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numerics

ipnvars = 177 module-attribute

total number of variables available for iteration

ipeqns = 92 module-attribute

number of constraint equations available

ipnfoms = 19 module-attribute

number of available figures of merit

ipvlam = ipeqns + 2 * ipnvars + 1 module-attribute

iptnt = ipeqns * (3 * ipeqns + 13) / 2 module-attribute

ipvp1 = ipnvars + 1 module-attribute

ioptimz = None module-attribute

Code operation switch: * -2 for evaluation mode (i.e. no optimisation) * 1 for optimisation mode (e.g. via VMCON)

minmax = None module-attribute

Switch for figure-of-merit (see FiguresOfMerit for descriptions) negative => maximise, positive => minimise

n_constraints = None module-attribute

Total number of constraints (neqns + nineqns)

ncalls = None module-attribute

number of function calls during solution

neqns = None module-attribute

number of equality constraints to be satisfied

nfev1 = None module-attribute

number of calls to FCNHYB (HYBRD function caller) made

nfev2 = None module-attribute

number of calls to FCNVMC1 (VMCON function caller) made

nineqns = None module-attribute

number of inequality constraints VMCON must satisfy (leave at zero for now)

nvar = None module-attribute

number of iteration variables to use

nviter = None module-attribute

number of optimisation iterations performed

icc = None module-attribute

active_constraints = True module-attribute

Logical array showing which constraints are active

lablcc = None module-attribute

Labels describing constraint equations (corresponding itvs)

