superconducting

SUPERCONDUCTING_TF_TYPES = {1: 'Nb3Sn ITER', 2: 'Bi-2212', 3: 'NbTi', 4: 'Nb3Sn user', 5: 'Nb3Sn WST', 6: 'REBCO Croco', 7: 'NbTi Ginzburg-Landau', 8: 'REBCO Ginzburg-Landau', 9: 'REBCO Hazelton-Zhai'} module-attribute

SuperconductingTFCoil

Bases: TFCoil

Source code in process/models/tfcoil/superconducting.py

class SuperconductingTFCoil(TFCoil):
    def __init__(self):
        self.outfile = constants.NOUT

    def run(self, output: bool):
        """Routine to call the superconductor module for the TF coils

        Parameters
        ----------
        output: bool

        """
        self.iprint = 0

        # Set up TF values share by all coil types
        self.run_base_tf()

        self.sc_tf_internal_geom(
            tfcoil_variables.i_tf_wp_geom,
            tfcoil_variables.i_tf_case_geom,
            tfcoil_variables.i_tf_turns_integer,
        )

        tfcoil_variables.ind_tf_coil = self.tf_coil_self_inductance(
            dr_tf_inboard=build_variables.dr_tf_inboard,
            r_tf_arc=tfcoil_variables.r_tf_arc,
            z_tf_arc=tfcoil_variables.z_tf_arc,
            itart=physics_variables.itart,
            i_tf_shape=tfcoil_variables.i_tf_shape,
            z_tf_inside_half=build_variables.z_tf_inside_half,
            dr_tf_outboard=build_variables.dr_tf_outboard,
            r_tf_outboard_mid=build_variables.r_tf_outboard_mid,
            r_tf_inboard_mid=build_variables.r_tf_inboard_mid,
        )

        (
            superconducting_tf_coil_variables.e_tf_magnetic_stored_total,
            tfcoil_variables.e_tf_magnetic_stored_total_gj,
            tfcoil_variables.e_tf_coil_magnetic_stored,
        ) = self.tf_stored_magnetic_energy(
            ind_tf_coil=tfcoil_variables.ind_tf_coil,
            c_tf_total=tfcoil_variables.c_tf_total,
            n_tf_coils=tfcoil_variables.n_tf_coils,
        )

        (
            tfcoil_variables.cforce,
            tfcoil_variables.vforce,
            tfcoil_variables.vforce_outboard,
            superconducting_tf_coil_variables.vforce_inboard_tot,
            tfcoil_variables.f_vforce_inboard,
        ) = self.tf_field_and_force(
            i_tf_sup=tfcoil_variables.i_tf_sup,
            r_tf_wp_inboard_outer=superconducting_tf_coil_variables.r_tf_wp_inboard_outer,
            r_tf_wp_inboard_inner=superconducting_tf_coil_variables.r_tf_wp_inboard_inner,
            r_tf_outboard_in=superconducting_tf_coil_variables.r_tf_outboard_in,
            dx_tf_wp_insulation=tfcoil_variables.dx_tf_wp_insulation,
            dx_tf_wp_insertion_gap=tfcoil_variables.dx_tf_wp_insertion_gap,
            b_tf_inboard_peak_symmetric=tfcoil_variables.b_tf_inboard_peak_symmetric,
            c_tf_total=tfcoil_variables.c_tf_total,
            n_tf_coils=tfcoil_variables.n_tf_coils,
            dr_tf_plasma_case=tfcoil_variables.dr_tf_plasma_case,
            rmajor=physics_variables.rmajor,
            b_plasma_toroidal_on_axis=physics_variables.b_plasma_toroidal_on_axis,
            r_cp_top=build_variables.r_cp_top,
            itart=physics_variables.itart,
            i_cp_joints=tfcoil_variables.i_cp_joints,
            f_vforce_inboard=tfcoil_variables.f_vforce_inboard,
        )

        # Calculate TF coil areas and masses
        self.generic_tf_coil_area_and_masses()
        self.superconducting_tf_coil_areas_and_masses()

        # Do stress calculations (writes the stress output)
        if output:
            tfcoil_variables.n_rad_per_layer = 500

        try:
            (
                sig_tf_r_max,
                sig_tf_t_max,
                sig_tf_z_max,
                sig_tf_vmises_max,
                s_shear_tf_peak,
                deflect,
                eyoung_axial,
                eyoung_trans,
                eyoung_wp_axial,
                eyoung_wp_trans,
                poisson_wp_trans,
                radial_array,
                s_shear_cea_tf_cond,
                poisson_wp_axial,
                sig_tf_r,
                sig_tf_smeared_r,
                sig_tf_smeared_t,
                sig_tf_smeared_z,
                sig_tf_t,
                s_shear_tf,
                sig_tf_vmises,
                sig_tf_z,
                str_tf_r,
                str_tf_t,
                str_tf_z,
                n_radial_array,
                n_tf_bucking,
                tfcoil_variables.sig_tf_wp,
                sig_tf_case,
                sig_tf_cs_bucked,
                str_wp,
                casestr,
                insstrain,
                sig_tf_wp_av_z,
            ) = self.stresscl(
                int(tfcoil_variables.n_tf_stress_layers),
                int(tfcoil_variables.n_rad_per_layer),
                int(tfcoil_variables.n_tf_wp_stress_layers),
                int(tfcoil_variables.i_tf_bucking),
                float(build_variables.r_tf_inboard_in),
                build_variables.dr_bore,
                build_variables.z_tf_inside_half,
                pfcoil_variables.f_z_cs_tf_internal,
                build_variables.dr_cs,
                build_variables.i_tf_inside_cs,
                build_variables.dr_tf_inboard,
                build_variables.dr_cs_tf_gap,
                pfcoil_variables.i_pf_conductor,
                pfcoil_variables.j_cs_flat_top_end,
                pfcoil_variables.j_cs_pulse_start,
                pfcoil_variables.c_pf_coil_turn_peak_input,
                pfcoil_variables.n_pf_coils_in_group,
                pfcoil_variables.f_dr_dz_cs_turn,
                pfcoil_variables.radius_cs_turn_corners,
                pfcoil_variables.f_a_cs_turn_steel,
                tfcoil_variables.eyoung_steel,
                tfcoil_variables.poisson_steel,
                tfcoil_variables.eyoung_cond_axial,
                tfcoil_variables.poisson_cond_axial,
                tfcoil_variables.eyoung_cond_trans,
                tfcoil_variables.poisson_cond_trans,
                tfcoil_variables.eyoung_ins,
                tfcoil_variables.poisson_ins,
                tfcoil_variables.dx_tf_turn_insulation,
                tfcoil_variables.eyoung_copper,
                tfcoil_variables.poisson_copper,
                tfcoil_variables.i_tf_sup,
                tfcoil_variables.eyoung_res_tf_buck,
                superconducting_tf_coil_variables.r_tf_wp_inboard_inner,
                superconducting_tf_coil_variables.tan_theta_coil,
                superconducting_tf_coil_variables.rad_tf_coil_inboard_toroidal_half,
                superconducting_tf_coil_variables.r_tf_wp_inboard_outer,
                superconducting_tf_coil_variables.a_tf_coil_inboard_steel,
                superconducting_tf_coil_variables.a_tf_plasma_case,
                superconducting_tf_coil_variables.a_tf_coil_nose_case,
                tfcoil_variables.dx_tf_wp_insertion_gap,
                tfcoil_variables.dx_tf_wp_insulation,
                tfcoil_variables.n_tf_coil_turns,
                int(tfcoil_variables.i_tf_turns_integer),
                superconducting_tf_coil_variables.dx_tf_turn_cable_space_average,
                superconducting_tf_coil_variables.dr_tf_turn_cable_space,
                tfcoil_variables.dia_tf_turn_coolant_channel,
                tfcoil_variables.f_a_tf_turn_cable_copper,
                tfcoil_variables.dx_tf_turn_steel,
                superconducting_tf_coil_variables.dx_tf_side_case_average,
                superconducting_tf_coil_variables.dx_tf_wp_toroidal_average,
                superconducting_tf_coil_variables.a_tf_coil_inboard_insulation,
                tfcoil_variables.a_tf_wp_steel,
                tfcoil_variables.a_tf_wp_conductor,
                superconducting_tf_coil_variables.a_tf_wp_with_insulation,
                tfcoil_variables.eyoung_al,
                tfcoil_variables.poisson_al,
                tfcoil_variables.fcoolcp,
                tfcoil_variables.n_tf_graded_layers,
                tfcoil_variables.c_tf_total,
                tfcoil_variables.dr_tf_plasma_case,
                tfcoil_variables.i_tf_stress_model,
                superconducting_tf_coil_variables.vforce_inboard_tot,
                tfcoil_variables.i_tf_tresca,
                tfcoil_variables.a_tf_coil_inboard_case,
                tfcoil_variables.vforce,
                tfcoil_variables.a_tf_turn_steel,
            )

            tfcoil_variables.sig_tf_case = (
                tfcoil_variables.sig_tf_case
                if tfcoil_variables.sig_tf_case is None
                else sig_tf_case
            )

            tfcoil_variables.sig_tf_cs_bucked = (
                tfcoil_variables.sig_tf_cs_bucked
                if tfcoil_variables.sig_tf_cs_bucked is None
                else sig_tf_cs_bucked
            )

            tfcoil_variables.str_wp = (
                tfcoil_variables.str_wp if tfcoil_variables.str_wp is None else str_wp
            )

            tfcoil_variables.casestr = (
                tfcoil_variables.casestr if tfcoil_variables.casestr is None else casestr
            )

            tfcoil_variables.insstrain = (
                tfcoil_variables.insstrain
                if tfcoil_variables.insstrain is None
                else insstrain
            )

            if output:
                self.out_stress(
                    sig_tf_r_max,
                    sig_tf_t_max,
                    sig_tf_z_max,
                    sig_tf_vmises_max,
                    s_shear_tf_peak,
                    deflect,
                    eyoung_axial,
                    eyoung_trans,
                    eyoung_wp_axial,
                    eyoung_wp_trans,
                    poisson_wp_trans,
                    radial_array,
                    s_shear_cea_tf_cond,
                    poisson_wp_axial,
                    sig_tf_r,
                    sig_tf_smeared_r,
                    sig_tf_smeared_t,
                    sig_tf_smeared_z,
                    sig_tf_t,
                    s_shear_tf,
                    sig_tf_vmises,
                    sig_tf_z,
                    str_tf_r,
                    str_tf_t,
                    str_tf_z,
                    n_radial_array,
                    n_tf_bucking,
                    sig_tf_wp_av_z,
                )
        except ValueError as e:
            if e.args[1] == 245 and e.args[2] == 0:
                logger.warning(
                    "Invalid stress model (r_tf_inboard = 0), stress constraint switched off"
                )
                tfcoil_variables.sig_tf_case = 0.0e0
                tfcoil_variables.sig_tf_wp = 0.0e0

        self.vv_stress_on_quench()

        # ======================================================

        # Peak inboard toroidal field including ripple
        tfcoil_variables.b_tf_inboard_peak_with_ripple = self.peak_b_tf_inboard_with_ripple(
            n_tf_coils=tfcoil_variables.n_tf_coils,
            dx_tf_wp_primary_toroidal=tfcoil_variables.dx_tf_wp_primary_toroidal,
            dr_tf_wp_no_insulation=superconducting_tf_coil_variables.dr_tf_wp_no_insulation,
            r_tf_wp_inboard_centre=superconducting_tf_coil_variables.r_tf_wp_inboard_centre,
            b_tf_inboard_peak_symmetric=tfcoil_variables.b_tf_inboard_peak_symmetric,
        )
        # ======================================================

        # Cross-sectional area per turn
        a_tf_turn = tfcoil_variables.c_tf_total / (
            tfcoil_variables.j_tf_wp
            * tfcoil_variables.n_tf_coils
            * tfcoil_variables.n_tf_coil_turns
        )

        if tfcoil_variables.i_tf_sc_mat == 6:
            (
                tfcoil_variables.j_tf_wp_critical,
                tfcoil_variables.temp_tf_superconductor_margin,
            ) = self.supercon_croco(
                a_tf_turn,
                tfcoil_variables.b_tf_inboard_peak_with_ripple,
                tfcoil_variables.c_tf_turn,
                tfcoil_variables.tftmp,
                output=output,
            )

            tfcoil_variables.v_tf_coil_dump_quench_kv = (
                self.croco_voltage() / 1.0e3
            )  # TFC Quench voltage in kV

        else:
            (
                tfcoil_variables.j_tf_wp_critical,
                superconducting_tf_coil_variables.j_tf_superconductor_critical,
                superconducting_tf_coil_variables.f_c_tf_turn_operating_critical,
                superconducting_tf_coil_variables.j_tf_superconductor,
                superconducting_tf_coil_variables.j_tf_coil_turn,
                superconducting_tf_coil_variables.b_tf_superconductor_critical_zero_temp_strain,
                superconducting_tf_coil_variables.temp_tf_superconductor_critical_zero_field_strain,
                superconducting_tf_coil_variables.c_tf_turn_cables_critical,
            ) = self.tf_cable_in_conduit_superconductor_properties(
                a_tf_turn_cable_space=tfcoil_variables.a_tf_turn_cable_space_no_void,
                a_tf_turn=a_tf_turn,
                a_tf_turn_cable_space_effective=superconducting_tf_coil_variables.a_tf_turn_cable_space_effective,
                f_a_tf_turn_cable_space_cooling=superconducting_tf_coil_variables.f_a_tf_turn_cable_space_cooling,
                b_tf_inboard_peak=tfcoil_variables.b_tf_inboard_peak_with_ripple,
                f_a_tf_turn_cable_copper=tfcoil_variables.f_a_tf_turn_cable_copper,
                c_tf_turn=tfcoil_variables.c_tf_turn,
                j_tf_wp=tfcoil_variables.j_tf_wp,
                i_tf_superconductor=tfcoil_variables.i_tf_sc_mat,
                f_strain_scale=tfcoil_variables.fhts,
                temp_tf_coolant_peak_field=tfcoil_variables.tftmp,
                bcritsc=tfcoil_variables.bcritsc,
                tcritsc=tfcoil_variables.tcritsc,
            )

        if tfcoil_variables.i_str_wp == 0:
            strain = tfcoil_variables.str_tf_con_res
        else:
            strain = tfcoil_variables.str_wp

        tfcoil_variables.temp_tf_superconductor_margin = self.calculate_superconductor_temperature_margin(
            i_tf_superconductor=tfcoil_variables.i_tf_sc_mat,
            j_superconductor=superconducting_tf_coil_variables.j_tf_superconductor,
            b_tf_inboard_peak=tfcoil_variables.b_tf_inboard_peak_with_ripple,
            strain=strain,
            bc20m=superconducting_tf_coil_variables.b_tf_superconductor_critical_zero_temp_strain,
            tc0m=superconducting_tf_coil_variables.temp_tf_superconductor_critical_zero_field_strain,
            c0=1.0e10,
            temp_tf_coolant_peak_field=tfcoil_variables.tftmp,
        )

        # Do current density protection calculation
        # Only setup for Nb3Sn at present.
        if tfcoil_variables.i_tf_sc_mat not in {1, 4, 5}:
            logger.warning(
                "Calculating current density protection limit for Nb3Sn TF coil (LTS windings only)"
            )
            # Find the current density limited by the protection limit
            # At present only valid for LTS windings (Nb3Sn properties assumed)
        tfcoil_variables.j_tf_wp_quench_heat_max, v_tf_coil_dump_quench = (
            self.quench_heat_protection_current_density(
                c_tf_turn=tfcoil_variables.c_tf_turn,
                e_tf_coil_magnetic_stored=tfcoil_variables.e_tf_coil_magnetic_stored,
                a_tf_turn_cable_space=tfcoil_variables.a_tf_turn_cable_space_no_void,
                a_tf_turn=a_tf_turn,
                t_tf_quench_dump=tfcoil_variables.t_tf_superconductor_quench,
                f_a_tf_turn_cable_space_conductor=1.0e0
                - superconducting_tf_coil_variables.f_a_tf_turn_cable_space_cooling,
                f_a_tf_turn_cable_copper=tfcoil_variables.f_a_tf_turn_cable_copper,
                temp_tf_coolant_peak_field=tfcoil_variables.tftmp,
                temp_tf_conductor_quench_max=tfcoil_variables.temp_tf_conductor_quench_max,
                b_tf_inboard_peak=tfcoil_variables.b_tf_inboard_peak_with_ripple,
                cu_rrr=tfcoil_variables.rrr_tf_cu,
                t_tf_quench_detection=tfcoil_variables.t_tf_quench_detection,
                nflutfmax=constraint_variables.nflutfmax,
            )
        )

        tfcoil_variables.v_tf_coil_dump_quench_kv = (
            v_tf_coil_dump_quench / 1.0e3
        )  # TFC Quench voltage in kV

        if output:
            self.outtf()

    def croco_voltage(self) -> float:
        if tfcoil_variables.quench_model == "linear":
            superconducting_tf_coil_variables.time2 = (
                tfcoil_variables.t_tf_superconductor_quench
            )
            croco_voltage = (
                2.0e0
                / superconducting_tf_coil_variables.time2
                * (
                    superconducting_tf_coil_variables.e_tf_magnetic_stored_total
                    / tfcoil_variables.n_tf_coils
                )
                / tfcoil_variables.c_tf_turn
            )
        elif tfcoil_variables.quench_model == "exponential":
            superconducting_tf_coil_variables.tau2 = (
                tfcoil_variables.t_tf_superconductor_quench
            )
            croco_voltage = (
                2.0e0
                / superconducting_tf_coil_variables.tau2
                * (
                    superconducting_tf_coil_variables.e_tf_magnetic_stored_total
                    / tfcoil_variables.n_tf_coils
                )
                / tfcoil_variables.c_tf_turn
            )
        else:
            return 0.0

        return croco_voltage

    def supercon_croco(
        self, a_tf_turn, b_tf_inboard_peak_symmetric, iop, thelium, output: bool
    ):
        """TF superconducting CroCo conductor using REBCO tape

        Parameters
        ----------
        a_tf_turn :

        b_tf_inboard_peak_symmetric :
            Peak field at conductor (T)
        iop :
            Operating current per turn (A)
        thelium :
            He temperature at peak field point (K)
        output:

        """

        j_crit_sc: float = 0.0
        #  Find critical current density in superconducting cable, j_crit_cable
        j_crit_sc, _ = superconductors.jcrit_rebco(thelium, b_tf_inboard_peak_symmetric)
        # tfcoil_variables.a_tf_turn_cable_space_no_void : Cable space - inside area (m2)
        # Set new rebco_variables.dia_croco_strand
        # allowing for scaling of rebco_variables.dia_croco_strand
        rebco_variables.dia_croco_strand = (
            tfcoil_variables.t_conductor / 3.0e0
            - tfcoil_variables.dx_tf_turn_steel * (2.0e0 / 3.0e0)
        )
        superconducting_tf_coil_variables.conductor_acs = (
            9.0e0 / 4.0e0 * np.pi * rebco_variables.dia_croco_strand**2
        )
        tfcoil_variables.a_tf_turn_cable_space_no_void = (
            superconducting_tf_coil_variables.conductor_acs
        )
        superconducting_tf_coil_variables.conductor_area = (
            tfcoil_variables.t_conductor**2
        )  # does this not assume it's a sqaure???

        superconducting_tf_coil_variables.conductor_jacket_area = (
            superconducting_tf_coil_variables.conductor_area
            - superconducting_tf_coil_variables.conductor_acs
        )
        tfcoil_variables.a_tf_turn_steel = (
            superconducting_tf_coil_variables.conductor_jacket_area
        )

        superconducting_tf_coil_variables.conductor_jacket_fraction = (
            superconducting_tf_coil_variables.conductor_jacket_area
            / superconducting_tf_coil_variables.conductor_area
        )
        (
            superconducting_tf_coil_variables.croco_strand_area,
            superconducting_tf_coil_variables.croco_strand_critical_current,
            superconducting_tf_coil_variables.conductor_copper_area,
            superconducting_tf_coil_variables.conductor_copper_fraction,
            superconducting_tf_coil_variables.conductor_copper_bar_area,
            superconducting_tf_coil_variables.conductor_hastelloy_area,
            superconducting_tf_coil_variables.conductor_hastelloy_fraction,
            superconducting_tf_coil_variables.conductor_helium_area,
            superconducting_tf_coil_variables.conductor_helium_fraction,
            superconducting_tf_coil_variables.conductor_solder_area,
            superconducting_tf_coil_variables.conductor_solder_fraction,
            superconducting_tf_coil_variables.conductor_rebco_area,
            superconducting_tf_coil_variables.conductor_rebco_fraction,
            superconducting_tf_coil_variables.conductor_critical_current,
        ) = superconductors.croco(
            j_crit_sc,
            superconducting_tf_coil_variables.conductor_area,
            rebco_variables.dia_croco_strand,
            rebco_variables.dx_croco_strand_copper,
        )

        rebco_variables.coppera_m2 = (
            iop / superconducting_tf_coil_variables.conductor_copper_area
        )

        icrit = superconducting_tf_coil_variables.conductor_critical_current
        j_crit_cable = (
            superconducting_tf_coil_variables.croco_strand_critical_current
            / superconducting_tf_coil_variables.croco_strand_area
        )

        # Critical current density in winding pack
        # a_tf_turn : Area per turn (i.e. entire jacketed conductor with insulation) (m2)
        j_tf_wp_critical = icrit / a_tf_turn
        #  Ratio of operating / critical current
        iooic = iop / icrit
        #  Operating current density
        jwdgop = iop / a_tf_turn
        #  Actual current density in superconductor,
        # which should be equal to jcrit(thelium+tmarg)

        #  when we have found the desired value of tmarg
        jsc = iooic * j_crit_sc

        # Temperature margin
        current_sharing_t = superconductors.current_sharing_rebco(
            b_tf_inboard_peak_symmetric, jsc
        )
        tmarg = current_sharing_t - thelium
        tfcoil_variables.temp_margin = (
            tmarg  # Only used in the availabilty routine - see comment to Issue #526
        )

        if output:  # Output ----------------------------------
            total = (
                superconducting_tf_coil_variables.conductor_copper_area
                + superconducting_tf_coil_variables.conductor_hastelloy_area
                + superconducting_tf_coil_variables.conductor_solder_area
                + superconducting_tf_coil_variables.conductor_jacket_area
                + superconducting_tf_coil_variables.conductor_helium_area
                + superconducting_tf_coil_variables.conductor_rebco_area
            )

            if tfcoil_variables.temp_margin <= 0.0e0:
                logger.error(
                    f"""Negative TFC temperature margin
                temp_margin: {tfcoil_variables.temp_margin}
                b_tf_inboard_peak_symmetric: {b_tf_inboard_peak_symmetric}"""
                )

            po.oheadr(self.outfile, "Superconducting TF Coils")
            po.ovarin(self.outfile, "Superconductor switch", "(isumat)", 6)
            po.ocmmnt(
                self.outfile, "Superconductor used: REBCO HTS tape in CroCo strand"
            )

            po.ovarre(
                self.outfile,
                "Thickness of REBCO layer in tape (m)",
                "(dx_hts_tape_rebco)",
                rebco_variables.dx_hts_tape_rebco,
            )
            po.ovarre(
                self.outfile,
                "Thickness of copper layer in tape (m)",
                "(dx_hts_tape_copper)",
                rebco_variables.dx_hts_tape_copper,
            )
            po.ovarre(
                self.outfile,
                "Thickness of Hastelloy layer in tape (m) ",
                "(dx_hts_tape_hastelloy)",
                rebco_variables.dx_hts_tape_hastelloy,
            )

            po.ovarre(
                self.outfile,
                "Mean width of tape (m)",
                "(dr_hts_tape)",
                rebco_variables.dr_hts_tape,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Diameter of a CroCo strand (m) ",
                "(dia_croco_strand)",
                rebco_variables.dia_croco_strand,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Inner diameter of CroCo copper tube (m) ",
                "(dia_croco_strand_tape_region)",
                rebco_variables.dia_croco_strand_tape_region,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Thickness of of o copper tube (m) ",
                "(dx_croco_strand_copper)",
                rebco_variables.dx_croco_strand_copper,
            )

            po.ovarre(
                self.outfile,
                "Thickness of each HTS tape ",
                "(dx_hts_tape_total)",
                rebco_variables.dx_hts_tape_total,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Thickness of stack of rebco_variables.n_croco_strand_hts_tapes (m) ",
                "(dx_croco_strand_tape_stack)",
                rebco_variables.dx_croco_strand_tape_stack,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Number of rebco_variables.n_croco_strand_hts_tapes in strand",
                "(n_croco_strand_hts_tapes)",
                rebco_variables.n_croco_strand_hts_tapes,
                "OP ",
            )
            po.oblnkl(self.outfile)
            po.ovarre(
                self.outfile,
                "Area of REBCO in strand (m2)",
                "(a_croco_strand_rebco)",
                rebco_variables.a_croco_strand_rebco,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Area of copper in strand (m2)",
                "(a_croco_strand_copper_total)",
                rebco_variables.a_croco_strand_copper_total,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Area of hastelloy substrate in strand (m2) ",
                "(a_croco_strand_hastelloy)",
                rebco_variables.a_croco_strand_hastelloy,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Area of solder in strand (m2)  ",
                "(a_croco_strand_solder)",
                rebco_variables.a_croco_strand_solder,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Total: area of CroCo strand (m2)  ",
                "(croco_strand_area)",
                superconducting_tf_coil_variables.croco_strand_area,
                "OP ",
            )
            if (
                abs(
                    superconducting_tf_coil_variables.croco_strand_area
                    - (
                        rebco_variables.a_croco_strand_rebco
                        + rebco_variables.a_croco_strand_copper_total
                        + rebco_variables.a_croco_strand_hastelloy
                        + rebco_variables.a_croco_strand_solder
                    )
                )
                > 1e-6
            ):
                po.ocmmnt(self.outfile, "ERROR: Areas in CroCo strand do not add up")
                logger.error("Areas in CroCo strand do not add up - see OUT.DAT")

            po.oblnkl(self.outfile)
            po.ocmmnt(self.outfile, "Cable information")
            po.ovarin(
                self.outfile,
                "Number of CroCo strands in the cable (fixed) ",
                "",
                6,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Total area of cable space (m2)",
                "(a_tf_turn_cable_space_no_void)",
                tfcoil_variables.a_tf_turn_cable_space_no_void,
                "OP ",
            )

