation i real(dp), optional, dimension(m), intent(out) :: con !! constraint value for equation i in physical units real(dp), optional, dimension(m), intent(out) :: err !! residual error in equation i in physical units character(len=1), optional, dimension(m), intent(out) :: symbol !! `=<`, `>`, `<` symbol for equation i denoting its type character*10, optional, dimension(m), intent(out) :: units !! constraint units in equation i ! Local variables integer :: i, i1, i2 real(dp) :: tmp_cc = 0 !! Residual error in constraint equation real(dp) :: tmp_con = 0 !! constraint value for constraint equation in physical units real(dp) :: tmp_err = 0 !! residual error in constraint equation in physical units character(len=1) :: tmp_symbol = ' ' !! `=<`, `>`, `<` symbol for constraint equation denoting its type character(len=10) :: tmp_units = ' ' !! constraint units in constraint equation ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! If ieqn is positive, only evaluate the 'ieqn'th constraint residue, ! otherwise evaluate all m constraint residues if (ieqn > 0) then i1 = ieqn ; i2 = ieqn else i1 = 1 ; i2 = m end if ! Consistency (equality) constraints should converge to zero. do i = i1,i2 ! The constraint value in physical units is ! a) for consistency equations, the quantity to be equated, or ! b) for limit equations, the limiting value. ! The symbol is = for a consistency equation, < for an upper limit ! or > for a lower limit. select case (icc(i)) ! Relationship between beta, temperature (keV) and density case (1); call constraint_eqn_001(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Global plasma power balance equation case (2); call constraint_eqn_002(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Global power balance equation for ions case (3); call constraint_eqn_003(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Global power balance equation for electrons case (4); call constraint_eqn_004(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for density upper limit case (5); call constraint_eqn_005(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for epsilon beta-poloidal upper limit case (6); call constraint_eqn_006(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for hot beam ion density case (7); call constraint_eqn_007(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for neutron wall load upper limit case (8); call constraint_eqn_008(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for fusion power upper limit case (9); call constraint_eqn_009(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Obsolete case (10); call constraint_eqn_010(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for radial build case (11); call constraint_eqn_011(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for volt-second capability lower limit case (12); call constraint_eqn_012(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for burn time lower limit case (13); call constraint_eqn_013(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation to fix number of NBI decay lengths to plasma centre case (14); call constraint_eqn_014(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for L-H power threshold limit case (15); call constraint_eqn_015(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for net electric power lower limit case (16); call constraint_eqn_016(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for radiation power upper limit case (17); call constraint_eqn_017(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for divertor heat load upper limit case (18); call constraint_eqn_018(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for MVA upper limit case (19); call constraint_eqn_019(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for neutral beam tangency radius upper limit case (20); call constraint_eqn_020(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for minor radius lower limit case (21); call constraint_eqn_021(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for divertor collision/connection length ratio upper limit case (22); call constraint_eqn_022(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for conducting shell radius / rminor upper limit case (23); call constraint_eqn_023(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for beta upper limit case (24); call constraint_eqn_024(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for peak toroidal field upper limit case (25); call constraint_eqn_025(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for Central Solenoid current density upper limit at EOF case (26); call constraint_eqn_026(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for Central Solenoid current density upper limit at BOP case (27); call constraint_eqn_027(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for fusion gain (big Q) lower limit case (28); call constraint_eqn_028(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for inboard major radius case (29); call constraint_eqn_029(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for injection power upper limit case (30); call constraint_eqn_030(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for TF coil case stress upper limit (SCTF) case (31); call constraint_eqn_031(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for TF coil conduit stress upper limit (SCTF) case (32); call constraint_eqn_032(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for TF coil operating/critical J upper limit (SCTF) case (33); call constraint_eqn_033(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for TF coil dump voltage upper limit (SCTF) case (34); call constraint_eqn_034(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for TF coil J_wp/J_prot upper limit (SCTF) case (35); call constraint_eqn_035(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for TF coil s/c temperature margin lower limit (SCTF) case (36); call constraint_eqn_036(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for current drive gamma upper limit case (37); call constraint_eqn_037(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for first wall temperature upper limit case (39); call constraint_eqn_039(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for auxiliary power lower limit case (40); call constraint_eqn_040(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for plasma current ramp-up time lower limit case (41); call constraint_eqn_041(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for cycle time lower limit case (42); call constraint_eqn_042(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for average centrepost temperature case (43); call constraint_eqn_043(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for centrepost temperature upper limit (TART) case (44); call constraint_eqn_044(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for edge safety factor lower limit (TART) case (45); call constraint_eqn_045(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for Ip/Irod upper limit (TART) case (46); call constraint_eqn_046(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for TF coil toroidal thickness upper limit case (47); call constraint_eqn_047(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for poloidal beta upper limit case (48); call constraint_eqn_048(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Issue #508 Remove RFP option Equation to ensure reversal parameter F is negative case (49); call constraint_eqn_049(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! IFE option: Equation for repetition rate upper limit case (50); call constraint_eqn_050(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation to enforce startup flux = available startup flux case (51); call constraint_eqn_051(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for tritium breeding ratio lower limit case (52); call constraint_eqn_052(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for fast neutron fluence on TF coil upper limit case (53); call constraint_eqn_053(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for peak TF coil nuclear heating upper limit case (54); call constraint_eqn_054(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for helium concentration in vacuum vessel upper limit case (55); call constraint_eqn_055(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for power through separatrix / major radius upper limit case (56); call constraint_eqn_056(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Obsolete case (57); call constraint_eqn_057(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Obsolete case (58); call constraint_eqn_058(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for neutral beam shine-through fraction upper limit case (59); call constraint_eqn_059(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for Central Solenoid s/c temperature margin lower limit case (60); call constraint_eqn_060(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for availability limit case (61); call constraint_eqn_061(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Lower limit on taup/taueff the ratio of alpha particle to energy confinement times case (62); call constraint_eqn_062(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Upper limit on niterpump (vacuum_model = simple) case (63); call constraint_eqn_063(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Upper limit on Zeff case (64); call constraint_eqn_064(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Limit TF dump time to calculated quench time case (65); call constraint_eqn_065(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Limit on rate of change of energy in poloidal field case (66); call constraint_eqn_066(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Simple upper limit on radiation wall load case (67); call constraint_eqn_067(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! New Psep scaling (PsepB/qAR) case (68); call constraint_eqn_068(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Ensure separatrix power is less than value from Kallenbach divertor case (69); call constraint_eqn_069(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Separatrix temperature consistency case (70); call constraint_eqn_070(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Separatrix density consistency case (71); call constraint_eqn_071(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Central Solenoid Tresca yield criterion case (72); call constraint_eqn_072(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! ensure separatrix power is greater than the L-H power + auxiliary power case (73); call constraint_eqn_073(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! ensure TF coil quench temperature < tmax_croco case (74); call constraint_eqn_074(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! ensure that TF coil current / copper area < Maximum value ONLY used for croco HTS coil case (75); call constraint_eqn_075(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Eich critical separatrix density model case (76); call constraint_eqn_076(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for maximum TF current per turn upper limit case (77); call constraint_eqn_077(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for Reinke criterion, divertor impurity fraction lower limit case (78); call constraint_eqn_078(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Equation for maximum CS field case (79); call constraint_eqn_079(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Lower limit pdivt case (80); call constraint_eqn_080(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Constraint equation making sure that ne(0) > ne(ped) case (81); call constraint_eqn_081(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Constraint equation making sure that stellarator coils dont touch in toroidal direction case (82); call constraint_eqn_082(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Constraint ensuring radial build consistency for stellarators case (83); call constraint_eqn_083(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Constraint for lower limit of beta case (84); call constraint_eqn_084(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Constraint for CP lifetime case (85); call constraint_eqn_085(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Constraint for turn dimension case (86); call constraint_eqn_086(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Constraint for cryogenic power case (87); call constraint_eqn_087(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Constraint for TF coil strain case (88); call constraint_eqn_088(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! ensure that OH coil current / copper area < Maximum value ONLY used for croco HTS coil case (89); call constraint_eqn_089(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Constraint for minimum CS stress load cycles case (90); call constraint_eqn_090(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) ! Constraint for indication of ECRH ignitability case (91); call constraint_eqn_091(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) case default idiags(1) = icc(i) call report_error(13) tmp_cc = 0 tmp_con = 0 tmp_err = 0 tmp_symbol = ' ' tmp_units = ' ' end select cc(i) = tmp_cc if (present(con)) then con(i) = tmp_con if (present(err)) err(i) = tmp_err if (present(symbol)) symbol(i) = tmp_symbol if (present(units)) units(i) = tmp_units end if ! Crude method of catching NaN errors !if ((abs(cc(i)) > 9.99D99).or.