    * ( 1) Beta (consistency equation) (itv 5) * ( 2) Global power balance (consistency equation) (itv 10,1,2,3,4,6,11) * ( 3) Ion power balance DEPRECATED (itv 10,1,2,3,4,6,11) * ( 4) Electron power balance DEPRECATED (itv 10,1,2,3,4,6,11) * ( 5) Density upper limit (itv 9,1,2,3,4,5,6) * ( 6) (Epsilon x beta poloidal) upper limit (itv 8,1,2,3,4,6) * ( 7) Beam ion density (NBI) (consistency equation) (itv 7) * ( 8) Neutron wall load upper limit (itv 14,1,2,3,4,6) * ( 9) Fusion power upper limit (itv 26,1,2,3,4,6) * (10) Toroidal field 1/R (consistency equation) (itv 12,1,2,3,13 ) * (11) Radial build (consistency equation) (itv 3,1,13,16,29,42,61) * (12) Volt second lower limit (STEADY STATE) (itv 15,1,2,3) * (13) Burn time lower limit (PULSE) (itv 21,1,16,17,29,42,44,61) (itv 19,1,2,3,6) * (14) Neutral beam decay lengths to plasma centre (NBI) (consistency equation) * (15) LH power threshold limit (itv 103) * (16) Net electric power lower limit (itv 25,1,2,3) * (17) Radiation fraction upper limit (itv 28) * (18) Divertor heat load upper limit (itv 27) * (19) MVA upper limit (itv 30) * (20) Neutral beam tangency radius upper limit (NBI) (itv 33,31,3,13) * (21) Plasma minor radius lower limit (itv 32) * (22) Divertor collisionality upper limit (itv 34,43) * (23) Conducting shell to plasma minor radius ratio upper limit (itv 104,1,74) * (24) Beta upper limit (itv 36,1,2,3,4,6,18) * (25) Peak toroidal field upper limit (itv 35,3,13,29) * (26) Central solenoid EOF current density upper limit (i_pf_conductor=0) (itv 38,37,41,12) * (27) Central solenoid BOP current density upper limit (i_pf_conductor=0) (itv 39,37,41,12) * (28) Fusion gain Q lower limit (itv 45,47,40) * (29) Inboard radial build consistency (itv 3,1,13,16,29,42,61) * (30) Injection power upper limit (itv 46,47,11) * (31) TF coil case stress upper limit (SCTF) (itv 48,56,57,58,59,60,24) * (32) TF coil conduit stress upper limit (SCTF) (itv 49,56,57,58,59,60,24) * (33) I_op / I_critical (TF coil) (SCTF) (itv 50,56,57,58,59,60,24) * (34) Dump voltage upper limit (SCTF) (itv 51,52,56,57,58,59,60,24) * (35) TF Quench Hotspot J limit (SCTF) (itv 53,56,57,58,59,60,24) * (36) TF coil temperature margin lower limit (SCTF) (itv 54,55,56,57,58,59,60,24) * (37) Current drive gamma upper limit (itv 40,47) * (38) First wall coolant temperature rise upper limit (itv 62) * (39) First wall peak temperature upper limit (itv 63) * (40) Start-up injection power lower limit (PULSE) (itv 64) * (41) Plasma current ramp-up time lower limit (PULSE) (itv 66,65) * (42) Cycle time lower limit (PULSE) (itv 17,67,65) * (43) Average centrepost temperature (TART) (consistency equation) (itv 13,20,69,70) * (44) Peak centrepost temperature upper limit (TART) (itv 68,69,70) * (45) Edge safety factor lower limit (TART) (itv 71,1,2,3) * (46) Equation for Ip/Irod upper limit (TART) (itv 72,2,60) * (47) NOT USED * (48) Poloidal beta upper limit (itv 79,2,3,18) * (49) NOT USED * (50) IFE repetition rate upper limit (IFE) * (51) Startup volt-seconds consistency (PULSE) (itv 16,29,3,1) * (52) Tritium breeding ratio lower limit (itv 89,90,91) * (53) Neutron fluence on TF coil upper limit (itv 92,93,94) * (54) Peak TF coil nuclear heating upper limit (itv 95,93,94) * (55) NOT USED * (56) Pseparatrix/Rmajor upper limit (itv 97,1,3) * (57) NOT USED * (58) NOT USED * (59) Neutral beam shine-through fraction upper limit (NBI) (itv 105,6,19,4 ) * (60) Central solenoid temperature margin lower limit (SCTF) (itv 106) * (61) Minimum availability value (itv 107) * (62) f_alpha_energy_confinement the ratio of particle to energy confinement times (itv 110) * (63) The number of ITER-like vacuum pumps n_iter_vacuum_pumps < tfno (itv 111) * (64) Zeff less than or equal to zeff_max (itv 112) * (65) Dump time set by VV loads (itv 56, 113) * (66) Limit on rate of change of energy in poloidal field (Use iteration variable 65(t_plant_pulse_plasma_current_ramp_up), 115) * (67) Simple Radiation Wall load limit (itv 116, 4,6) * (68) Psep * Bt / qAR upper limit (itv 117) * (69) ensure separatrix power = the value from Kallenbach divertor (itv 118) * (70) ensure that teomp = separatrix temperature in the pedestal profile, (itv 119 (temp_plasma_separatrix_kev)) * (71) ensure that neomp = separatrix density (nd_plasma_separatrix_electron) x neratio * (72) central solenoid shear stress limit (Tresca yield criterion) * (73) Psep >= Plh + Paux * (74) TFC quench < temp_croco_quench_max * (75) TFC current/copper area < Maximum * (76) Eich critical separatrix density * (77) TF coil current per turn upper limit * (78) Reinke criterion impurity fraction lower limit * (79) Peak CS field upper limit * (80) Divertor power lower limit p_plasma_separatrix_mw * (81) Ne(0) > ne(ped) constraint * (82) toroidalgap > dx_tf_inboard_out_toroidal constraint * (83) Radial build consistency for stellarators * (84) Lower limit for beta (itv 173 fbeta_min) * (85) Constraint for CP lifetime * (86) Constraint for TF coil turn dimension * (87) Constraint for cryogenic power * (88) Constraint for TF coil strain absolute value * (89) Constraint for CS coil quench protection * (90) Lower Limit on number of stress load cycles for CS * (91) Checking if the design point is ECRH ignitable * (92) D/T/He3 ratio in fuel sums to 1

ixc = None module-attribute

Array defining which iteration variables to activate (see lablxc for descriptions)