            po.oblnkl(self.outfile)
            po.ocmmnt(
                self.outfile,
                "Conductor information (includes jacket, not including insulation)",
            )
            po.ovarre(
                self.outfile,
                "Width of square conductor (cable + steel jacket) (m)",
                "(t_conductor)",
                tfcoil_variables.t_conductor,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Area of conductor (m2)",
                "(area)",
                superconducting_tf_coil_variables.conductor_area,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "REBCO area of conductor (mm2)",
                "(a_croco_strand_rebco)",
                superconducting_tf_coil_variables.conductor_rebco_area,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Area of central copper bar (mm2)",
                "(copper_bar_area)",
                superconducting_tf_coil_variables.conductor_copper_bar_area,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Total copper area of conductor, total (mm2)",
                "(a_croco_strand_copper_total)",
                superconducting_tf_coil_variables.conductor_copper_area,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Hastelloy area of conductor (mm2)",
                "(a_croco_strand_hastelloy)",
                superconducting_tf_coil_variables.conductor_hastelloy_area,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Solder area of conductor (mm2)",
                "(a_croco_strand_solder)",
                superconducting_tf_coil_variables.conductor_solder_area,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Jacket area of conductor (mm2)",
                "(jacket_area)",
                superconducting_tf_coil_variables.conductor_jacket_area,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Helium area of conductor (mm2)",
                "(helium_area)",
                superconducting_tf_coil_variables.conductor_helium_area,
                "OP ",
            )
            if abs(total - superconducting_tf_coil_variables.conductor_area) > 1e-8:
                po.ovarre(
                    self.outfile,
                    "ERROR: conductor areas do not add up:",
                    "(total)",
                    total,
                    "OP ",
                )
                logger.error(f"conductor areas do not add up. total: {total}")

            po.ovarre(
                self.outfile,
                "Critical current of CroCo strand (A)",
                "(croco_strand_critical_current)",
                superconducting_tf_coil_variables.croco_strand_critical_current,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Critical current of conductor (A) ",
                "(conductor_critical_current)",
                superconducting_tf_coil_variables.conductor_critical_current,
                "OP ",
            )

            if global_variables.run_tests == 1:
                po.oblnkl(self.outfile)
                po.ocmmnt(
                    self.outfile,
                    "PROCESS TF Coil peak field fit. Values for t, z and y:",
                )
                po.oblnkl(self.outfile)
                po.ovarre(
                    self.outfile,
                    "Dimensionless winding pack width",
                    "(tf_fit_t)",
                    superconducting_tf_coil_variables.tf_fit_t,
                    "OP ",
                )
                po.ovarre(
                    self.outfile,
                    "Dimensionless winding pack radial thickness",
                    "(tf_fit_z)",
                    superconducting_tf_coil_variables.tf_fit_z,
                    "OP ",
                )
                po.ovarre(
                    self.outfile,
                    "Ratio of actual peak field to nominal axisymmetric peak field",
                    "(f_b_tf_inboard_peak_ripple_symmetric)",
                    superconducting_tf_coil_variables.f_b_tf_inboard_peak_ripple_symmetric,
                    "OP ",
                )

            po.oblnkl(self.outfile)
            po.ovarre(
                self.outfile,
                "Helium temperature at peak field (= superconductor temperature) (K)",
                "(thelium)",
                thelium,
            )
            po.ovarre(
                self.outfile,
                "Critical current density in superconductor (A/m2)",
                "(j_crit_sc)",
                j_crit_sc,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Critical current density in cable (A/m2)",
                "(j_crit_cable)",
                j_crit_cable,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Critical current density in winding pack (A/m2)",
                "(j_tf_wp_critical)",
                j_tf_wp_critical,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Actual current density in winding pack (A/m2)",
                "(jwdgop)",
                jwdgop,
                "OP ",
            )

            po.ovarre(
                self.outfile,
                "Minimum allowed temperature margin in superconductor (K)",
                "(temp_tf_superconductor_margin_min)",
                tfcoil_variables.temp_tf_superconductor_margin_min,
            )

            po.ovarre(
                self.outfile,
                "Actual temperature margin in superconductor (K)",
                "(tmarg)",
                tmarg,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Current sharing temperature (K)",
                "(current_sharing_t)",
                current_sharing_t,
                "OP ",
            )
            po.ovarre(self.outfile, "Critical current (A)", "(icrit)", icrit, "OP ")
            po.ovarre(
                self.outfile,
                "Actual current (A)",
                "(c_tf_turn)",
                tfcoil_variables.c_tf_turn,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Actual current / critical current",
                "(iooic)",
                iooic,
                "OP ",
            )

        return j_tf_wp_critical, tmarg

    def tf_cable_in_conduit_superconductor_properties(
        self,
        a_tf_turn_cable_space: float,
        a_tf_turn: float,
        a_tf_turn_cable_space_effective: float,
        f_a_tf_turn_cable_space_cooling: float,
        b_tf_inboard_peak: float,
        f_a_tf_turn_cable_copper: float,
        c_tf_turn: float,
        j_tf_wp: float,
        i_tf_superconductor: int,
        f_strain_scale: float,
        temp_tf_coolant_peak_field: float,
        bcritsc: float,
        tcritsc: float,
    ) -> tuple[float, float, float, float, float, float, float, float]:
        """Calculates the properties of the TF superconducting conductor.

        Parameters
        ----------
        a_tf_turn_cable_space:
            Cable space - inside area (m²).
        a_tf_turn:
            Area per turn (i.e. entire jacketed conductor) (m²).
        a_tf_turn_cable_space_effective:
            Effective cable space area per turn (m²).
        f_a_tf_turn_cable_space_cooling:
            Fraction of cable space used for cooling.
        b_tf_inboard_peak:
            Peak field at conductor (T).
        f_a_tf_turn_cable_copper:
            Fraction of conductor that is copper.
        c_tf_turn:
            Operating current per turn (A).
        j_tf_wp:
            Actual winding pack current density (A/m²).
        i_tf_superconductor:
            Switch for conductor type:
            - 1: ITER Nb3Sn, standard parameters
            - 2: Bi-2212 High Temperature Superconductor
            - 3: NbTi
            - 4: ITER Nb3Sn, user-defined parameters
            - 5: WST Nb3Sn parameterisation
            - 7: Durham Ginzburg-Landau Nb-Ti parameterisation
            - 8: Durham Ginzburg-Landau critical surface model for REBCO
            - 9: Hazelton experimental data + Zhai conceptual model for REBCO
        f_strain_scale:
            Adjustment factor (<= 1) to account for strain, radiation damage, fatigue or AC losses.
        temp_tf_coolant_peak_field:
            He temperature at peak field point (K).
        bcritsc:
            Critical field at zero temperature and strain (T) (used only if i_tf_superconductor=4).
        tcritsc:
            Critical temperature at zero field and strain (K) (used only if i_tf_superconductor=4).

        Returns
        -------
        type
            tuple (float, float, float, float, float, float, float, float, float)
            - j_tf_wp_critical (float): Critical winding pack current density (A/m²).
            - j_superconductor_critical (float): Critical current density in superconductor (A/m²).
            - f_c_tf_turn_operating_critical (float): Ratio of operating / critical current.
            - j_superconductor_turn (float): Actual current density in superconductor (A/m²).
            - j_tf_coil_turn (float): Actual current density in superconductor (A/m²).
            - b_tf_superconductor_critical_zero_temp_strain (float): Critical field at zero temperature and strain (T).
            - temp_tf_superconductor_critical_zero_field_strain (float): Critical temperature at zero field and strain (K).
            - c_tf_turn_cables_critical (float): Critical current in cable (A).

        Notes
        -----
        This routine calculates the superconductor properties for the TF coils.
        It was originally programmed by J. Galambos (1991), from algorithms provided by J. Miller.
        The routine calculates the critical current density (winding pack) and also the protection
        information (for a quench). Not used for the CroCo conductor.

        The critical current density for a superconductor (``j_superconductor_critical``) is for the superconducting
        strands/tape, not including copper. The critical current density for a cable (``j_crit_cable``)
        accounts for both the fraction of the cable taken up by helium coolant channels, and the cable
        conductor copper fraction (i.e., the copper in the superconducting strands and any additional
        copper, such as REBCO tape support).
        """

        # Guard against negative conductor fraction f_a_tf_turn_cable_space_conductor
        # Kludge to allow solver to continue and hopefully be constrained away
        # from this point
        if f_a_tf_turn_cable_space_cooling > 0.99:
            f_a_tf_turn_cable_space_cooling = 0.99

        #  Conductor fraction (including central helium channel)
        f_a_tf_turn_cable_space_conductor = 1.0e0 - f_a_tf_turn_cable_space_cooling

        if tfcoil_variables.i_str_wp == 0:
            strain = tfcoil_variables.str_tf_con_res
        else:
            strain = tfcoil_variables.str_wp

        # =================================================================

        # ITER Nb3Sn critical surface parameterization
        if i_tf_superconductor == 1:
            # Peak field and temperature at zero strain
            bc20m = 32.97e0  # [T]
            tc0m = 16.06e0  # [K]

            # If strain limit achieved, throw a warning and use the lower strain
            if abs(strain) > 0.5e-2:
                logger.error(
                    f"TF strain={strain} was outside the region of applicability. Used lower strain."
                )
                strain = np.sign(strain) * 0.5e-2

            #  j_superconductor_critical returned by superconductors.itersc is the critical current density in the
            #  superconductor - not the whole strand, which contains copper
            j_superconductor_critical, _, _ = superconductors.itersc(
                temp_conductor=temp_tf_coolant_peak_field,
                b_conductor=b_tf_inboard_peak,
                strain=strain,
                b_c20max=bc20m,
                temp_c0max=tc0m,
            )

            # Scale for the copper area fraction of the cable
            j_cables_critical = j_superconductor_critical * (
                1.0e0 - f_a_tf_turn_cable_copper
            )

            #  Critical current in turn all turn cables
            c_turn_cables_critical = j_cables_critical * a_tf_turn_cable_space_effective

            # Strand critical current calculation for costing in $/kAm
            # = Superconducting filaments jc * (1 - strand copper fraction)
            tfcoil_variables.j_crit_str_tf = j_superconductor_critical * (
                1.0e0 - f_a_tf_turn_cable_copper
            )

        # =================================================================

        # Bi-2212 high temperature superconductor parameterization
        elif i_tf_superconductor == 2:
            #  Current density in a strand of Bi-2212 conductor
            #  N.B. jcrit returned by superconductors.bi2212 is the critical current density
            #  in the strand, not just the superconducting portion.
            #  The parameterization for j_crit_cable assumes a particular strand
            #  composition that does not require a user-defined copper fraction,
            #  so this is irrelevant in this model
            j_strand = (
                j_tf_wp
                * a_tf_turn
                / (a_tf_turn_cable_space * f_a_tf_turn_cable_space_conductor)
            )

            j_crit_cable, _ = superconductors.bi2212(
                b_conductor=b_tf_inboard_peak,
                jstrand=j_strand,
                temp_conductor=temp_tf_coolant_peak_field,
                f_strain=f_strain_scale,
            )
            j_superconductor_critical = j_crit_cable / (1.0e0 - f_a_tf_turn_cable_copper)
            #  Critical current in cable
            c_turn_cables_critical = (
                j_crit_cable * a_tf_turn_cable_space * f_a_tf_turn_cable_space_conductor
            )

            # Strand critical current calulation for costing in $ / kAm
            # Copper in the strand is already accounted for
            tfcoil_variables.j_crit_str_tf = j_superconductor_critical
        # =================================================================

        # NbTi data
        elif i_tf_superconductor == 3:
            bc20m = 15.0e0  # [T]
            tc0m = 9.3e0  # [K]
            c0 = 1.0e10  # [A/m2]

            j_superconductor_critical, _ = superconductors.jcrit_nbti(
                temp_conductor=temp_tf_coolant_peak_field,
                b_conductor=b_tf_inboard_peak,
                c0=c0,
                b_c20m=bc20m,
                temp_c0max=tc0m,
            )

            # Scale for the copper area fraction of the cable
            j_cables_critical = j_superconductor_critical * (
                1.0e0 - f_a_tf_turn_cable_copper
            )

            #  Critical current in turn all turn cables
            c_turn_cables_critical = j_cables_critical * a_tf_turn_cable_space_effective

            # Strand critical current calulation for costing in $ / kAm
            # = superconducting filaments jc * (1 -strand copper fraction)
            tfcoil_variables.j_crit_str_tf = j_superconductor_critical * (
                1.0e0 - f_a_tf_turn_cable_copper
            )

        # =================================================================

        # ITER Nb3Sn parameterization, but user-defined parameters
        elif i_tf_superconductor == 4:
            bc20m = bcritsc  # [T]
            tc0m = tcritsc  # [K]

            # If strain limit achieved, throw a warning and use the lower strain
            if abs(strain) > 0.5e-2:
                logger.error(
                    f"TF strain={strain} was outside the region of applicability. Used lower strain."
                )
                strain = np.sign(strain) * 0.5e-2

            j_superconductor_critical, _, _ = superconductors.itersc(
                temp_conductor=temp_tf_coolant_peak_field,
                b_conductor=b_tf_inboard_peak,
                strain=strain,
                b_c20max=bc20m,
                temp_c0max=tc0m,
            )
            # Scale for the copper area fraction of the cable
            j_cables_critical = j_superconductor_critical * (
                1.0e0 - f_a_tf_turn_cable_copper
            )

            #  Critical current in turn all turn cables
            c_turn_cables_critical = j_cables_critical * a_tf_turn_cable_space_effective

            # Strand critical current calulation for costing in $ / kAm
            # = superconducting filaments jc * (1 -strand copper fraction)
            tfcoil_variables.j_crit_str_tf = j_superconductor_critical * (
                1.0e0 - f_a_tf_turn_cable_copper
            )

        # =================================================================

        # WST Nb3Sn parameterisation
        elif i_tf_superconductor == 5:
            bc20m = 32.97e0  # [T]
            tc0m = 16.06e0  # [K]

            # If strain limit achieved, throw a warning and use the lower strain
            if abs(strain) > 0.5e-2:
                logger.error(
                    f"TF strain={strain} was outside the region of applicability. Used lower strain."
                )
                strain = np.sign(strain) * 0.5e-2

            #  j_superconductor_critical returned by superconductors.itersc is the critical current density in the
            #  superconductor - not the whole strand, which contains copper
            j_superconductor_critical, _, _ = (
                superconductors.western_superconducting_nb3sn(
                    temp_conductor=temp_tf_coolant_peak_field,
                    b_conductor=b_tf_inboard_peak,
                    strain=strain,
                    b_c20max=bc20m,
                    temp_c0max=tc0m,
                )
            )
            # Scale for the copper area fraction of the cable
            j_cables_critical = j_superconductor_critical * (
                1.0e0 - f_a_tf_turn_cable_copper
            )

            #  Critical current in turn all turn cables
            c_turn_cables_critical = j_cables_critical * a_tf_turn_cable_space_effective

            # Strand critical current calulation for costing in $ / kAm
            # = superconducting filaments jc * (1 -strand copper fraction)
            tfcoil_variables.j_crit_str_tf = j_superconductor_critical * (
                1.0e0 - f_a_tf_turn_cable_copper
            )

        # =================================================================

        # "REBCO" 2nd generation HTS superconductor in CrCo strand
        elif i_tf_superconductor == 6:
            raise ProcessValueError(
                "sctfcoil.supercon has been called but tfcoil_variables.i_tf_sc_mat=6"
            )

        # =================================================================

        # Durham Ginzburg-Landau Nb-Ti parameterisation
        elif i_tf_superconductor == 7:
            bc20m = tfcoil_variables.b_crit_upper_nbti  # [T]
            tc0m = tfcoil_variables.t_crit_nbti  # [K]

            j_superconductor_critical, _, _ = superconductors.gl_nbti(
                temp_conductor=temp_tf_coolant_peak_field,
                b_conductor=b_tf_inboard_peak,
                strain=strain,
                b_c20max=bc20m,
                t_c0=tc0m,
            )
            # Scale for the copper area fraction of the cable
            j_cables_critical = j_superconductor_critical * (
                1.0e0 - f_a_tf_turn_cable_copper
            )

            #  Critical current in turn all turn cables
            c_turn_cables_critical = j_cables_critical * a_tf_turn_cable_space_effective

            # Strand critical current calulation for costing in $ / kAm
            # = superconducting filaments jc * (1 -strand copper fraction)
            tfcoil_variables.j_crit_str_tf = j_superconductor_critical * (
                1.0e0 - f_a_tf_turn_cable_copper
            )

        # =================================================================

        # Durham Ginzburg-Landau critical surface model for REBCO
        elif i_tf_superconductor == 8:
            bc20m = 430  # [T]
            tc0m = 185  # [K]

            # If strain limit achieved, throw a warning and use the lower strain
            if abs(strain) > 0.7e-2:
                logger.error(
                    f"TF strain={strain} was outside the region of applicability. Used lower strain."
                )
                strain = np.sign(strain) * 0.7e-2

            j_superconductor_critical, _, _ = superconductors.gl_rebco(
                temp_conductor=temp_tf_coolant_peak_field,
                b_conductor=b_tf_inboard_peak,
                strain=strain,
                b_c20max=bc20m,
                t_c0=tc0m,
            )
            # Scale for the copper area fraction of the cable
            j_cables_critical = j_superconductor_critical * (
                1.0e0 - f_a_tf_turn_cable_copper
            )

            #  Critical current in turn all turn cables
            c_turn_cables_critical = j_cables_critical * a_tf_turn_cable_space_effective

            # Strand critical current calulation for costing in $ / kAm
            # Already includes buffer and support layers so no need to include f_a_tf_turn_cable_copper here
            tfcoil_variables.j_crit_str_tf = j_superconductor_critical

            # REBCO measurements from 2 T to 14 T, extrapolating outside this
            if (b_tf_inboard_peak) >= 14.0:
                logger.error(
                    "Field on superconductor > 14 T (outside of interpolation range)"
                )

        # =================================================================

        # Hazelton experimental data + Zhai conceptual model for REBCO
        elif i_tf_superconductor == 9:
            bc20m = 138  # [T]
            tc0m = 92  # [K]

            # If strain limit achieved, throw a warning and use the lower strain
            if abs(strain) > 0.7e-2:
                logger.error(
                    f"TF strain={strain} was outside the region of applicability. Used lower strain."
                )
                strain = np.sign(strain) * 0.7e-2

            # 'high current density' as per parameterisation described in Wolf,
            #  and based on Hazelton experimental data and Zhai conceptual model;
            #  see subroutine for full references
            j_superconductor_critical, _, _ = superconductors.hijc_rebco(
                temp_conductor=temp_tf_coolant_peak_field,
                b_conductor=b_tf_inboard_peak,
                b_c20max=bc20m,
                t_c0=tc0m,
                dr_hts_tape=rebco_variables.dr_hts_tape,
                dx_hts_tape_rebco=rebco_variables.dx_hts_tape_rebco,
                dx_hts_tape_total=rebco_variables.dx_hts_tape_total,
            )
            # Scale for the copper area fraction of the cable
            j_cables_critical = j_superconductor_critical * (
                1.0e0 - f_a_tf_turn_cable_copper
            )

            #  Critical current in turn all turn cables
            c_turn_cables_critical = j_cables_critical * a_tf_turn_cable_space_effective

            # Strand critical current calulation for costing in $ / kAm
            # = superconducting filaments jc * (1 -strand copper fraction)
            tfcoil_variables.j_crit_str_tf = j_superconductor_critical * (
                1.0e0 - f_a_tf_turn_cable_copper
            )

        else:
            raise ProcessValueError(
                "Illegal value for i_tf_sc_mat", i_tf_superconductor=i_tf_superconductor
            )

        # =================================================================

        # Critical current density in winding pack
        # a_tf_turn : Area per turn (i.e. entire jacketed conductor with insulation) (m2)
        j_tf_wp_critical = c_turn_cables_critical / a_tf_turn

        #  Ratio of operating / critical current
        f_c_tf_turn_operating_critical = c_tf_turn / c_turn_cables_critical

        #  Operating current density
        j_tf_coil_turn = c_tf_turn / a_tf_turn

        #  Actual current density in superconductor, not including copper

        j_superconductor = f_c_tf_turn_operating_critical * j_superconductor_critical

        # =================================================================

        if f_c_tf_turn_operating_critical <= 0e0:
            logger.error(
                f"""Negative Iop/Icrit for TF coil
            jsc: {j_superconductor}
            f_c_tf_turn_operating_critical: {f_c_tf_turn_operating_critical}
            j_superconductor_critical: {j_superconductor_critical}
            Check conductor dimensions. Cable space area a_tf_turn_cable_space likely gone negative. a_tf_turn_cable_space: {a_tf_turn_cable_space}
            This is likely because dr_tf_turn_cable_space or dx_tf_turn_cable_space has gone negative:
            dr_tf_turn_cable_space: {superconducting_tf_coil_variables.dr_tf_turn_cable_space}
            dx_tf_turn_cable_space: {superconducting_tf_coil_variables.dx_tf_turn_cable_space}
            """
            )

        return (
            j_tf_wp_critical,
            j_superconductor_critical,
            f_c_tf_turn_operating_critical,
            j_superconductor,
            j_tf_coil_turn,
            bc20m,
            tc0m,
            c_turn_cables_critical,
        )

    def calculate_cable_in_conduit_strand_count(
        self,
        a_cable_space: float,
        dia_superconductor_strand: float,
    ) -> int:
        """Calculates the maximum number of superconducting strands that can fit into a cable-in-conduit conductor,
        based on the available cable space, strand diameter, and desired void fraction.

        Parameters
        ----------
        a_cable_space : float
            Total cross-sectional area available for the cable (in m²).
        dia_superconductor_strand : float
            Diameter of a single superconducting strand (in meters).

        Returns
        -------
        int
            The maximum number of strands that can fit in the available space, accounting for the void fraction.
        """

        # Effective area available for strands (excluding voids)
        effective_area = a_cable_space

        # Area per strand (circular)
        strand_area = np.pi * (dia_superconductor_strand / 2) ** 2

        # Number of strands that fit
        return int(effective_area / strand_area)

    def calculate_cable_in_conduit_superconductor_length(
        self,
        n_tf_coils: int,
        n_tf_coil_turns: int,
        len_tf_coil: float,
        n_tf_turn_superconducting_cables: int,
    ) -> float:
        """Calculates the total length of superconducting material required for the TF coils.

        Parameters
        ----------
        n_tf_coils: int :
            n_tf_coils: Number of TF coils.
        n_tf_coil_turns: int :
            n_tf_coil_turns: Total number of turns in the TF coil winding pack.
        len_tf_coil:
            len_tf_coil: Length of a single TF coil (in meters).
        n_tf_turn_superconducting_cables: int :
            n_tf_turn_superconducting_cables: Number of superconducting cables per turn in the TF coil.

        Returns
        -------
        tuple[float, float]
            Tuple containing:
            - Length of superconductor in one TF coil (in meters).
            - Total length of superconductor in all TF coils (in meters).
        """

        # Length of superconductor in one TF coil
        len_tf_coil_superconductor = (
            n_tf_coil_turns * len_tf_coil * n_tf_turn_superconducting_cables
        )

        # Total length of superconductor in all TF coils
        len_tf_superconductor_total = len_tf_coil_superconductor * n_tf_coils

        return len_tf_coil_superconductor, len_tf_superconductor_total

    def output_tf_superconductor_info(self):
        """Output TF superconductor information"""

        po.oheadr(self.outfile, "TF Coils Superconductor Information")
        po.ovarin(
            self.outfile,
            "TF superconductor switch",
            "(i_tf_sc_mat)",
            tfcoil_variables.i_tf_sc_mat,
        )

        po.ocmmnt(
            self.outfile,
            f"Superconductor used: {SUPERCONDUCTING_TF_TYPES[tfcoil_variables.i_tf_sc_mat]}",
        )

        po.ovarre(
            self.outfile,
            "Critical field at zero temperature and strain (T)",
            "(b_tf_superconductor_critical_zero_temp_strain)",
            superconducting_tf_coil_variables.b_tf_superconductor_critical_zero_temp_strain,
        )
        po.ovarre(
            self.outfile,
            "Critical temperature at zero field and strain (K)",
            "(temp_tf_superconductor_critical_zero_field_strain)",
            superconducting_tf_coil_variables.temp_tf_superconductor_critical_zero_field_strain,
        )

        if global_variables.run_tests == 1:
            po.oblnkl(self.outfile)
            po.ocmmnt(
                self.outfile,
                "PROCESS TF Coil peak field fit. Values for t, z and y:",
            )
            po.oblnkl(self.outfile)
            po.ovarre(
                self.outfile,
                "Dimensionless winding pack width",
                "(tf_fit_t)",
                superconducting_tf_coil_variables.tf_fit_t,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Dimensionless winding pack radial thickness",
                "(tf_fit_z)",
                superconducting_tf_coil_variables.tf_fit_z,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Ratio of peak field with ripple to nominal axisymmetric peak field",
                "(f_b_tf_inboard_peak_ripple_symmetric)",
                superconducting_tf_coil_variables.f_b_tf_inboard_peak_ripple_symmetric,
                "OP ",
            )

        po.oblnkl(self.outfile)
        po.ovarre(
            self.outfile,
            "Helium temperature at peak field (= superconductor temperature) (K)",
            "(tftmp)",
            tfcoil_variables.tftmp,
        )
        po.ovarre(
            self.outfile,
            "Total cooling area fraction inside cable space",
            "(f_a_tf_turn_cable_space_cooling)",
            superconducting_tf_coil_variables.f_a_tf_turn_cable_space_cooling,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Copper fraction of conductor",
            "(f_a_tf_turn_cable_copper)",
            tfcoil_variables.f_a_tf_turn_cable_copper,
        )
        po.ovarre(
            self.outfile,
            "Residual manufacturing strain on superconductor",
            "(str_tf_con_res)",
            tfcoil_variables.str_tf_con_res,
        )
        po.ovarre(
            self.outfile,
            "Self-consistent strain on superconductor",
            "(str_wp)",
            tfcoil_variables.str_wp,
        )
        po.ovarre(
            self.outfile,
            "Critical current density in superconductor (A/m2)",
            "(j_tf_superconductor_critical)",
            superconducting_tf_coil_variables.j_tf_superconductor_critical,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Critical current density in winding pack (A/m2)",
            "(j_tf_wp_critical)",
            tfcoil_variables.j_tf_wp_critical,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Actual current density in winding pack (A/m2)",
            "(j_tf_coil_turn)",
            superconducting_tf_coil_variables.j_tf_coil_turn,
            "OP ",
        )

        po.ovarre(
            self.outfile,
            "Minimum allowed temperature margin in superconductor (K)",
            "(temp_tf_superconductor_margin_min)",
            tfcoil_variables.temp_tf_superconductor_margin_min,
        )
        po.ovarre(
            self.outfile,
            "Actual temperature margin in superconductor (K)",
            "(temp_tf_superconductor_margin)",
            tfcoil_variables.temp_tf_superconductor_margin,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Critical current (A)",
            "(c_turn_cables_critical)",
            superconducting_tf_coil_variables.c_tf_turn_cables_critical,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Actual current (A)",
            "(c_tf_turn)",
            tfcoil_variables.c_tf_turn,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Actual current / critical current",
            "(f_c_tf_turn_operating_critical)",
            superconducting_tf_coil_variables.f_c_tf_turn_operating_critical,
            "OP ",
        )
        if superconducting_tf_coil_variables.f_c_tf_turn_operating_critical > 0.7:
            logger.error(
                "f_c_tf_turn_operating_critical shouldn't be above 0.7 for engineering reliability"
            )

        po.ovarre(
            self.outfile,
            "TF Superconductor quench dump time (s)",
            "(t_tf_superconductor_quench)",
            tfcoil_variables.t_tf_superconductor_quench,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "TF Superconductor quench detection time (s)",
            "(t_tf_quench_detection)",
            tfcoil_variables.t_tf_quench_detection,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Maximum winding pack current density for protection (A/m2)",
            "(j_tf_wp_quench_heat_max)",
            tfcoil_variables.j_tf_wp_quench_heat_max,
            "OP ",
        )

    def calculate_superconductor_temperature_margin(
        self,
        i_tf_superconductor: int,
        j_superconductor: float,
        b_tf_inboard_peak: float,
        strain: float,
        bc20m: float,
        tc0m: float,
        c0: float,
        temp_tf_coolant_peak_field: float,
    ):
        """Calculate the temperature margin of the TF superconductor.