(cc(i) /= cc(i))) then if (variable_error(cc(i))) then ! Add debugging lines as appropriate... select case (icc(i)) ! Relationship between beta, temperature (keV) and density (consistency equation) case (1); call constraint_err_001() ! Equation for net electric power lower limit case (16); call constraint_err_016() ! Equation for injection power upper limit case (30); call constraint_err_030() ! Limit on rate of change of energy in poloidal field case (66); call constraint_err_066() end select idiags(1) = icc(i) ; fdiags(1) = cc(i) call report_error(14) end if end do ! Issue 505 Reverse the sign so it works as an inequality constraint (cc(i) > 0) ! This will have no effect if it is used as an equality constraint because it will be squared. cc = -cc end subroutine constraint_eqns !--- Error-handling routines subroutine constraint_err_001() !! Error in: Relationship between beta, temperature (keV) and density (consistency equation) !! author: P B Lloyd, CCFE, Culham Science Centre use physics_variables, only: betaft, beta_beam, dene, ten, dnitot, tin, btot, beta write(*,*) 'betaft = ', betaft write(*,*) 'beta_beam = ', beta_beam write(*,*) 'dene = ', dene write(*,*) 'ten = ', ten write(*,*) 'dnitot = ', dnitot write(*,*) 'tin = ', tin write(*,*) 'btot = ',btot write(*,*) 'beta = ', beta end subroutine subroutine constraint_err_016() !! Error in: Equation for net electric power lower limit !! author: P B Lloyd, CCFE, Culham Science Centre use constraint_variables, only: fpnetel, pnetelin use heat_transport_variables, only: pnetelmw implicit none write(*,*) 'fpnetel = ', fpnetel write(*,*) 'pnetelmw = ', pnetelmw write(*,*) 'pnetelin = ', pnetelin end subroutine subroutine constraint_err_030() !! Error in: Equation for injection power upper limit !! author: P B Lloyd, CCFE, Culham Science Centre use current_drive_variables, only: pinjmw, pinjalw use constraint_variables, only: fpinj implicit none write(*,*) 'fpinj = ', fpinj write(*,*) 'pinjalw = ', pinjalw write(*,*) 'pinjmw = ', pinjmw end subroutine subroutine constraint_err_066() !! Error in: Limit on rate of change of energy in poloidal field !! author: P B Lloyd, CCFE, Culham Science Centre use constraint_variables, only: fpoloidalpower use pf_power_variables, only: maxpoloidalpower, peakpoloidalpower implicit none write(*,*) 'fpoloidalpower = ', fpoloidalpower write(*,*) 'maxpoloidalpower = ', maxpoloidalpower write(*,*) 'peakpoloidalpower = ', peakpoloidalpower end subroutine constraint_err_066 !--- subroutine constraint_eqn_001(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! author: J Morris !! category: equality constraint !! !! Relationship between beta, temperature (keV) and density !! !! \begin{equation} !! c_i = 1 - \frac{1}{\beta}\left( \beta_{ft} + \beta_{NBI} + 2 \times 10^3 \mu_0 e !! \left( \frac{n_e T_e + n_i T_i}{B_{tot}^2} \right) \right) !! \end{equation} !! !! - \( \beta \) -- total plasma beta !! - \( \beta_{ft} \) -- fast alpha beta component !! - \( \beta_{NBI} \) -- neutral beam beta component !! - \( n_e \) -- electron density [m\(^3\)] !! - \( n_i \) -- total ion density [m\(^3\)] !! - \( T_e \) -- density weighted average electron temperature [keV] !! - \( T_i \) -- density weighted average ion temperature [keV] !! - \( B_{tot} \) -- total toroidal + poloidal field [T] use physics_variables, only: betaft, beta_beam, dene, ten, dnitot, tin, btot, beta use constants, only: electron_charge,rmu0 implicit none ! type(constraint_args_type), intent(out) :: args real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units !! constraint derived type tmp_cc = 1.0D0 - (betaft + beta_beam + & 2.0D3*rmu0*electron_charge * (dene*ten + dnitot*tin)/btot**2 )/beta tmp_con = beta * (1.0D0 - tmp_cc) tmp_err = beta * tmp_cc tmp_symbol = '=' tmp_units = '' end subroutine constraint_eqn_001 subroutine constraint_eqn_002(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! author: J. Morris !! category: equality constraint !! !! Global plasma power balance equation !! !! \begin{equation} c_i = !! \end{equation} !! !! iradloss : input integer : switch for radiation loss term usage in power balance (see User Guide):<UL> !! <LI> = 0 total power lost is scaling power plus radiation (needed for ipedestal=2,3) !! <LI> = 1 total power lost is scaling power plus core radiation only !! <LI> = 2 total power lost is scaling power only, with no additional !! allowance for radiation. This is not recommended for power plant models.</UL> !! ignite : input integer : switch for ignition assumption:<UL> !! <LI> = 0 do not assume plasma ignition; !! <LI> = 1 assume ignited (but include auxiliary power in costs)</UL> !! ptrepv : input real : electron transport power per volume (MW/m3) !! ptripv : input real : ion transport power per volume (MW/m3) !! pradpv : input real : total radiation power per volume (MW/m3) !! pcoreradpv : input real : total core radiation power per volume (MW/m3) !! f_alpha_plasma : input real : fraction of alpha power deposited in plasma !! alpha_power_density_total : input real : alpha power per volume (MW/m3) !! charged_power_density : input real : non-alpha charged particle fusion power per volume (MW/m3) !! pohmpv : input real : ohmic heating power per volume (MW/m3) !! pinjmw : input real : total auxiliary injected power (MW) !! plasma_volume : input real : plasma volume (m3) use physics_variables, only: iradloss, ignite, ptrepv, ptripv, pradpv, & pcoreradpv, f_alpha_plasma, alpha_power_density_total, charged_power_density, & pohmpv, plasma_volume use current_drive_variables, only: pinjmw implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units !! constraint derived type ! pscaling : Local real : total transport power per volume (MW/m3) real(dp) :: pscaling real(dp) :: pnumerator, pdenom pscaling = ptrepv + ptripv ! Total power lost is scaling power plus radiation: if (iradloss == 0) then pnumerator = pscaling + pradpv else if (iradloss == 1) then pnumerator = pscaling + pcoreradpv else pnumerator = pscaling end if ! if plasma not ignited include injected power if (ignite == 0) then pdenom = f_alpha_plasma*alpha_power_density_total + charged_power_density + pohmpv + pinjmw/plasma_volume else ! if plasma ignited pdenom = f_alpha_plasma*alpha_power_density_total + charged_power_density + pohmpv end if tmp_cc = 1.0D0 - pnumerator / pdenom tmp_con = pdenom * (1.0D0 - tmp_cc) tmp_err = pdenom * tmp_cc tmp_symbol = '=' tmp_units = 'MW/m3' end subroutine constraint_eqn_002 subroutine constraint_eqn_003(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Global power balance equation for ions !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Global power balance equation for ions !! This is a consistency equation (NBI) !! #=# physics !! #=#=# consistency !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! ignite : input integer : switch for ignition assumption:<UL> !! <LI> = 0 do not assume plasma ignition; !! <LI> = 1 assume ignited (but include auxiliary power in costs)</UL> !! ptripv : input real : ion transport power per volume (MW/m3) !! piepv : input real : ion/electron equilibration power per volume (MW/m3) !! f_alpha_plasma : input real : fraction of alpha power deposited in plasma !! alpha_power_ions_density : input real : alpha power per volume to ions (MW/m3) !! pinjimw : input real : auxiliary injected power to ions (MW) !! plasma_volume : input real : plasma volume (m3) use physics_variables, only: ignite, ptripv, piepv, f_alpha_plasma, alpha_power_ions_density, plasma_volume use current_drive_variables, only: pinjimw implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! No assume plasma ignition: if (ignite == 0) then tmp_cc = 1.0D0 - (ptripv + piepv) / (f_alpha_plasma*alpha_power_ions_density + pinjimw/plasma_volume) tmp_con = (f_alpha_plasma*alpha_power_ions_density + pinjimw/plasma_volume) * (1.0D0 - tmp_cc) tmp_err = (f_alpha_plasma*alpha_power_ions_density + pinjimw/plasma_volume) * tmp_cc tmp_symbol = '=' tmp_units = 'MW/m3' ! Plasma ignited: else tmp_cc = 1.0D0 - (ptripv+piepv) / (f_alpha_plasma*alpha_power_ions_density) tmp_con = (f_alpha_plasma*alpha_power_ions_density) * (1.0D0 - tmp_cc) tmp_err = (f_alpha_plasma*alpha_power_ions_density) * tmp_cc tmp_symbol = '=' tmp_units = 'MW/m3' end if end subroutine constraint_eqn_003 subroutine constraint_eqn_004(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Global power balance equation for electrons !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Global power balance equation for electrons !! This is a consistency equation !! N.B. This constraint is currently NOT RECOMMENDED for use. !! #=# physics !! #=#=# consistency !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! iradloss : input integer : switch for radiation loss term usage in power balance (see User Guide):<UL> !! <LI> = 0 total power lost is scaling power plus radiation (needed for ipedestal=2,3) !! <LI> = 1 total power lost is scaling power plus core radiation only !! <LI> = 2 total power lost is scaling power only, with no additional !! allowance for radiation. This is not recommended for power plant models.</UL> !! ignite : input integer : switch for ignition assumption:<UL> !! <LI> = 0 do not assume plasma ignition; !! <LI> = 1 assume ignited (but include auxiliary power in costs)</UL> !! ptrepv : input real : electron transport power per volume (MW/m3) !! pradpv : input real : total radiation power per volume (MW/m3) !! pcoreradpv : input real : total core radiation power per volume (MW/m3) !! f_alpha_plasma : input real : fraction of alpha power deposited in plasma !! alpha_power_electron_density : input real : alpha power per volume to electrons (MW/m3) !! piepv : input real : ion/electron equilibration power per volume (MW/m3) !! pinjemw : input real : auxiliary injected power to electrons (MW) !! plasma_volume : input real : plasma volume (m3) use physics_variables, only: iradloss, ignite, ptrepv, pcoreradpv, f_alpha_plasma, & alpha_power_electron_density, piepv, plasma_volume, pradpv use current_drive_variables, only: pinjemw implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! pscaling : Local real : total transport power per volume (MW/m3) real(dp) :: pscaling real(dp) :: pnumerator, pdenom pscaling = ptrepv ! Total power lost is scaling power plus radiation: if (iradloss == 0) then pnumerator = pscaling + pradpv else if (iradloss == 1) then pnumerator = pscaling + pcoreradpv else pnumerator = pscaling end if ! if plasma not ignited include injected power if (ignite == 0) then pdenom = f_alpha_plasma*alpha_power_electron_density + piepv + pinjemw/plasma_volume else ! if plasma ignited pdenom = f_alpha_plasma*alpha_power_electron_density + piepv end if tmp_cc = 1.0D0 - pnumerator / pdenom tmp_con = pdenom * (1.0D0 - tmp_cc) tmp_err = pdenom * tmp_cc tmp_symbol = '=' tmp_units = 'MW/m3' end subroutine constraint_eqn_004 subroutine constraint_eqn_005(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for density upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for density upper limit !! #=# physics !! #=#=# fdene, dnelimt !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! idensl : input integer : switch for density limit to enforce (constraint equation 5):<UL> !! <LI> = 1 old ASDEX; !! <LI> = 2 Borrass model for ITER (I); !! <LI> = 3 Borrass model for ITER (II); !! <LI> = 4 JET edge radiation; !! <LI> = 5 JET simplified; !! <LI> = 6 Hugill-Murakami Mq limit; !! <LI> = 7 Greenwald limit</UL> !! fdene : input real : f-value for density limit !! dene : input real : electron density (/m3) !! dnelimt : input real : density limit (/m3) !! dnla : input real : line averaged electron density (m-3) use physics_variables, only: idensl, dnelimt, dnla, dene use constraint_variables, only: fdene implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! Apply Greenwald limit to line-averaged density if (idensl == 7) then tmp_cc = 1.0D0 - fdene * dnelimt/dnla tmp_con = fdene * dnelimt tmp_err = fdene * dnelimt - dnla tmp_symbol = '<' tmp_units = '/m3' else tmp_cc = 1.0D0 - fdene * dnelimt/dene tmp_con = dnelimt * (1.0D0 - tmp_cc) tmp_err = dene * tmp_cc tmp_symbol = '<' tmp_units = '/m3' end if end subroutine constraint_eqn_005 subroutine constraint_eqn_006(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for epsilon beta-poloidal upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for epsilon beta-poloidal upper limit !! #=# physics !! #=#=# fbeta, epbetmax !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fbeta : input real : f-value for epsilon beta-poloidal !! epbetmax : input real : maximum (eps*beta_poloidal) !! eps : input real : inverse aspect ratio !! betap : input real : poloidal beta use physics_variables, only: epbetmax, eps, betap use constraint_variables, only: fbeta, fbeta implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fbeta * epbetmax/(eps*betap) tmp_con = epbetmax * (1.0D0 - tmp_cc) tmp_err = (eps*betap) * tmp_cc tmp_symbol = '<' tmp_units = '' end subroutine constraint_eqn_006 subroutine constraint_eqn_007(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for hot beam ion density !