lablxc = None module-attribute

Labels describing iteration variables

    * ( 1) aspect * ( 2) b_plasma_toroidal_on_axis * ( 3) rmajor * ( 4) temp_plasma_electron_vol_avg_kev * ( 5) beta_total_vol_avg * ( 6) nd_plasma_electrons_vol_avg * ( 7) f_nd_beam_electron * ( 8) NOT USED * ( 9) NOT USED * (10) hfact * (11) p_hcd_primary_extra_heat_mw * (12) j_tf_coil_full_area * (13) dr_tf_inboard (NOT RECOMMENDED) * (14) NOT USED * (15) NOT USED * (16) dr_cs * (17) t_plant_pulse_dwell * (18) q * (19) e_beam_kev * (20) temp_cp_average * (21) NOT USED * (22) NOT USED * (23) fcoolcp * (24) NOT USED * (25) NOT USED * (26) NOT USED * (27) NOT USED * (28) NOT USED * (29) dr_bore * (30) NOT USED * (31) gapomin * (32) NOT USED * (33) NOT USED * (34) NOT USED * (35) NOT USED * (36) NOT USED * (37) j_cs_flat_top_end * (38) NOT USED * (39) NOT USED * (40) NOT USED * (41) f_j_cs_start_pulse_end_flat_top * (42) dr_cs_tf_gap * (43) NOT USED * (44) f_c_plasma_non_inductive * (45) NOT USED * (46) NOT USED * (47) feffcd * (48) NOT USED * (49) NOT USED * (50) NOT USED * (51) NOT USED * (52) NOT USED * (53) NOT USED * (54) NOT USED * (55) NOT USED * (56) t_tf_superconductor_quench * (57) dr_tf_nose_case * (58) dx_tf_turn_steel * (59) f_a_tf_turn_cable_copper * (60) c_tf_turn * (61) dr_shld_vv_gap_inboard * (62) NOT USED * (63) NOT USED * (64) NOT USED * (65) t_plant_pulse_plasma_current_ramp_up * (66) NOT USED * (67) NOT USED * (68) NOT USED * (69) radius_cp_coolant_channel * (70) vel_cp_coolant_midplane * (71) NOT USED * (72) NOT USED * (73) dr_fw_plasma_gap_inboard * (74) dr_fw_plasma_gap_outboard * (75) f_dr_tf_outboard_inboard * (76) NOT USED * (77) NOT USED * (78) NOT USED * (79) NOT USED * (80) NOT USED * (81) edrive * (82) drveff * (83) tgain * (84) chrad * (85) pdrive * (86) NOT USED * (87) NOT USED * (88) NOT USED * (89) NOT USED * (90) blbuith * (91) blbuoth * (92) NOT USED * (93) dr_shld_inboard * (94) dr_shld_outboard * (95) NOT USED * (96) NOT USED * (97) NOT USED * (98) f_blkt_li6_enrichment * (99) NOT USED * (100) NOT USED * (101) NOT USED * (102) f_nd_impurity_electronsvar # OBSOLETE * (103) NOT USED * (104) NOT USED * (105) NOT USED * (106) NOT USED * (107) NOT USED * (108) breeder_f: Volume of Li4SiO4 / (Volume of Be12Ti + Li4SiO4) * (109) f_nd_alpha_electron: thermal alpha density / electron density * (110) NOT USED * (111) NOT USED * (112) NOT USED * (113) NOT USED * (114) len_fw_channel: Length of a single first wall channel * (115) NOT USED * (116) NOT USED * (117) NOT USED * (119) temp_plasma_separatrix_kev: separatrix temperature calculated by the Kallenbach divertor model * (120) ttarget: Plasma temperature adjacent to divertor sheath [eV] * (121) neratio: ratio of mean SOL density at OMP to separatrix density at OMP * (122) f_a_cs_turn_steel : streel fraction of Central Solenoid * (123) NOT USED * (124) qtargettotal : Power density on target including surface recombination [W/m2] * (125) f_nd_impurity_electrons(3) : Beryllium density fraction relative to electron density * (126) f_nd_impurity_electrons(4) : Carbon density fraction relative to electron density * (127) f_nd_impurity_electrons(5) : Nitrogen fraction relative to electron density * (128) f_nd_impurity_electrons(6) : Oxygen density fraction relative to electron density * (129) f_nd_impurity_electrons(7) : Neon density fraction relative to electron density * (130) f_nd_impurity_electrons(8) : Silicon density fraction relative to electron density * (131) f_nd_impurity_electrons(9) : Argon density fraction relative to electron density * (132) f_nd_impurity_electrons(10) : Iron density fraction relative to electron density * (133) f_nd_impurity_electrons(11) : Nickel density fraction relative to electron density * (134) f_nd_impurity_electrons(12) : Krypton density fraction relative to electron density * (135) f_nd_impurity_electrons(13) : Xenon density fraction relative to electron density * (136) f_nd_impurity_electrons(14) : Tungsten density fraction relative to electron density * (137) NOT USED * (138) dx_tf_hts_tape_rebco : thickness of REBCO layer in tape (m) * (139) dx_tf_hts_tape_copper : thickness of copper layer in tape (m) * (140) dr_tf_wp_with_insulation : radial thickness of TFC winding pack (m) * (141) NOT USED * (142) nd_plasma_separatrix_electron : electron density at separatrix [m-3] * (143) f_copperA_m2 : TF coil current / copper area < Maximum value * (144) NOT USED * (145) f_nd_plasma_pedestal_greenwald : fraction of Greenwald density to set as pedestal-top density * (146) NOT USED * (147) NOT USED * (148) fzactual : fraction of impurity at SOL with Reinke detachment criterion * (149) NOT USED * (150) NOT USED * (151) NOT USED * (152) f_nd_plasma_separatrix_greenwald : Ratio of separatrix density to Greenwald density * (153) NOT USED * (154) NOT USED * (155) pfusife : IFE input fusion power (MW) (ifedrv=3 only) * (156) rrin : Input IFE repetition rate (Hz) (ifedrv=3 only) * (157) NOT USED * (158) dx_tf_croco_strand_copper : Thickness of CroCo copper tube (m) * (159) NOT USED * (160) NOT USED * (161) NOT USED * (162) r_cp_top : Top outer radius of the centropost (ST only) (m) * (163) NOT USED * (164) NOT USED * (165) NOT USED * (166) NOT USED * (167) NOT USED * (168) NOT USED * (169) te0_ecrh_achievable: Max. achievable electron temperature at ignition point * (170) deg_div_field_plate : field line angle wrt divertor target plate (degrees) * (171) casths_fraction : TF side case thickness as fraction of toridal case thickness * (172) dx_tf_side_case_min : TF side case thickness [m] * (173) f_plasma_fuel_deuterium : Deuterium fraction in fuel * (174) NOT USED * (175) NOT USED