        Parameters
        ----------
        i_tf_superconductor:
            Switch for conductor type:
            - 1: ITER Nb3Sn, standard parameters
            - 2: Bi-2212 High Temperature Superconductor
            - 3: NbTi
            - 4: ITER Nb3Sn, user-defined parameters
            - 5: WST Nb3Sn parameterisation
            - 7: Durham Ginzburg-Landau Nb-Ti parameterisation
            - 8: Durham Ginzburg-Landau critical surface model for REBCO
            - 9: Hazelton experimental data + Zhai conceptual model for REBCO
        j_superconductor:
            Current density in superconductor (A/m²).
        b_tf_inboard_peak:
            Peak field at conductor (T).
        strain:
            Strain on superconductor.
        bc20m:
            Critical field at zero temperature and strain (T).
        tc0m:
            Critical temperature at zero field and strain (K).
        c0:
            Constant used in NbTi critical current density calculation (A/m²).
        temp_tf_coolant_peak_field:
            He temperature at peak field point (K).

        Returns
        -------
        type
            temp_tf_superconductor_margin.
        """

        # =================================================================
        # Calculate temperature margin of superconductor

        #  Temperature margin (already calculated in superconductors.bi2212 for i_tf_superconductor=2)

        if i_tf_superconductor in (
            1,
            3,
            4,
            5,
            7,
            8,
            9,
        ):  # Find temperature at which current density margin = 0
            if i_tf_superconductor == 3:
                arguments = (
                    i_tf_superconductor,
                    j_superconductor,
                    b_tf_inboard_peak,
                    strain,
                    bc20m,
                    tc0m,
                    c0,
                )
            else:
                arguments = (
                    i_tf_superconductor,
                    j_superconductor,
                    b_tf_inboard_peak,
                    strain,
                    bc20m,
                    tc0m,
                )

            another_estimate = 2 * temp_tf_coolant_peak_field
            (
                t_zero_margin,
                _root_result,
            ) = optimize.newton(
                superconductors.superconductor_current_density_margin,
                temp_tf_coolant_peak_field,
                fprime=None,
                args=arguments,
                tol=1.0e-06,
                maxiter=50,
                fprime2=None,
                x1=another_estimate,
                rtol=1.0e-6,
                full_output=True,
                disp=True,
            )
            # print(root_result)  # Diagnostic for newton method
            temp_tf_superconductor_margin = t_zero_margin - temp_tf_coolant_peak_field
            tfcoil_variables.temp_margin = temp_tf_superconductor_margin

            if temp_tf_superconductor_margin <= 0.0e0:
                logger.error(
                    """Negative TFC temperature margin
                temp_tf_superconductor_margin: {temp_tf_superconductor_margin}
                b_tf_inboard_peak: {b_tf_inboard_peak}
                j_superconductor: {j_superconductor}
                """
                )

        return temp_tf_superconductor_margin

    def quench_heat_protection_current_density(
        self,
        c_tf_turn: float,
        e_tf_coil_magnetic_stored: float,
        a_tf_turn_cable_space: float,
        a_tf_turn: float,
        t_tf_quench_dump: float,
        f_a_tf_turn_cable_space_conductor: float,
        f_a_tf_turn_cable_copper: float,
        temp_tf_coolant_peak_field: float,
        temp_tf_conductor_quench_max: float,
        b_tf_inboard_peak: float,
        cu_rrr: float,
        t_tf_quench_detection: float,
        nflutfmax: float,
    ) -> tuple[float, float]:
        """Calculates the maximum conductor current density limited by the protection limit,
        and the discharge voltage for a TF coil.

        Parameters
        ----------
        c_tf_turn : float
            Operating current (A)
        e_tf_coil_magnetic_stored : float
            Energy stored in one TF coil (J)
        a_tf_turn_cable_space : float
            Cable space - inside area (m²)
        a_tf_turn : float
            Area per turn (i.e. entire cable) (m²)
        t_tf_quench_dump : float
            Dump time (s)
        f_a_tf_turn_cable_space_conductor : float
            Fraction of cable space containing conductor
        f_a_tf_turn_cable_copper : float
            Fraction of conductor that is copper
        temp_tf_coolant_peak_field : float
            Helium temperature at peak field point (K)
        temp_tf_conductor_quench_max : float
            Maximum conductor temperature during quench (K)
        b_tf_inboard_peak : float
            Peak magnetic field at conductor (T)
        cu_rrr : float
            Copper residual-resistance-ratio
        t_tf_quench_detection : float
            Quench detection time (s)
        nflutfmax : float
            End-of-life neutron fluence in the copper (1/m²)

        Returns
        -------
        tuple[float, float]
            j_tf_wp_quench_protection_max (float): Winding pack current density from temperature rise protection (A/m²)
            - v_tf_dump_voltage_peak (float): Discharge voltage imposed on a TF coil (V)

        References
        ----------
        - L. Bottura, “Magnet Quench 101,” arXiv (Cornell University), Jan. 2014,
        doi: https://doi.org/10.48550/arxiv.1401.3927.
        """

        #  Peak Dump voltage
        v_tf_dump_voltage_peak = (
            2.0e0 * e_tf_coil_magnetic_stored / (t_tf_quench_dump * c_tf_turn)
        )

        # Winding pack current density from temperature rise protection
        j_tf_wp_quench_protection_max = (
            a_tf_turn_cable_space
            / a_tf_turn
            * quench.calculate_quench_protection_current_density(
                t_tf_quench_dump,
                b_tf_inboard_peak,
                f_a_tf_turn_cable_copper,
                1.0 - f_a_tf_turn_cable_space_conductor,
                temp_tf_coolant_peak_field,
                temp_tf_conductor_quench_max,
                cu_rrr,
                t_tf_quench_detection,
                nflutfmax,
            )
        )

        return j_tf_wp_quench_protection_max, v_tf_dump_voltage_peak

    def vv_stress_on_quench(self):
        """Calculate the Tresca stress [Pa] of the Vacuum Vessel (VV)
        experienced when the TF coil quenches.

        Assumes the current center line (CCL) of the TF coil is the
        middle of the coil.

        We assume vertical symmetry which is only true for double null
        machines.
        """
        H_coil = build_variables.z_tf_inside_half + (build_variables.dr_tf_inboard / 2)
        ri_coil = build_variables.r_tf_inboard_mid
        ro_coil = build_variables.r_tf_outboard_mid
        # NOTE: rm is measured from the outside edge of the coil because thats where
        # the radius of the first ellipse is measured from
        rm_coil = build_variables.r_tf_inboard_out + tfcoil_variables.tfa[0]

        H_vv = (
            build_variables.z_plasma_xpoint_upper
            + build_variables.dz_xpoint_divertor
            + divertor_variables.dz_divertor
            + build_variables.dz_shld_upper
            + (build_variables.dz_vv_upper / 2)
        )
        # ri and ro for VV dont consider the shield widths
        # because it is assumed the shield is on the plasma side
        # of the VV
        ri_vv = build_variables.r_vv_inboard_out - (build_variables.dr_vv_outboard / 2)
        ro_vv = (
            build_variables.r_tf_outboard_mid
            - (build_variables.dr_tf_outboard / 2)
            - build_variables.dr_tf_shld_gap
            - build_variables.dr_shld_thermal_outboard
            - build_variables.dr_shld_vv_gap_outboard
            - (build_variables.dr_vv_outboard / 2)
        )

        # Assume the radius of the first ellipse of the VV is in the same proportion to
        # that of the plasma facing radii of the two structures
        tf_vv_frac = build_variables.r_tf_inboard_out / build_variables.r_vv_inboard_out
        rm_vv = build_variables.r_vv_inboard_out + (tfcoil_variables.tfa[0] * tf_vv_frac)

        superconducting_tf_coil_variables.vv_stress_quench = vv_stress_on_quench(
            # TF shape
            H_coil=H_coil,
            ri_coil=ri_coil,
            ro_coil=ro_coil,
            rm_coil=rm_coil,
            ccl_length_coil=tfcoil_variables.len_tf_coil,
            theta1_coil=tfcoil_variables.theta1_coil,
            # VV shape
            H_vv=H_vv,
            ri_vv=ri_vv,
            ro_vv=ro_vv,
            rm_vv=rm_vv,
            theta1_vv=tfcoil_variables.theta1_vv,
            # TF properties
            n_tf_coils=tfcoil_variables.n_tf_coils,
            n_tf_coil_turns=tfcoil_variables.n_tf_coil_turns,
            # Area of the radial plate taken to be the area of steel in the WP
            # TODO: value clipped due to #1883
            s_rp=np.clip(
                superconducting_tf_coil_variables.a_tf_coil_inboard_steel, 0, None
            ),
            s_cc=superconducting_tf_coil_variables.a_tf_plasma_case
            + superconducting_tf_coil_variables.a_tf_coil_nose_case
            + 2.0 * superconducting_tf_coil_variables.dx_tf_side_case_average,
            taud=tfcoil_variables.t_tf_superconductor_quench,
            # TODO: is this the correct current?
            i_op=superconducting_tf_coil_variables.c_tf_coil
            / tfcoil_variables.n_tf_coil_turns,
            # VV properties
            d_vv=build_variables.dr_vv_shells,
        )

    def peak_b_tf_inboard_with_ripple(
        self,
        n_tf_coils: float,
        dx_tf_wp_primary_toroidal: float,
        dr_tf_wp_no_insulation: float,
        r_tf_wp_inboard_centre: float,
        b_tf_inboard_peak_symmetric: float,
    ) -> tuple[float, int]:
        """Calculates the peak toroidal field at the outboard edge of the inboard TF coil winding pack,
        including the effects of ripple.

        For 16, 18, or 20 coils, uses fitting formulae derived by M. Kovari using MAGINT calculations
        on coil sets based on a DEMO1 case. For other numbers of coils, uses a 9% increase due to ripple
        from the axisymmetric calculation.

        Parameters
        ----------
        n_tf_coils : float
            Number of TF coils.
        dx_tf_wp_primary_toroidal : float
            Width of plasma-facing face of winding pack (m).
        dr_tf_wp_no_insulation : float
            Radial thickness of winding pack with no insulation (e.g. conductor region) (m).
        r_tf_wp_inboard_centre : float
            Major radius of centre of winding pack (m).
        b_tf_inboard_peak_symmetric : float
            Nominal (axisymmetric) peak toroidal field (T).

        Returns
        -------
        tuple[float]
            Tuple containing:
            - b_tf_inboard_peak_with_ripple (float): Peak toroidal field including ripple (T).

        Notes
        -----
        - M. Kovari, Toroidal Field Coils - Maximum Field and Ripple - Parametric Calculation, July 2014.
        """
        a = np.zeros((4,))

        #  Set fitting coefficients for different numbers of TF coils

        int_n_tf = np.round(n_tf_coils)

        if int_n_tf == 16:
            a[0] = 0.28101e0
            a[1] = 1.8481e0
            a[2] = -0.88159e0
            a[3] = 0.93834e0
        elif int_n_tf == 18:
            a[0] = 0.29153e0
            a[1] = 1.81600e0
            a[2] = -0.84178e0
            a[3] = 0.90426e0
        elif int_n_tf == 20:
            a[0] = 0.29853e0
            a[1] = 1.82130e0
            a[2] = -0.85031e0
            a[3] = 0.89808e0

        else:
            return 1.09e0 * b_tf_inboard_peak_symmetric

        #  Maximum winding pack width before adjacent packs touch
        #  (ignoring the external case and ground wall thicknesses)

        dx_tf_wp_toroidal_max = (
            2.0e0 * r_tf_wp_inboard_centre + dr_tf_wp_no_insulation
        ) * np.tan(np.pi / n_tf_coils)

        #  Dimensionless winding pack width

        superconducting_tf_coil_variables.tf_fit_t = (
            dx_tf_wp_primary_toroidal / dx_tf_wp_toroidal_max
        )
        if (superconducting_tf_coil_variables.tf_fit_t < 0.3e0) or (
            superconducting_tf_coil_variables.tf_fit_t > 1.1e0
        ):
            logger.warning(
                "(TF coil peak field calculation) Winding pack width out of fitted range"
            )

        #  Dimensionless winding pack radial thickness

        superconducting_tf_coil_variables.tf_fit_z = (
            dr_tf_wp_no_insulation / dx_tf_wp_toroidal_max
        )
        if (superconducting_tf_coil_variables.tf_fit_z < 0.26e0) or (
            superconducting_tf_coil_variables.tf_fit_z > 0.7e0
        ):
            # write(*,*) 'PEAK_TF_WITH_RIPPLE: fitting problem; z = ',z
            logger.warning(
                "(TF coil peak field calculation) Winding pack radial thickness out of fitted range"
            )

        #  Ratio of peak field with ripple to nominal axisymmetric peak field

        superconducting_tf_coil_variables.f_b_tf_inboard_peak_ripple_symmetric = (
            a[0]
            + a[1] * np.exp(-superconducting_tf_coil_variables.tf_fit_t)
            + a[2] * superconducting_tf_coil_variables.tf_fit_z
            + a[3]
            * superconducting_tf_coil_variables.tf_fit_z
            * superconducting_tf_coil_variables.tf_fit_t
        )

        return (
            superconducting_tf_coil_variables.f_b_tf_inboard_peak_ripple_symmetric
            * b_tf_inboard_peak_symmetric
        )

    def sc_tf_internal_geom(self, i_tf_wp_geom, i_tf_case_geom, i_tf_turns_integer):
        """
        Seting the WP, case and turns geometry for SC magnets

        Parameters
        ----------
        i_tf_wp_geom :

        i_tf_case_geom :

        i_tf_turns_integer :

        """

        # Calculating the WP / ground insulation areas
        (
            superconducting_tf_coil_variables.r_tf_wp_inboard_inner,
            superconducting_tf_coil_variables.r_tf_wp_inboard_outer,
            superconducting_tf_coil_variables.r_tf_wp_inboard_centre,
            superconducting_tf_coil_variables.dx_tf_wp_toroidal_min,
            superconducting_tf_coil_variables.dr_tf_wp_no_insulation,
            tfcoil_variables.dx_tf_wp_primary_toroidal,
            tfcoil_variables.dx_tf_wp_secondary_toroidal,
            superconducting_tf_coil_variables.dx_tf_wp_toroidal_average,
            superconducting_tf_coil_variables.a_tf_wp_with_insulation,
            superconducting_tf_coil_variables.a_tf_wp_no_insulation,
            superconducting_tf_coil_variables.a_tf_wp_ground_insulation,
        ) = self.superconducting_tf_wp_geometry(
            i_tf_wp_geom=i_tf_wp_geom,
            r_tf_inboard_in=build_variables.r_tf_inboard_in,
            dr_tf_nose_case=tfcoil_variables.dr_tf_nose_case,
            dr_tf_wp_with_insulation=tfcoil_variables.dr_tf_wp_with_insulation,
            tan_theta_coil=superconducting_tf_coil_variables.tan_theta_coil,
            dx_tf_side_case_min=tfcoil_variables.dx_tf_side_case_min,
            dx_tf_wp_insulation=tfcoil_variables.dx_tf_wp_insulation,
            dx_tf_wp_insertion_gap=tfcoil_variables.dx_tf_wp_insertion_gap,
        )

        # Calculating the TF steel casing areas
        (
            tfcoil_variables.a_tf_coil_inboard_case,
            tfcoil_variables.a_tf_coil_outboard_case,
            superconducting_tf_coil_variables.a_tf_plasma_case,
            superconducting_tf_coil_variables.a_tf_coil_nose_case,
            superconducting_tf_coil_variables.dx_tf_side_case_average,
            superconducting_tf_coil_variables.dx_tf_side_case_peak,
        ) = self.superconducting_tf_case_geometry(
            i_tf_case_geom=i_tf_case_geom,
            i_tf_wp_geom=i_tf_wp_geom,
            a_tf_inboard_total=tfcoil_variables.a_tf_inboard_total,
            n_tf_coils=tfcoil_variables.n_tf_coils,
            a_tf_wp_with_insulation=superconducting_tf_coil_variables.a_tf_wp_with_insulation,
            a_tf_leg_outboard=tfcoil_variables.a_tf_leg_outboard,
            rad_tf_coil_inboard_toroidal_half=superconducting_tf_coil_variables.rad_tf_coil_inboard_toroidal_half,
            r_tf_inboard_out=build_variables.r_tf_inboard_out,
            tan_theta_coil=superconducting_tf_coil_variables.tan_theta_coil,
            r_tf_wp_inboard_outer=superconducting_tf_coil_variables.r_tf_wp_inboard_outer,
            dr_tf_plasma_case=tfcoil_variables.dr_tf_plasma_case,
            r_tf_wp_inboard_inner=superconducting_tf_coil_variables.r_tf_wp_inboard_inner,
            r_tf_inboard_in=build_variables.r_tf_inboard_in,
            dx_tf_side_case_min=tfcoil_variables.dx_tf_side_case_min,
            dr_tf_wp_with_insulation=tfcoil_variables.dr_tf_wp_with_insulation,
        )

        # WP/trun currents
        self.tf_wp_currents()

        # Setting the WP turn geometry / areas
        if i_tf_turns_integer == 0:
            # Non-ingeger number of turns
            (
                tfcoil_variables.a_tf_turn_cable_space_no_void,
                tfcoil_variables.a_tf_turn_steel,
                tfcoil_variables.a_tf_turn_insulation,
                tfcoil_variables.n_tf_coil_turns,
                tfcoil_variables.dx_tf_turn_general,
                tfcoil_variables.c_tf_turn,
                tfcoil_variables.dx_tf_turn_general,
                superconducting_tf_coil_variables.dr_tf_turn,
                superconducting_tf_coil_variables.dx_tf_turn,
                tfcoil_variables.t_conductor,
                superconducting_tf_coil_variables.radius_tf_turn_cable_space_corners,
                superconducting_tf_coil_variables.dx_tf_turn_cable_space_average,
                superconducting_tf_coil_variables.a_tf_turn_cable_space_effective,
                superconducting_tf_coil_variables.f_a_tf_turn_cable_space_cooling,
            ) = self.tf_cable_in_conduit_averaged_turn_geometry(
                j_tf_wp=tfcoil_variables.j_tf_wp,
                dx_tf_turn_steel=tfcoil_variables.dx_tf_turn_steel,
                dx_tf_turn_insulation=tfcoil_variables.dx_tf_turn_insulation,
                i_tf_sc_mat=tfcoil_variables.i_tf_sc_mat,
                dx_tf_turn_general=tfcoil_variables.dx_tf_turn_general,
                c_tf_turn=tfcoil_variables.c_tf_turn,
                i_dx_tf_turn_general_input=tfcoil_variables.i_dx_tf_turn_general_input,
                i_dx_tf_turn_cable_space_general_input=tfcoil_variables.i_dx_tf_turn_cable_space_general_input,
                dx_tf_turn_cable_space_general=tfcoil_variables.dx_tf_turn_cable_space_general,
                layer_ins=tfcoil_variables.layer_ins,
                a_tf_wp_no_insulation=superconducting_tf_coil_variables.a_tf_wp_no_insulation,
                dia_tf_turn_coolant_channel=tfcoil_variables.dia_tf_turn_coolant_channel,
                f_a_tf_turn_cable_space_extra_void=tfcoil_variables.f_a_tf_turn_cable_space_extra_void,
            )

        else:
            # Integer number of turns
            (
                superconducting_tf_coil_variables.radius_tf_turn_cable_space_corners,
                superconducting_tf_coil_variables.dr_tf_turn,
                superconducting_tf_coil_variables.dx_tf_turn,
                tfcoil_variables.a_tf_turn_cable_space_no_void,
                tfcoil_variables.a_tf_turn_steel,
                tfcoil_variables.a_tf_turn_insulation,
                tfcoil_variables.c_tf_turn,
                tfcoil_variables.n_tf_coil_turns,
                superconducting_tf_coil_variables.t_conductor_radial,
                superconducting_tf_coil_variables.t_conductor_toroidal,
                tfcoil_variables.t_conductor,
                superconducting_tf_coil_variables.dr_tf_turn_cable_space,
                superconducting_tf_coil_variables.dx_tf_turn_cable_space,
                superconducting_tf_coil_variables.dx_tf_turn_cable_space_average,
            ) = self.tf_cable_in_conduit_integer_turn_geometry(
                dr_tf_wp_with_insulation=tfcoil_variables.dr_tf_wp_with_insulation,
                dx_tf_wp_insulation=tfcoil_variables.dx_tf_wp_insulation,
                dx_tf_wp_insertion_gap=tfcoil_variables.dx_tf_wp_insertion_gap,
                n_tf_wp_layers=tfcoil_variables.n_tf_wp_layers,
                dx_tf_wp_toroidal_min=superconducting_tf_coil_variables.dx_tf_wp_toroidal_min,
                n_tf_wp_pancakes=tfcoil_variables.n_tf_wp_pancakes,
                c_tf_coil=superconducting_tf_coil_variables.c_tf_coil,
                dx_tf_turn_steel=tfcoil_variables.dx_tf_turn_steel,
                dx_tf_turn_insulation=tfcoil_variables.dx_tf_turn_insulation,
            )

        # Calculate number of cables in turn if CICC conductor
        # ---------------------------------------------------
        if tfcoil_variables.i_tf_sc_mat != 6:
            superconducting_tf_coil_variables.n_tf_turn_superconducting_cables = self.calculate_cable_in_conduit_strand_count(
                a_cable_space=superconducting_tf_coil_variables.a_tf_turn_cable_space_effective,
                dia_superconductor_strand=superconducting_tf_coil_variables.dia_tf_turn_superconducting_cable,
            )

            (
                superconducting_tf_coil_variables.len_tf_coil_superconductor,
                superconducting_tf_coil_variables.len_tf_superconductor_total,
            ) = self.calculate_cable_in_conduit_superconductor_length(
                n_tf_coils=tfcoil_variables.n_tf_coils,
                n_tf_coil_turns=tfcoil_variables.n_tf_coil_turns,
                len_tf_coil=tfcoil_variables.len_tf_coil,
                n_tf_turn_superconducting_cables=superconducting_tf_coil_variables.n_tf_turn_superconducting_cables,
            )

        # Areas and fractions
        # -------------------
        # Central helium channel down the conductor core [m2]
        tfcoil_variables.a_tf_wp_coolant_channels = (
            0.25e0
            * tfcoil_variables.n_tf_coil_turns
            * np.pi
            * tfcoil_variables.dia_tf_turn_coolant_channel**2
        )

        # Total conductor cross-sectional area, taking account of void area
        # and central helium channel [m2]
        tfcoil_variables.a_tf_wp_conductor = (
            tfcoil_variables.a_tf_turn_cable_space_no_void
            * tfcoil_variables.n_tf_coil_turns
            * (1.0e0 - tfcoil_variables.f_a_tf_turn_cable_space_extra_void)
            - tfcoil_variables.a_tf_wp_coolant_channels
        )

        # Void area in conductor for He, not including central channel [m2]
        tfcoil_variables.a_tf_wp_extra_void = (
            tfcoil_variables.a_tf_turn_cable_space_no_void
            * tfcoil_variables.n_tf_coil_turns
            * tfcoil_variables.f_a_tf_turn_cable_space_extra_void
        )

        # Area of inter-turn insulation: total [m2]
        tfcoil_variables.a_tf_coil_wp_turn_insulation = (
            tfcoil_variables.n_tf_coil_turns * tfcoil_variables.a_tf_turn_insulation
        )

        # Area of steel structure in winding pack [m2]
        tfcoil_variables.a_tf_wp_steel = (
            tfcoil_variables.n_tf_coil_turns * tfcoil_variables.a_tf_turn_steel
        )

        # Inboard coil steel area [m2]
        superconducting_tf_coil_variables.a_tf_coil_inboard_steel = (
            tfcoil_variables.a_tf_coil_inboard_case + tfcoil_variables.a_tf_wp_steel
        )

        # Inboard coil steel fraction [-]
        superconducting_tf_coil_variables.f_a_tf_coil_inboard_steel = (
            tfcoil_variables.n_tf_coils
            * superconducting_tf_coil_variables.a_tf_coil_inboard_steel
            / tfcoil_variables.a_tf_inboard_total
        )

        # Inboard coil insulation cross-section [m2]
        superconducting_tf_coil_variables.a_tf_coil_inboard_insulation = (
            tfcoil_variables.a_tf_coil_wp_turn_insulation
            + superconducting_tf_coil_variables.a_tf_wp_ground_insulation
        )

        #  Inboard coil insulation fraction [-]
        superconducting_tf_coil_variables.f_a_tf_coil_inboard_insulation = (
            tfcoil_variables.n_tf_coils
            * superconducting_tf_coil_variables.a_tf_coil_inboard_insulation
            / tfcoil_variables.a_tf_inboard_total
        )

        # Negative areas or fractions error reporting
        if (
            tfcoil_variables.a_tf_wp_conductor <= 0.0e0
            or tfcoil_variables.a_tf_wp_extra_void <= 0.0e0
            or tfcoil_variables.a_tf_coil_wp_turn_insulation <= 0.0e0
            or tfcoil_variables.a_tf_wp_steel <= 0.0e0
            or superconducting_tf_coil_variables.a_tf_coil_inboard_steel <= 0.0e0
            or superconducting_tf_coil_variables.f_a_tf_coil_inboard_steel <= 0.0e0
            or superconducting_tf_coil_variables.a_tf_coil_inboard_insulation <= 0.0e0
            or superconducting_tf_coil_variables.f_a_tf_coil_inboard_insulation <= 0.0e0
        ):
            logger.error(
                "One of the areas or fractions is negative in the internal SC TF coil geometry"
                f"{tfcoil_variables.a_tf_wp_conductor=} {tfcoil_variables.a_tf_wp_extra_void=}"
                f"{tfcoil_variables.a_tf_coil_wp_turn_insulation=} {tfcoil_variables.a_tf_wp_steel=}"
                f"{superconducting_tf_coil_variables.a_tf_coil_inboard_steel=} {superconducting_tf_coil_variables.f_a_tf_coil_inboard_steel=}"
                f"{superconducting_tf_coil_variables.a_tf_coil_inboard_insulation=} {superconducting_tf_coil_variables.f_a_tf_coil_inboard_insulation=}"
            )

    def superconducting_tf_wp_geometry(
        self,
        i_tf_wp_geom: int,
        r_tf_inboard_in: float,
        dr_tf_nose_case: float,
        dr_tf_wp_with_insulation: float,
        tan_theta_coil: float,
        dx_tf_side_case_min: float,
        dx_tf_wp_insulation: float,
        dx_tf_wp_insertion_gap: float,
    ) -> tuple[
        float,  # r_tf_wp_inboard_inner
        float,  # r_tf_wp_inboard_outer
        float,  # r_tf_wp_inboard_centre
        float,  # dx_tf_wp_toroidal_min
        float,  # dr_tf_wp_no_insulation
        float,  # dx_tf_wp_primary_toroidal
        float,  # dx_tf_wp_secondary_toroidal
        float,  # dx_tf_wp_toroidal_average
        float,  # a_tf_wp_with_insulation
        float,  # a_tf_wp_no_insulation
        float,  # a_tf_wp_ground_insulation
    ]:
        """Calculates the winding pack (WP) geometry and cross-sectional areas for superconducting toroidal field (TF) coils.