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for hot beam ion density !! This is a consistency equation (NBI) !! #=# physics !! #=#=# consistency !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! ignite : input integer : switch for ignition assumption:<UL> !! <LI> = 0 do not assume plasma ignition; !! <LI> = 1 assume ignited (but include auxiliary power in costs)</UL> !! Obviously, ignite must be zero if current drive is required. !! If ignite=1, any auxiliary power is assumed to be used only !! during plasma start-up, and is excluded from all steady-state !! power balance calculations. !! beam_density_out : input real : hot beam ion density from calculation (/m3) !! dnbeam : input real : hot beam ion density, variable (/m3) use physics_variables, only: ignite, beam_density_out, dnbeam implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! Do not assume plasma ignition: if (ignite == 0) then tmp_cc = 1.0D0 - beam_density_out/dnbeam tmp_con = dnbeam * (1.0D0 - tmp_cc) tmp_err = dnbeam * tmp_cc tmp_symbol = '=' tmp_units = '/m3' else tmp_cc = 0 tmp_con = 0 tmp_err = 0 tmp_symbol = '' tmp_units = '' call report_error(1) end if end subroutine constraint_eqn_007 subroutine constraint_eqn_008(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for neutron wall load upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for neutron wall load upper limit !! #=# physics !! #=#=# fwalld, walalw !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fwalld : input real : f-value for maximum wall load !! walalw : input real : allowable wall-load (MW/m2) !! wallmw : input real : average neutron wall load (MW/m2) use constraint_variables, only: fwalld, walalw use physics_variables, only: wallmw implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fwalld * walalw/wallmw tmp_con = fwalld * walalw tmp_err = fwalld * walalw - wallmw tmp_symbol = '<' tmp_units = 'MW/m2' end subroutine constraint_eqn_008 subroutine constraint_eqn_009(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for fusion power upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for fusion power upper limit !! #=# physics !! #=#=# ffuspow, powfmax !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! ffuspow : input real : f-value for maximum fusion power !! powfmax : input real : maximum fusion power (MW) !! fusion_power : input real : fusion power (MW) use constraint_variables, only: ffuspow, powfmax use physics_variables, only: fusion_power implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - ffuspow * powfmax/fusion_power tmp_con = powfmax * (1.0D0 - tmp_cc) tmp_err = fusion_power * tmp_cc tmp_symbol = '<' tmp_units = 'MW' end subroutine constraint_eqn_009 subroutine constraint_eqn_010(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! author: P B Lloyd, CCFE, Culham Science Centre !! Equation for field at TF coil !! This is a consistency equation !! (do not use for stellarators) !! #=# tfcoil !! #=#=# consistency !! rmajor | plasma major radius (m) !! bt | toroidal field on axis (T) !! rbmax | radius of maximum toroidal field (m) !! bmaxtf | peak field at toroidal field coil (T) !! This constraint is depreciated implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units !! Constraints output ! This constraint is depreciated call report_error(236) tmp_con = 1.0D0 tmp_err = 0.0D0 tmp_symbol = '=' tmp_units = '' end subroutine constraint_eqn_010 subroutine constraint_eqn_011(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for radial build !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for radial build !! (This is a consistency equation.) !! #=# build !! #=#=# consistency !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! rbld : input real : sum of thicknesses to the major radius (m) !! rmajor : input real : plasma major radius (m) use build_variables, only: rbld use physics_variables, only: rmajor implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - rbld/rmajor tmp_con = rmajor * (1.0D0 - tmp_cc) tmp_err = rmajor * tmp_cc tmp_symbol = '=' tmp_units = 'm' end subroutine constraint_eqn_011 subroutine constraint_eqn_012(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for volt-second capability lower limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for volt-second capability lower limit !! #=# pfcoil !! #=#=# fvs, vsstt !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! vsstt : input real : total V-s needed (Wb) !! vsstt (lower limit) is positive; vstot (available) is negative !! fvs : input real : f-value for flux-swing (V-s) requirement (STEADY STATE) !! vstot : input real : total flux swing for pulse (Wb) use physics_variables, only: vsstt use constraint_variables, only: fvs use pfcoil_variables, only: vstot implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 + fvs * vstot/vsstt tmp_con = vsstt * (1.0D0 - tmp_cc) tmp_err = vsstt * tmp_cc tmp_symbol = '>' tmp_units = 'V.sec' end subroutine constraint_eqn_012 subroutine constraint_eqn_013(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for burn time lower limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for burn time lower limit !! #=# times !! #=#=# ftburn, tbrnmn !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! ftburn : input real : f-value for minimum burn time !! tburn : input real : burn time (s) (calculated if lpulse=1) !! tbrnmn : input real : minimum burn time (s) use constraint_variables, only: ftburn,tbrnmn use times_variables, only: tburn implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - ftburn * tburn/tbrnmn tmp_con = tbrnmn / ftburn tmp_err = tbrnmn / ftburn - tburn tmp_symbol = '>' tmp_units = 'sec' end subroutine constraint_eqn_013 subroutine constraint_eqn_014(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation to fix number of NBI decay lengths to plasma centre !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation to fix number of NBI decay lengths to plasma centre !! This is a consistency equation !! #=# current_drive !! #=#=# consistency !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! taubeam : input real : neutral beam e-decay lengths to plasma centre !! tbeamin : input real : permitted neutral beam e-decay lengths to plasma centre use current_drive_variables, only: taubeam, tbeamin implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - taubeam/tbeamin tmp_con = tbeamin * (1.0D0 - tmp_cc) tmp_err = tbeamin * tmp_cc tmp_symbol = '=' tmp_units = '' end subroutine constraint_eqn_014 subroutine constraint_eqn_015(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for L-H power threshold limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for L-H power threshold limit !! #=# physics !! #=#=# flhthresh, plhthresh !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! flhthresh : input real : f-value for L-H power threshold !! plhthresh : input real : L-H mode power threshold (MW) !! pdivt : input real : power to conducted to the divertor region (MW) use constraint_variables, only: flhthresh use physics_variables, only: plhthresh, pdivt implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = -(1.0D0 - flhthresh * plhthresh / pdivt) tmp_con = plhthresh tmp_err = plhthresh - pdivt / flhthresh if (flhthresh > 1.0D0) then tmp_symbol = '>' else tmp_symbol = '<' end if tmp_units = 'MW' end subroutine constraint_eqn_015 subroutine constraint_eqn_016(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for net electric power lower limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for net electric power lower limit !! #=# heat_transport !! #=#=# fpnetel, pnetelin !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fpnetel : input real : f-value for net electric power !! pnetelmw : input real : net electric power (MW) !! pnetelin : input real : required net electric power (MW) use constraint_variables, only: fpnetel, pnetelin use heat_transport_variables, only: pnetelmw implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fpnetel * pnetelmw / pnetelin tmp_con = pnetelin tmp_err = pnetelmw - pnetelin / fpnetel tmp_symbol = '>' tmp_units = 'MW' end subroutine constraint_eqn_016 subroutine constraint_eqn_017(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for radiation power upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for radiation power upper limit !! #=# physics !! #=#=# fradpwr, pradmaxpv !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! f_alpha_plasma : input real : fraction of alpha power deposited in plasma !! pinjmw : input real : total auxiliary injected power (MW) !! plasma_volume : input real : plasma volume (m3) !! alpha_power_density_total : input real : alpha power per volume (MW/m3) !! charged_power_density : input real : non-alpha charged particle fusion power per volume (MW/m3) !! pohmpv : input real : ohmic heating power per volume (MW/m3) !! fradpwr : input real : f-value for core radiation power limit !! pradpv : input real : total radiation power per volume (MW/m3) use physics_variables, only: f_alpha_plasma, plasma_volume, alpha_power_density_total, charged_power_density, pohmpv, pradpv use current_drive_variables, only: pinjmw use constraint_variables, only: fradpwr implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units real(dp) :: pradmaxpv !! Maximum possible power/plasma_volume that can be radiated (local) pradmaxpv = pinjmw/plasma_volume + alpha_power_density_total*f_alpha_plasma + charged_power_density + pohmpv tmp_cc = 1.0D0 - fradpwr * pradmaxpv / pradpv tmp_con = pradmaxpv * (1.0D0 - tmp_cc) tmp_err = pradpv * tmp_cc tmp_symbol = '<' tmp_units = 'MW/m3' end subroutine constraint_eqn_017 subroutine constraint_eqn_018(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for divertor heat load upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for divertor heat load upper limit !! #=# divertor !! #=#=# fhldiv, hldivlim !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fhldiv : input real : f-value for divertor heat load !! hldivlim : input real : heat load limit (MW/m2) !! hldiv : input real : divertor heat load (MW/m2) use constraint_variables, only: fhldiv use divertor_variables, only: hldivlim, hldiv implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fhldiv * hldivlim/hldiv tmp_con = hldivlim * (1.0D0 - tmp_cc) tmp_err = hldiv * tmp_cc tmp_symbol = '<' tmp_units = 'MW/m2' end subroutine constraint_eqn_018 subroutine constraint_eqn_019(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for MVA (power) upper limit: resistive TF coil set !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for MVA upper limit !! #=# tfcoil !! #=#=# fmva, mvalim !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! tfcpmw : input real : peak resistive TF coil inboard leg power (total) (MW) !! tflegmw : input real : TF coil outboard leg resistive power (total) (MW) !! fmva : input real : f-value for maximum MVA !! mvalim : input real : MVA limit for resistive TF coil set (total) (MW) use tfcoil_variables, only: tfcpmw, tflegmw use constraint_variables, only: fmva, mvalim implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! totmva : local real : total MVA in TF coil (MW) real(dp) :: totmva totmva = tfcpmw + tflegmw tmp_cc = 1.0D0 - fmva * mvalim/totmva tmp_con = mvalim * (1.0D0 - tmp_cc) tmp_err = totmva * tmp_cc tmp_symbol = '<' tmp_units = 'MVA' end subroutine constraint_eqn_019 subroutine constraint_eqn_020(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for neutral beam tangency radius upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for neutral beam tangency radius upper limit !! #=# current_drive !! #=#=# fportsz, rtanmax !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fportsz : input real : f-value for neutral beam tangency radius limit !! rtanmax : input real : maximum tangency radius for centreline of beam (m) !! rtanbeam : input real : neutral beam centreline tangency radius (m) use constraint_variables, only: fportsz use current_drive_variables, only: rtanmax, rtanbeam implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fportsz * rtanmax/rtanbeam tmp_con = rtanmax * (1.0D0 - tmp_cc) tmp_err = rtanbeam * tmp_cc tmp_symbol = '<' tmp_units = 'm' end subroutine constraint_eqn_020 subroutine constraint_eqn_021(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for minor radius lower limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for minor radius lower limit !! #=# physics !! #=#=# frminor, aplasmin !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! frminor : input real : f-value for minor radius limit !! rminor : input real : plasma minor radius (m) !! aplasmin : input real : minimum minor radius (m) use constraint_variables, only: frminor use physics_variables, only: rminor use build_variables, only: aplasmin implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - frminor * rminor/aplasmin tmp_con = aplasmin * (1.0D0 - tmp_cc) tmp_err = aplasmin * tmp_cc tmp_symbol = '>' tmp_units = '' end subroutine constraint_eqn_021 subroutine constraint_eqn_022(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for divertor collision/connection length ratio upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for divertor collision/connection length ratio upper limit !! #=# divertor !! #=#=# fdivcol, rlenmax !