name_xc = None module-attribute

sqsumsq = None module-attribute

sqrt of the sum of the square of the constraint residuals

objf_name = None module-attribute

Description of the objective function

norm_objf = None module-attribute

Normalised objective function (figure of merit)

epsfcn = None module-attribute

Finite difference step length for calculating derivatives

epsvmc = None module-attribute

Error tolerance for optimiser

boundl = None module-attribute

Lower bounds used on ixc variables during optimisation runs

boundu = None module-attribute

Upper bounds used on ixc variables

itv_scaled_lower_bounds = None module-attribute

Lower bound of the ixc variables scaled to (divided by) the initial value of the corresponding ixc

itv_scaled_upper_bounds = None module-attribute

Upper bound of the ixc variables scaled to (divided by) the initial value of the corresponding ixc

rcm = None module-attribute

resdl = None module-attribute

scafc = None module-attribute

The initial value of each ixc variable

scale = None module-attribute

The reciprocal of the initial value of each ixc variable

xcm = None module-attribute

xcs = None module-attribute

vlam = None module-attribute

force_vmcon_inequality_satisfication = None module-attribute

If 1, adds an additional convergence criteria to the VMCON solver that enforces a margin on the inequality constraints. I.e. VMCON cannot converge until all inequality constraints are satisfied to within a tolerance of force_vmcon_inequality_tolerance.

Default is 1 (enabled).

NOTE: this only affects the VMCON solver.

force_vmcon_inequality_tolerance = None module-attribute

The relative tolerance for the additional VMCON convergence criteria that forces inequality constraints to be satisfied within a tolerance.

Default is 1e-8.

NOTE: has no effect if force_vmcon_inequality_satisfication is 0 NOTE: this only affects the VMCON solver.

factor = None module-attribute

ftol = None module-attribute

PROCESSRunMode

Bases: IntEnum

Enumeration of the available PROCESS run modes, which determine the behaviour of the code in various places. This is controlled by the ioptimz variable

Source code in process/data_structure/numerics.py 
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class PROCESSRunMode(IntEnum):
    """Enumeration of the available PROCESS run modes, which determine the behaviour
    of the code in various places. This is controlled by the `ioptimz` variable
    """

    EVALUATION = (-2, "Evaluation mode (no optimisation)")
    """In this mode, the code will not perform any optimisation, and will instead
    simply evaluate the constraints for the given input parameters, which is useful
    for testing and for evaluating the performance of a given design point without
    trying to optimise it. Internally, PROCESS uses `fsolve` (a Newton-Krylov/hybrd
    root-finding method from `scipy.optimize`) to seek a *consistent* solution by
    varying a subset of the iteration variables until the consistency constraints
    (equality constraints whose residuals must be driven to zero) are simultaneously
    satisfied; no figure-of-merit is optimised, and the solver simply tries to find
    a root of the constraint-residual vector.
    """
    OPTIMISATION = (1, "Optimisation mode (e.g. via VMCON)")
    """In this mode, the code will perform optimisation using the VMCON solver
    (or a custom solver if specified) to try to find a design point that optimises
    the figure of merit while satisfying the constraints.  This is the default mode
    of operation for PROCESS.
    """

    def __new__(cls, value: int, description: str):
        """Create a new PROCESSRunMode enum member with description.