        Parameters
        ----------
        i_tf_wp_geom : int
            0: Rectangular
            - 1: Double rectangular
            - 2: Trapezoidal
        r_tf_inboard_in : float
            Inboard inner radius [m].
        dr_tf_nose_case : float
            Radial thickness of nose case [m].
        dr_tf_wp_with_insulation : float
            Radial thickness of winding pack including insulation [m].
        tan_theta_coil : float
            Tangent of coil half angle [-].
        dx_tf_side_case_min : float
            Side case thickness [m].
        dx_tf_wp_insulation : float
            Insulation thickness [m].
        dx_tf_wp_insertion_gap : float
            Insertion gap thickness [m].

        Returns
        -------
        tuple[float, float, float, float, float, float, float, float, float, float]
            Tuple containing:
            - r_tf_wp_inboard_inner (float): WP inboard inner radius [m]
            - r_tf_wp_inboard_outer (float): WP inboard outer radius [m]
            - r_tf_wp_inboard_centre (float): WP inboard centre radius [m]
            - dx_tf_wp_toroidal_min (float): Minimal toroidal thickness of WP [m]
            - dr_tf_wp_no_insulation (float): Radial thickness of winding pack without insulation [m]
            - dx_tf_wp_primary_toroidal (float): Primary toroidal thickness [m]
            - dx_tf_wp_secondary_toroidal (float): Secondary toroidal thickness [m]
            - dx_tf_wp_toroidal_average (float): Averaged toroidal thickness [m]
            - a_tf_wp_with_insulation (float): WP cross-sectional area with insulation [m²]
            - a_tf_wp_no_insulation (float): WP cross-sectional area without insulation [m²]
            - a_tf_wp_ground_insulation (float): WP ground insulation cross-sectional area [m²]

        Raises
        ------
        ValueError
            If calculated winding pack area (with or without insulation) is non-positive.
        """

        r_tf_wp_inboard_inner = r_tf_inboard_in + dr_tf_nose_case

        # Radial position of outer edge of winding pack [m]
        r_tf_wp_inboard_outer = r_tf_wp_inboard_inner + dr_tf_wp_with_insulation

        # Radius of geometrical centre of winding pack [m]
        r_tf_wp_inboard_centre = 0.5e0 * (r_tf_wp_inboard_inner + r_tf_wp_inboard_outer)

        # TF toroidal thickness at the WP inner radius [m]
        dx_tf_wp_inner_toroidal = 2.0e0 * r_tf_wp_inboard_inner * tan_theta_coil

        # Minimal toroidal thickness of winding pack [m]
        dx_tf_wp_toroidal_min = dx_tf_wp_inner_toroidal - 2.0e0 * dx_tf_side_case_min

        # Radial thickness of winding pack without insulation (e.g. the conductor region) [m]
        dr_tf_wp_no_insulation = dr_tf_wp_with_insulation - 2.0e0 * (
            dx_tf_wp_insulation + dx_tf_wp_insertion_gap
        )

        # Rectangular WP
        # --------------
        if i_tf_wp_geom == 0:
            # Outer WP layer toroidal thickness [m]
            dx_tf_wp_primary_toroidal = dx_tf_wp_toroidal_min

            # No secondary WP here but will set for consistency
            dx_tf_wp_secondary_toroidal = dx_tf_wp_toroidal_min

            # Averaged toroidal thickness of of winding pack [m]
            dx_tf_wp_toroidal_average = dx_tf_wp_toroidal_min

            # Total cross-sectional area of winding pack [m²]
            a_tf_wp_with_insulation = (
                dr_tf_wp_with_insulation * dx_tf_wp_primary_toroidal
            )

            # WP cross-section without insertion gap and ground insulation [m²]
            a_tf_wp_no_insulation = (
                dr_tf_wp_with_insulation
                - 2.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
            ) * (
                dx_tf_wp_primary_toroidal
                - 2.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
            )

            # Cross-section area of the WP ground insulation [m²]
            a_tf_wp_ground_insulation = (
                dr_tf_wp_with_insulation - 2.0e0 * dx_tf_wp_insertion_gap
            ) * (
                dx_tf_wp_primary_toroidal - 2.0e0 * dx_tf_wp_insertion_gap
            ) - a_tf_wp_no_insulation

        # Double rectangular WP
        # ---------------------
        elif i_tf_wp_geom == 1:
            # Thickness of winding pack section at R > superconducting_tf_coil_variables.r_tf_wp_inboard_centre [m]
            dx_tf_wp_primary_toroidal = 2.0e0 * (
                r_tf_wp_inboard_centre * tan_theta_coil - dx_tf_side_case_min
            )

            # Thickness of winding pack section at R < superconducting_tf_coil_variables.r_tf_wp_inboard_centre [m]
            dx_tf_wp_secondary_toroidal = 2.0e0 * (
                r_tf_wp_inboard_inner * tan_theta_coil - dx_tf_side_case_min
            )

            # Averaged toroidal thickness of of winding pack [m]
            dx_tf_wp_toroidal_average = 0.5e0 * (
                dx_tf_wp_primary_toroidal + dx_tf_wp_secondary_toroidal
            )

            # Total cross-sectional area of winding pack [m²]
            # Including ground insulation and insertion gap
            a_tf_wp_with_insulation = (
                dr_tf_wp_with_insulation * dx_tf_wp_toroidal_average
            )

            # WP cross-section without insertion gap and ground insulation [m²]
            a_tf_wp_no_insulation = (
                0.5e0
                * (
                    dr_tf_wp_with_insulation
                    - 2.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
                )
                * (
                    dx_tf_wp_primary_toroidal
                    + dx_tf_wp_secondary_toroidal
                    - 4.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
                )
            )

            # Cross-section area of the WP ground insulation [m²]
            a_tf_wp_ground_insulation = (
                0.5e0
                * (dr_tf_wp_with_insulation - 2.0e0 * dx_tf_wp_insertion_gap)
                * (
                    dx_tf_wp_primary_toroidal
                    + dx_tf_wp_secondary_toroidal
                    - 4.0e0 * dx_tf_wp_insertion_gap
                )
                - a_tf_wp_no_insulation
            )

        # Trapezoidal WP
        # --------------
        else:
            # Thickness of winding pack section at r_tf_wp_inboard_outer [m]
            dx_tf_wp_primary_toroidal = 2.0e0 * (
                r_tf_wp_inboard_outer * tan_theta_coil - dx_tf_side_case_min
            )

            # Thickness of winding pack section at r_tf_wp_inboard_inner [m]
            dx_tf_wp_secondary_toroidal = 2.0e0 * (
                r_tf_wp_inboard_inner * tan_theta_coil - dx_tf_side_case_min
            )

            # Averaged toroidal thickness of of winding pack [m]
            dx_tf_wp_toroidal_average = 0.5e0 * (
                dx_tf_wp_primary_toroidal + dx_tf_wp_secondary_toroidal
            )

            # Total cross-sectional area of winding pack [m²]
            # Including ground insulation and insertion gap
            a_tf_wp_with_insulation = (
                dr_tf_wp_with_insulation
                * 0.5
                * (dx_tf_wp_primary_toroidal + dx_tf_wp_secondary_toroidal)
            )

            # WP cross-section without insertion gap and ground insulation [m²]
            a_tf_wp_no_insulation = (
                (
                    dr_tf_wp_with_insulation
                    - 2.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
                )
                * (
                    (
                        dx_tf_wp_secondary_toroidal
                        - 2.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
                    )
                    + (
                        dx_tf_wp_primary_toroidal
                        - 2.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
                    )
                )
                / 2
            )

            # Cross-section area of the WP ground insulation [m²]
            a_tf_wp_ground_insulation = (
                dr_tf_wp_with_insulation - 2.0e0 * dx_tf_wp_insertion_gap
            ) * (
                (
                    (dx_tf_wp_primary_toroidal - 2.0e0 * dx_tf_wp_insertion_gap)
                    + (dx_tf_wp_secondary_toroidal - 2.0e0 * dx_tf_wp_insertion_gap)
                )
                / 2
            ) - a_tf_wp_no_insulation

        # --------------
        # Negative WP area error reporting
        if a_tf_wp_no_insulation <= 0.0e0 or a_tf_wp_with_insulation <= 0.0e0:
            logger.error(
                f"Winding pack cross-section problem... {a_tf_wp_no_insulation=} {a_tf_wp_with_insulation=}"
            )

        return (
            r_tf_wp_inboard_inner,
            r_tf_wp_inboard_outer,
            r_tf_wp_inboard_centre,
            dx_tf_wp_toroidal_min,
            dr_tf_wp_no_insulation,
            dx_tf_wp_primary_toroidal,
            dx_tf_wp_secondary_toroidal,
            dx_tf_wp_toroidal_average,
            a_tf_wp_with_insulation,
            a_tf_wp_no_insulation,
            a_tf_wp_ground_insulation,
        )

    def superconducting_tf_case_geometry(
        self,
        i_tf_wp_geom: int,
        i_tf_case_geom: int,
        a_tf_inboard_total: float,
        n_tf_coils: float,
        a_tf_wp_with_insulation: float,
        a_tf_leg_outboard: float,
        rad_tf_coil_inboard_toroidal_half: float,
        r_tf_inboard_out: float,
        tan_theta_coil: float,
        r_tf_wp_inboard_outer: float,
        dr_tf_plasma_case: float,
        r_tf_wp_inboard_inner: float,
        r_tf_inboard_in: float,
        dx_tf_side_case_min: float,
        dr_tf_wp_with_insulation: float,
    ) -> tuple[float, float, float, float, float, float]:
        """Setting the case geometry and area for SC magnets

        Parameters
        ----------
        i_tf_wp_geom : int
            Index specifying winding pack geometry (0: rectangular, 1: double rectangular, else: trapezoidal).
        i_tf_case_geom : int
            Index specifying case geometry (0: circular, else: straight).
        a_tf_inboard_total : float
            Total inboard area for TF coils [m²].
        n_tf_coils : float
            Number of TF coils.
        a_tf_wp_with_insulation : float
            Area of winding pack with insulation [m²].
        a_tf_leg_outboard : float
            Outboard leg cross-sectional area [m²].
        rad_tf_coil_inboard_toroidal_half : float
            Half toroidal radius of inboard coil [m].
        r_tf_inboard_out : float
            Outer radius of inboard TF coil [m].
        tan_theta_coil : float
            Tangent of coil angle theta.
        r_tf_wp_inboard_outer : float
            Outer radius of inboard winding pack [m].
        dr_tf_plasma_case : float
            Radial thickness of plasma case [m].
        r_tf_wp_inboard_inner : float
            Inner radius of inboard winding pack [m].
        r_tf_inboard_in : float
            Inner radius of inboard TF coil [m].
        dx_tf_side_case_min : float
            Minimum lateral casing thickness [m].
        dr_tf_wp_with_insulation : float
            Radial thickness of winding pack with insulation [m].

        Returns
        -------
        tuple[float, float, float, float, float]
            Tuple containing:
            - a_tf_coil_inboard_case (float): Inboard case area [m²].
            - a_tf_coil_outboard_case (float): Outboard case area [m²].
            - a_tf_plasma_case (float): Front casing area [m²].
            - a_tf_coil_nose_case (float): Nose casing area [m²].
            - dx_tf_side_case_average (float): Average lateral casing thickness [m].
            - dx_tf_side_case_peak (float): Peak lateral casing thickness [m].
        """

        # Total area of inboard TF coil case [m²]
        a_tf_coil_inboard_case = (
            a_tf_inboard_total / n_tf_coils
        ) - a_tf_wp_with_insulation

        # Outboard leg cross-sectional area of surrounding case [m²]
        a_tf_coil_outboard_case = a_tf_leg_outboard - a_tf_wp_with_insulation

        # Front casing area [m²]
        if i_tf_case_geom == 0:
            # Circular front case
            a_tf_plasma_case = (
                rad_tf_coil_inboard_toroidal_half * r_tf_inboard_out**2
            ) - (tan_theta_coil * r_tf_wp_inboard_outer**2)
        else:
            # Straight front case [m²]
            a_tf_plasma_case = (
                (r_tf_wp_inboard_outer + dr_tf_plasma_case) ** 2
                - r_tf_wp_inboard_outer**2
            ) * tan_theta_coil

        # Nose casing area [m²]
        a_tf_coil_nose_case = (
            tan_theta_coil * r_tf_wp_inboard_inner**2
            - rad_tf_coil_inboard_toroidal_half * r_tf_inboard_in**2
        )

        # Report error if the casing area is negative
        if a_tf_coil_inboard_case <= 0.0e0 or a_tf_coil_outboard_case <= 0.0e0:
            logger.error(
                f"Winding pack cross-section problem... {a_tf_coil_inboard_case=} {a_tf_coil_outboard_case=}"
            )

        # Average lateral casing thickness [m]
        # --------------
        # Rectangular casing
        if i_tf_wp_geom == 0:
            dx_tf_side_case_average = (
                dx_tf_side_case_min + 0.5e0 * tan_theta_coil * dr_tf_wp_with_insulation
            )

        # Double rectangular WP
        elif i_tf_wp_geom == 1:
            dx_tf_side_case_average = (
                dx_tf_side_case_min + 0.25e0 * tan_theta_coil * dr_tf_wp_with_insulation
            )

        # Trapezoidal WP
        else:
            dx_tf_side_case_average = dx_tf_side_case_min

        # Peak lateral casing thickness [m]
        # --------------
        # Rectangular casing

        if i_tf_wp_geom == 0:
            dx_tf_side_case_peak = (
                dx_tf_side_case_min + tan_theta_coil * dr_tf_wp_with_insulation
            )
        # Double rectangular WP
        elif i_tf_wp_geom == 1:
            dx_tf_side_case_peak = (
                dx_tf_side_case_min + 0.5 * tan_theta_coil * dr_tf_wp_with_insulation
            )

        # Trapezoidal WP
        # Constant thickness so min = average
        else:
            dx_tf_side_case_peak = dx_tf_side_case_min

        return (
            a_tf_coil_inboard_case,
            a_tf_coil_outboard_case,
            a_tf_plasma_case,
            a_tf_coil_nose_case,
            dx_tf_side_case_average,
            dx_tf_side_case_peak,
        )

    def tf_cable_in_conduit_integer_turn_geometry(
        self,
        dr_tf_wp_with_insulation: float,
        dx_tf_wp_insulation: float,
        dx_tf_wp_insertion_gap: float,
        n_tf_wp_layers: int,
        dx_tf_wp_toroidal_min: float,
        n_tf_wp_pancakes: int,
        c_tf_coil: float,
        dx_tf_turn_steel: float,
        dx_tf_turn_insulation: float,
    ) -> tuple[
        float,  # radius_tf_turn_cable_space_corners
        float,  # dr_tf_turn
        float,  # dx_tf_turn
        float,  # a_tf_turn_cable_space_no_void
        float,  # a_tf_turn_steel
        float,  # a_tf_turn_insulation
        float,  # c_tf_turn
        float,  # n_tf_coil_turns
        float,  # t_conductor_radial
        float,  # t_conductor_toroidal
        float,  # t_conductor
        float,  # dr_tf_turn_cable_space
        float,  # dx_tf_turn_cable_space
        float,  # dx_tf_turn_cable_space_average
    ]:
        """Set the TF WP turn geometry for superconducting magnets using the number of turn rows in the radial direction.
        The turns can have any rectangular shape.

        This calculation checks if a turn can exist (positive cable space) and provides its dimensions, areas, and associated current.

        Parameters
        ----------
        dr_tf_wp_with_insulation : float
            Radial thickness of winding pack with insulation [m].
        dx_tf_wp_insulation : float
            Thickness of winding pack insulation [m].
        dx_tf_wp_insertion_gap : float
            Thickness of winding pack insertion gap [m].
        n_tf_wp_layers : int
            Number of winding pack layers (radial direction).
        dx_tf_wp_toroidal_min : float
            Minimum toroidal thickness of winding pack [m].
        n_tf_wp_pancakes : int
            Number of winding pack pancakes (toroidal direction).
        c_tf_coil : float
            Total TF coil current [A].
        dx_tf_turn_steel : float
            Thickness of turn steel [m].
        dx_tf_turn_insulation : float
            Thickness of turn insulation [m].

        Returns
        -------
        type
            tuple containing:
            - radius_tf_turn_cable_space_corners
            - dr_tf_turn
            - dx_tf_turn
            - a_tf_turn_cable_space_no_void
            - a_tf_turn_steel
            - a_tf_turn_insulation
            - c_tf_turn
            - n_tf_coil_turns
            - t_conductor_radial
            - t_conductor_toroidal
            - t_conductor
            - dr_tf_turn_cable_space
            - dx_tf_turn_cable_space
            - dx_tf_turn_cable_space_average
        """

        # Radius of rounded corners in the cable space [m]
        radius_tf_turn_cable_space_corners = dx_tf_turn_steel * 0.75e0

        # Radial turn dimension [m]
        dr_tf_turn = (
            dr_tf_wp_with_insulation
            - 2.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
        ) / n_tf_wp_layers

        if dr_tf_turn <= (2.0e0 * dx_tf_turn_insulation + 2.0e0 * dx_tf_turn_steel):
            logger.error(
                "Negative cable space dimension; reduce conduit thicknesses or raise c_tf_turn. "
                f"{dr_tf_turn=} {dx_tf_turn_insulation=} {dx_tf_turn_steel=}"
            )

        # Toroidal turn dimension [m]
        dx_tf_turn = (
            dx_tf_wp_toroidal_min
            - 2.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
        ) / n_tf_wp_pancakes

        if dx_tf_turn <= (2.0e0 * dx_tf_turn_insulation + 2.0e0 * dx_tf_turn_steel):
            logger.error(
                "Negative cable space dimension; reduce conduit thicknesses or raise c_tf_turn. "
                f"{dx_tf_turn=} {dx_tf_turn_insulation=} {dx_tf_turn_steel=}"
            )

        # Average turn dimension [m]
        tfcoil_variables.dx_tf_turn_general = np.sqrt(dr_tf_turn * dx_tf_turn)

        # Number of TF turns
        n_tf_coil_turns = np.double(n_tf_wp_layers * n_tf_wp_pancakes)

        # Current per turn [A/turn]
        c_tf_turn = c_tf_coil / n_tf_coil_turns

        # Radial and toroidal dimension of conductor [m]
        t_conductor_radial = dr_tf_turn - 2.0e0 * dx_tf_turn_insulation
        t_conductor_toroidal = dx_tf_turn - 2.0e0 * dx_tf_turn_insulation
        t_conductor = np.sqrt(t_conductor_radial * t_conductor_toroidal)

        # Dimension of square cable space inside conduit [m]
        dr_tf_turn_cable_space = t_conductor_radial - 2.0e0 * dx_tf_turn_steel
        dx_tf_turn_cable_space = t_conductor_toroidal - 2.0e0 * dx_tf_turn_steel
        dx_tf_turn_cable_space_average = np.sqrt(
            dr_tf_turn_cable_space * dx_tf_turn_cable_space
        )

        # Cross-sectional area of cable space per turn
        # taking account of rounded inside corners [m²]
        a_tf_turn_cable_space_no_void = (
            dr_tf_turn_cable_space * dx_tf_turn_cable_space
        ) - (4.0e0 - np.pi) * radius_tf_turn_cable_space_corners**2

        # Calculate the true effective cable space by taking away the cooling
        # channel and the extra void fraction
        superconducting_tf_coil_variables.a_tf_turn_cable_space_effective = (
            a_tf_turn_cable_space_no_void
            -
            # Coolant channel area
            (
                (np.pi / 4.0e0)
                * tfcoil_variables.dia_tf_turn_coolant_channel
                * tfcoil_variables.dia_tf_turn_coolant_channel
            )
            # Additional void area deduction
            - (
                a_tf_turn_cable_space_no_void
                * tfcoil_variables.f_a_tf_turn_cable_space_extra_void
            )
        )

        superconducting_tf_coil_variables.f_a_tf_turn_cable_space_cooling = 1 - (
            superconducting_tf_coil_variables.a_tf_turn_cable_space_effective
            / a_tf_turn_cable_space_no_void
        )

        if a_tf_turn_cable_space_no_void <= 0.0e0:
            if (dr_tf_turn_cable_space < 0.0e0) or (dx_tf_turn_cable_space < 0.0e0):
                logger.error(
                    f"Negative cable space dimension. {a_tf_turn_cable_space_no_void=} "
                    f"{dr_tf_turn_cable_space=} {dx_tf_turn_cable_space=}"
                )
            else:
                logger.error(
                    "Cable space area problem; artificially set rounded corner radius to 0. "
                    f"{a_tf_turn_cable_space_no_void=} {dr_tf_turn_cable_space=}"
                    f" {dx_tf_turn_cable_space=}"
                )
                radius_tf_turn_cable_space_corners = 0.0e0
                a_tf_turn_cable_space_no_void = (
                    dr_tf_turn_cable_space * dx_tf_turn_cable_space
                )

        # Cross-sectional area of conduit jacket per turn [m²]
        a_tf_turn_steel = (
            t_conductor_radial * t_conductor_toroidal - a_tf_turn_cable_space_no_void
        )

        # Area of inter-turn insulation: single turn [m²]
        a_tf_turn_insulation = (
            dr_tf_turn * dx_tf_turn - a_tf_turn_steel - a_tf_turn_cable_space_no_void
        )
        return (
            radius_tf_turn_cable_space_corners,
            dr_tf_turn,
            dx_tf_turn,
            a_tf_turn_cable_space_no_void,
            a_tf_turn_steel,
            a_tf_turn_insulation,
            c_tf_turn,
            n_tf_coil_turns,
            t_conductor_radial,
            t_conductor_toroidal,
            t_conductor,
            dr_tf_turn_cable_space,
            dx_tf_turn_cable_space,
            dx_tf_turn_cable_space_average,
        )

        # -------------

    def tf_wp_currents(self):
        """
        Turn engineering turn currents/densities
        """
        tfcoil_variables.j_tf_wp = max(
            1.0e0,
            tfcoil_variables.c_tf_total
            / (
                tfcoil_variables.n_tf_coils
                * superconducting_tf_coil_variables.a_tf_wp_no_insulation
            ),
        )

    def tf_cable_in_conduit_averaged_turn_geometry(
        self,
        j_tf_wp,
        dx_tf_turn_steel,
        dx_tf_turn_insulation,
        i_tf_sc_mat,
        dx_tf_turn_general,
        c_tf_turn,
        i_dx_tf_turn_general_input,
        i_dx_tf_turn_cable_space_general_input,
        dx_tf_turn_cable_space_general,
        layer_ins,
        a_tf_wp_no_insulation,
        dia_tf_turn_coolant_channel,
        f_a_tf_turn_cable_space_extra_void,
    ):
        """subroutine straight from Python, see comments in tf_averaged_turn_geom_wrapper
        Setting the TF WP turn geometry for SC magnets from the number
        the current per turn.
        This calculation has two purposes, first to check if a turn can exist
        (positive cable space) and the second to provide its dimensions,
        areas and the (float) number of turns

        Parameters
        ----------
        j_tf_wp :

        dx_tf_turn_steel :

        dx_tf_turn_insulation :

        i_tf_sc_mat :

        dx_tf_turn_general :

        c_tf_turn :

        i_dx_tf_turn_general_input :

        i_dx_tf_turn_cable_space_general_input :

        dx_tf_turn_cable_space_general :

        layer_ins :

        a_tf_wp_no_insulation :

        dia_tf_turn_coolant_channel :

        f_a_tf_turn_cable_space_extra_void :

        """

        # Turn dimension is a an input
        if i_dx_tf_turn_general_input:
            # Turn area [m2]
            a_tf_turn = dx_tf_turn_general**2

            # Current per turn [A]
            c_tf_turn = a_tf_turn * j_tf_wp

        # Turn cable dimension is an input
        elif i_dx_tf_turn_cable_space_general_input:
            # Turn squared dimension [m]
            dx_tf_turn_general = dx_tf_turn_cable_space_general + 2.0e0 * (
                dx_tf_turn_insulation + dx_tf_turn_steel
            )

            # Turn area [m2]
            a_tf_turn = dx_tf_turn_general**2

            # Current per turn [A]
            c_tf_turn = a_tf_turn * j_tf_wp

        # Current per turn is an input
        else:
            # Turn area [m2]
            # Allow for additional inter-layer insulation MDK 13/11/18
            # Area of turn including conduit and inter-layer insulation
            a_tf_turn = c_tf_turn / j_tf_wp

            # Dimension of square cross-section of each turn including inter-turn insulation [m]
            dx_tf_turn_general = np.sqrt(a_tf_turn)

        # Square turn assumption
        dr_tf_turn = dx_tf_turn_general
        dx_tf_turn = dx_tf_turn_general

        # See derivation in the following document
        # k:\power plant physics and technology\process\hts\hts coil module for process.docx
        t_conductor = (
            -layer_ins + np.sqrt(layer_ins**2 + 4.0e00 * a_tf_turn)
        ) / 2 - 2.0e0 * dx_tf_turn_insulation

        # Total number of turns per TF coil (not required to be an integer)
        n_tf_coil_turns = a_tf_wp_no_insulation / a_tf_turn

        # Area of inter-turn insulation: single turn [m2]
        a_tf_turn_insulation = a_tf_turn - t_conductor**2

        # NOTE: Fortran has a_tf_turn_cable_space_no_void as an intent(out) variable that was outputting
        # into tfcoil_variables.a_tf_turn_cable_space_no_void. The local variable, however, appears to
        # initially hold the value of tfcoil_variables.a_tf_turn_cable_space_no_void despite not being
        # intent(in). I have replicated this behaviour in Python for now.
        a_tf_turn_cable_space_no_void = copy.copy(
            tfcoil_variables.a_tf_turn_cable_space_no_void
        )

        # ITER like turn structure
        if i_tf_sc_mat != 6:
            # Radius of rounded corners of cable space inside conduit [m]
            radius_tf_turn_cable_space_corners = dx_tf_turn_steel * 0.75e0

            # Dimension of square cable space inside conduit [m]
            dx_tf_turn_cable_space_average = t_conductor - 2.0e0 * dx_tf_turn_steel

            # Cross-sectional area of cable space per turn
            # taking account of rounded inside corners [m2]
            a_tf_turn_cable_space_no_void = (
                dx_tf_turn_cable_space_average**2
                - (4.0e0 - np.pi) * radius_tf_turn_cable_space_corners**2
            )