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fdivcol : input real : f-value for divertor collisionality !! rlenmax : input real : maximum value for length ratio (rlclolcn) !! rlclolcn : input real : ratio of collision length / connection length use constraint_variables, only: fdivcol use divertor_variables, only: rlenmax, rlclolcn implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fdivcol * rlenmax / rlclolcn tmp_con = rlenmax * (1.0D0 - tmp_cc) tmp_err = rlclolcn * tmp_cc tmp_symbol = '<' tmp_units = '' end subroutine constraint_eqn_022 subroutine constraint_eqn_023(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for conducting shell radius / rminor upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for conducting shell radius / rminor upper limit !! #=# physics !! #=#=# fcwr, cwrmax !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! rminor : input real : plasma minor radius (m) !! scraplo : input real : gap between plasma and first wall, outboard side (m) !! fwoth : input real : outboard first wall thickness, initial estimate (m) !! blnkoth : input real : outboard blanket thickness (m) !! fcwr : input real : f-value for conducting wall radius / rminor limit !! cwrmax : input real : maximum ratio of conducting wall distance to plasma minor radius for vertical stability use physics_variables, only: rminor, cwrmax use build_variables, only: scraplo, fwoth, blnkoth use constraint_variables, only: fcwr implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! rcw : local real : conducting shell radius (m) real(dp) :: rcw rcw = rminor + scraplo + fwoth + blnkoth tmp_cc = 1.0D0 - fcwr * cwrmax*rminor / rcw tmp_con = cwrmax*rminor * (1.0D0 - tmp_cc) tmp_err = rcw * tmp_cc tmp_symbol = '<' tmp_units = 'm' end subroutine constraint_eqn_023 subroutine constraint_eqn_024(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for beta upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for beta upper limit !! #=# physics !! #=#=# fbetatry, betalim !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! iculbl : input integer : switch for beta limit scaling (constraint equation 24):<UL> !! <LI> = 0 apply limit to total beta; !! <LI> = 1 apply limit to thermal beta; !! <LI> = 2 apply limit to thermal + neutral beam beta !! <LI> = 3 apply limit to toroidal beta </UL> !! istell : input integer : switch for stellarator option (set via <CODE>device.dat</CODE>):<UL> !! <LI> = 0 use tokamak model; !! <LI> = 1 use stellarator model</UL> !! fbetatry : input real : f-value for beta limit !! betalim : input real : allowable beta !! beta : input real : total plasma beta (calculated if ipedestal =3) !! betaft : input real : fast alpha beta component !! beta_beam : input real : neutral beam beta component !! bt : input real : toroidal field !! btot : input real : total field use physics_variables, only: iculbl, betalim, beta, beta_beam, betaft, bt, btot use stellarator_variables, only: istell use constraint_variables, only: fbetatry implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! Include all beta components: relevant for both tokamaks and stellarators if ((iculbl == 0).or.(istell /= 0)) then tmp_cc = 1.0D0 - fbetatry * betalim/beta tmp_con = betalim tmp_err = betalim - beta / fbetatry tmp_symbol = '<' tmp_units = '' ! Here, the beta limit applies to only the thermal component, not the fast alpha or neutral beam parts else if (iculbl == 1) then tmp_cc = 1.0D0 - fbetatry * betalim/(beta-betaft-beta_beam) tmp_con = betalim tmp_err = betalim - (beta-betaft-beta_beam) / fbetatry tmp_symbol = '<' tmp_units = '' ! Beta limit applies to thermal + neutral beam: components of the total beta, i.e. excludes alphas else if (iculbl == 2) then tmp_cc = 1.0D0 - fbetatry * betalim/(beta-betaft) tmp_con = betalim * (1.0D0 - tmp_cc) tmp_err = (beta-betaft) * tmp_cc tmp_symbol = '<' tmp_units = '' ! Beta limit applies to toroidal beta else if (iculbl == 3) then tmp_cc = 1.0D0 - fbetatry * betalim/(beta*(btot/bt)**2) tmp_con = betalim tmp_err = betalim - (beta*(btot/bt)**2) / fbetatry tmp_symbol = '<' tmp_units = '' end if end subroutine constraint_eqn_024 subroutine constraint_eqn_025(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for peak toroidal field upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for peak toroidal field upper limit !! #=# tfcoil !! #=#=# fpeakb, bmxlim !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fpeakb : input real : f-value for maximum toroidal field !! bmxlim : input real : maximum peak toroidal field (T) !! bmaxtf : input real : mean peak field at TF coil (T) use constraint_variables, only: fpeakb, bmxlim use tfcoil_variables, only: bmaxtf implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fpeakb * bmxlim/bmaxtf tmp_con = bmxlim * (1.0D0 - tmp_cc) tmp_err = bmaxtf * tmp_cc tmp_symbol = '<' tmp_units = 'T' end subroutine constraint_eqn_025 subroutine constraint_eqn_026(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for Central Solenoid current density upper limit at EOF !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for Central Solenoid current density upper limit at EOF !! #=# pfcoil !! #=#=# fjohc, rjohc !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fjohc : input real : f-value for central solenoid current at end-of-flattop !! rjohc : input real : allowable central solenoid current density at end of flat-top (A/m2) !! coheof : input real : central solenoid overall current density at end of flat-top (A/m2) use constraint_variables, only: fjohc use pfcoil_variables, only: rjohc, coheof implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fjohc * rjohc/coheof tmp_con = rjohc tmp_err = rjohc - coheof / fjohc tmp_symbol = '<' tmp_units = 'A/m2' end subroutine constraint_eqn_026 subroutine constraint_eqn_027(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for Central Solenoid current density upper limit at BOP !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for Central Solenoid current density upper limit at BOP !! #=# pfcoil !! #=#=# fjohc0, rjohc0 !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fjohc0 : input real : f-value for central solenoid current at beginning of pulse !! rjohc0 : input real : allowable central solenoid current density at beginning of pulse (A/m2) !! cohbop : input real : central solenoid overall current density at beginning of pulse (A/m2) use constraint_variables, only: fjohc0 use pfcoil_variables, only: rjohc0, cohbop implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fjohc0 * rjohc0/cohbop tmp_con = rjohc0 tmp_err = rjohc0 - cohbop / fjohc0 tmp_symbol = '<' tmp_units = 'A/m2' end subroutine constraint_eqn_027 subroutine constraint_eqn_028(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for fusion gain (big Q) lower limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for fusion gain (big Q) lower limit !! #=# physics !! #=#=# fqval, bigqmin !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fqval : input real : pf-value for Q !! bigq : input real : Fusion gain; P_fusion / (P_injection + P_ohmic) !! bigqmin : input real : minimum fusion gain Q !! ignite : input integer : switch for ignition assumption:<UL> !! <LI> = 0 do not assume plasma ignition; !! <LI> = 1 assume ignited (but include auxiliary power in costs)</UL> !! Obviously, ignite must be zero if current drive is required. !! If ignite=1, any auxiliary power is assumed to be used only !! during plasma start-up, and is excluded from all steady-state !! power balance calculations. use constraint_variables, only: fqval, bigqmin use current_drive_variables, only: bigq use physics_variables, only: ignite implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! if plasma is not ignited ... if (ignite == 0) then tmp_cc = 1.0D0 - fqval * bigq/bigqmin tmp_con = bigqmin * (1.0D0 - tmp_cc) tmp_err = bigqmin * tmp_cc tmp_symbol = '>' tmp_units = '' ! if plasma is ignited report error else tmp_cc = 0 tmp_con = 0 tmp_err = 0 tmp_symbol = '' tmp_units = '' call report_error(4) end if end subroutine constraint_eqn_028 subroutine constraint_eqn_029(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for inboard major radius: This is a consistency equation !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for inboard major radius: This is a consistency equation !! #=# build !! #=#=# consistency !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! rmajor : input real : plasma major radius (m) (iteration variable 3) !! rminor : input real : plasma minor radius (m) !! rinboard : input real : plasma inboard radius (m) use physics_variables, only: rmajor, rminor use build_variables, only: rinboard implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - (rmajor - rminor) / rinboard tmp_con = rinboard * (1.0D0 - tmp_cc) tmp_err = rinboard * tmp_cc tmp_symbol = '=' tmp_units = 'm' end subroutine constraint_eqn_029 subroutine constraint_eqn_030(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for injection power upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for injection power upper limit !! #=# current_drive !! #=#=# fpinj, pinjalw !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! pinjmw : input real : total auxiliary injected power (MW) !! fpinj : input real : f-value for injection power !! pinjalw : input real : Maximum allowable value for injected power (MW) use current_drive_variables, only: pinjmw, pinjalw use constraint_variables, only: fpinj implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fpinj*pinjalw/pinjmw tmp_con = pinjalw tmp_err = pinjalw - pinjmw / fpinj tmp_symbol = '<' tmp_units = 'MW' end subroutine constraint_eqn_030 subroutine constraint_eqn_031(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for TF coil case stress upper limit (SCTF) !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for TF coil case stress upper limit (SCTF) !! #=# tfcoil !! #=#=# fstrcase, sig_tf_case_max !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fstrcase : input real : f-value for TF coil case stress !! sig_tf_case_max : input real : Allowable maximum shear stress in TF coil case (Tresca criterion) (Pa) !! sig_tf_case : input real : Constrained stress in TF coil case (Pa) use constraint_variables, only: fstrcase use tfcoil_variables, only: sig_tf_case_max, sig_tf_case implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fstrcase * sig_tf_case_max/sig_tf_case tmp_con = sig_tf_case_max tmp_err = sig_tf_case_max - sig_tf_case / fstrcase tmp_symbol = '<' tmp_units = 'Pa' end subroutine constraint_eqn_031 subroutine constraint_eqn_032(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for TF coil conduit stress upper limit (SCTF) !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for TF coil conduit stress upper limit (SCTF) !! #=# tfcoil !! #=#=# fstrcond, sig_tf_wp_max !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fstrcond : input real : f-value for TF coil conduit stress !! sig_tf_wp_max : input real : Allowable maximum shear stress in TF coil conduit (Tresca criterion) (Pa) !! sig_tf_wp : input real : Constrained stress in TF conductor conduit (Pa) use constraint_variables, only: fstrcond use tfcoil_variables, only: sig_tf_wp_max, sig_tf_wp implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fstrcond * sig_tf_wp_max/sig_tf_wp tmp_con = sig_tf_wp_max tmp_err = sig_tf_wp_max - sig_tf_wp / fstrcond tmp_symbol = '<' tmp_units = 'Pa' end subroutine constraint_eqn_032 subroutine constraint_eqn_033(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for TF coil operating/critical J upper limit (SCTF) !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for TF coil operating/critical J upper limit (SCTF) !! #=# tfcoil !! #=#=# fiooic, jwdgcrt !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fiooic : input real : f-value for TF coil operating current / critical !! jwdgcrt : input real : critical current density for winding pack (A/m2) !! jwptf : input real : winding pack current density (A/m2) use constraint_variables, only: fiooic use tfcoil_variables, only: jwdgcrt, jwptf implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units if (fiooic > 0.7D0) call report_error(285) tmp_cc = 1.0D0 - fiooic * jwdgcrt/jwptf tmp_con = jwdgcrt * (1.0D0 - tmp_cc) tmp_err = jwptf * tmp_cc tmp_symbol = '<' tmp_units = 'A/m2' end subroutine constraint_eqn_033 subroutine constraint_eqn_034(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for TF coil dump voltage upper limit (SCTF) !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for TF coil dump voltage upper limit (SCTF) !! #=# tfcoil !! #=#=# fvdump, vdalw !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fvdump : input real : f-value for dump voltage !! vdalw : input real : max voltage across TF coil during quench (kV) !! vtfskv : input real : voltage across a TF coil during quench (kV) use constraint_variables, only: fvdump use tfcoil_variables, only: vdalw, vtfskv implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fvdump * vdalw/vtfskv tmp_con = vdalw tmp_err = vdalw - vtfskv tmp_symbol = '<' tmp_units = 'V' end subroutine constraint_eqn_034 subroutine constraint_eqn_035(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for TF coil J_wp/J_prot upper limit (SCTF) !