        Args:
            value: The integer value of the enum member.
            description: The description for this run mode.

        Returns
        -------
            The new enum member with attached description.
        """
        obj = int.__new__(cls, value)
        obj._value_ = value
        obj._description_ = description
        return obj

    @DynamicClassAttribute
    def description(self):
        """Return the description for this run mode."""
        return self._description_

EVALUATION = (-2, 'Evaluation mode (no optimisation)') class-attribute instance-attribute

In this mode, the code will not perform any optimisation, and will instead simply evaluate the constraints for the given input parameters, which is useful for testing and for evaluating the performance of a given design point without trying to optimise it. Internally, PROCESS uses fsolve (a Newton-Krylov/hybrd root-finding method from scipy.optimize) to seek a consistent solution by varying a subset of the iteration variables until the consistency constraints (equality constraints whose residuals must be driven to zero) are simultaneously satisfied; no figure-of-merit is optimised, and the solver simply tries to find a root of the constraint-residual vector.

OPTIMISATION = (1, 'Optimisation mode (e.g. via VMCON)') class-attribute instance-attribute

In this mode, the code will perform optimisation using the VMCON solver (or a custom solver if specified) to try to find a design point that optimises the figure of merit while satisfying the constraints. This is the default mode of operation for PROCESS.

description()

Return the description for this run mode.

Source code in process/data_structure/numerics.py 
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@DynamicClassAttribute
def description(self):
    """Return the description for this run mode."""
    return self._description_

FiguresOfMerit

Bases: IntEnum

Enumeration of the available figures of merit (FoM) that can be used as objective functions for optimisation in PROCESS.

Source code in process/data_structure/numerics.py 
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class FiguresOfMerit(IntEnum):
    """Enumeration of the available figures of merit (FoM) that can be used as
    objective functions for optimisation in PROCESS.
    """

    MAJOR_RADIUS = (1, "Plasma major radius (R₀)")
    NEUTRON_WALL_LOAD = (3, "Neutron wall load")
    P_TF_PLUS_P_PF = (4, "TF & PF coil power")
    FUSION_GAIN_Q = (5, "Fusion gain (Qₚₗₐₛₘₐ)")
    COST_OF_ELECTRICITY = (6, "Cost of electricity")
    CAPITAL_COST = (7, "Plant capital cost")
    ASPECT_RATIO = (8, "Plasma aspect ratio")
    DIVERTOR_HEAT_LOAD = (9, "Divertor heat load")
    TOROIDAL_FIELD = (10, "Plasma toroidal field on axis (B₀)")
    TOTAL_INJECTED_POWER = (11, "Plasma total injected power (Pᵢₙⱼ)")
    PULSE_LENGTH = (14, "Pulse length")
    PLANT_AVAILABILITY_FACTOR = (15, "Plant availability factor")
    MIN_R0_MAX_TAU_BURN = (
        16,
        "Linear combination of major radius (minimised) and pulse length (maximised)",
    )
    NET_ELECTRICAL_OUTPUT = (17, "Plant net electrical output")
    NULL_FIGURE_OF_MERIT = (18, "Null Figure of Merit")
    MAX_Q_MAX_T_PLANT_PULSE_BURN = (
        19,
        "Linear combination of big Q and pulse length (maximised)",
    )

    def __new__(cls, value: int, description: str):
        """Create a new FiguresOfMerit enum member with description.

        Args:
            value: The integer value of the enum member.
            description: The description for this figure of merit.