            # Calculate the true effective cable space by taking away the cooling
            # channel and the extra void fraction

            a_tf_turn_cable_space_effective = (
                a_tf_turn_cable_space_no_void
                -
                # Coolant channel area
                (
                    (np.pi / 4.0e0)
                    * dia_tf_turn_coolant_channel
                    * dia_tf_turn_coolant_channel
                )
                # Additional void area deduction
                - (a_tf_turn_cable_space_no_void * f_a_tf_turn_cable_space_extra_void)
            )

            f_a_tf_turn_cable_space_cooling = 1 - (
                a_tf_turn_cable_space_effective / a_tf_turn_cable_space_no_void
            )

            if a_tf_turn_cable_space_no_void <= 0.0e0:
                if t_conductor < 0.0e0:
                    logger.error(
                        f"Negative cable space dimension. {a_tf_turn_cable_space_no_void=} "
                        f"{dx_tf_turn_cable_space_average=}"
                    )
                else:
                    logger.error(
                        "Cable space area problem; artificially set rounded corner radius to 0. "
                        f"{a_tf_turn_cable_space_no_void=} {dx_tf_turn_cable_space_average=}"
                    )
                    radius_tf_turn_cable_space_corners = 0.0e0
                    a_tf_turn_cable_space_no_void = dx_tf_turn_cable_space_average**2

            # Cross-sectional area of conduit jacket per turn [m2]
            a_tf_turn_steel = t_conductor**2 - a_tf_turn_cable_space_no_void

        # REBCO turn structure
        elif i_tf_sc_mat == 6:
            # Diameter of circular cable space inside conduit [m]
            dx_tf_turn_cable_space_average = t_conductor - 2.0e0 * dx_tf_turn_steel

            # Cross-sectional area of conduit jacket per turn [m2]
            a_tf_turn_steel = t_conductor**2 - a_tf_turn_cable_space_no_void

        return (
            a_tf_turn_cable_space_no_void,
            a_tf_turn_steel,
            a_tf_turn_insulation,
            n_tf_coil_turns,
            dx_tf_turn_general,
            c_tf_turn,
            dx_tf_turn_general,
            dr_tf_turn,
            dx_tf_turn,
            t_conductor,
            radius_tf_turn_cable_space_corners,
            dx_tf_turn_cable_space_average,
            a_tf_turn_cable_space_effective,
            f_a_tf_turn_cable_space_cooling,
        )

    def superconducting_tf_coil_areas_and_masses(self):
        # Mass of case [kg]
        # ***

        # Mass of ground-wall insulation [kg]
        # (assumed to be same density/material as turn insulation)
        tfcoil_variables.m_tf_coil_wp_insulation = (
            tfcoil_variables.len_tf_coil
            * (
                superconducting_tf_coil_variables.a_tf_wp_with_insulation
                - superconducting_tf_coil_variables.a_tf_wp_no_insulation
            )
            * tfcoil_variables.den_tf_wp_turn_insulation
        )

        # The length of the vertical section is that of the first (inboard) segment
        # = height of TF coil inner edge + (2 * coil thickness)
        tfcoil_variables.cplen = (2.0e0 * build_variables.z_tf_inside_half) + (
            2.0e0 * build_variables.dr_tf_inboard
        )

        # The 2.2 factor is used as a scaling factor to fit
        # to the ITER-FDR value of 450 tonnes; see CCFE note T&M/PKNIGHT/PROCESS/026
        if physics_variables.itart == 1:
            # tfcoil_variables.len_tf_coil does not include inboard leg ('centrepost') length in TART
            tfcoil_variables.m_tf_coil_case = (
                2.2e0
                * tfcoil_variables.den_tf_coil_case
                * (
                    tfcoil_variables.cplen * tfcoil_variables.a_tf_coil_inboard_case
                    + tfcoil_variables.len_tf_coil
                    * tfcoil_variables.a_tf_coil_outboard_case
                )
            )
        else:
            tfcoil_variables.m_tf_coil_case = (
                2.2e0
                * tfcoil_variables.den_tf_coil_case
                * (
                    tfcoil_variables.cplen * tfcoil_variables.a_tf_coil_inboard_case
                    + (tfcoil_variables.len_tf_coil - tfcoil_variables.cplen)
                    * tfcoil_variables.a_tf_coil_outboard_case
                )
            )

        # ***

        # Masses of conductor constituents
        # ---------------------------------
        # Superconductor mass [kg]
        # Includes space allowance for central helium channel, area tfcoil_variables.a_tf_wp_coolant_channels
        tfcoil_variables.m_tf_coil_superconductor = (
            tfcoil_variables.len_tf_coil
            * tfcoil_variables.n_tf_coil_turns
            * tfcoil_variables.a_tf_turn_cable_space_no_void
            * (1.0e0 - tfcoil_variables.f_a_tf_turn_cable_space_extra_void)
            * (1.0e0 - tfcoil_variables.f_a_tf_turn_cable_copper)
            - tfcoil_variables.len_tf_coil * tfcoil_variables.a_tf_wp_coolant_channels
        ) * tfcoil_variables.dcond[tfcoil_variables.i_tf_sc_mat - 1]

        # Copper mass [kg]
        tfcoil_variables.m_tf_coil_copper = (
            tfcoil_variables.len_tf_coil
            * tfcoil_variables.n_tf_coil_turns
            * tfcoil_variables.a_tf_turn_cable_space_no_void
            * (1.0e0 - tfcoil_variables.f_a_tf_turn_cable_space_extra_void)
            * tfcoil_variables.f_a_tf_turn_cable_copper
            - tfcoil_variables.len_tf_coil * tfcoil_variables.a_tf_wp_coolant_channels
        ) * constants.den_copper
        if tfcoil_variables.m_tf_coil_copper <= 0.0e0:
            tfcoil_variables.m_tf_coil_copper = 0.0e0

        # Steel conduit (sheath) mass [kg]
        tfcoil_variables.m_tf_wp_steel_conduit = (
            tfcoil_variables.len_tf_coil
            * tfcoil_variables.n_tf_coil_turns
            * tfcoil_variables.a_tf_turn_steel
            * fwbs_variables.den_steel
        )

        # Conduit insulation mass [kg]
        # (tfcoil_variables.a_tf_coil_wp_turn_insulation already contains tfcoil_variables.n_tf_coil_turns)
        tfcoil_variables.m_tf_coil_wp_turn_insulation = (
            tfcoil_variables.len_tf_coil
            * tfcoil_variables.a_tf_coil_wp_turn_insulation
            * tfcoil_variables.den_tf_wp_turn_insulation
        )

        # Total conductor mass [kg]
        tfcoil_variables.m_tf_coil_conductor = (
            tfcoil_variables.m_tf_coil_superconductor
            + tfcoil_variables.m_tf_coil_copper
            + tfcoil_variables.m_tf_wp_steel_conduit
            + tfcoil_variables.m_tf_coil_wp_turn_insulation
        )
        # ---------------------------------

        # Total TF coil mass [kg] (all coils)
        tfcoil_variables.m_tf_coils_total = (
            tfcoil_variables.m_tf_coil_case
            + tfcoil_variables.m_tf_coil_conductor
            + tfcoil_variables.m_tf_coil_wp_insulation
        ) * tfcoil_variables.n_tf_coils

        # If spherical tokamak, distribute between centrepost and outboard legs
        # (in this case, total TF coil length = inboard `cplen` + outboard `len_tf_coil`)
        if physics_variables.itart == 1:
            tfleng_sph = tfcoil_variables.cplen + tfcoil_variables.len_tf_coil
            tfcoil_variables.whtcp = tfcoil_variables.m_tf_coils_total * (
                tfcoil_variables.cplen / tfleng_sph
            )
            tfcoil_variables.whttflgs = tfcoil_variables.m_tf_coils_total * (
                tfcoil_variables.len_tf_coil / tfleng_sph
            )

outfile = constants.NOUT instance-attribute

run(output)

Routine to call the superconductor module for the TF coils

Parameters:

Name	Type	Description	Default
output	bool		required

Source code in process/models/tfcoil/superconducting.py

def run(self, output: bool):
    """Routine to call the superconductor module for the TF coils

    Parameters
    ----------
    output: bool

    """
    self.iprint = 0

    # Set up TF values share by all coil types
    self.run_base_tf()

    self.sc_tf_internal_geom(
        tfcoil_variables.i_tf_wp_geom,
        tfcoil_variables.i_tf_case_geom,
        tfcoil_variables.i_tf_turns_integer,
    )

    tfcoil_variables.ind_tf_coil = self.tf_coil_self_inductance(
        dr_tf_inboard=build_variables.dr_tf_inboard,
        r_tf_arc=tfcoil_variables.r_tf_arc,
        z_tf_arc=tfcoil_variables.z_tf_arc,
        itart=physics_variables.itart,
        i_tf_shape=tfcoil_variables.i_tf_shape,
        z_tf_inside_half=build_variables.z_tf_inside_half,
        dr_tf_outboard=build_variables.dr_tf_outboard,
        r_tf_outboard_mid=build_variables.r_tf_outboard_mid,
        r_tf_inboard_mid=build_variables.r_tf_inboard_mid,
    )

    (
        superconducting_tf_coil_variables.e_tf_magnetic_stored_total,
        tfcoil_variables.e_tf_magnetic_stored_total_gj,
        tfcoil_variables.e_tf_coil_magnetic_stored,
    ) = self.tf_stored_magnetic_energy(
        ind_tf_coil=tfcoil_variables.ind_tf_coil,
        c_tf_total=tfcoil_variables.c_tf_total,
        n_tf_coils=tfcoil_variables.n_tf_coils,
    )

    (
        tfcoil_variables.cforce,
        tfcoil_variables.vforce,
        tfcoil_variables.vforce_outboard,
        superconducting_tf_coil_variables.vforce_inboard_tot,
        tfcoil_variables.f_vforce_inboard,
    ) = self.tf_field_and_force(
        i_tf_sup=tfcoil_variables.i_tf_sup,
        r_tf_wp_inboard_outer=superconducting_tf_coil_variables.r_tf_wp_inboard_outer,
        r_tf_wp_inboard_inner=superconducting_tf_coil_variables.r_tf_wp_inboard_inner,
        r_tf_outboard_in=superconducting_tf_coil_variables.r_tf_outboard_in,
        dx_tf_wp_insulation=tfcoil_variables.dx_tf_wp_insulation,
        dx_tf_wp_insertion_gap=tfcoil_variables.dx_tf_wp_insertion_gap,
        b_tf_inboard_peak_symmetric=tfcoil_variables.b_tf_inboard_peak_symmetric,
        c_tf_total=tfcoil_variables.c_tf_total,
        n_tf_coils=tfcoil_variables.n_tf_coils,
        dr_tf_plasma_case=tfcoil_variables.dr_tf_plasma_case,
        rmajor=physics_variables.rmajor,
        b_plasma_toroidal_on_axis=physics_variables.b_plasma_toroidal_on_axis,
        r_cp_top=build_variables.r_cp_top,
        itart=physics_variables.itart,
        i_cp_joints=tfcoil_variables.i_cp_joints,
        f_vforce_inboard=tfcoil_variables.f_vforce_inboard,
    )

    # Calculate TF coil areas and masses
    self.generic_tf_coil_area_and_masses()
    self.superconducting_tf_coil_areas_and_masses()

    # Do stress calculations (writes the stress output)
    if output:
        tfcoil_variables.n_rad_per_layer = 500

    try:
        (
            sig_tf_r_max,
            sig_tf_t_max,
            sig_tf_z_max,
            sig_tf_vmises_max,
            s_shear_tf_peak,
            deflect,
            eyoung_axial,
            eyoung_trans,
            eyoung_wp_axial,
            eyoung_wp_trans,
            poisson_wp_trans,
            radial_array,
            s_shear_cea_tf_cond,
            poisson_wp_axial,
            sig_tf_r,
            sig_tf_smeared_r,
            sig_tf_smeared_t,
            sig_tf_smeared_z,
            sig_tf_t,
            s_shear_tf,
            sig_tf_vmises,
            sig_tf_z,
            str_tf_r,
            str_tf_t,
            str_tf_z,
            n_radial_array,
            n_tf_bucking,
            tfcoil_variables.sig_tf_wp,
            sig_tf_case,
            sig_tf_cs_bucked,
            str_wp,
            casestr,
            insstrain,
            sig_tf_wp_av_z,
        ) = self.stresscl(
            int(tfcoil_variables.n_tf_stress_layers),
            int(tfcoil_variables.n_rad_per_layer),
            int(tfcoil_variables.n_tf_wp_stress_layers),
            int(tfcoil_variables.i_tf_bucking),
            float(build_variables.r_tf_inboard_in),
            build_variables.dr_bore,
            build_variables.z_tf_inside_half,
            pfcoil_variables.f_z_cs_tf_internal,
            build_variables.dr_cs,
            build_variables.i_tf_inside_cs,
            build_variables.dr_tf_inboard,
            build_variables.dr_cs_tf_gap,
            pfcoil_variables.i_pf_conductor,
            pfcoil_variables.j_cs_flat_top_end,
            pfcoil_variables.j_cs_pulse_start,
            pfcoil_variables.c_pf_coil_turn_peak_input,
            pfcoil_variables.n_pf_coils_in_group,
            pfcoil_variables.f_dr_dz_cs_turn,
            pfcoil_variables.radius_cs_turn_corners,
            pfcoil_variables.f_a_cs_turn_steel,
            tfcoil_variables.eyoung_steel,
            tfcoil_variables.poisson_steel,
            tfcoil_variables.eyoung_cond_axial,
            tfcoil_variables.poisson_cond_axial,
            tfcoil_variables.eyoung_cond_trans,
            tfcoil_variables.poisson_cond_trans,
            tfcoil_variables.eyoung_ins,
            tfcoil_variables.poisson_ins,
            tfcoil_variables.dx_tf_turn_insulation,
            tfcoil_variables.eyoung_copper,
            tfcoil_variables.poisson_copper,
            tfcoil_variables.i_tf_sup,
            tfcoil_variables.eyoung_res_tf_buck,
            superconducting_tf_coil_variables.r_tf_wp_inboard_inner,
            superconducting_tf_coil_variables.tan_theta_coil,
            superconducting_tf_coil_variables.rad_tf_coil_inboard_toroidal_half,
            superconducting_tf_coil_variables.r_tf_wp_inboard_outer,
            superconducting_tf_coil_variables.a_tf_coil_inboard_steel,
            superconducting_tf_coil_variables.a_tf_plasma_case,
            superconducting_tf_coil_variables.a_tf_coil_nose_case,
            tfcoil_variables.dx_tf_wp_insertion_gap,
            tfcoil_variables.dx_tf_wp_insulation,
            tfcoil_variables.n_tf_coil_turns,
            int(tfcoil_variables.i_tf_turns_integer),
            superconducting_tf_coil_variables.dx_tf_turn_cable_space_average,
            superconducting_tf_coil_variables.dr_tf_turn_cable_space,
            tfcoil_variables.dia_tf_turn_coolant_channel,
            tfcoil_variables.f_a_tf_turn_cable_copper,
            tfcoil_variables.dx_tf_turn_steel,
            superconducting_tf_coil_variables.dx_tf_side_case_average,
            superconducting_tf_coil_variables.dx_tf_wp_toroidal_average,
            superconducting_tf_coil_variables.a_tf_coil_inboard_insulation,
            tfcoil_variables.a_tf_wp_steel,
            tfcoil_variables.a_tf_wp_conductor,
            superconducting_tf_coil_variables.a_tf_wp_with_insulation,
            tfcoil_variables.eyoung_al,
            tfcoil_variables.poisson_al,
            tfcoil_variables.fcoolcp,
            tfcoil_variables.n_tf_graded_layers,
            tfcoil_variables.c_tf_total,
            tfcoil_variables.dr_tf_plasma_case,
            tfcoil_variables.i_tf_stress_model,
            superconducting_tf_coil_variables.vforce_inboard_tot,
            tfcoil_variables.i_tf_tresca,
            tfcoil_variables.a_tf_coil_inboard_case,
            tfcoil_variables.vforce,
            tfcoil_variables.a_tf_turn_steel,
        )

        tfcoil_variables.sig_tf_case = (
            tfcoil_variables.sig_tf_case
            if tfcoil_variables.sig_tf_case is None
            else sig_tf_case
        )

        tfcoil_variables.sig_tf_cs_bucked = (
            tfcoil_variables.sig_tf_cs_bucked
            if tfcoil_variables.sig_tf_cs_bucked is None
            else sig_tf_cs_bucked
        )

        tfcoil_variables.str_wp = (
            tfcoil_variables.str_wp if tfcoil_variables.str_wp is None else str_wp
        )

        tfcoil_variables.casestr = (
            tfcoil_variables.casestr if tfcoil_variables.casestr is None else casestr
        )

        tfcoil_variables.insstrain = (
            tfcoil_variables.insstrain
            if tfcoil_variables.insstrain is None
            else insstrain
        )

        if output:
            self.out_stress(
                sig_tf_r_max,
                sig_tf_t_max,
                sig_tf_z_max,
                sig_tf_vmises_max,
                s_shear_tf_peak,
                deflect,
                eyoung_axial,
                eyoung_trans,
                eyoung_wp_axial,
                eyoung_wp_trans,
                poisson_wp_trans,
                radial_array,
                s_shear_cea_tf_cond,
                poisson_wp_axial,
                sig_tf_r,
                sig_tf_smeared_r,
                sig_tf_smeared_t,
                sig_tf_smeared_z,
                sig_tf_t,
                s_shear_tf,
                sig_tf_vmises,
                sig_tf_z,
                str_tf_r,
                str_tf_t,
                str_tf_z,
                n_radial_array,
                n_tf_bucking,
                sig_tf_wp_av_z,
            )
    except ValueError as e:
        if e.args[1] == 245 and e.args[2] == 0:
            logger.warning(
                "Invalid stress model (r_tf_inboard = 0), stress constraint switched off"
            )
            tfcoil_variables.sig_tf_case = 0.0e0
            tfcoil_variables.sig_tf_wp = 0.0e0

    self.vv_stress_on_quench()

    # ======================================================

    # Peak inboard toroidal field including ripple
    tfcoil_variables.b_tf_inboard_peak_with_ripple = self.peak_b_tf_inboard_with_ripple(
        n_tf_coils=tfcoil_variables.n_tf_coils,
        dx_tf_wp_primary_toroidal=tfcoil_variables.dx_tf_wp_primary_toroidal,
        dr_tf_wp_no_insulation=superconducting_tf_coil_variables.dr_tf_wp_no_insulation,
        r_tf_wp_inboard_centre=superconducting_tf_coil_variables.r_tf_wp_inboard_centre,
        b_tf_inboard_peak_symmetric=tfcoil_variables.b_tf_inboard_peak_symmetric,
    )
    # ======================================================

    # Cross-sectional area per turn
    a_tf_turn = tfcoil_variables.c_tf_total / (
        tfcoil_variables.j_tf_wp
        * tfcoil_variables.n_tf_coils
        * tfcoil_variables.n_tf_coil_turns
    )

    if tfcoil_variables.i_tf_sc_mat == 6:
        (
            tfcoil_variables.j_tf_wp_critical,
            tfcoil_variables.temp_tf_superconductor_margin,
        ) = self.supercon_croco(
            a_tf_turn,
            tfcoil_variables.b_tf_inboard_peak_with_ripple,
            tfcoil_variables.c_tf_turn,
            tfcoil_variables.tftmp,
            output=output,
        )

        tfcoil_variables.v_tf_coil_dump_quench_kv = (
            self.croco_voltage() / 1.0e3
        )  # TFC Quench voltage in kV

    else:
        (
            tfcoil_variables.j_tf_wp_critical,
            superconducting_tf_coil_variables.j_tf_superconductor_critical,
            superconducting_tf_coil_variables.f_c_tf_turn_operating_critical,
            superconducting_tf_coil_variables.j_tf_superconductor,
            superconducting_tf_coil_variables.j_tf_coil_turn,
            superconducting_tf_coil_variables.b_tf_superconductor_critical_zero_temp_strain,
            superconducting_tf_coil_variables.temp_tf_superconductor_critical_zero_field_strain,
            superconducting_tf_coil_variables.c_tf_turn_cables_critical,
        ) = self.tf_cable_in_conduit_superconductor_properties(
            a_tf_turn_cable_space=tfcoil_variables.a_tf_turn_cable_space_no_void,
            a_tf_turn=a_tf_turn,
            a_tf_turn_cable_space_effective=superconducting_tf_coil_variables.a_tf_turn_cable_space_effective,
            f_a_tf_turn_cable_space_cooling=superconducting_tf_coil_variables.f_a_tf_turn_cable_space_cooling,
            b_tf_inboard_peak=tfcoil_variables.b_tf_inboard_peak_with_ripple,
            f_a_tf_turn_cable_copper=tfcoil_variables.f_a_tf_turn_cable_copper,
            c_tf_turn=tfcoil_variables.c_tf_turn,
            j_tf_wp=tfcoil_variables.j_tf_wp,
            i_tf_superconductor=tfcoil_variables.i_tf_sc_mat,
            f_strain_scale=tfcoil_variables.fhts,
            temp_tf_coolant_peak_field=tfcoil_variables.tftmp,
            bcritsc=tfcoil_variables.bcritsc,
            tcritsc=tfcoil_variables.tcritsc,
        )

    if tfcoil_variables.i_str_wp == 0:
        strain = tfcoil_variables.str_tf_con_res
    else:
        strain = tfcoil_variables.str_wp

    tfcoil_variables.temp_tf_superconductor_margin = self.calculate_superconductor_temperature_margin(
        i_tf_superconductor=tfcoil_variables.i_tf_sc_mat,
        j_superconductor=superconducting_tf_coil_variables.j_tf_superconductor,
        b_tf_inboard_peak=tfcoil_variables.b_tf_inboard_peak_with_ripple,
        strain=strain,
        bc20m=superconducting_tf_coil_variables.b_tf_superconductor_critical_zero_temp_strain,
        tc0m=superconducting_tf_coil_variables.temp_tf_superconductor_critical_zero_field_strain,
        c0=1.0e10,
        temp_tf_coolant_peak_field=tfcoil_variables.tftmp,
    )

    # Do current density protection calculation
    # Only setup for Nb3Sn at present.
    if tfcoil_variables.i_tf_sc_mat not in {1, 4, 5}:
        logger.warning(
            "Calculating current density protection limit for Nb3Sn TF coil (LTS windings only)"
        )
        # Find the current density limited by the protection limit
        # At present only valid for LTS windings (Nb3Sn properties assumed)
    tfcoil_variables.j_tf_wp_quench_heat_max, v_tf_coil_dump_quench = (
        self.quench_heat_protection_current_density(
            c_tf_turn=tfcoil_variables.c_tf_turn,
            e_tf_coil_magnetic_stored=tfcoil_variables.e_tf_coil_magnetic_stored,
            a_tf_turn_cable_space=tfcoil_variables.a_tf_turn_cable_space_no_void,
            a_tf_turn=a_tf_turn,
            t_tf_quench_dump=tfcoil_variables.t_tf_superconductor_quench,
            f_a_tf_turn_cable_space_conductor=1.0e0
            - superconducting_tf_coil_variables.f_a_tf_turn_cable_space_cooling,
            f_a_tf_turn_cable_copper=tfcoil_variables.f_a_tf_turn_cable_copper,
            temp_tf_coolant_peak_field=tfcoil_variables.tftmp,
            temp_tf_conductor_quench_max=tfcoil_variables.temp_tf_conductor_quench_max,
            b_tf_inboard_peak=tfcoil_variables.b_tf_inboard_peak_with_ripple,
            cu_rrr=tfcoil_variables.rrr_tf_cu,
            t_tf_quench_detection=tfcoil_variables.t_tf_quench_detection,
            nflutfmax=constraint_variables.nflutfmax,
        )
    )

    tfcoil_variables.v_tf_coil_dump_quench_kv = (
        v_tf_coil_dump_quench / 1.0e3
    )  # TFC Quench voltage in kV

    if output:
        self.outtf()

croco_voltage()

Source code in process/models/tfcoil/superconducting.py

def croco_voltage(self) -> float:
    if tfcoil_variables.quench_model == "linear":
        superconducting_tf_coil_variables.time2 = (
            tfcoil_variables.t_tf_superconductor_quench
        )
        croco_voltage = (
            2.0e0
            / superconducting_tf_coil_variables.time2
            * (
                superconducting_tf_coil_variables.e_tf_magnetic_stored_total
                / tfcoil_variables.n_tf_coils
            )
            / tfcoil_variables.c_tf_turn
        )
    elif tfcoil_variables.quench_model == "exponential":
        superconducting_tf_coil_variables.tau2 = (
            tfcoil_variables.t_tf_superconductor_quench
        )
        croco_voltage = (
            2.0e0
            / superconducting_tf_coil_variables.tau2
            * (
                superconducting_tf_coil_variables.e_tf_magnetic_stored_total
                / tfcoil_variables.n_tf_coils
            )
            / tfcoil_variables.c_tf_turn
        )
    else:
        return 0.0

    return croco_voltage

supercon_croco(a_tf_turn, b_tf_inboard_peak_symmetric, iop, thelium, output)

TF superconducting CroCo conductor using REBCO tape

Parameters:

Name	Type	Description	Default
a_tf_turn			required
b_tf_inboard_peak_symmetric		Peak field at conductor (T)	required
iop		Operating current per turn (A)	required
thelium		He temperature at peak field point (K)	required
output	bool		required

Source code in process/models/tfcoil/superconducting.py

def supercon_croco(
    self, a_tf_turn, b_tf_inboard_peak_symmetric, iop, thelium, output: bool
):
    """TF superconducting CroCo conductor using REBCO tape

    Parameters
    ----------
    a_tf_turn :

    b_tf_inboard_peak_symmetric :
        Peak field at conductor (T)
    iop :
        Operating current per turn (A)
    thelium :
        He temperature at peak field point (K)
    output:

    """

    j_crit_sc: float = 0.0
    #  Find critical current density in superconducting cable, j_crit_cable
    j_crit_sc, _ = superconductors.jcrit_rebco(thelium, b_tf_inboard_peak_symmetric)
    # tfcoil_variables.a_tf_turn_cable_space_no_void : Cable space - inside area (m2)
    # Set new rebco_variables.dia_croco_strand
    # allowing for scaling of rebco_variables.dia_croco_strand
    rebco_variables.dia_croco_strand = (
        tfcoil_variables.t_conductor / 3.0e0
        - tfcoil_variables.dx_tf_turn_steel * (2.0e0 / 3.0e0)
    )
    superconducting_tf_coil_variables.conductor_acs = (
        9.0e0 / 4.0e0 * np.pi * rebco_variables.dia_croco_strand**2
    )
    tfcoil_variables.a_tf_turn_cable_space_no_void = (
        superconducting_tf_coil_variables.conductor_acs
    )
    superconducting_tf_coil_variables.conductor_area = (
        tfcoil_variables.t_conductor**2
    )  # does this not assume it's a sqaure???