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for TF coil J_wp/J_prot upper limit (SCTF) !! #=# tfcoil !! #=#=# fjprot, jwdgpro !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fjprot : input real : f-value for TF coil winding pack current density !! jwdgpro : input real : allowable TF coil winding pack current density, for dump temperature rise protection (A/m2) !! jwptf : input real : winding pack current density (A/m2) use constraint_variables, only: fjprot use tfcoil_variables, only: jwdgpro, jwptf implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fjprot * jwdgpro/jwptf tmp_con = jwdgpro tmp_err = jwptf - jwdgpro tmp_symbol = '<' tmp_units = 'A/m2' end subroutine constraint_eqn_035 subroutine constraint_eqn_036(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for TF coil s/c temperature margin lower limit (SCTF) !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for TF coil s/c temperature margin lower limit (SCTF) !! #=# tfcoil !! #=#=# ftmargtf, tmargmin_tf !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! ftmargtf : input real : f-value for TF coil temperature margin !! tmargtf : input real : TF coil temperature margin (K) !! tmargmin_tf : input real : minimum allowable temperature margin : TF coils (K) use constraint_variables, only: ftmargtf use tfcoil_variables, only: tmargtf, tmargmin_tf implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - ftmargtf * tmargtf/tmargmin_tf tmp_con = tmargmin_tf tmp_err = tmargmin_tf - tmargtf tmp_symbol = '>' tmp_units = 'K' end subroutine constraint_eqn_036 subroutine constraint_eqn_037(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for current drive gamma upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for current drive gamma upper limit !! #=# current_drive !! #=#=# fgamcd, gammax !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fgamcd : input real : f-value for current drive gamma !! gammax : input real : maximum current drive gamma !! gamcd : input real : normalised current drive efficiency (1.0e20 A/W-m2) use constraint_variables, only: fgamcd, gammax use current_drive_variables, only: gamcd implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fgamcd * gammax/gamcd tmp_con = gammax * (1.0D0 - tmp_cc) tmp_err = gamcd * tmp_cc tmp_symbol = '<' tmp_units = '1E20 A/Wm2' end subroutine constraint_eqn_037 subroutine constraint_eqn_038(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Obsolete !! author: P B Lloyd, CCFE, Culham Science Centre !! Obsolete !! #=# empty !! #=#=# empty implicit none ! Dummy formal arguments, for compliance with interface real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 0 tmp_con = 0 tmp_err = 0 tmp_symbol = '' tmp_units = '' end subroutine constraint_eqn_038 subroutine constraint_eqn_039(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for first wall temperature upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for first wall temperature upper limit !! #=# fwbs !! #=#=# ftpeak, tfwmatmax !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! ftpeak : input real : f-value for first wall peak temperature !! tfwmatmax : input real : maximum temperature of first wall material (K) (secondary_cycle>1) !! tpeak : input real : peak first wall temperature (K) use constraint_variables, only: ftpeak use fwbs_variables, only: tfwmatmax, tpeak implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! If the temperature peak == 0 then report an error if (tpeak < 1.0D0) call report_error(5) tmp_cc = 1.0D0 - ftpeak * tfwmatmax/tpeak tmp_con = tfwmatmax * (1.0D0 - tmp_cc) tmp_err = tpeak * tmp_cc tmp_symbol = '<' tmp_units = 'K' end subroutine constraint_eqn_039 subroutine constraint_eqn_040(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for auxiliary power lower limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for auxiliary power lower limit !! #=# current_drive !! #=#=# fauxmn, auxmin !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fauxmn : input real : f-value for minimum auxiliary power !! pinjmw : input real : total auxiliary injected power (MW) !! auxmin : input real : minimum auxiliary power (MW) use constraint_variables, only: fauxmn, auxmin use current_drive_variables, only: pinjmw implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fauxmn * pinjmw/auxmin tmp_con = auxmin * (1.0D0 - tmp_cc) tmp_err = auxmin * tmp_cc tmp_symbol = '>' tmp_units = 'MW' end subroutine constraint_eqn_040 subroutine constraint_eqn_041(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for plasma current ramp-up time lower limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for plasma current ramp-up time lower limit !! #=# times !! #=#=# ftohs, tohsmn !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! ftohs : input real : f-value for plasma current ramp-up time !! tohs : input real : plasma current ramp-up time for current initiation (s) !! tohsmn : input real : minimum plasma current ramp-up time (s) use constraint_variables, only: ftohs, tohsmn use times_variables, only: tohs implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - ftohs * tohs/tohsmn tmp_con = tohsmn * (1.0D0 - tmp_cc) tmp_err = tohsmn * tmp_cc tmp_symbol = '>' tmp_units = 'sec' end subroutine constraint_eqn_041 subroutine constraint_eqn_042(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for cycle time lower limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for cycle time lower limit !! #=# times !! #=#=# ftcycl, tcycmn !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! ftcycl : input real : f-value for cycle time !! tcycle : input real : full cycle time (s) !! tcycmn : input real : minimum cycle time (s) use constraint_variables, only: ftcycl, tcycmn use times_variables, only: tcycle implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! if the minimum cycle time == 0 report an error if (tcycmn < 1.0D0) call report_error(6) tmp_cc = 1.0D0 - ftcycl * tcycle/tcycmn tmp_con = tcycmn * (1.0D0 - tmp_cc) tmp_err = tcycmn * tmp_cc tmp_symbol = '>' tmp_units = 'sec' end subroutine constraint_eqn_042 subroutine constraint_eqn_043(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for average centrepost temperature: This is a consistency equation (TART) !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for average centrepost temperature: This is a consistency equation (TART) !! #=# tfcoil !! #=#=# consistency !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! tcpav : input real : average temp of TF coil inboard leg conductor (C)e !! tcpav2 : input real : centrepost average temperature (C) (for consistency) !! itart : input integer : switch for spherical tokamak (ST) models:<UL> !! <LI> = 0 use conventional aspect ratio models; !! <LI> = 1 use spherical tokamak models</UL> use tfcoil_variables, only: tcpav, tcpav2 use physics_variables, only: itart use tfcoil_variables, only: i_tf_sup implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! if the machine isn't a ST then report error if (itart == 0) call report_error(7) ! For some reasons these lines are needed to make VMCON CONVERGE .... if ( i_tf_sup == 0 ) then ! Copper case tcpav = tcpav - 273.15D0 tcpav2 = tcpav2 - 273.15D0 end if tmp_cc = 1.0D0 - tcpav/tcpav2 tmp_con = tcpav2 * (1.0D0 - tmp_cc) tmp_err = tcpav2 * tmp_cc tmp_symbol = '=' tmp_units = 'deg C' ! For some reasons these lines are needed to make VMCON CONVERGE .... if ( i_tf_sup == 0 ) then ! Copper case tcpav = tcpav + 273.15D0 tcpav2 = tcpav2 + 273.15D0 end if end subroutine constraint_eqn_043 subroutine constraint_eqn_044(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for centrepost temperature upper limit (TART) !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for centrepost temperature upper limit (TART) !! #=# tfcoil !! #=#=# fptemp, ptempalw !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fptemp : input real : f-value for peak centrepost temperature !! ptempalw : input real : maximum peak centrepost temperature (K) !! tcpmax : input real : peak centrepost temperature (K) !! itart : input integer : switch for spherical tokamak (ST) models:<UL> !! <LI> = 0 use conventional aspect ratio models; !! <LI> = 1 use spherical tokamak models</UL> use constraint_variables, only: fptemp use tfcoil_variables, only: ptempalw, tcpmax use physics_variables, only: itart use tfcoil_variables, only: i_tf_sup implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! if the machine isn't a ST then report error if (itart == 0) call report_error(8) ! For some reasons these lines are needed to make VMCON CONVERGE .... if ( i_tf_sup == 0 ) then ! Copper case ptempalw = ptempalw - 273.15D0 tcpmax = tcpmax - 273.15D0 end if tmp_cc = 1.0D0 - fptemp * ptempalw / tcpmax tmp_con = ptempalw * (1.0D0 - tmp_cc) tmp_err = tcpmax * tmp_cc tmp_symbol = '<' tmp_units = 'deg C' ! For some reasons these lines are needed to make VMCON CONVERGE .... if ( i_tf_sup == 0 ) then ! Copper case ptempalw = ptempalw + 273.15D0 tcpmax = tcpmax + 273.15D0 end if end subroutine constraint_eqn_044 subroutine constraint_eqn_045(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for edge safety factor lower limit (TART) !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for edge safety factor lower limit (TART) !! #=# tfcoil !! #=#=# fq, qlim !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fq : input real : f-value for edge safety factor !! q : safety factor 'near' plasma edge: equal to q95 !! (unless i_plasma_current = 2 (ST current scaling), in which case q = mean edge safety factor qbar) !! qlim : input real : lower limit for edge safety factor !! itart : input integer : switch for spherical tokamak (ST) models:<UL> !! <LI> = 0 use conventional aspect ratio models; !! <LI> = 1 use spherical tokamak models</UL> use constraint_variables, only: fq use physics_variables, only: q, qlim, itart implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! if the machine isn't a ST then report error if (itart == 0) call report_error(9) tmp_cc = 1.0D0 - fq * q/qlim tmp_con = qlim * (1.0D0 - tmp_cc) tmp_err = qlim * tmp_cc tmp_symbol = '<' tmp_units = '' end subroutine constraint_eqn_045 subroutine constraint_eqn_046(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for Ip/Irod upper limit (TART) !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for Ip/Irod upper limit (TART) !! #=# tfcoil !! #=#=# fipir, cratmx !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! eps : input real : inverse aspect ratio !! fipir : input real : f-value for Ip/Irod upper limit !! ritfc : input real : total (summed) current in TF coils (A) !! plasma_current : input real : plasma current (A) !! itart : input integer : switch for spherical tokamak (ST) models:<UL> !! <LI> = 0 use conventional aspect ratio models; !! <LI> = 1 use spherical tokamak models</UL> use physics_variables, only: eps, plasma_current, itart use constraint_variables, only: fipir use tfcoil_variables, only: ritfc implicit none ! cratmx : local real : maximum ratio of plasma current to centrepost current real(dp) :: cratmx real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! if the machine isn't a ST then report error if (itart == 0) call report_error(10) cratmx = 1.0D0 + 4.91D0*(eps-0.62D0) tmp_cc = 1.0D0 - fipir * cratmx * ritfc/plasma_current tmp_con = cratmx * (1.0D0 - tmp_cc) tmp_err = plasma_current/ritfc * tmp_cc tmp_symbol = '<' tmp_units = '' end subroutine constraint_eqn_046 subroutine constraint_eqn_047(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Issue #508 Remove RFP option: Relevant only to reversed field pinch devices !! author: P B Lloyd, CCFE, Culham Science Centre !! Issue #508 Remove RFP option: Relevant only to reversed field pinch devices !! Equation for TF coil toroidal thickness upper limit !! #=# empty !! #=#=# empty implicit none ! Dummy formal arguments, just to comply with the subroutine interface real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 0 tmp_con = 0 tmp_err = 0 tmp_symbol = '' tmp_units = '' end subroutine constraint_eqn_047 subroutine constraint_eqn_048(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for poloidal beta upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for poloidal beta upper limit !! #=# physics !! #=#=# fbetap, betpmx !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fbetap : input real : rf-value for poloidal beta !! betpmx : input real : maximum poloidal beta !! betap : input real : poloidal beta use constraint_variables, only: fbetap, betpmx use physics_variables, only: betap implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fbetap * betpmx/betap tmp_con = betpmx * (1.0D0 - tmp_cc) tmp_err = betap * tmp_cc tmp_symbol = '<' tmp_units = '' end subroutine constraint_eqn_048 subroutine constraint_eqn_049(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Issue #508 Remove IFE option: Equation for repetition rate upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! Issue #508 Remove IFE option: Equation for repetition rate upper limit !! #=# empty !! #=#=# empty ! Dummy formal arguments, just to comply with the subroutine interface real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 0 tmp_con = 0 tmp_err = 0 tmp_symbol = '' tmp_units = '' end subroutine constraint_eqn_049 subroutine constraint_eqn_050(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! IFE option: Equation for repetition rate upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! author: S I Muldrew, CCFE, Culham Science Centre !! IFE option: Equation for repetition rate upper limit !! #=# IFE !! #=#=# frrmax, rrmax use ife_variables, only: frrmax, ife, rrmax, reprat implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units if (ife /= 1) then call report_error(12) end if tmp_cc = 1.0D0 - frrmax * rrmax/reprat tmp_con = rrmax * (1.0D0 - tmp_cc) tmp_err = reprat * tmp_cc tmp_symbol = '<' tmp_units = 'Hz' end subroutine constraint_eqn_050 subroutine constraint_eqn_051(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation to enforce startup flux = available startup flux !