        Returns
        -------
            The new enum member with attached description.
        """
        obj = int.__new__(cls, value)
        obj._value_ = value
        obj._description_ = description
        return obj

    @DynamicClassAttribute
    def description(self):
        """Return the description for this figure of merit."""
        return self._description_

MAJOR_RADIUS = (1, 'Plasma major radius (R₀)') class-attribute instance-attribute

NEUTRON_WALL_LOAD = (3, 'Neutron wall load') class-attribute instance-attribute

P_TF_PLUS_P_PF = (4, 'TF & PF coil power') class-attribute instance-attribute

FUSION_GAIN_Q = (5, 'Fusion gain (Qₚₗₐₛₘₐ)') class-attribute instance-attribute

COST_OF_ELECTRICITY = (6, 'Cost of electricity') class-attribute instance-attribute

CAPITAL_COST = (7, 'Plant capital cost') class-attribute instance-attribute

ASPECT_RATIO = (8, 'Plasma aspect ratio') class-attribute instance-attribute

DIVERTOR_HEAT_LOAD = (9, 'Divertor heat load') class-attribute instance-attribute

TOROIDAL_FIELD = (10, 'Plasma toroidal field on axis (B₀)') class-attribute instance-attribute

TOTAL_INJECTED_POWER = (11, 'Plasma total injected power (Pᵢₙⱼ)') class-attribute instance-attribute

PULSE_LENGTH = (14, 'Pulse length') class-attribute instance-attribute

PLANT_AVAILABILITY_FACTOR = (15, 'Plant availability factor') class-attribute instance-attribute

MIN_R0_MAX_TAU_BURN = (16, 'Linear combination of major radius (minimised) and pulse length (maximised)') class-attribute instance-attribute

NET_ELECTRICAL_OUTPUT = (17, 'Plant net electrical output') class-attribute instance-attribute

NULL_FIGURE_OF_MERIT = (18, 'Null Figure of Merit') class-attribute instance-attribute

MAX_Q_MAX_T_PLANT_PULSE_BURN = (19, 'Linear combination of big Q and pulse length (maximised)') class-attribute instance-attribute

description()

Return the description for this figure of merit.

Source code in process/data_structure/numerics.py 
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@DynamicClassAttribute
def description(self):
    """Return the description for this figure of merit."""
    return self._description_

init_numerics()

Source code in process/data_structure/numerics.py 
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def init_numerics():
    global \
        ioptimz, \
        minmax, \
        n_constraints, \
        ncalls, \
        neqns, \
        nfev1, \
        nfev2, \
        nineqns, \
        nvar, \
        nviter, \
        icc, \
        active_constraints, \
        lablcc, \
        ixc, \
        lablxc, \
        name_xc, \
        sqsumsq, \
        objf_name, \
        norm_objf, \
        epsfcn, \
        epsvmc, \
        factor, \
        ftol, \
        boundl, \
        boundu, \
        itv_scaled_lower_bounds, \
        itv_scaled_upper_bounds, \
        rcm, \
        resdl, \
        scafc, \
        scale, \
        xcm, \
        xcs, \
        vlam, \
        force_vmcon_inequality_satisfication, \
        force_vmcon_inequality_tolerance
    """Initialise module variables"""
    ioptimz = 1
    minmax = 7

    ncalls = 0
    neqns = -1
    nfev1 = 0
    nfev2 = 0
    nineqns = 0
    nvar = 0
    n_constraints = 0
    nviter = 0
    icc = np.array([0] * ipeqns)
    active_constraints = [False] * ipeqns