    superconducting_tf_coil_variables.conductor_jacket_area = (
        superconducting_tf_coil_variables.conductor_area
        - superconducting_tf_coil_variables.conductor_acs
    )
    tfcoil_variables.a_tf_turn_steel = (
        superconducting_tf_coil_variables.conductor_jacket_area
    )

    superconducting_tf_coil_variables.conductor_jacket_fraction = (
        superconducting_tf_coil_variables.conductor_jacket_area
        / superconducting_tf_coil_variables.conductor_area
    )
    (
        superconducting_tf_coil_variables.croco_strand_area,
        superconducting_tf_coil_variables.croco_strand_critical_current,
        superconducting_tf_coil_variables.conductor_copper_area,
        superconducting_tf_coil_variables.conductor_copper_fraction,
        superconducting_tf_coil_variables.conductor_copper_bar_area,
        superconducting_tf_coil_variables.conductor_hastelloy_area,
        superconducting_tf_coil_variables.conductor_hastelloy_fraction,
        superconducting_tf_coil_variables.conductor_helium_area,
        superconducting_tf_coil_variables.conductor_helium_fraction,
        superconducting_tf_coil_variables.conductor_solder_area,
        superconducting_tf_coil_variables.conductor_solder_fraction,
        superconducting_tf_coil_variables.conductor_rebco_area,
        superconducting_tf_coil_variables.conductor_rebco_fraction,
        superconducting_tf_coil_variables.conductor_critical_current,
    ) = superconductors.croco(
        j_crit_sc,
        superconducting_tf_coil_variables.conductor_area,
        rebco_variables.dia_croco_strand,
        rebco_variables.dx_croco_strand_copper,
    )

    rebco_variables.coppera_m2 = (
        iop / superconducting_tf_coil_variables.conductor_copper_area
    )

    icrit = superconducting_tf_coil_variables.conductor_critical_current
    j_crit_cable = (
        superconducting_tf_coil_variables.croco_strand_critical_current
        / superconducting_tf_coil_variables.croco_strand_area
    )

    # Critical current density in winding pack
    # a_tf_turn : Area per turn (i.e. entire jacketed conductor with insulation) (m2)
    j_tf_wp_critical = icrit / a_tf_turn
    #  Ratio of operating / critical current
    iooic = iop / icrit
    #  Operating current density
    jwdgop = iop / a_tf_turn
    #  Actual current density in superconductor,
    # which should be equal to jcrit(thelium+tmarg)

    #  when we have found the desired value of tmarg
    jsc = iooic * j_crit_sc

    # Temperature margin
    current_sharing_t = superconductors.current_sharing_rebco(
        b_tf_inboard_peak_symmetric, jsc
    )
    tmarg = current_sharing_t - thelium
    tfcoil_variables.temp_margin = (
        tmarg  # Only used in the availabilty routine - see comment to Issue #526
    )

    if output:  # Output ----------------------------------
        total = (
            superconducting_tf_coil_variables.conductor_copper_area
            + superconducting_tf_coil_variables.conductor_hastelloy_area
            + superconducting_tf_coil_variables.conductor_solder_area
            + superconducting_tf_coil_variables.conductor_jacket_area
            + superconducting_tf_coil_variables.conductor_helium_area
            + superconducting_tf_coil_variables.conductor_rebco_area
        )

        if tfcoil_variables.temp_margin <= 0.0e0:
            logger.error(
                f"""Negative TFC temperature margin
            temp_margin: {tfcoil_variables.temp_margin}
            b_tf_inboard_peak_symmetric: {b_tf_inboard_peak_symmetric}"""
            )

        po.oheadr(self.outfile, "Superconducting TF Coils")
        po.ovarin(self.outfile, "Superconductor switch", "(isumat)", 6)
        po.ocmmnt(
            self.outfile, "Superconductor used: REBCO HTS tape in CroCo strand"
        )

        po.ovarre(
            self.outfile,
            "Thickness of REBCO layer in tape (m)",
            "(dx_hts_tape_rebco)",
            rebco_variables.dx_hts_tape_rebco,
        )
        po.ovarre(
            self.outfile,
            "Thickness of copper layer in tape (m)",
            "(dx_hts_tape_copper)",
            rebco_variables.dx_hts_tape_copper,
        )
        po.ovarre(
            self.outfile,
            "Thickness of Hastelloy layer in tape (m) ",
            "(dx_hts_tape_hastelloy)",
            rebco_variables.dx_hts_tape_hastelloy,
        )

        po.ovarre(
            self.outfile,
            "Mean width of tape (m)",
            "(dr_hts_tape)",
            rebco_variables.dr_hts_tape,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Diameter of a CroCo strand (m) ",
            "(dia_croco_strand)",
            rebco_variables.dia_croco_strand,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Inner diameter of CroCo copper tube (m) ",
            "(dia_croco_strand_tape_region)",
            rebco_variables.dia_croco_strand_tape_region,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Thickness of of o copper tube (m) ",
            "(dx_croco_strand_copper)",
            rebco_variables.dx_croco_strand_copper,
        )

        po.ovarre(
            self.outfile,
            "Thickness of each HTS tape ",
            "(dx_hts_tape_total)",
            rebco_variables.dx_hts_tape_total,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Thickness of stack of rebco_variables.n_croco_strand_hts_tapes (m) ",
            "(dx_croco_strand_tape_stack)",
            rebco_variables.dx_croco_strand_tape_stack,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Number of rebco_variables.n_croco_strand_hts_tapes in strand",
            "(n_croco_strand_hts_tapes)",
            rebco_variables.n_croco_strand_hts_tapes,
            "OP ",
        )
        po.oblnkl(self.outfile)
        po.ovarre(
            self.outfile,
            "Area of REBCO in strand (m2)",
            "(a_croco_strand_rebco)",
            rebco_variables.a_croco_strand_rebco,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Area of copper in strand (m2)",
            "(a_croco_strand_copper_total)",
            rebco_variables.a_croco_strand_copper_total,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Area of hastelloy substrate in strand (m2) ",
            "(a_croco_strand_hastelloy)",
            rebco_variables.a_croco_strand_hastelloy,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Area of solder in strand (m2)  ",
            "(a_croco_strand_solder)",
            rebco_variables.a_croco_strand_solder,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Total: area of CroCo strand (m2)  ",
            "(croco_strand_area)",
            superconducting_tf_coil_variables.croco_strand_area,
            "OP ",
        )
        if (
            abs(
                superconducting_tf_coil_variables.croco_strand_area
                - (
                    rebco_variables.a_croco_strand_rebco
                    + rebco_variables.a_croco_strand_copper_total
                    + rebco_variables.a_croco_strand_hastelloy
                    + rebco_variables.a_croco_strand_solder
                )
            )
            > 1e-6
        ):
            po.ocmmnt(self.outfile, "ERROR: Areas in CroCo strand do not add up")
            logger.error("Areas in CroCo strand do not add up - see OUT.DAT")

        po.oblnkl(self.outfile)
        po.ocmmnt(self.outfile, "Cable information")
        po.ovarin(
            self.outfile,
            "Number of CroCo strands in the cable (fixed) ",
            "",
            6,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Total area of cable space (m2)",
            "(a_tf_turn_cable_space_no_void)",
            tfcoil_variables.a_tf_turn_cable_space_no_void,
            "OP ",
        )

        po.oblnkl(self.outfile)
        po.ocmmnt(
            self.outfile,
            "Conductor information (includes jacket, not including insulation)",
        )
        po.ovarre(
            self.outfile,
            "Width of square conductor (cable + steel jacket) (m)",
            "(t_conductor)",
            tfcoil_variables.t_conductor,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Area of conductor (m2)",
            "(area)",
            superconducting_tf_coil_variables.conductor_area,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "REBCO area of conductor (mm2)",
            "(a_croco_strand_rebco)",
            superconducting_tf_coil_variables.conductor_rebco_area,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Area of central copper bar (mm2)",
            "(copper_bar_area)",
            superconducting_tf_coil_variables.conductor_copper_bar_area,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Total copper area of conductor, total (mm2)",
            "(a_croco_strand_copper_total)",
            superconducting_tf_coil_variables.conductor_copper_area,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Hastelloy area of conductor (mm2)",
            "(a_croco_strand_hastelloy)",
            superconducting_tf_coil_variables.conductor_hastelloy_area,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Solder area of conductor (mm2)",
            "(a_croco_strand_solder)",
            superconducting_tf_coil_variables.conductor_solder_area,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Jacket area of conductor (mm2)",
            "(jacket_area)",
            superconducting_tf_coil_variables.conductor_jacket_area,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Helium area of conductor (mm2)",
            "(helium_area)",
            superconducting_tf_coil_variables.conductor_helium_area,
            "OP ",
        )
        if abs(total - superconducting_tf_coil_variables.conductor_area) > 1e-8:
            po.ovarre(
                self.outfile,
                "ERROR: conductor areas do not add up:",
                "(total)",
                total,
                "OP ",
            )
            logger.error(f"conductor areas do not add up. total: {total}")

        po.ovarre(
            self.outfile,
            "Critical current of CroCo strand (A)",
            "(croco_strand_critical_current)",
            superconducting_tf_coil_variables.croco_strand_critical_current,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Critical current of conductor (A) ",
            "(conductor_critical_current)",
            superconducting_tf_coil_variables.conductor_critical_current,
            "OP ",
        )

        if global_variables.run_tests == 1:
            po.oblnkl(self.outfile)
            po.ocmmnt(
                self.outfile,
                "PROCESS TF Coil peak field fit. Values for t, z and y:",
            )
            po.oblnkl(self.outfile)
            po.ovarre(
                self.outfile,
                "Dimensionless winding pack width",
                "(tf_fit_t)",
                superconducting_tf_coil_variables.tf_fit_t,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Dimensionless winding pack radial thickness",
                "(tf_fit_z)",
                superconducting_tf_coil_variables.tf_fit_z,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Ratio of actual peak field to nominal axisymmetric peak field",
                "(f_b_tf_inboard_peak_ripple_symmetric)",
                superconducting_tf_coil_variables.f_b_tf_inboard_peak_ripple_symmetric,
                "OP ",
            )

        po.oblnkl(self.outfile)
        po.ovarre(
            self.outfile,
            "Helium temperature at peak field (= superconductor temperature) (K)",
            "(thelium)",
            thelium,
        )
        po.ovarre(
            self.outfile,
            "Critical current density in superconductor (A/m2)",
            "(j_crit_sc)",
            j_crit_sc,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Critical current density in cable (A/m2)",
            "(j_crit_cable)",
            j_crit_cable,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Critical current density in winding pack (A/m2)",
            "(j_tf_wp_critical)",
            j_tf_wp_critical,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Actual current density in winding pack (A/m2)",
            "(jwdgop)",
            jwdgop,
            "OP ",
        )

        po.ovarre(
            self.outfile,
            "Minimum allowed temperature margin in superconductor (K)",
            "(temp_tf_superconductor_margin_min)",
            tfcoil_variables.temp_tf_superconductor_margin_min,
        )

        po.ovarre(
            self.outfile,
            "Actual temperature margin in superconductor (K)",
            "(tmarg)",
            tmarg,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Current sharing temperature (K)",
            "(current_sharing_t)",
            current_sharing_t,
            "OP ",
        )
        po.ovarre(self.outfile, "Critical current (A)", "(icrit)", icrit, "OP ")
        po.ovarre(
            self.outfile,
            "Actual current (A)",
            "(c_tf_turn)",
            tfcoil_variables.c_tf_turn,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Actual current / critical current",
            "(iooic)",
            iooic,
            "OP ",
        )

    return j_tf_wp_critical, tmarg

tf_cable_in_conduit_superconductor_properties(a_tf_turn_cable_space, a_tf_turn, a_tf_turn_cable_space_effective, f_a_tf_turn_cable_space_cooling, b_tf_inboard_peak, f_a_tf_turn_cable_copper, c_tf_turn, j_tf_wp, i_tf_superconductor, f_strain_scale, temp_tf_coolant_peak_field, bcritsc, tcritsc)

Calculates the properties of the TF superconducting conductor.

Parameters:

Name	Type	Description	Default
a_tf_turn_cable_space	float	Cable space - inside area (m²).	required
a_tf_turn	float	Area per turn (i.e. entire jacketed conductor) (m²).	required
a_tf_turn_cable_space_effective	float	Effective cable space area per turn (m²).	required
f_a_tf_turn_cable_space_cooling	float	Fraction of cable space used for cooling.	required
b_tf_inboard_peak	float	Peak field at conductor (T).	required
f_a_tf_turn_cable_copper	float	Fraction of conductor that is copper.	required
c_tf_turn	float	Operating current per turn (A).	required
j_tf_wp	float	Actual winding pack current density (A/m²).	required
i_tf_superconductor	int	Switch for conductor type: - 1: ITER Nb3Sn, standard parameters - 2: Bi-2212 High Temperature Superconductor - 3: NbTi - 4: ITER Nb3Sn, user-defined parameters - 5: WST Nb3Sn parameterisation - 7: Durham Ginzburg-Landau Nb-Ti parameterisation - 8: Durham Ginzburg-Landau critical surface model for REBCO - 9: Hazelton experimental data + Zhai conceptual model for REBCO	required
f_strain_scale	float	Adjustment factor (<= 1) to account for strain, radiation damage, fatigue or AC losses.	required
temp_tf_coolant_peak_field	float	He temperature at peak field point (K).	required
bcritsc	float	Critical field at zero temperature and strain (T) (used only if i_tf_superconductor=4).	required
tcritsc	float	Critical temperature at zero field and strain (K) (used only if i_tf_superconductor=4).	required

Returns:

Type

Description

type

tuple (float, float, float, float, float, float, float, float, float) - j_tf_wp_critical (float): Critical winding pack current density (A/m²). - j_superconductor_critical (float): Critical current density in superconductor (A/m²). - f_c_tf_turn_operating_critical (float): Ratio of operating / critical current. - j_superconductor_turn (float): Actual current density in superconductor (A/m²). - j_tf_coil_turn (float): Actual current density in superconductor (A/m²). - b_tf_superconductor_critical_zero_temp_strain (float): Critical field at zero temperature and strain (T). - temp_tf_superconductor_critical_zero_field_strain (float): Critical temperature at zero field and strain (K). - c_tf_turn_cables_critical (float): Critical current in cable (A).

Notes

This routine calculates the superconductor properties for the TF coils. It was originally programmed by J. Galambos (1991), from algorithms provided by J. Miller. The routine calculates the critical current density (winding pack) and also the protection information (for a quench). Not used for the CroCo conductor.

The critical current density for a superconductor (j_superconductor_critical) is for the superconducting strands/tape, not including copper. The critical current density for a cable (j_crit_cable) accounts for both the fraction of the cable taken up by helium coolant channels, and the cable conductor copper fraction (i.e., the copper in the superconducting strands and any additional copper, such as REBCO tape support).

Source code in process/models/tfcoil/superconducting.py

def tf_cable_in_conduit_superconductor_properties(
    self,
    a_tf_turn_cable_space: float,
    a_tf_turn: float,
    a_tf_turn_cable_space_effective: float,
    f_a_tf_turn_cable_space_cooling: float,
    b_tf_inboard_peak: float,
    f_a_tf_turn_cable_copper: float,
    c_tf_turn: float,
    j_tf_wp: float,
    i_tf_superconductor: int,
    f_strain_scale: float,
    temp_tf_coolant_peak_field: float,
    bcritsc: float,
    tcritsc: float,
) -> tuple[float, float, float, float, float, float, float, float]:
    """Calculates the properties of the TF superconducting conductor.

    Parameters
    ----------
    a_tf_turn_cable_space:
        Cable space - inside area (m²).
    a_tf_turn:
        Area per turn (i.e. entire jacketed conductor) (m²).
    a_tf_turn_cable_space_effective:
        Effective cable space area per turn (m²).
    f_a_tf_turn_cable_space_cooling:
        Fraction of cable space used for cooling.
    b_tf_inboard_peak:
        Peak field at conductor (T).
    f_a_tf_turn_cable_copper:
        Fraction of conductor that is copper.
    c_tf_turn:
        Operating current per turn (A).
    j_tf_wp:
        Actual winding pack current density (A/m²).
    i_tf_superconductor:
        Switch for conductor type:
        - 1: ITER Nb3Sn, standard parameters
        - 2: Bi-2212 High Temperature Superconductor
        - 3: NbTi
        - 4: ITER Nb3Sn, user-defined parameters
        - 5: WST Nb3Sn parameterisation
        - 7: Durham Ginzburg-Landau Nb-Ti parameterisation
        - 8: Durham Ginzburg-Landau critical surface model for REBCO
        - 9: Hazelton experimental data + Zhai conceptual model for REBCO
    f_strain_scale:
        Adjustment factor (<= 1) to account for strain, radiation damage, fatigue or AC losses.
    temp_tf_coolant_peak_field:
        He temperature at peak field point (K).
    bcritsc:
        Critical field at zero temperature and strain (T) (used only if i_tf_superconductor=4).
    tcritsc:
        Critical temperature at zero field and strain (K) (used only if i_tf_superconductor=4).

    Returns
    -------
    type
        tuple (float, float, float, float, float, float, float, float, float)
        - j_tf_wp_critical (float): Critical winding pack current density (A/m²).
        - j_superconductor_critical (float): Critical current density in superconductor (A/m²).
        - f_c_tf_turn_operating_critical (float): Ratio of operating / critical current.
        - j_superconductor_turn (float): Actual current density in superconductor (A/m²).
        - j_tf_coil_turn (float): Actual current density in superconductor (A/m²).
        - b_tf_superconductor_critical_zero_temp_strain (float): Critical field at zero temperature and strain (T).
        - temp_tf_superconductor_critical_zero_field_strain (float): Critical temperature at zero field and strain (K).
        - c_tf_turn_cables_critical (float): Critical current in cable (A).

    Notes
    -----
    This routine calculates the superconductor properties for the TF coils.
    It was originally programmed by J. Galambos (1991), from algorithms provided by J. Miller.
    The routine calculates the critical current density (winding pack) and also the protection
    information (for a quench). Not used for the CroCo conductor.

    The critical current density for a superconductor (``j_superconductor_critical``) is for the superconducting
    strands/tape, not including copper. The critical current density for a cable (``j_crit_cable``)
    accounts for both the fraction of the cable taken up by helium coolant channels, and the cable
    conductor copper fraction (i.e., the copper in the superconducting strands and any additional
    copper, such as REBCO tape support).
    """

    # Guard against negative conductor fraction f_a_tf_turn_cable_space_conductor
    # Kludge to allow solver to continue and hopefully be constrained away
    # from this point
    if f_a_tf_turn_cable_space_cooling > 0.99:
        f_a_tf_turn_cable_space_cooling = 0.99

    #  Conductor fraction (including central helium channel)
    f_a_tf_turn_cable_space_conductor = 1.0e0 - f_a_tf_turn_cable_space_cooling

    if tfcoil_variables.i_str_wp == 0:
        strain = tfcoil_variables.str_tf_con_res
    else:
        strain = tfcoil_variables.str_wp

    # =================================================================

    # ITER Nb3Sn critical surface parameterization
    if i_tf_superconductor == 1:
        # Peak field and temperature at zero strain
        bc20m = 32.97e0  # [T]
        tc0m = 16.06e0  # [K]

        # If strain limit achieved, throw a warning and use the lower strain
        if abs(strain) > 0.5e-2:
            logger.error(
                f"TF strain={strain} was outside the region of applicability. Used lower strain."
            )
            strain = np.sign(strain) * 0.5e-2

        #  j_superconductor_critical returned by superconductors.itersc is the critical current density in the
        #  superconductor - not the whole strand, which contains copper
        j_superconductor_critical, _, _ = superconductors.itersc(
            temp_conductor=temp_tf_coolant_peak_field,
            b_conductor=b_tf_inboard_peak,
            strain=strain,
            b_c20max=bc20m,
            temp_c0max=tc0m,
        )

        # Scale for the copper area fraction of the cable
        j_cables_critical = j_superconductor_critical * (
            1.0e0 - f_a_tf_turn_cable_copper
        )

        #  Critical current in turn all turn cables
        c_turn_cables_critical = j_cables_critical * a_tf_turn_cable_space_effective

        # Strand critical current calculation for costing in $/kAm
        # = Superconducting filaments jc * (1 - strand copper fraction)
        tfcoil_variables.j_crit_str_tf = j_superconductor_critical * (
            1.0e0 - f_a_tf_turn_cable_copper
        )

    # =================================================================

    # Bi-2212 high temperature superconductor parameterization
    elif i_tf_superconductor == 2:
        #  Current density in a strand of Bi-2212 conductor
        #  N.B. jcrit returned by superconductors.bi2212 is the critical current density
        #  in the strand, not just the superconducting portion.
        #  The parameterization for j_crit_cable assumes a particular strand
        #  composition that does not require a user-defined copper fraction,
        #  so this is irrelevant in this model
        j_strand = (
            j_tf_wp
            * a_tf_turn
            / (a_tf_turn_cable_space * f_a_tf_turn_cable_space_conductor)
        )

        j_crit_cable, _ = superconductors.bi2212(
            b_conductor=b_tf_inboard_peak,
            jstrand=j_strand,
            temp_conductor=temp_tf_coolant_peak_field,
            f_strain=f_strain_scale,
        )
        j_superconductor_critical = j_crit_cable / (1.0e0 - f_a_tf_turn_cable_copper)
        #  Critical current in cable
        c_turn_cables_critical = (
            j_crit_cable * a_tf_turn_cable_space * f_a_tf_turn_cable_space_conductor
        )

        # Strand critical current calulation for costing in $ / kAm
        # Copper in the strand is already accounted for
        tfcoil_variables.j_crit_str_tf = j_superconductor_critical
    # =================================================================

    # NbTi data
    elif i_tf_superconductor == 3:
        bc20m = 15.0e0  # [T]
        tc0m = 9.3e0  # [K]
        c0 = 1.0e10  # [A/m2]

        j_superconductor_critical, _ = superconductors.jcrit_nbti(
            temp_conductor=temp_tf_coolant_peak_field,
            b_conductor=b_tf_inboard_peak,
            c0=c0,
            b_c20m=bc20m,
            temp_c0max=tc0m,
        )

        # Scale for the copper area fraction of the cable
        j_cables_critical = j_superconductor_critical * (
            1.0e0 - f_a_tf_turn_cable_copper
        )

        #  Critical current in turn all turn cables
        c_turn_cables_critical = j_cables_critical * a_tf_turn_cable_space_effective

        # Strand critical current calulation for costing in $ / kAm
        # = superconducting filaments jc * (1 -strand copper fraction)
        tfcoil_variables.j_crit_str_tf = j_superconductor_critical * (
            1.0e0 - f_a_tf_turn_cable_copper
        )

    # =================================================================

    # ITER Nb3Sn parameterization, but user-defined parameters
    elif i_tf_superconductor == 4:
        bc20m = bcritsc  # [T]
        tc0m = tcritsc  # [K]

        # If strain limit achieved, throw a warning and use the lower strain
        if abs(strain) > 0.5e-2:
            logger.error(
                f"TF strain={strain} was outside the region of applicability. Used lower strain."
            )
            strain = np.sign(strain) * 0.5e-2

        j_superconductor_critical, _, _ = superconductors.itersc(
            temp_conductor=temp_tf_coolant_peak_field,
            b_conductor=b_tf_inboard_peak,
            strain=strain,
            b_c20max=bc20m,
            temp_c0max=tc0m,
        )
        # Scale for the copper area fraction of the cable
        j_cables_critical = j_superconductor_critical * (
            1.0e0 - f_a_tf_turn_cable_copper
        )

        #  Critical current in turn all turn cables
        c_turn_cables_critical = j_cables_critical * a_tf_turn_cable_space_effective

        # Strand critical current calulation for costing in $ / kAm
        # = superconducting filaments jc * (1 -strand copper fraction)
        tfcoil_variables.j_crit_str_tf = j_superconductor_critical * (
            1.0e0 - f_a_tf_turn_cable_copper
        )

    # =================================================================

    # WST Nb3Sn parameterisation
    elif i_tf_superconductor == 5:
        bc20m = 32.97e0  # [T]
        tc0m = 16.06e0  # [K]

        # If strain limit achieved, throw a warning and use the lower strain
        if abs(strain) > 0.5e-2:
            logger.error(
                f"TF strain={strain} was outside the region of applicability. Used lower strain."
            )
            strain = np.sign(strain) * 0.5e-2

        #  j_superconductor_critical returned by superconductors.itersc is the critical current density in the
        #  superconductor - not the whole strand, which contains copper
        j_superconductor_critical, _, _ = (
            superconductors.western_superconducting_nb3sn(
                temp_conductor=temp_tf_coolant_peak_field,
                b_conductor=b_tf_inboard_peak,
                strain=strain,
                b_c20max=bc20m,
                temp_c0max=tc0m,
            )
        )
        # Scale for the copper area fraction of the cable
        j_cables_critical = j_superconductor_critical * (
            1.0e0 - f_a_tf_turn_cable_copper
        )

        #  Critical current in turn all turn cables
        c_turn_cables_critical = j_cables_critical * a_tf_turn_cable_space_effective

        # Strand critical current calulation for costing in $ / kAm
        # = superconducting filaments jc * (1 -strand copper fraction)
        tfcoil_variables.j_crit_str_tf = j_superconductor_critical * (
            1.0e0 - f_a_tf_turn_cable_copper
        )

    # =================================================================

    # "REBCO" 2nd generation HTS superconductor in CrCo strand
    elif i_tf_superconductor == 6:
        raise ProcessValueError(
            "sctfcoil.supercon has been called but tfcoil_variables.i_tf_sc_mat=6"
        )

    # =================================================================

    # Durham Ginzburg-Landau Nb-Ti parameterisation
    elif i_tf_superconductor == 7:
        bc20m = tfcoil_variables.b_crit_upper_nbti  # [T]
        tc0m = tfcoil_variables.t_crit_nbti  # [K]

        j_superconductor_critical, _, _ = superconductors.gl_nbti(
            temp_conductor=temp_tf_coolant_peak_field,
            b_conductor=b_tf_inboard_peak,
            strain=strain,
            b_c20max=bc20m,
            t_c0=tc0m,
        )
        # Scale for the copper area fraction of the cable
        j_cables_critical = j_superconductor_critical * (
            1.0e0 - f_a_tf_turn_cable_copper
        )

        #  Critical current in turn all turn cables
        c_turn_cables_critical = j_cables_critical * a_tf_turn_cable_space_effective

        # Strand critical current calulation for costing in $ / kAm
        # = superconducting filaments jc * (1 -strand copper fraction)
        tfcoil_variables.j_crit_str_tf = j_superconductor_critical * (
            1.0e0 - f_a_tf_turn_cable_copper
        )

    # =================================================================

    # Durham Ginzburg-Landau critical surface model for REBCO
    elif i_tf_superconductor == 8:
        bc20m = 430  # [T]
        tc0m = 185  # [K]

        # If strain limit achieved, throw a warning and use the lower strain
        if abs(strain) > 0.7e-2:
            logger.error(
                f"TF strain={strain} was outside the region of applicability. Used lower strain."
            )
            strain = np.sign(strain) * 0.7e-2

        j_superconductor_critical, _, _ = superconductors.gl_rebco(
            temp_conductor=temp_tf_coolant_peak_field,
            b_conductor=b_tf_inboard_peak,
            strain=strain,
            b_c20max=bc20m,
            t_c0=tc0m,
        )
        # Scale for the copper area fraction of the cable
        j_cables_critical = j_superconductor_critical * (
            1.0e0 - f_a_tf_turn_cable_copper
        )