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation to enforce startup flux = available startup flux !! #=# pfcoil !! #=#=# consistency !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! vsres : input real : resistive losses in startup V-s (Wb) !! vsind : input real : internal and external plasma inductance V-s (Wb)) !! vssu : input real : total flux swing for startup (Wb) use physics_variables, only: vsres, vsind use pfcoil_variables, only: vssu, fvssu implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fvssu * abs((vsres+vsind) / vssu) tmp_con = vssu * (1.0D0 - tmp_cc) tmp_err = vssu * tmp_cc tmp_symbol = '=' tmp_units = 'V.s' end subroutine constraint_eqn_051 subroutine constraint_eqn_052(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for tritium breeding ratio lower limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for tritium breeding ratio lower limit !! #=# fwbs !! #=#=# ftbr, tbrmin !! ? TODO should this only be for certain blanket models ? !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! ftbr : input real : f-value for minimum tritium breeding ratio !! tbr : input real : tritium breeding ratio (iblanket=2,3 (KIT HCPB/HCLL)) !! tbrmin : input real : minimum tritium breeding ratio (If iblanket=1, tbrmin=minimum 5-year time-averaged tritium breeding ratio) use constraint_variables, only: ftbr, tbrmin use fwbs_variables, only: tbr implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - ftbr * tbr/tbrmin tmp_con = tbrmin * (1.0D0 - tmp_cc) tmp_err = tbrmin * tmp_cc tmp_symbol = '>' tmp_units = '' end subroutine constraint_eqn_052 subroutine constraint_eqn_053(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for fast neutron fluence on TF coil upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for fast neutron fluence on TF coil upper limit !! #=# fwbs !! #=#=# fflutf, nflutfmax !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fflutf : input real : f-value for maximum TF coil nuclear heating !! nflutfmax : input real : max fast neutron fluence on TF coil (n/m2) !! nflutf : input real : peak fast neutron fluence on TF coil superconductor (n/m2) use constraint_variables, only: fflutf, nflutfmax use fwbs_variables, only: nflutf implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fflutf * nflutfmax/nflutf tmp_con = nflutfmax * (1.0D0 - tmp_cc) tmp_err = nflutf * tmp_cc tmp_symbol = '<' tmp_units = 'neutron/m2' end subroutine constraint_eqn_053 subroutine constraint_eqn_054(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for peak TF coil nuclear heating upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for peak TF coil nuclear heating upper limit !! #=# fwbs !! #=#=# fptfnuc, ptfnucmax !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fptfnuc : input real : f-value for maximum TF coil nuclear heating !! ptfnucmax : input real : maximum nuclear heating in TF coil (MW/m3) !! ptfnucpm3 : input real : nuclear heating in the TF coil (MW/m3) (blktmodel>0) use constraint_variables, only: fptfnuc, ptfnucmax use fwbs_variables, only: ptfnucpm3 implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fptfnuc * ptfnucmax/ptfnucpm3 tmp_con = ptfnucmax * (1.0D0 - tmp_cc) tmp_err = ptfnucpm3 * tmp_cc tmp_symbol = '<' tmp_units = 'MW/m3' end subroutine constraint_eqn_054 subroutine constraint_eqn_055(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! vvhemax is no longer calculated in PROCESS and this constraint is disabled implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units call report_error(173) end subroutine constraint_eqn_055 subroutine constraint_eqn_056(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for power through separatrix / major radius upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for power through separatrix / major radius upper limit !! #=# current_drive !! #=#=# fnbshinef, nbshinefmax !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fpsepr : input real : f-value for maximum Psep/R limit !! pseprmax : input real : maximum ratio of power crossing the separatrix to plasma major radius (Psep/R) (MW/m) !! pdivt : input real : power to be conducted to the divertor region (MW) !! rmajor : input real : plasma major radius (m) use constraint_variables, only: fpsepr, pseprmax use physics_variables, only: pdivt, rmajor implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fpsepr * pseprmax / (pdivt/rmajor) tmp_con = pseprmax * (1.0D0 - tmp_cc) tmp_err = (pdivt/rmajor) * tmp_cc tmp_symbol = '<' tmp_units = 'MW/m' end subroutine constraint_eqn_056 subroutine constraint_eqn_057(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Obsolete !! author: P B Lloyd, CCFE, Culham Science Centre !! Obsolete !! #=# empty !! #=#=# empty ! Dummy formal arguments, just to comply with the subroutine interface real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 0 tmp_con = 0 tmp_err = 0 tmp_symbol = '' tmp_units = '' end subroutine constraint_eqn_057 subroutine constraint_eqn_058(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Obsolete !! author: P B Lloyd, CCFE, Culham Science Centre !! Obsolete !! #=# empty !! #=#=# empty ! Dummy formal arguments, just to comply with the subroutine interface real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 0 tmp_con = 0 tmp_err = 0 tmp_symbol = '' tmp_units = '' end subroutine constraint_eqn_058 subroutine constraint_eqn_059(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for neutral beam shine-through fraction upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for neutral beam shine-through fraction upper limit !! #=# current_drive !! #=#=# fnbshinef, nbshinefmax !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fnbshinef : input real : f-value for maximum neutral beam shine-through fraction !! nbshinefmax : input real : maximum neutral beam shine-through fraction !! nbshinef : input real : neutral beam shine-through fraction use constraint_variables, only: fnbshinef, nbshinefmax use current_drive_variables, only: nbshinef implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fnbshinef * nbshinefmax / nbshinef tmp_con = nbshinefmax * (1.0D0 - tmp_cc) tmp_err = nbshinef * tmp_cc tmp_symbol = '<' tmp_units = '' end subroutine constraint_eqn_059 subroutine constraint_eqn_060(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for Central Solenoid s/c temperature margin lower limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for Central Solenoid s/c temperature margin lower limit !! #=# tfcoil !! #=#=# ftmargoh, tmargmin_cs !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! ftmargoh : input real : f-value for central solenoid temperature margin !! tmargoh : input real : Central solenoid temperature margin (K) !! tmargmin_cs : input real : Minimum allowable temperature margin : CS (K) use constraint_variables, only: ftmargoh use pfcoil_variables, only: tmargoh use tfcoil_variables, only: tmargmin_cs implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - ftmargoh * tmargoh/tmargmin_cs tmp_con = tmargmin_cs tmp_err = tmargmin_cs - tmargoh tmp_symbol = '>' tmp_units = 'K' end subroutine constraint_eqn_060 subroutine constraint_eqn_061(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for availability limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for availability limit !! #=# cost !! #=#=# favail, avail_min !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! favail : input real : F-value for minimum availability !! cfactr : input real : Total plant availability fraction !! avail_min : input real : Minimum availability use cost_variables, only: favail, cfactr, avail_min implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - favail * cfactr / avail_min tmp_con = avail_min * (1.0D0 - tmp_cc) tmp_err = cfactr * tmp_cc tmp_symbol = '>' tmp_units = '' end subroutine constraint_eqn_061 subroutine constraint_eqn_062(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Lower limit on taup/taueff the ratio of alpha particle to energy confinement times !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Lower limit on taup/taueff the ratio of alpha particle to energy confinement times !! #=# physics !! #=#=# ftaulimit, taulimit !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! ftaulimit : input real : f-value for lower limit on taup/taueff the ratio of alpha particle to energy confinement !! taup : input real : alpha particle confinement time (s) !! taueff : input real : global thermal energy confinement time (sec) !! taulimit : input real : Lower limit on taup/taueff the ratio of alpha particle to energy confinement times use constraint_variables, only: ftaulimit, taulimit use physics_variables, only: taup, taueff implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - ftaulimit * (taup / taueff) / taulimit tmp_con = taulimit tmp_err = (taup / taueff) * tmp_cc tmp_symbol = '>' tmp_units = '' end subroutine constraint_eqn_062 subroutine constraint_eqn_063(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Upper limit on niterpump (vacuum_model = simple) !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Upper limit on niterpump (vacuum_model = simple) !! #=# vacuum !! #=#=# fniterpump, tfno !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fniterpump : input real : f-value for constraint that number of pumps < tfno !! tfno : input real : number of TF coils (default = 50 for stellarators) !! niterpump : input real : number of high vacuum pumps (real number), each with the throughput use constraint_variables, only: fniterpump use tfcoil_variables, only: n_tf use vacuum_variables, only: niterpump implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fniterpump * n_tf / niterpump tmp_con = n_tf tmp_err = n_tf * tmp_cc tmp_symbol = '<' tmp_units = '' end subroutine constraint_eqn_063 subroutine constraint_eqn_064(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Upper limit on Zeff !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Upper limit on Zeff !! #=# physics !! #=#=# fzeffmax, zeffmax !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fzeffmax : input real : f-value for maximum zeff !! zeffmax : input real : maximum value for Zeff !! zeff : input real : plasma effective charge use constraint_variables, only: fzeffmax, zeffmax use physics_variables, only: zeff implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fzeffmax * (zeffmax/zeff) tmp_con = zeffmax tmp_err = zeffmax * tmp_cc tmp_symbol = '<' tmp_units = '' end subroutine constraint_eqn_064 subroutine constraint_eqn_065(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Limit the stress of the vacuum vessel that occurs when the TF coil quenches. !! author: Timothy Nunn, UKAEA !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fmaxvvstress : input real : f-value for constraint on maximum VV stress !! max_vv_stress : input real : Maximum permitted stress of the VV (Pa) !! vv_stress_quench : input real : Stress of the VV (Pa) use constraint_variables, only: fmaxvvstress use tfcoil_variables, only: max_vv_stress use sctfcoil_module, only: vv_stress_quench implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0d0 - fmaxvvstress * max_vv_stress / vv_stress_quench tmp_con = max_vv_stress tmp_err = max_vv_stress * tmp_cc tmp_symbol = '<' tmp_units = 'Pa' end subroutine constraint_eqn_065 subroutine constraint_eqn_066(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Limit on rate of change of energy in poloidal field !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Limit on rate of change of energy in poloidal field !! #=# pfcoil !! #=#=# fpoloidalpower, maxpoloidalpower !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fpoloidalpower : input real : f-value for constraint on rate of change of energy in poloidal field !! maxpoloidalpower : input real : Maximum permitted absolute rate of change of stored energy in poloidal field (MW) !! peakpoloidalpower : input real : Peak absolute rate of change of stored energy in poloidal field (MW) (11/01/16) use constraint_variables, only: fpoloidalpower use pf_power_variables, only: maxpoloidalpower, peakpoloidalpower implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0d0 - fpoloidalpower * maxpoloidalpower / peakpoloidalpower tmp_con = maxpoloidalpower tmp_err = maxpoloidalpower * tmp_cc tmp_symbol = '<' tmp_units = 'MW' end subroutine constraint_eqn_066 subroutine constraint_eqn_067(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Simple upper limit on radiation wall load !