    lablcc = [
        "⟨β⟩ consistency                   ",
        "Global power balance consistency ",
        "Ion power balance                ",
        "Electron power balance           ",
        "Electron density upper limit (nₑ<) ",
        "(βₚε) upper limit ",
        "Beam ion density consistency     ",
        "Neutron wall load upper limit    ",
        "Fusion power upper limit         ",
        "NOT USED",
        "Radial build consistency         ",
        "CS & PF system whole pulse Vs lower limit          ",
        "Burn time lower limit            ",
        "NBI decay lengths consistency    ",
        "Pₛₑₚ > Pₗₕ consistency    ",
        "Net electric power lower limit   ",
        "Radiation fraction (fᵧ) upper limit   ",
        "Divertor heat load upper limit   ",
        "Resistive TF MVA upper limit                  ",
        "Beam tangency radius upper limit ",
        "Plasma minor radius (a) lower limit  ",
        "Divertor collisionality upper limit",
        "Conducting shell radius upper limit",
        "⟨β⟩ upper limit                 ",
        "TF peak symmetric toroidal field upper limit  ",
        "CS coil EOF current density limit",
        "CS coil BOP current density limit",
        "Fusion gain (Qₚₗₐₛₘₐ) lower limit        ",
        "Inboard radial build consistency ",
        "Plasma injected power (Pₐᵤₓ) upper limit      ",
        "TF coil case stress upper limit  ",
        "TF coil conduit stress upper limit ",
        "TF coil superconductor critical current density upper limit  ",
        "TF quench dump voltage upper limit         ",
        "TF quench hotspot current density upper limit         ",
        "TF coil superconductor temperature margin lower limit ",
        "HCD normalised current drive efficiency (γ) upper limit        ",  # noqa: RUF001
        "FW coolant temperature rise upper limit ",
        "FW peak temperature limit",
        "Plasma injected power lower limit  ",
        "Plasma current (Iₚ) ramp time lower limit ",
        "Pulse cycle time lower limit           ",
        "Average CP temperature consistency  ",
        "Peak CP temperature upper limit",
        "Edge safety factor (q₉₅) lower limit   ",
        "Iₚ/I_rod upper limit              ",
        "NOT USED",
        "⟨βₚ⟩ upper limit        ",
        "NOT USED",
        "IFE repetition rate upper limit  ",
        "CS & PF system ramp-up Vs consistency ",
        "Tritium breeding ratio lower limit ",
        "TF fast neutron fluence upper limit ",
        "TF peak nuclear heating upper limit ",
        "NOT USED",
        "Pₛₑₚ / R₀ upper limit             ",
        "NOT USED",
        "NOT USED",
        "NB shine-through fraction upper limit",
        "CS superconductor temperature margin lower limit",
        "Plant availability lower limit",
        "Alpha to energy confinement ratio (τ_α/τₑ) lower limit       ",  # noqa: RUF001
        "ITER-like vacuum pump number upper limit",
        "Plasma volume averaged effective charge (⟨Zₑ⟩) upper limit                       ",
        "VV stress during TF quench upper limit     ",
        "Rate of change of energy in PF system upper limit",
        "FW radiation wall load upper limit",
        "(PₛₑₚBₜ / q₉₅AR₀) upper limit      ",
        "NOT USED",
        "NOT USED",
        "NOT USED",
        "CS Tresca yield criterion upper limit     ",
        "Pₛₑₚ > Pₗₕ + Pₐᵤₓ consistency           ",
        "TF quench temperature < temp_croco_quench_max",
        "TF current/copper area < Max    ",
        "Eich critical separatrix density upper limit ",
        "TF current per turn upper limit ",
        "Reinke criterion divertor impurity fraction lower limit",
        "Peak CS field upper limit        ",
        "Pₛₑₚ lower limit                ",
        "nₑ₀ > nₑ_pedestal constraint     ",
        "toroidalgap > dx_tf_inboard_out_t",  # Stellarator constraint
        "available_space > required_space ",  # Stellarator constraint
        "⟨β⟩ lower limit                   ",
        "CP lifetime consistency                  ",
        "TF turn dimension upper limit              ",
        "Cryogenic plant power upper limit           ",
        "TF WP vertical strain upper limit    ",
        "CS current to copper area upper limit   ",
        "CS achievable stress load cycles lower limit           ",
        "ECRH ignitability                ",  # Stellarator constraint
        "Fuel composition consistency     ",
    ]

    ixc = np.array([0] * ipnvars)

    # WARNING These labels are used as variable names by write_new_in_dat.py, and possibly
    # other python utilities, so they cannot easily be changed.
    lablxc = [""] * ipnvars

    sqsumsq = 0.0
    objf_name = ""
    norm_objf = 0.0
    epsfcn = 1.0e-3
    epsvmc = 1.0e-6
    factor = 0.1e0
    ftol = 1.0e-4

    boundl = np.array([9.0e-99] * ipnvars)
    boundu = np.array([9.0e99] * ipnvars)

    itv_scaled_lower_bounds = np.array([0.0] * ipnvars)
    itv_scaled_upper_bounds = np.array([0.0] * ipnvars)
    rcm = np.array([0.0] * ipnvars)
    resdl = np.array([0.0] * ipnvars)
    scafc = np.array([0.0] * ipnvars)
    scale = np.array([0.0] * ipnvars)
    xcm = np.array([0.0] * ipnvars)
    xcs = np.array([0.0] * ipnvars)
    vlam = np.array([0.0] * ipnvars)
    name_xc = [""] * ipnvars
    force_vmcon_inequality_satisfication = 1
    force_vmcon_inequality_tolerance = 1e-8