        #  Critical current in turn all turn cables
        c_turn_cables_critical = j_cables_critical * a_tf_turn_cable_space_effective

        # Strand critical current calulation for costing in $ / kAm
        # Already includes buffer and support layers so no need to include f_a_tf_turn_cable_copper here
        tfcoil_variables.j_crit_str_tf = j_superconductor_critical

        # REBCO measurements from 2 T to 14 T, extrapolating outside this
        if (b_tf_inboard_peak) >= 14.0:
            logger.error(
                "Field on superconductor > 14 T (outside of interpolation range)"
            )

    # =================================================================

    # Hazelton experimental data + Zhai conceptual model for REBCO
    elif i_tf_superconductor == 9:
        bc20m = 138  # [T]
        tc0m = 92  # [K]

        # If strain limit achieved, throw a warning and use the lower strain
        if abs(strain) > 0.7e-2:
            logger.error(
                f"TF strain={strain} was outside the region of applicability. Used lower strain."
            )
            strain = np.sign(strain) * 0.7e-2

        # 'high current density' as per parameterisation described in Wolf,
        #  and based on Hazelton experimental data and Zhai conceptual model;
        #  see subroutine for full references
        j_superconductor_critical, _, _ = superconductors.hijc_rebco(
            temp_conductor=temp_tf_coolant_peak_field,
            b_conductor=b_tf_inboard_peak,
            b_c20max=bc20m,
            t_c0=tc0m,
            dr_hts_tape=rebco_variables.dr_hts_tape,
            dx_hts_tape_rebco=rebco_variables.dx_hts_tape_rebco,
            dx_hts_tape_total=rebco_variables.dx_hts_tape_total,
        )
        # Scale for the copper area fraction of the cable
        j_cables_critical = j_superconductor_critical * (
            1.0e0 - f_a_tf_turn_cable_copper
        )

        #  Critical current in turn all turn cables
        c_turn_cables_critical = j_cables_critical * a_tf_turn_cable_space_effective

        # Strand critical current calulation for costing in $ / kAm
        # = superconducting filaments jc * (1 -strand copper fraction)
        tfcoil_variables.j_crit_str_tf = j_superconductor_critical * (
            1.0e0 - f_a_tf_turn_cable_copper
        )

    else:
        raise ProcessValueError(
            "Illegal value for i_tf_sc_mat", i_tf_superconductor=i_tf_superconductor
        )

    # =================================================================

    # Critical current density in winding pack
    # a_tf_turn : Area per turn (i.e. entire jacketed conductor with insulation) (m2)
    j_tf_wp_critical = c_turn_cables_critical / a_tf_turn

    #  Ratio of operating / critical current
    f_c_tf_turn_operating_critical = c_tf_turn / c_turn_cables_critical

    #  Operating current density
    j_tf_coil_turn = c_tf_turn / a_tf_turn

    #  Actual current density in superconductor, not including copper

    j_superconductor = f_c_tf_turn_operating_critical * j_superconductor_critical

    # =================================================================

    if f_c_tf_turn_operating_critical <= 0e0:
        logger.error(
            f"""Negative Iop/Icrit for TF coil
        jsc: {j_superconductor}
        f_c_tf_turn_operating_critical: {f_c_tf_turn_operating_critical}
        j_superconductor_critical: {j_superconductor_critical}
        Check conductor dimensions. Cable space area a_tf_turn_cable_space likely gone negative. a_tf_turn_cable_space: {a_tf_turn_cable_space}
        This is likely because dr_tf_turn_cable_space or dx_tf_turn_cable_space has gone negative:
        dr_tf_turn_cable_space: {superconducting_tf_coil_variables.dr_tf_turn_cable_space}
        dx_tf_turn_cable_space: {superconducting_tf_coil_variables.dx_tf_turn_cable_space}
        """
        )

    return (
        j_tf_wp_critical,
        j_superconductor_critical,
        f_c_tf_turn_operating_critical,
        j_superconductor,
        j_tf_coil_turn,
        bc20m,
        tc0m,
        c_turn_cables_critical,
    )

calculate_cable_in_conduit_strand_count(a_cable_space, dia_superconductor_strand)

Calculates the maximum number of superconducting strands that can fit into a cable-in-conduit conductor, based on the available cable space, strand diameter, and desired void fraction.

Parameters:

Name	Type	Description	Default
a_cable_space	float	Total cross-sectional area available for the cable (in m²).	required
dia_superconductor_strand	float	Diameter of a single superconducting strand (in meters).	required

Returns:

Type	Description
int	The maximum number of strands that can fit in the available space, accounting for the void fraction.

Source code in process/models/tfcoil/superconducting.py

def calculate_cable_in_conduit_strand_count(
    self,
    a_cable_space: float,
    dia_superconductor_strand: float,
) -> int:
    """Calculates the maximum number of superconducting strands that can fit into a cable-in-conduit conductor,
    based on the available cable space, strand diameter, and desired void fraction.

    Parameters
    ----------
    a_cable_space : float
        Total cross-sectional area available for the cable (in m²).
    dia_superconductor_strand : float
        Diameter of a single superconducting strand (in meters).

    Returns
    -------
    int
        The maximum number of strands that can fit in the available space, accounting for the void fraction.
    """

    # Effective area available for strands (excluding voids)
    effective_area = a_cable_space

    # Area per strand (circular)
    strand_area = np.pi * (dia_superconductor_strand / 2) ** 2

    # Number of strands that fit
    return int(effective_area / strand_area)

calculate_cable_in_conduit_superconductor_length(n_tf_coils, n_tf_coil_turns, len_tf_coil, n_tf_turn_superconducting_cables)

Calculates the total length of superconducting material required for the TF coils.

Parameters:

Name	Type	Description	Default
n_tf_coils	int	n_tf_coils: Number of TF coils.	required
n_tf_coil_turns	int	n_tf_coil_turns: Total number of turns in the TF coil winding pack.	required
len_tf_coil	float	len_tf_coil: Length of a single TF coil (in meters).	required
n_tf_turn_superconducting_cables	int	n_tf_turn_superconducting_cables: Number of superconducting cables per turn in the TF coil.	required

Returns:

Type	Description
tuple[float, float]	Tuple containing: - Length of superconductor in one TF coil (in meters). - Total length of superconductor in all TF coils (in meters).

Source code in process/models/tfcoil/superconducting.py

def calculate_cable_in_conduit_superconductor_length(
    self,
    n_tf_coils: int,
    n_tf_coil_turns: int,
    len_tf_coil: float,
    n_tf_turn_superconducting_cables: int,
) -> float:
    """Calculates the total length of superconducting material required for the TF coils.

    Parameters
    ----------
    n_tf_coils: int :
        n_tf_coils: Number of TF coils.
    n_tf_coil_turns: int :
        n_tf_coil_turns: Total number of turns in the TF coil winding pack.
    len_tf_coil:
        len_tf_coil: Length of a single TF coil (in meters).
    n_tf_turn_superconducting_cables: int :
        n_tf_turn_superconducting_cables: Number of superconducting cables per turn in the TF coil.

    Returns
    -------
    tuple[float, float]
        Tuple containing:
        - Length of superconductor in one TF coil (in meters).
        - Total length of superconductor in all TF coils (in meters).
    """

    # Length of superconductor in one TF coil
    len_tf_coil_superconductor = (
        n_tf_coil_turns * len_tf_coil * n_tf_turn_superconducting_cables
    )

    # Total length of superconductor in all TF coils
    len_tf_superconductor_total = len_tf_coil_superconductor * n_tf_coils

    return len_tf_coil_superconductor, len_tf_superconductor_total

output_tf_superconductor_info()

Output TF superconductor information

Source code in process/models/tfcoil/superconducting.py

def output_tf_superconductor_info(self):
    """Output TF superconductor information"""

    po.oheadr(self.outfile, "TF Coils Superconductor Information")
    po.ovarin(
        self.outfile,
        "TF superconductor switch",
        "(i_tf_sc_mat)",
        tfcoil_variables.i_tf_sc_mat,
    )

    po.ocmmnt(
        self.outfile,
        f"Superconductor used: {SUPERCONDUCTING_TF_TYPES[tfcoil_variables.i_tf_sc_mat]}",
    )

    po.ovarre(
        self.outfile,
        "Critical field at zero temperature and strain (T)",
        "(b_tf_superconductor_critical_zero_temp_strain)",
        superconducting_tf_coil_variables.b_tf_superconductor_critical_zero_temp_strain,
    )
    po.ovarre(
        self.outfile,
        "Critical temperature at zero field and strain (K)",
        "(temp_tf_superconductor_critical_zero_field_strain)",
        superconducting_tf_coil_variables.temp_tf_superconductor_critical_zero_field_strain,
    )

    if global_variables.run_tests == 1:
        po.oblnkl(self.outfile)
        po.ocmmnt(
            self.outfile,
            "PROCESS TF Coil peak field fit. Values for t, z and y:",
        )
        po.oblnkl(self.outfile)
        po.ovarre(
            self.outfile,
            "Dimensionless winding pack width",
            "(tf_fit_t)",
            superconducting_tf_coil_variables.tf_fit_t,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Dimensionless winding pack radial thickness",
            "(tf_fit_z)",
            superconducting_tf_coil_variables.tf_fit_z,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Ratio of peak field with ripple to nominal axisymmetric peak field",
            "(f_b_tf_inboard_peak_ripple_symmetric)",
            superconducting_tf_coil_variables.f_b_tf_inboard_peak_ripple_symmetric,
            "OP ",
        )

    po.oblnkl(self.outfile)
    po.ovarre(
        self.outfile,
        "Helium temperature at peak field (= superconductor temperature) (K)",
        "(tftmp)",
        tfcoil_variables.tftmp,
    )
    po.ovarre(
        self.outfile,
        "Total cooling area fraction inside cable space",
        "(f_a_tf_turn_cable_space_cooling)",
        superconducting_tf_coil_variables.f_a_tf_turn_cable_space_cooling,
        "OP ",
    )
    po.ovarre(
        self.outfile,
        "Copper fraction of conductor",
        "(f_a_tf_turn_cable_copper)",
        tfcoil_variables.f_a_tf_turn_cable_copper,
    )
    po.ovarre(
        self.outfile,
        "Residual manufacturing strain on superconductor",
        "(str_tf_con_res)",
        tfcoil_variables.str_tf_con_res,
    )
    po.ovarre(
        self.outfile,
        "Self-consistent strain on superconductor",
        "(str_wp)",
        tfcoil_variables.str_wp,
    )
    po.ovarre(
        self.outfile,
        "Critical current density in superconductor (A/m2)",
        "(j_tf_superconductor_critical)",
        superconducting_tf_coil_variables.j_tf_superconductor_critical,
        "OP ",
    )
    po.ovarre(
        self.outfile,
        "Critical current density in winding pack (A/m2)",
        "(j_tf_wp_critical)",
        tfcoil_variables.j_tf_wp_critical,
        "OP ",
    )
    po.ovarre(
        self.outfile,
        "Actual current density in winding pack (A/m2)",
        "(j_tf_coil_turn)",
        superconducting_tf_coil_variables.j_tf_coil_turn,
        "OP ",
    )

    po.ovarre(
        self.outfile,
        "Minimum allowed temperature margin in superconductor (K)",
        "(temp_tf_superconductor_margin_min)",
        tfcoil_variables.temp_tf_superconductor_margin_min,
    )
    po.ovarre(
        self.outfile,
        "Actual temperature margin in superconductor (K)",
        "(temp_tf_superconductor_margin)",
        tfcoil_variables.temp_tf_superconductor_margin,
        "OP ",
    )
    po.ovarre(
        self.outfile,
        "Critical current (A)",
        "(c_turn_cables_critical)",
        superconducting_tf_coil_variables.c_tf_turn_cables_critical,
        "OP ",
    )
    po.ovarre(
        self.outfile,
        "Actual current (A)",
        "(c_tf_turn)",
        tfcoil_variables.c_tf_turn,
        "OP ",
    )
    po.ovarre(
        self.outfile,
        "Actual current / critical current",
        "(f_c_tf_turn_operating_critical)",
        superconducting_tf_coil_variables.f_c_tf_turn_operating_critical,
        "OP ",
    )
    if superconducting_tf_coil_variables.f_c_tf_turn_operating_critical > 0.7:
        logger.error(
            "f_c_tf_turn_operating_critical shouldn't be above 0.7 for engineering reliability"
        )

    po.ovarre(
        self.outfile,
        "TF Superconductor quench dump time (s)",
        "(t_tf_superconductor_quench)",
        tfcoil_variables.t_tf_superconductor_quench,
        "OP ",
    )
    po.ovarre(
        self.outfile,
        "TF Superconductor quench detection time (s)",
        "(t_tf_quench_detection)",
        tfcoil_variables.t_tf_quench_detection,
        "OP ",
    )
    po.ovarre(
        self.outfile,
        "Maximum winding pack current density for protection (A/m2)",
        "(j_tf_wp_quench_heat_max)",
        tfcoil_variables.j_tf_wp_quench_heat_max,
        "OP ",
    )

calculate_superconductor_temperature_margin(i_tf_superconductor, j_superconductor, b_tf_inboard_peak, strain, bc20m, tc0m, c0, temp_tf_coolant_peak_field)

Calculate the temperature margin of the TF superconductor.

Parameters:

Name	Type	Description	Default
i_tf_superconductor	int	Switch for conductor type: - 1: ITER Nb3Sn, standard parameters - 2: Bi-2212 High Temperature Superconductor - 3: NbTi - 4: ITER Nb3Sn, user-defined parameters - 5: WST Nb3Sn parameterisation - 7: Durham Ginzburg-Landau Nb-Ti parameterisation - 8: Durham Ginzburg-Landau critical surface model for REBCO - 9: Hazelton experimental data + Zhai conceptual model for REBCO	required
j_superconductor	float	Current density in superconductor (A/m²).	required
b_tf_inboard_peak	float	Peak field at conductor (T).	required
strain	float	Strain on superconductor.	required
bc20m	float	Critical field at zero temperature and strain (T).	required
tc0m	float	Critical temperature at zero field and strain (K).	required
c0	float	Constant used in NbTi critical current density calculation (A/m²).	required
temp_tf_coolant_peak_field	float	He temperature at peak field point (K).	required

Returns:

Type	Description
type	temp_tf_superconductor_margin.

Source code in process/models/tfcoil/superconducting.py

def calculate_superconductor_temperature_margin(
    self,
    i_tf_superconductor: int,
    j_superconductor: float,
    b_tf_inboard_peak: float,
    strain: float,
    bc20m: float,
    tc0m: float,
    c0: float,
    temp_tf_coolant_peak_field: float,
):
    """Calculate the temperature margin of the TF superconductor.

    Parameters
    ----------
    i_tf_superconductor:
        Switch for conductor type:
        - 1: ITER Nb3Sn, standard parameters
        - 2: Bi-2212 High Temperature Superconductor
        - 3: NbTi
        - 4: ITER Nb3Sn, user-defined parameters
        - 5: WST Nb3Sn parameterisation
        - 7: Durham Ginzburg-Landau Nb-Ti parameterisation
        - 8: Durham Ginzburg-Landau critical surface model for REBCO
        - 9: Hazelton experimental data + Zhai conceptual model for REBCO
    j_superconductor:
        Current density in superconductor (A/m²).
    b_tf_inboard_peak:
        Peak field at conductor (T).
    strain:
        Strain on superconductor.
    bc20m:
        Critical field at zero temperature and strain (T).
    tc0m:
        Critical temperature at zero field and strain (K).
    c0:
        Constant used in NbTi critical current density calculation (A/m²).
    temp_tf_coolant_peak_field:
        He temperature at peak field point (K).

    Returns
    -------
    type
        temp_tf_superconductor_margin.
    """

    # =================================================================
    # Calculate temperature margin of superconductor

    #  Temperature margin (already calculated in superconductors.bi2212 for i_tf_superconductor=2)

    if i_tf_superconductor in (
        1,
        3,
        4,
        5,
        7,
        8,
        9,
    ):  # Find temperature at which current density margin = 0
        if i_tf_superconductor == 3:
            arguments = (
                i_tf_superconductor,
                j_superconductor,
                b_tf_inboard_peak,
                strain,
                bc20m,
                tc0m,
                c0,
            )
        else:
            arguments = (
                i_tf_superconductor,
                j_superconductor,
                b_tf_inboard_peak,
                strain,
                bc20m,
                tc0m,
            )

        another_estimate = 2 * temp_tf_coolant_peak_field
        (
            t_zero_margin,
            _root_result,
        ) = optimize.newton(
            superconductors.superconductor_current_density_margin,
            temp_tf_coolant_peak_field,
            fprime=None,
            args=arguments,
            tol=1.0e-06,
            maxiter=50,
            fprime2=None,
            x1=another_estimate,
            rtol=1.0e-6,
            full_output=True,
            disp=True,
        )
        # print(root_result)  # Diagnostic for newton method
        temp_tf_superconductor_margin = t_zero_margin - temp_tf_coolant_peak_field
        tfcoil_variables.temp_margin = temp_tf_superconductor_margin

        if temp_tf_superconductor_margin <= 0.0e0:
            logger.error(
                """Negative TFC temperature margin
            temp_tf_superconductor_margin: {temp_tf_superconductor_margin}
            b_tf_inboard_peak: {b_tf_inboard_peak}
            j_superconductor: {j_superconductor}
            """
            )

    return temp_tf_superconductor_margin

quench_heat_protection_current_density(c_tf_turn, e_tf_coil_magnetic_stored, a_tf_turn_cable_space, a_tf_turn, t_tf_quench_dump, f_a_tf_turn_cable_space_conductor, f_a_tf_turn_cable_copper, temp_tf_coolant_peak_field, temp_tf_conductor_quench_max, b_tf_inboard_peak, cu_rrr, t_tf_quench_detection, nflutfmax)

Calculates the maximum conductor current density limited by the protection limit, and the discharge voltage for a TF coil.

Parameters:

Name	Type	Description	Default
c_tf_turn	float	Operating current (A)	required
e_tf_coil_magnetic_stored	float	Energy stored in one TF coil (J)	required
a_tf_turn_cable_space	float	Cable space - inside area (m²)	required
a_tf_turn	float	Area per turn (i.e. entire cable) (m²)	required
t_tf_quench_dump	float	Dump time (s)	required
f_a_tf_turn_cable_space_conductor	float	Fraction of cable space containing conductor	required
f_a_tf_turn_cable_copper	float	Fraction of conductor that is copper	required
temp_tf_coolant_peak_field	float	Helium temperature at peak field point (K)	required
temp_tf_conductor_quench_max	float	Maximum conductor temperature during quench (K)	required
b_tf_inboard_peak	float	Peak magnetic field at conductor (T)	required
cu_rrr	float	Copper residual-resistance-ratio	required
t_tf_quench_detection	float	Quench detection time (s)	required
nflutfmax	float	End-of-life neutron fluence in the copper (1/m²)	required

Returns:

Type	Description
tuple[float, float]	j_tf_wp_quench_protection_max (float): Winding pack current density from temperature rise protection (A/m²) - v_tf_dump_voltage_peak (float): Discharge voltage imposed on a TF coil (V)

References

• L. Bottura, “Magnet Quench 101,” arXiv (Cornell University), Jan. 2014, doi: https://doi.org/10.48550/arxiv.1401.3927.

Source code in process/models/tfcoil/superconducting.py

def quench_heat_protection_current_density(
    self,
    c_tf_turn: float,
    e_tf_coil_magnetic_stored: float,
    a_tf_turn_cable_space: float,
    a_tf_turn: float,
    t_tf_quench_dump: float,
    f_a_tf_turn_cable_space_conductor: float,
    f_a_tf_turn_cable_copper: float,
    temp_tf_coolant_peak_field: float,
    temp_tf_conductor_quench_max: float,
    b_tf_inboard_peak: float,
    cu_rrr: float,
    t_tf_quench_detection: float,
    nflutfmax: float,
) -> tuple[float, float]:
    """Calculates the maximum conductor current density limited by the protection limit,
    and the discharge voltage for a TF coil.

    Parameters
    ----------
    c_tf_turn : float
        Operating current (A)
    e_tf_coil_magnetic_stored : float
        Energy stored in one TF coil (J)
    a_tf_turn_cable_space : float
        Cable space - inside area (m²)
    a_tf_turn : float
        Area per turn (i.e. entire cable) (m²)
    t_tf_quench_dump : float
        Dump time (s)
    f_a_tf_turn_cable_space_conductor : float
        Fraction of cable space containing conductor
    f_a_tf_turn_cable_copper : float
        Fraction of conductor that is copper
    temp_tf_coolant_peak_field : float
        Helium temperature at peak field point (K)
    temp_tf_conductor_quench_max : float
        Maximum conductor temperature during quench (K)
    b_tf_inboard_peak : float
        Peak magnetic field at conductor (T)
    cu_rrr : float
        Copper residual-resistance-ratio
    t_tf_quench_detection : float
        Quench detection time (s)
    nflutfmax : float
        End-of-life neutron fluence in the copper (1/m²)

    Returns
    -------
    tuple[float, float]
        j_tf_wp_quench_protection_max (float): Winding pack current density from temperature rise protection (A/m²)
        - v_tf_dump_voltage_peak (float): Discharge voltage imposed on a TF coil (V)

    References
    ----------
    - L. Bottura, “Magnet Quench 101,” arXiv (Cornell University), Jan. 2014,
    doi: https://doi.org/10.48550/arxiv.1401.3927.
    """

    #  Peak Dump voltage
    v_tf_dump_voltage_peak = (
        2.0e0 * e_tf_coil_magnetic_stored / (t_tf_quench_dump * c_tf_turn)
    )

    # Winding pack current density from temperature rise protection
    j_tf_wp_quench_protection_max = (
        a_tf_turn_cable_space
        / a_tf_turn
        * quench.calculate_quench_protection_current_density(
            t_tf_quench_dump,
            b_tf_inboard_peak,
            f_a_tf_turn_cable_copper,
            1.0 - f_a_tf_turn_cable_space_conductor,
            temp_tf_coolant_peak_field,
            temp_tf_conductor_quench_max,
            cu_rrr,
            t_tf_quench_detection,
            nflutfmax,
        )
    )

    return j_tf_wp_quench_protection_max, v_tf_dump_voltage_peak

vv_stress_on_quench()

Calculate the Tresca stress [Pa] of the Vacuum Vessel (VV) experienced when the TF coil quenches.

Assumes the current center line (CCL) of the TF coil is the middle of the coil.

We assume vertical symmetry which is only true for double null machines.

Source code in process/models/tfcoil/superconducting.py

def vv_stress_on_quench(self):
    """Calculate the Tresca stress [Pa] of the Vacuum Vessel (VV)
    experienced when the TF coil quenches.

    Assumes the current center line (CCL) of the TF coil is the
    middle of the coil.

    We assume vertical symmetry which is only true for double null
    machines.
    """
    H_coil = build_variables.z_tf_inside_half + (build_variables.dr_tf_inboard / 2)
    ri_coil = build_variables.r_tf_inboard_mid
    ro_coil = build_variables.r_tf_outboard_mid
    # NOTE: rm is measured from the outside edge of the coil because thats where
    # the radius of the first ellipse is measured from
    rm_coil = build_variables.r_tf_inboard_out + tfcoil_variables.tfa[0]

    H_vv = (
        build_variables.z_plasma_xpoint_upper
        + build_variables.dz_xpoint_divertor
        + divertor_variables.dz_divertor
        + build_variables.dz_shld_upper
        + (build_variables.dz_vv_upper / 2)
    )
    # ri and ro for VV dont consider the shield widths
    # because it is assumed the shield is on the plasma side
    # of the VV
    ri_vv = build_variables.r_vv_inboard_out - (build_variables.dr_vv_outboard / 2)
    ro_vv = (
        build_variables.r_tf_outboard_mid
        - (build_variables.dr_tf_outboard / 2)
        - build_variables.dr_tf_shld_gap
        - build_variables.dr_shld_thermal_outboard
        - build_variables.dr_shld_vv_gap_outboard
        - (build_variables.dr_vv_outboard / 2)
    )

    # Assume the radius of the first ellipse of the VV is in the same proportion to
    # that of the plasma facing radii of the two structures
    tf_vv_frac = build_variables.r_tf_inboard_out / build_variables.r_vv_inboard_out
    rm_vv = build_variables.r_vv_inboard_out + (tfcoil_variables.tfa[0] * tf_vv_frac)

    superconducting_tf_coil_variables.vv_stress_quench = vv_stress_on_quench(
        # TF shape
        H_coil=H_coil,
        ri_coil=ri_coil,
        ro_coil=ro_coil,
        rm_coil=rm_coil,
        ccl_length_coil=tfcoil_variables.len_tf_coil,
        theta1_coil=tfcoil_variables.theta1_coil,
        # VV shape
        H_vv=H_vv,
        ri_vv=ri_vv,
        ro_vv=ro_vv,
        rm_vv=rm_vv,
        theta1_vv=tfcoil_variables.theta1_vv,
        # TF properties
        n_tf_coils=tfcoil_variables.n_tf_coils,
        n_tf_coil_turns=tfcoil_variables.n_tf_coil_turns,
        # Area of the radial plate taken to be the area of steel in the WP
        # TODO: value clipped due to #1883
        s_rp=np.clip(
            superconducting_tf_coil_variables.a_tf_coil_inboard_steel, 0, None
        ),
        s_cc=superconducting_tf_coil_variables.a_tf_plasma_case
        + superconducting_tf_coil_variables.a_tf_coil_nose_case
        + 2.0 * superconducting_tf_coil_variables.dx_tf_side_case_average,
        taud=tfcoil_variables.t_tf_superconductor_quench,
        # TODO: is this the correct current?
        i_op=superconducting_tf_coil_variables.c_tf_coil
        / tfcoil_variables.n_tf_coil_turns,
        # VV properties
        d_vv=build_variables.dr_vv_shells,
    )

peak_b_tf_inboard_with_ripple(n_tf_coils, dx_tf_wp_primary_toroidal, dr_tf_wp_no_insulation, r_tf_wp_inboard_centre, b_tf_inboard_peak_symmetric)

Calculates the peak toroidal field at the outboard edge of the inboard TF coil winding pack, including the effects of ripple.

For 16, 18, or 20 coils, uses fitting formulae derived by M. Kovari using MAGINT calculations on coil sets based on a DEMO1 case. For other numbers of coils, uses a 9% increase due to ripple from the axisymmetric calculation.

Parameters:

Name	Type	Description	Default
n_tf_coils	float	Number of TF coils.	required
dx_tf_wp_primary_toroidal	float	Width of plasma-facing face of winding pack (m).	required
dr_tf_wp_no_insulation	float	Radial thickness of winding pack with no insulation (e.g. conductor region) (m).	required
r_tf_wp_inboard_centre	float	Major radius of centre of winding pack (m).	required
b_tf_inboard_peak_symmetric	float	Nominal (axisymmetric) peak toroidal field (T).	required

Returns:

Type	Description
tuple[float]	Tuple containing: - b_tf_inboard_peak_with_ripple (float): Peak toroidal field including ripple (T).

Notes

• M. Kovari, Toroidal Field Coils - Maximum Field and Ripple - Parametric Calculation, July 2014.