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Simple upper limit on radiation wall load !! #=# physics !! #=#=# fradwall, maxradwallload !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fradwall : input real : f-value for upper limit on radiation wall load !! maxradwallload : input real : Maximum permitted radiation wall load (MW/m^2) !! peakradwallload : input real : Peak radiation wall load (MW/m^2) use constraint_variables, only: fradwall, maxradwallload, peakradwallload implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0d0 - fradwall * maxradwallload / peakradwallload tmp_con = maxradwallload tmp_err = maxradwallload * tmp_cc tmp_symbol = '<' tmp_units = 'MW/m^2' end subroutine constraint_eqn_067 subroutine constraint_eqn_068(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! New Psep scaling (PsepB/qAR) !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! New Psep scaling (PsepB/qAR) !! Issue #464 !! #=# physics !! #=#=# fpsepbqar, psepbqarmax !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fpsepbqar : input real : f-value for upper limit on psepbqar, maximum Psep*Bt/qAR limit !! psepbqarmax : input real : maximum permitted value of ratio of Psep*Bt/qAR (MWT/m) !! pdivt : input real : Power to conducted to the divertor region (MW) !! bt : input real : toroidal field on axis (T) (iteration variable 2) !! q95 : input real : safety factor q at 95% flux surface !! aspect : input real : aspect ratio (iteration variable 1) !! rmajor : input real : plasma major radius (m) (iteration variable 3) use constraint_variables, only: fpsepbqar, psepbqarmax use physics_variables, only: pdivt, bt, q95, aspect, rmajor implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0d0 - fpsepbqar * psepbqarmax / ((pdivt*bt)/(q95*aspect*rmajor)) tmp_con = psepbqarmax tmp_err = (pdivt*bt)/(q95*aspect*rmajor) - psepbqarmax tmp_symbol = '<' tmp_units = 'MWT/m' end subroutine constraint_eqn_068 subroutine constraint_eqn_069(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Ensure separatrix power is less than value from Kallenbach divertor !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Ensure separatrix power is less than value from Kallenbach divertor !! #=# divertor_kallenbach !! #=#=# consistency, psep_kallenbach !! fpsep has been removed from the equation. !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! psep_kallenbach : input real : Power conducted through the separatrix, as calculated by the divertor model [W] !! pdivt : input real : power to conducted to the divertor region (MW) ! use div_kal_vars, only: psep_kallenbach use physics_variables, only: pdivt implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! From Kallenbach model, should be reserved if the model is going to be added back end subroutine constraint_eqn_069 subroutine constraint_eqn_070(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Separatrix density consistency !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Separatrix density consistency !! #=# divertor_kallenbach !! #=#=# consistency !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! teomp : input real : Separatrix temperature calculated by the Kallenbach divertor model [eV] !! tesep : input real : Electron temperature at separatrix [keV] ! use div_kal_vars, only: teomp use physics_variables, only: tesep implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! From Kallenbach model, should be reserved if the model is going to be added back end subroutine constraint_eqn_070 subroutine constraint_eqn_071(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Separatrix density consistency !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Separatrix density consistency !! #=# divertor_kallenbach !! #=#=# consistency !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! neomp : input real : Mean SOL density at OMP calculated by the Kallenbach divertor model [m-3] !! nesep : input real : electron density at separatrix [m-3] (ipedestal=1,2, calculated if 3) !! neratio : input real : Ratio of mean SOL density at OMP to separatrix density at OMP (iteration variable 121) ! use div_kal_vars, only: neomp, neratio use physics_variables, only: nesep implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! From Kallenbach model, should be reserved if the model is going to be added back end subroutine constraint_eqn_071 subroutine constraint_eqn_072(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Central Solenoid Tresca yield criterion !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Central Solenoid Tresca yield criterion !! #=# pfcoil !! #=#=# foh_stress, alstroh !! In the case if the bucked and wedged option ( i_tf_bucking >= 2 ) the constrained !! stress is the largest the largest stress of the !! - CS stress at maximum current (conservative as the TF inward pressure is not taken !! into account) !! - CS stress at flux swing (no current in CS) from the TF inward pressure !! This allow to cover the 2 worst stress scenario in the bucked and wedged design !! Otherwise (free standing TF), the stress limits are only set by the CS stress at max current !! Reverse the sign so it works as an inequality constraint (tmp_cc > 0) !! This will have no effect if it is used as an equality constraint because it will be squared. !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! foh_stress : input real : f-value for Tresca yield criterion in Central Solenoid !! alstroh : input real : allowable hoop stress in Central Solenoid structural material (Pa) !! s_tresca_oh : input real : Maximum shear stress coils/central solenoid (Pa) !! sig_tf_cs_bucked : input real : Maximum shear stress in CS case at flux swing (no current in CS) !! can be significant for the bucked and weged design !! i_tf_bucking : input integer : switch for TF structure design use constraint_variables, only: foh_stress use pfcoil_variables, only: alstroh, s_tresca_oh use tfcoil_variables, only: sig_tf_cs_bucked, i_tf_bucking use build_variables, only: tf_in_cs implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! bucked and wedged desing (see subroutine comment) if ( i_tf_bucking >= 2 .and. tf_in_cs == 0 ) then tmp_cc = 1.0d0 - foh_stress * alstroh / max(s_tresca_oh, sig_tf_cs_bucked) tmp_err = alstroh - max(s_tresca_oh, sig_tf_cs_bucked) ! Free standing CS else tmp_cc = 1.0d0 - foh_stress * alstroh / s_tresca_oh tmp_err = alstroh - s_tresca_oh end if tmp_con = alstroh tmp_symbol = '<' tmp_units = 'Pa' end subroutine constraint_eqn_072 subroutine constraint_eqn_073(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Ensure separatrix power is greater than the L-H power + auxiliary power !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Ensure separatrix power is greater than the L-H power + auxiliary power !! #=# physics !! #=#=# fplhsep, pdivt !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fplhsep : input real : F-value for Psep >= Plh + Paux : for consistency of two values of separatrix power !! plhthresh : input real : L-H mode power threshold (MW) !! pdivt : input real : power to be conducted to the divertor region (MW) !! pinjmw : inout real : total auxiliary injected power (MW) use physics_variables, only: fplhsep, plhthresh, pdivt use current_drive_variables, only: pinjmw implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0d0 - fplhsep * pdivt / (plhthresh+pinjmw) tmp_con = pdivt tmp_err = pdivt * tmp_cc tmp_symbol = '>' tmp_units = 'MW' end subroutine constraint_eqn_073 subroutine constraint_eqn_074(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Ensure TF coil quench temperature < tmax_croco ONLY used for croco HTS coil !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Ensure TF coil quench temperature < tmax_croco ONLY used for croco HTS coil !! #=# physics !! #=#=# fcqt, tmax_croco !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fcqt : input real : f-value: TF coil quench temparature remains below tmax_croco !! croco_quench_temperature : input real : CroCo strand: Actual temp reached during a quench (K) !! tmax_croco : input real : CroCo strand: maximum permitted temp during a quench (K) use constraint_variables, only: fcqt use tfcoil_variables, only: croco_quench_temperature, tmax_croco implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0d0 - fcqt * tmax_croco / croco_quench_temperature tmp_con = croco_quench_temperature tmp_err = croco_quench_temperature * tmp_cc tmp_symbol = '<' tmp_units = 'K' end subroutine constraint_eqn_074 subroutine constraint_eqn_075(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Ensure that TF coil current / copper area < Maximum value !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Ensure that TF coil current / copper area < Maximum value !! ONLY used for croco HTS coil !! #=# physics !! #=#=# f_coppera_m2, copperA_m2_max !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! copperA_m2 : input real : TF coil current / copper area (A/m2) !! copperA_m2_max : input real : Maximum TF coil current / copper area (A/m2) !! f_coppera_m2 : input real : f-value for TF coil current / copper area < copperA_m2_max use rebco_variables, only: copperA_m2, copperA_m2_max, f_coppera_m2 implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0d0 - f_coppera_m2 * copperA_m2_max / copperA_m2 tmp_con = copperA_m2 tmp_err = copperA_m2 * tmp_cc tmp_symbol = '<' tmp_units = 'A/m2' end subroutine constraint_eqn_075 subroutine constraint_eqn_076(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Eich critical separatrix density model: Added for issue 558 !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Eich critical separatrix density model !! Added for issue 558 with ref to http://iopscience.iop.org/article/10.1088/1741-4326/aaa340/pdf !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! alpha_crit : output real : critical ballooning parameter value !! nesep_crit : output real : critical electron density at separatrix [m-3] !! kappa : input real : plasma separatrix elongation (calculated if ishape = 1-5, 7 or 9) !! triang : input real : plasma separatrix triangularity (calculated if ishape = 1, 3-5 or 7) !! aspect : input real : aspect ratio (iteration variable 1) !! pdivt : input real : power to conducted to the divertor region (MW) !! dlimit(7) : input real array : density limit (/m3) as calculated using various models !! fnesep : input real : f-value for Eich critical separatrix density use physics_variables, only: alpha_crit, nesep_crit, kappa, triang, & aspect, pdivt, dlimit, nesep use constraint_variables, only: fnesep implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units alpha_crit = (kappa ** 1.2D0) * (1.0D0 + 1.5D0 * triang) nesep_crit = 5.9D0 * alpha_crit * (aspect ** (-2.0D0/7.0D0)) * & (((1.0D0 + (kappa ** 2.0D0)) / 2.0D0) ** (-6.0D0/7.0D0)) & * ((pdivt* 1.0D6) ** (-11.0D0/70.0D0)) * dlimit(7) tmp_cc = 1.0D0 - fnesep * nesep_crit/nesep tmp_con = nesep tmp_err = nesep * tmp_cc tmp_symbol = '<' tmp_units = 'm-3' end subroutine constraint_eqn_076 subroutine constraint_eqn_077(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for maximum TF current per turn upper limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; residual error in physical units; output string; units string !! Equation for maximum TF current per turn upper limit !! #=# tfcoil !! #=#=# fcpttf, cpttf, cpttf_max !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fcpttf : input : f-value for TF coil current per turn !! cpttf_max : input : allowable TF coil current per turn [A/turn] !! cpttf : input : TF coil current per turn [A/turn] use constraint_variables, only: fcpttf use tfcoil_variables, only: cpttf_max, cpttf implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fcpttf * cpttf_max/cpttf tmp_con = cpttf_max tmp_err = cpttf_max * tmp_cc tmp_symbol = '<' tmp_units = 'A/turn' end subroutine constraint_eqn_077 subroutine constraint_eqn_078(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for Reinke criterion, divertor impurity fraction lower limit !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; residual error in physical units; output string; units string !! Equation for Reinke criterion, divertor impurity fraction lower limit !! #=# divertor !! #=#=# freinke, fzactual, fzmin !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present; !! and con will be printed out only if present. Thesw conditions were missing. !! freinke : input : f-value for Reinke criterion (itv 147) !! fzmin : input : minimum impurity fraction from Reinke model !! fzactual : input : actual impurity fraction use constraint_variables, only: freinke use reinke_variables, only: fzactual, fzmin implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! write(*,*) 'freinke, fzact, fzmin = ', freinke, ', ', fzactual, ', ', fzmin ! 1.0, 0.0, value tmp_cc = 1.0D0 - freinke * fzactual/fzmin !The following two pre-existing lines are not understood: !KE note - cc is always 1, code never enters IF statement... tmp_con = fzmin * (1.0D0 - tmp_cc) tmp_err = fzmin * tmp_cc tmp_symbol = '>' tmp_units = '' ! write(*,*) 'cc, con = ', tmp_cc, ', ', tmp_con ! write(*,*) 'freinke, fzactual, fzmin = ', freinke, ', ', fzactual, ', ', fzmin end subroutine constraint_eqn_078 subroutine constraint_eqn_079(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for maximum CS field !! author: P B Lloyd, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; residual error in physical units; output string; units string !! Equation for maximum CS field !! #=# pfcoil !! #=#=# fbmaxcs, bmaxoh, bmaxoh0, bmaxcs_lim !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fbmaxcs : input : F-value for CS mmax field (cons. 79, itvar 149) !! bmaxcs_lim : input : Central solenoid max field limit [T] !! bmaxoh0 : input : maximum field in central solenoid at beginning of pulse (T) !! bmaxoh : input real : maximum field in central solenoid at end of flat-top (EoF) (T) !! (Note: original code has "bmaxoh/bmaxoh0 | peak CS field [T]".) use pfcoil_variables, only: fbmaxcs, bmaxcs_lim, bmaxoh0, bmaxoh implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fbmaxcs * bmaxcs_lim/max(bmaxoh, bmaxoh0) tmp_con = bmaxcs_lim tmp_err = max(bmaxoh, bmaxoh0) * tmp_cc tmp_symbol = '<' tmp_units = 'A/turn' end subroutine constraint_eqn_079 subroutine constraint_eqn_080(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for pdivt lower limit !! author: J Morris, Culham Science Centre !! args : output structure : residual error; constraint value; residual error in physical units; !! output string; units string !! Lower limit pdivt !! #=# physics !! #=#=# fpdivlim, pdivt !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fpdivlim : input : F-value for lower limit on pdivt (cons. 80, itvar 153) !! pdivtlim : input : Minimum power crossing separatrix pdivt [MW] !! pdivt : input : Power crossing separatrix [MW] use physics_variables, only: fpdivlim, pdivt use constraint_variables, only : pdivtlim implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fpdivlim * pdivt / pdivtlim tmp_con = pdivtlim tmp_err = pdivt * tmp_cc tmp_symbol = '>' tmp_units = 'MW' end subroutine constraint_eqn_080 subroutine constraint_eqn_081(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Make sure that the central density is larger that the pedestal one !! author: S Kahn, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Lower limit ne0 > neped !! !#=# physics !! !#=#=# ne0, neped !! Logic change during pre-factoring: err, symbol, units will be !! assigned only if present. !! fne0 : input : F-value for constraint on ne0 > neped !! ne0 : input : Central electron density [m-3] !! neped : input : Electron density at pedestal [m-3] use physics_variables, only: ne0, fne0, neped implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fne0 * ne0/neped tmp_con = fne0 tmp_err = fne0 * tmp_cc tmp_symbol = '>' tmp_units = '/m3' end subroutine constraint_eqn_081 subroutine constraint_eqn_082(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for toroidal consistency of stellarator build !! author: J Lion, IPP Greifswald !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! toroidalgap > tftort !! #=# tfcoil !! #=#=# tftort, ftoroidalgap !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! ftoroidalgap : input real : f-value for constraint toroidalgap > tftort !! toroidalgap : input real : minimal gap between two stellarator coils !! tftort : input real : total toroidal width of a tf coil use tfcoil_variables, only: tftort,ftoroidalgap,toroidalgap implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - ftoroidalgap * toroidalgap/tftort tmp_con = toroidalgap tmp_err = toroidalgap - tftort/ftoroidalgap tmp_symbol = '<' tmp_units = 'm' end subroutine constraint_eqn_082 subroutine constraint_eqn_083(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for radial consistency of stellarator build !! author: J Lion, IPP Greifswald !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! available_radial_space > required_radial_space !! #=# build !! #=#=# required_radial_space, f_avspace !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! f_avspace : input real : f-value for constraint available_radial_space > required_radial_space !! available_radial_space : input real : avaible space in radial direction as given by each s.-configuration !! required_radial_space : input real : required space in radial direction use build_variables, only: available_radial_space, required_radial_space, f_avspace implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - f_avspace * available_radial_space/required_radial_space tmp_con = available_radial_space * (1.0D0 - tmp_cc) tmp_err = required_radial_space * tmp_cc tmp_symbol = '<' tmp_units = 'm' end subroutine constraint_eqn_083 subroutine constraint_eqn_084(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for the lower limit of beta !! author: J Lion, IPP Greifswald !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! (beta-betaft) > betalim_lower !! #=# physics !! #=#=# betaft, beta, fbetatry_lower !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fbetatry_lower : input real : f-value for constraint beta-betaft > betalim_lower !! betalim_lower : input real : Lower limit for beta !! beta : input real : plasma beta !! betaft : input real : Alpha particle beta use physics_variables, only: betalim_lower, beta, betaft use constraint_variables, only: fbetatry_lower implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fbetatry_lower * (beta-betaft)/betalim_lower tmp_con = betalim_lower * (1.0D0 - tmp_cc) tmp_err = (beta-betaft) * tmp_cc tmp_symbol = '>' tmp_units = '' end subroutine constraint_eqn_084 subroutine constraint_eqn_085(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Author : S Kahn !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation constraining the centerpost (CP) lifetime !! Depending on the chosen option : i_cp_lifetime !! - 0 : The CP full power year lifelime is set by the user (cplife_input) !! - 1 : The CP lifelime is equal to the divertor one !! - 2 : The CP lifetime is equal to the breeding blankets one !! - 3 : The CP lifetime is equal to the plant one !! #=# availability !! #=#=# consistency !! Logic change during pre-factoring: err, symbol, units will be assigned !! only if present. !! cplife : input real : calculated CP full power year lifetime (years) !! bktlife : input real : calculated first wall/blanket power year lifetime (years) !! divlife : input real : calculated divertor power year lifetime (years) !! i_cp_lifetime : input integer : switch chosing which plant element the CP !! the CP lifetime must equate use cost_variables, only : cplife, divlife, cplife_input, & tlife, i_cp_lifetime use fwbs_variables, only : bktlife implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units !! Constraints output ! The CP lifetime is equal to the the divertor one if ( i_cp_lifetime == 0 ) then tmp_cc = 1.0D0 - cplife/cplife_input else if ( i_cp_lifetime == 1 ) then tmp_cc = 1.0D0 - cplife/divlife ! The CP lifetime is equal to the tritium breeding blankets / FW one else if ( i_cp_lifetime == 2 ) then tmp_cc = 1.0D0 - cplife/bktlife ! The CP lifetime is equal to the else if ( i_cp_lifetime == 3 ) then tmp_cc = 1.0D0 - cplife/tlife end if tmp_con = divlife * (1.0D0 - tmp_cc) tmp_err = divlife * tmp_cc tmp_symbol = '=' tmp_units = 'years' end subroutine constraint_eqn_085 subroutine constraint_eqn_086(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Author : S Kahn !! args : output structure : residual error; constraint value; !! residual error in physical units; !! Equation constraining the turn edge length in the TF winding pack !! t_turn_tf : input real : TF coil turn edge length including turn insulation [m] !! f_t_turn_tf : input real : f-value for TF turn edge length constraint !! t_turn_tf_max : input real : TF turn edge length including turn insulation upper limit [m] use tfcoil_variables, only : t_turn_tf, f_t_turn_tf, t_turn_tf_max implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units !! Constraints output tmp_cc = 1.0D0 - t_turn_tf / ( f_t_turn_tf * t_turn_tf_max ) tmp_con = t_turn_tf_max * (1.0D0 - tmp_cc) tmp_err = t_turn_tf_max * tmp_cc tmp_symbol = '<' tmp_units = 'm' end subroutine constraint_eqn_086 subroutine constraint_eqn_087(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! author: S. Kahn, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for TF coil cryogenic power upper limit !! crypmw : input real : cryogenic plant power (MW) !! f_crypmw : input real : f-value for maximum cryogenic plant power !! crypmw_max : input real : Maximum cryogenic plant power (MW) use heat_transport_variables, only: crypmw, crypmw_max, f_crypmw implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - f_crypmw * crypmw_max/crypmw tmp_con = crypmw_max * (1.0D0 - tmp_cc) tmp_err = crypmw * tmp_cc tmp_symbol = '<' tmp_units = 'MW' end subroutine constraint_eqn_087 subroutine constraint_eqn_088(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for TF coil vertical strain upper limit (absolute value) !! author: CPS Swanson, PPPL, USA !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for TF coil vertical strain upper limit (absolute value) !! #=# tfcoil !! #=#=# fstr_wp, str_wp_max !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! fstr_wp : input real : f-value for TF coil strain !! str_wp_max : input real : Allowable maximum TF coil vertical strain !! str_wp : input real : Constrained TF coil vertical strain use constraint_variables, only: fstr_wp use tfcoil_variables, only: str_wp_max, str_wp implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0D0 - fstr_wp * str_wp_max/abs(str_wp) tmp_con = str_wp_max tmp_err = str_wp_max - abs(str_wp) / fstr_wp tmp_symbol = '<' tmp_units = '' end subroutine constraint_eqn_088 subroutine constraint_eqn_089(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Ensure that the Central Solenoid [OH] coil current / copper area < Maximum value !! author: G Turkington, CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! #=# physics !! #=#=# f_copperaoh_m2, copperaoh_m2_max !! and hence also optional here. !! Logic change during pre-factoring: err, symbol, units will be assigned only if present. !! copperaoh_m2 : input real : CS coil current at EOF / copper area [A/m2] !! copperaoh_m2_max : input real : maximum coil current / copper area [A/m2] !! f_copperaoh_m2 : input real : f-value for CS coil current / copper area use rebco_variables, only: copperaoh_m2, copperaoh_m2_max, f_copperaoh_m2 implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units tmp_cc = 1.0d0 - f_copperaoh_m2 * copperaoh_m2_max / copperaoh_m2 tmp_con = copperaoh_m2 tmp_err = copperaoh_m2 * tmp_cc tmp_symbol = '<' tmp_units = 'A/m2' end subroutine constraint_eqn_089 subroutine constraint_eqn_090(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! author: A. Pearce, G Turkington CCFE, Culham Science Centre !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! Equation for minimum CS coil stress load cycles !! fncycle : input real : f-value for constraint n_cycle > n_cycle_min !! n_cycle : input real : Allowable number of cycles for CS !! n_cycle_min : input real : Minimum required cycles for CS use CS_fatigue_variables, only: n_cycle, n_cycle_min, bkt_life_csf use constraint_variables, only: fncycle use cost_variables, only: ibkt_life, bktcycles implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units !! Switch to relay the calculated fw/blanket lifetime cycles as the minimum required CS stress cycles. !! bkt_life_cycle = 1 turns on the relay. Otherwise the models run independently. if (ibkt_life == 1 .and. bkt_life_csf == 1 ) then n_cycle_min = bktcycles end if tmp_cc = 1.0D0 - fncycle * n_cycle / n_cycle_min tmp_con = n_cycle_min * (1.0D0 - tmp_cc) tmp_err = n_cycle * tmp_cc tmp_symbol = '>' tmp_units = '' end subroutine constraint_eqn_090 subroutine constraint_eqn_091(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units) !! Equation for checking if the design point is ECRH ignitable !! at lower values for n and B. Or if the design point is ECRH heatable (if ignite==0) !! stellarators only (but in principle usable also for tokamaks). !! author: J Lion, IPP Greifswald !! args : output structure : residual error; constraint value; !! residual error in physical units; output string; units string !! powerht_local > powerscaling !! #=# physics !! #=#=# fecrh_ignition, powerht_local, powerscaling !! fecrh_ignition : input real : f-value for constraint powerht_local > powerscaling !! max_gyrotron_frequency : input real : Max. av. gyrotron frequency !! te0_ecrh_achievable : input real : Max. achievable electron temperature at ignition point use constraint_variables, only: fecrh_ignition use stellarator_variables, only: max_gyrotron_frequency, te0_ecrh_achievable, powerscaling_constraint, powerht_constraint use physics_variables, only: ignite use current_drive_variables, only: pheat implicit none real(dp), intent(out) :: tmp_cc real(dp), intent(out) :: tmp_con real(dp), intent(out) :: tmp_err character(len=1), intent(out) :: tmp_symbol character(len=10), intent(out) :: tmp_units ! Achievable ECRH te needs to be larger than needed te for igntion if(ignite==0) then tmp_cc = 1.0D0 - fecrh_ignition* (powerht_constraint+pheat)/powerscaling_constraint else tmp_cc = 1.0D0 - fecrh_ignition* powerht_constraint/powerscaling_constraint endif tmp_con = powerscaling_constraint * (1.0D0 - tmp_cc) tmp_err = powerht_constraint * tmp_cc tmp_symbol = '<' tmp_units = 'MW' end subroutine constraint_eqn_091 end module constraints