Source code in process/models/tfcoil/superconducting.py

def peak_b_tf_inboard_with_ripple(
    self,
    n_tf_coils: float,
    dx_tf_wp_primary_toroidal: float,
    dr_tf_wp_no_insulation: float,
    r_tf_wp_inboard_centre: float,
    b_tf_inboard_peak_symmetric: float,
) -> tuple[float, int]:
    """Calculates the peak toroidal field at the outboard edge of the inboard TF coil winding pack,
    including the effects of ripple.

    For 16, 18, or 20 coils, uses fitting formulae derived by M. Kovari using MAGINT calculations
    on coil sets based on a DEMO1 case. For other numbers of coils, uses a 9% increase due to ripple
    from the axisymmetric calculation.

    Parameters
    ----------
    n_tf_coils : float
        Number of TF coils.
    dx_tf_wp_primary_toroidal : float
        Width of plasma-facing face of winding pack (m).
    dr_tf_wp_no_insulation : float
        Radial thickness of winding pack with no insulation (e.g. conductor region) (m).
    r_tf_wp_inboard_centre : float
        Major radius of centre of winding pack (m).
    b_tf_inboard_peak_symmetric : float
        Nominal (axisymmetric) peak toroidal field (T).

    Returns
    -------
    tuple[float]
        Tuple containing:
        - b_tf_inboard_peak_with_ripple (float): Peak toroidal field including ripple (T).

    Notes
    -----
    - M. Kovari, Toroidal Field Coils - Maximum Field and Ripple - Parametric Calculation, July 2014.
    """
    a = np.zeros((4,))

    #  Set fitting coefficients for different numbers of TF coils

    int_n_tf = np.round(n_tf_coils)

    if int_n_tf == 16:
        a[0] = 0.28101e0
        a[1] = 1.8481e0
        a[2] = -0.88159e0
        a[3] = 0.93834e0
    elif int_n_tf == 18:
        a[0] = 0.29153e0
        a[1] = 1.81600e0
        a[2] = -0.84178e0
        a[3] = 0.90426e0
    elif int_n_tf == 20:
        a[0] = 0.29853e0
        a[1] = 1.82130e0
        a[2] = -0.85031e0
        a[3] = 0.89808e0

    else:
        return 1.09e0 * b_tf_inboard_peak_symmetric

    #  Maximum winding pack width before adjacent packs touch
    #  (ignoring the external case and ground wall thicknesses)

    dx_tf_wp_toroidal_max = (
        2.0e0 * r_tf_wp_inboard_centre + dr_tf_wp_no_insulation
    ) * np.tan(np.pi / n_tf_coils)

    #  Dimensionless winding pack width

    superconducting_tf_coil_variables.tf_fit_t = (
        dx_tf_wp_primary_toroidal / dx_tf_wp_toroidal_max
    )
    if (superconducting_tf_coil_variables.tf_fit_t < 0.3e0) or (
        superconducting_tf_coil_variables.tf_fit_t > 1.1e0
    ):
        logger.warning(
            "(TF coil peak field calculation) Winding pack width out of fitted range"
        )

    #  Dimensionless winding pack radial thickness

    superconducting_tf_coil_variables.tf_fit_z = (
        dr_tf_wp_no_insulation / dx_tf_wp_toroidal_max
    )
    if (superconducting_tf_coil_variables.tf_fit_z < 0.26e0) or (
        superconducting_tf_coil_variables.tf_fit_z > 0.7e0
    ):
        # write(*,*) 'PEAK_TF_WITH_RIPPLE: fitting problem; z = ',z
        logger.warning(
            "(TF coil peak field calculation) Winding pack radial thickness out of fitted range"
        )

    #  Ratio of peak field with ripple to nominal axisymmetric peak field

    superconducting_tf_coil_variables.f_b_tf_inboard_peak_ripple_symmetric = (
        a[0]
        + a[1] * np.exp(-superconducting_tf_coil_variables.tf_fit_t)
        + a[2] * superconducting_tf_coil_variables.tf_fit_z
        + a[3]
        * superconducting_tf_coil_variables.tf_fit_z
        * superconducting_tf_coil_variables.tf_fit_t
    )

    return (
        superconducting_tf_coil_variables.f_b_tf_inboard_peak_ripple_symmetric
        * b_tf_inboard_peak_symmetric
    )

sc_tf_internal_geom(i_tf_wp_geom, i_tf_case_geom, i_tf_turns_integer)

Seting the WP, case and turns geometry for SC magnets

Parameters:

Name	Type	Description	Default
i_tf_wp_geom			required
i_tf_case_geom			required
i_tf_turns_integer			required

Source code in process/models/tfcoil/superconducting.py

def sc_tf_internal_geom(self, i_tf_wp_geom, i_tf_case_geom, i_tf_turns_integer):
    """
    Seting the WP, case and turns geometry for SC magnets

    Parameters
    ----------
    i_tf_wp_geom :

    i_tf_case_geom :

    i_tf_turns_integer :

    """

    # Calculating the WP / ground insulation areas
    (
        superconducting_tf_coil_variables.r_tf_wp_inboard_inner,
        superconducting_tf_coil_variables.r_tf_wp_inboard_outer,
        superconducting_tf_coil_variables.r_tf_wp_inboard_centre,
        superconducting_tf_coil_variables.dx_tf_wp_toroidal_min,
        superconducting_tf_coil_variables.dr_tf_wp_no_insulation,
        tfcoil_variables.dx_tf_wp_primary_toroidal,
        tfcoil_variables.dx_tf_wp_secondary_toroidal,
        superconducting_tf_coil_variables.dx_tf_wp_toroidal_average,
        superconducting_tf_coil_variables.a_tf_wp_with_insulation,
        superconducting_tf_coil_variables.a_tf_wp_no_insulation,
        superconducting_tf_coil_variables.a_tf_wp_ground_insulation,
    ) = self.superconducting_tf_wp_geometry(
        i_tf_wp_geom=i_tf_wp_geom,
        r_tf_inboard_in=build_variables.r_tf_inboard_in,
        dr_tf_nose_case=tfcoil_variables.dr_tf_nose_case,
        dr_tf_wp_with_insulation=tfcoil_variables.dr_tf_wp_with_insulation,
        tan_theta_coil=superconducting_tf_coil_variables.tan_theta_coil,
        dx_tf_side_case_min=tfcoil_variables.dx_tf_side_case_min,
        dx_tf_wp_insulation=tfcoil_variables.dx_tf_wp_insulation,
        dx_tf_wp_insertion_gap=tfcoil_variables.dx_tf_wp_insertion_gap,
    )

    # Calculating the TF steel casing areas
    (
        tfcoil_variables.a_tf_coil_inboard_case,
        tfcoil_variables.a_tf_coil_outboard_case,
        superconducting_tf_coil_variables.a_tf_plasma_case,
        superconducting_tf_coil_variables.a_tf_coil_nose_case,
        superconducting_tf_coil_variables.dx_tf_side_case_average,
        superconducting_tf_coil_variables.dx_tf_side_case_peak,
    ) = self.superconducting_tf_case_geometry(
        i_tf_case_geom=i_tf_case_geom,
        i_tf_wp_geom=i_tf_wp_geom,
        a_tf_inboard_total=tfcoil_variables.a_tf_inboard_total,
        n_tf_coils=tfcoil_variables.n_tf_coils,
        a_tf_wp_with_insulation=superconducting_tf_coil_variables.a_tf_wp_with_insulation,
        a_tf_leg_outboard=tfcoil_variables.a_tf_leg_outboard,
        rad_tf_coil_inboard_toroidal_half=superconducting_tf_coil_variables.rad_tf_coil_inboard_toroidal_half,
        r_tf_inboard_out=build_variables.r_tf_inboard_out,
        tan_theta_coil=superconducting_tf_coil_variables.tan_theta_coil,
        r_tf_wp_inboard_outer=superconducting_tf_coil_variables.r_tf_wp_inboard_outer,
        dr_tf_plasma_case=tfcoil_variables.dr_tf_plasma_case,
        r_tf_wp_inboard_inner=superconducting_tf_coil_variables.r_tf_wp_inboard_inner,
        r_tf_inboard_in=build_variables.r_tf_inboard_in,
        dx_tf_side_case_min=tfcoil_variables.dx_tf_side_case_min,
        dr_tf_wp_with_insulation=tfcoil_variables.dr_tf_wp_with_insulation,
    )

    # WP/trun currents
    self.tf_wp_currents()

    # Setting the WP turn geometry / areas
    if i_tf_turns_integer == 0:
        # Non-ingeger number of turns
        (
            tfcoil_variables.a_tf_turn_cable_space_no_void,
            tfcoil_variables.a_tf_turn_steel,
            tfcoil_variables.a_tf_turn_insulation,
            tfcoil_variables.n_tf_coil_turns,
            tfcoil_variables.dx_tf_turn_general,
            tfcoil_variables.c_tf_turn,
            tfcoil_variables.dx_tf_turn_general,
            superconducting_tf_coil_variables.dr_tf_turn,
            superconducting_tf_coil_variables.dx_tf_turn,
            tfcoil_variables.t_conductor,
            superconducting_tf_coil_variables.radius_tf_turn_cable_space_corners,
            superconducting_tf_coil_variables.dx_tf_turn_cable_space_average,
            superconducting_tf_coil_variables.a_tf_turn_cable_space_effective,
            superconducting_tf_coil_variables.f_a_tf_turn_cable_space_cooling,
        ) = self.tf_cable_in_conduit_averaged_turn_geometry(
            j_tf_wp=tfcoil_variables.j_tf_wp,
            dx_tf_turn_steel=tfcoil_variables.dx_tf_turn_steel,
            dx_tf_turn_insulation=tfcoil_variables.dx_tf_turn_insulation,
            i_tf_sc_mat=tfcoil_variables.i_tf_sc_mat,
            dx_tf_turn_general=tfcoil_variables.dx_tf_turn_general,
            c_tf_turn=tfcoil_variables.c_tf_turn,
            i_dx_tf_turn_general_input=tfcoil_variables.i_dx_tf_turn_general_input,
            i_dx_tf_turn_cable_space_general_input=tfcoil_variables.i_dx_tf_turn_cable_space_general_input,
            dx_tf_turn_cable_space_general=tfcoil_variables.dx_tf_turn_cable_space_general,
            layer_ins=tfcoil_variables.layer_ins,
            a_tf_wp_no_insulation=superconducting_tf_coil_variables.a_tf_wp_no_insulation,
            dia_tf_turn_coolant_channel=tfcoil_variables.dia_tf_turn_coolant_channel,
            f_a_tf_turn_cable_space_extra_void=tfcoil_variables.f_a_tf_turn_cable_space_extra_void,
        )

    else:
        # Integer number of turns
        (
            superconducting_tf_coil_variables.radius_tf_turn_cable_space_corners,
            superconducting_tf_coil_variables.dr_tf_turn,
            superconducting_tf_coil_variables.dx_tf_turn,
            tfcoil_variables.a_tf_turn_cable_space_no_void,
            tfcoil_variables.a_tf_turn_steel,
            tfcoil_variables.a_tf_turn_insulation,
            tfcoil_variables.c_tf_turn,
            tfcoil_variables.n_tf_coil_turns,
            superconducting_tf_coil_variables.t_conductor_radial,
            superconducting_tf_coil_variables.t_conductor_toroidal,
            tfcoil_variables.t_conductor,
            superconducting_tf_coil_variables.dr_tf_turn_cable_space,
            superconducting_tf_coil_variables.dx_tf_turn_cable_space,
            superconducting_tf_coil_variables.dx_tf_turn_cable_space_average,
        ) = self.tf_cable_in_conduit_integer_turn_geometry(
            dr_tf_wp_with_insulation=tfcoil_variables.dr_tf_wp_with_insulation,
            dx_tf_wp_insulation=tfcoil_variables.dx_tf_wp_insulation,
            dx_tf_wp_insertion_gap=tfcoil_variables.dx_tf_wp_insertion_gap,
            n_tf_wp_layers=tfcoil_variables.n_tf_wp_layers,
            dx_tf_wp_toroidal_min=superconducting_tf_coil_variables.dx_tf_wp_toroidal_min,
            n_tf_wp_pancakes=tfcoil_variables.n_tf_wp_pancakes,
            c_tf_coil=superconducting_tf_coil_variables.c_tf_coil,
            dx_tf_turn_steel=tfcoil_variables.dx_tf_turn_steel,
            dx_tf_turn_insulation=tfcoil_variables.dx_tf_turn_insulation,
        )

    # Calculate number of cables in turn if CICC conductor
    # ---------------------------------------------------
    if tfcoil_variables.i_tf_sc_mat != 6:
        superconducting_tf_coil_variables.n_tf_turn_superconducting_cables = self.calculate_cable_in_conduit_strand_count(
            a_cable_space=superconducting_tf_coil_variables.a_tf_turn_cable_space_effective,
            dia_superconductor_strand=superconducting_tf_coil_variables.dia_tf_turn_superconducting_cable,
        )

        (
            superconducting_tf_coil_variables.len_tf_coil_superconductor,
            superconducting_tf_coil_variables.len_tf_superconductor_total,
        ) = self.calculate_cable_in_conduit_superconductor_length(
            n_tf_coils=tfcoil_variables.n_tf_coils,
            n_tf_coil_turns=tfcoil_variables.n_tf_coil_turns,
            len_tf_coil=tfcoil_variables.len_tf_coil,
            n_tf_turn_superconducting_cables=superconducting_tf_coil_variables.n_tf_turn_superconducting_cables,
        )

    # Areas and fractions
    # -------------------
    # Central helium channel down the conductor core [m2]
    tfcoil_variables.a_tf_wp_coolant_channels = (
        0.25e0
        * tfcoil_variables.n_tf_coil_turns
        * np.pi
        * tfcoil_variables.dia_tf_turn_coolant_channel**2
    )

    # Total conductor cross-sectional area, taking account of void area
    # and central helium channel [m2]
    tfcoil_variables.a_tf_wp_conductor = (
        tfcoil_variables.a_tf_turn_cable_space_no_void
        * tfcoil_variables.n_tf_coil_turns
        * (1.0e0 - tfcoil_variables.f_a_tf_turn_cable_space_extra_void)
        - tfcoil_variables.a_tf_wp_coolant_channels
    )

    # Void area in conductor for He, not including central channel [m2]
    tfcoil_variables.a_tf_wp_extra_void = (
        tfcoil_variables.a_tf_turn_cable_space_no_void
        * tfcoil_variables.n_tf_coil_turns
        * tfcoil_variables.f_a_tf_turn_cable_space_extra_void
    )

    # Area of inter-turn insulation: total [m2]
    tfcoil_variables.a_tf_coil_wp_turn_insulation = (
        tfcoil_variables.n_tf_coil_turns * tfcoil_variables.a_tf_turn_insulation
    )

    # Area of steel structure in winding pack [m2]
    tfcoil_variables.a_tf_wp_steel = (
        tfcoil_variables.n_tf_coil_turns * tfcoil_variables.a_tf_turn_steel
    )

    # Inboard coil steel area [m2]
    superconducting_tf_coil_variables.a_tf_coil_inboard_steel = (
        tfcoil_variables.a_tf_coil_inboard_case + tfcoil_variables.a_tf_wp_steel
    )

    # Inboard coil steel fraction [-]
    superconducting_tf_coil_variables.f_a_tf_coil_inboard_steel = (
        tfcoil_variables.n_tf_coils
        * superconducting_tf_coil_variables.a_tf_coil_inboard_steel
        / tfcoil_variables.a_tf_inboard_total
    )

    # Inboard coil insulation cross-section [m2]
    superconducting_tf_coil_variables.a_tf_coil_inboard_insulation = (
        tfcoil_variables.a_tf_coil_wp_turn_insulation
        + superconducting_tf_coil_variables.a_tf_wp_ground_insulation
    )

    #  Inboard coil insulation fraction [-]
    superconducting_tf_coil_variables.f_a_tf_coil_inboard_insulation = (
        tfcoil_variables.n_tf_coils
        * superconducting_tf_coil_variables.a_tf_coil_inboard_insulation
        / tfcoil_variables.a_tf_inboard_total
    )

    # Negative areas or fractions error reporting
    if (
        tfcoil_variables.a_tf_wp_conductor <= 0.0e0
        or tfcoil_variables.a_tf_wp_extra_void <= 0.0e0
        or tfcoil_variables.a_tf_coil_wp_turn_insulation <= 0.0e0
        or tfcoil_variables.a_tf_wp_steel <= 0.0e0
        or superconducting_tf_coil_variables.a_tf_coil_inboard_steel <= 0.0e0
        or superconducting_tf_coil_variables.f_a_tf_coil_inboard_steel <= 0.0e0
        or superconducting_tf_coil_variables.a_tf_coil_inboard_insulation <= 0.0e0
        or superconducting_tf_coil_variables.f_a_tf_coil_inboard_insulation <= 0.0e0
    ):
        logger.error(
            "One of the areas or fractions is negative in the internal SC TF coil geometry"
            f"{tfcoil_variables.a_tf_wp_conductor=} {tfcoil_variables.a_tf_wp_extra_void=}"
            f"{tfcoil_variables.a_tf_coil_wp_turn_insulation=} {tfcoil_variables.a_tf_wp_steel=}"
            f"{superconducting_tf_coil_variables.a_tf_coil_inboard_steel=} {superconducting_tf_coil_variables.f_a_tf_coil_inboard_steel=}"
            f"{superconducting_tf_coil_variables.a_tf_coil_inboard_insulation=} {superconducting_tf_coil_variables.f_a_tf_coil_inboard_insulation=}"
        )

superconducting_tf_wp_geometry(i_tf_wp_geom, r_tf_inboard_in, dr_tf_nose_case, dr_tf_wp_with_insulation, tan_theta_coil, dx_tf_side_case_min, dx_tf_wp_insulation, dx_tf_wp_insertion_gap)

Calculates the winding pack (WP) geometry and cross-sectional areas for superconducting toroidal field (TF) coils.

Parameters:

Name	Type	Description	Default
i_tf_wp_geom	int	0: Rectangular - 1: Double rectangular - 2: Trapezoidal	required
r_tf_inboard_in	float	Inboard inner radius [m].	required
dr_tf_nose_case	float	Radial thickness of nose case [m].	required
dr_tf_wp_with_insulation	float	Radial thickness of winding pack including insulation [m].	required
tan_theta_coil	float	Tangent of coil half angle [-].	required
dx_tf_side_case_min	float	Side case thickness [m].	required
dx_tf_wp_insulation	float	Insulation thickness [m].	required
dx_tf_wp_insertion_gap	float	Insertion gap thickness [m].	required

Returns:

Type

Description

tuple[float, float, float, float, float, float, float, float, float, float]

Tuple containing: - r_tf_wp_inboard_inner (float): WP inboard inner radius [m] - r_tf_wp_inboard_outer (float): WP inboard outer radius [m] - r_tf_wp_inboard_centre (float): WP inboard centre radius [m] - dx_tf_wp_toroidal_min (float): Minimal toroidal thickness of WP [m] - dr_tf_wp_no_insulation (float): Radial thickness of winding pack without insulation [m] - dx_tf_wp_primary_toroidal (float): Primary toroidal thickness [m] - dx_tf_wp_secondary_toroidal (float): Secondary toroidal thickness [m] - dx_tf_wp_toroidal_average (float): Averaged toroidal thickness [m] - a_tf_wp_with_insulation (float): WP cross-sectional area with insulation [m²] - a_tf_wp_no_insulation (float): WP cross-sectional area without insulation [m²] - a_tf_wp_ground_insulation (float): WP ground insulation cross-sectional area [m²]

Raises:

Type	Description
ValueError	If calculated winding pack area (with or without insulation) is non-positive.

Source code in process/models/tfcoil/superconducting.py

def superconducting_tf_wp_geometry(
    self,
    i_tf_wp_geom: int,
    r_tf_inboard_in: float,
    dr_tf_nose_case: float,
    dr_tf_wp_with_insulation: float,
    tan_theta_coil: float,
    dx_tf_side_case_min: float,
    dx_tf_wp_insulation: float,
    dx_tf_wp_insertion_gap: float,
) -> tuple[
    float,  # r_tf_wp_inboard_inner
    float,  # r_tf_wp_inboard_outer
    float,  # r_tf_wp_inboard_centre
    float,  # dx_tf_wp_toroidal_min
    float,  # dr_tf_wp_no_insulation
    float,  # dx_tf_wp_primary_toroidal
    float,  # dx_tf_wp_secondary_toroidal
    float,  # dx_tf_wp_toroidal_average
    float,  # a_tf_wp_with_insulation
    float,  # a_tf_wp_no_insulation
    float,  # a_tf_wp_ground_insulation
]:
    """Calculates the winding pack (WP) geometry and cross-sectional areas for superconducting toroidal field (TF) coils.

    Parameters
    ----------
    i_tf_wp_geom : int
        0: Rectangular
        - 1: Double rectangular
        - 2: Trapezoidal
    r_tf_inboard_in : float
        Inboard inner radius [m].
    dr_tf_nose_case : float
        Radial thickness of nose case [m].
    dr_tf_wp_with_insulation : float
        Radial thickness of winding pack including insulation [m].
    tan_theta_coil : float
        Tangent of coil half angle [-].
    dx_tf_side_case_min : float
        Side case thickness [m].
    dx_tf_wp_insulation : float
        Insulation thickness [m].
    dx_tf_wp_insertion_gap : float
        Insertion gap thickness [m].

    Returns
    -------
    tuple[float, float, float, float, float, float, float, float, float, float]
        Tuple containing:
        - r_tf_wp_inboard_inner (float): WP inboard inner radius [m]
        - r_tf_wp_inboard_outer (float): WP inboard outer radius [m]
        - r_tf_wp_inboard_centre (float): WP inboard centre radius [m]
        - dx_tf_wp_toroidal_min (float): Minimal toroidal thickness of WP [m]
        - dr_tf_wp_no_insulation (float): Radial thickness of winding pack without insulation [m]
        - dx_tf_wp_primary_toroidal (float): Primary toroidal thickness [m]
        - dx_tf_wp_secondary_toroidal (float): Secondary toroidal thickness [m]
        - dx_tf_wp_toroidal_average (float): Averaged toroidal thickness [m]
        - a_tf_wp_with_insulation (float): WP cross-sectional area with insulation [m²]
        - a_tf_wp_no_insulation (float): WP cross-sectional area without insulation [m²]
        - a_tf_wp_ground_insulation (float): WP ground insulation cross-sectional area [m²]

    Raises
    ------
    ValueError
        If calculated winding pack area (with or without insulation) is non-positive.
    """

    r_tf_wp_inboard_inner = r_tf_inboard_in + dr_tf_nose_case

    # Radial position of outer edge of winding pack [m]
    r_tf_wp_inboard_outer = r_tf_wp_inboard_inner + dr_tf_wp_with_insulation

    # Radius of geometrical centre of winding pack [m]
    r_tf_wp_inboard_centre = 0.5e0 * (r_tf_wp_inboard_inner + r_tf_wp_inboard_outer)

    # TF toroidal thickness at the WP inner radius [m]
    dx_tf_wp_inner_toroidal = 2.0e0 * r_tf_wp_inboard_inner * tan_theta_coil

    # Minimal toroidal thickness of winding pack [m]
    dx_tf_wp_toroidal_min = dx_tf_wp_inner_toroidal - 2.0e0 * dx_tf_side_case_min

    # Radial thickness of winding pack without insulation (e.g. the conductor region) [m]
    dr_tf_wp_no_insulation = dr_tf_wp_with_insulation - 2.0e0 * (
        dx_tf_wp_insulation + dx_tf_wp_insertion_gap
    )

    # Rectangular WP
    # --------------
    if i_tf_wp_geom == 0:
        # Outer WP layer toroidal thickness [m]
        dx_tf_wp_primary_toroidal = dx_tf_wp_toroidal_min

        # No secondary WP here but will set for consistency
        dx_tf_wp_secondary_toroidal = dx_tf_wp_toroidal_min

        # Averaged toroidal thickness of of winding pack [m]
        dx_tf_wp_toroidal_average = dx_tf_wp_toroidal_min

        # Total cross-sectional area of winding pack [m²]
        a_tf_wp_with_insulation = (
            dr_tf_wp_with_insulation * dx_tf_wp_primary_toroidal
        )

        # WP cross-section without insertion gap and ground insulation [m²]
        a_tf_wp_no_insulation = (
            dr_tf_wp_with_insulation
            - 2.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
        ) * (
            dx_tf_wp_primary_toroidal
            - 2.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
        )

        # Cross-section area of the WP ground insulation [m²]
        a_tf_wp_ground_insulation = (
            dr_tf_wp_with_insulation - 2.0e0 * dx_tf_wp_insertion_gap
        ) * (
            dx_tf_wp_primary_toroidal - 2.0e0 * dx_tf_wp_insertion_gap
        ) - a_tf_wp_no_insulation

    # Double rectangular WP
    # ---------------------
    elif i_tf_wp_geom == 1:
        # Thickness of winding pack section at R > superconducting_tf_coil_variables.r_tf_wp_inboard_centre [m]
        dx_tf_wp_primary_toroidal = 2.0e0 * (
            r_tf_wp_inboard_centre * tan_theta_coil - dx_tf_side_case_min
        )

        # Thickness of winding pack section at R < superconducting_tf_coil_variables.r_tf_wp_inboard_centre [m]
        dx_tf_wp_secondary_toroidal = 2.0e0 * (
            r_tf_wp_inboard_inner * tan_theta_coil - dx_tf_side_case_min
        )

        # Averaged toroidal thickness of of winding pack [m]
        dx_tf_wp_toroidal_average = 0.5e0 * (
            dx_tf_wp_primary_toroidal + dx_tf_wp_secondary_toroidal
        )

        # Total cross-sectional area of winding pack [m²]
        # Including ground insulation and insertion gap
        a_tf_wp_with_insulation = (
            dr_tf_wp_with_insulation * dx_tf_wp_toroidal_average
        )

        # WP cross-section without insertion gap and ground insulation [m²]
        a_tf_wp_no_insulation = (
            0.5e0
            * (
                dr_tf_wp_with_insulation
                - 2.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
            )
            * (
                dx_tf_wp_primary_toroidal
                + dx_tf_wp_secondary_toroidal
                - 4.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
            )
        )

        # Cross-section area of the WP ground insulation [m²]
        a_tf_wp_ground_insulation = (
            0.5e0
            * (dr_tf_wp_with_insulation - 2.0e0 * dx_tf_wp_insertion_gap)
            * (
                dx_tf_wp_primary_toroidal
                + dx_tf_wp_secondary_toroidal
                - 4.0e0 * dx_tf_wp_insertion_gap
            )
            - a_tf_wp_no_insulation
        )

    # Trapezoidal WP
    # --------------
    else:
        # Thickness of winding pack section at r_tf_wp_inboard_outer [m]
        dx_tf_wp_primary_toroidal = 2.0e0 * (
            r_tf_wp_inboard_outer * tan_theta_coil - dx_tf_side_case_min
        )

        # Thickness of winding pack section at r_tf_wp_inboard_inner [m]
        dx_tf_wp_secondary_toroidal = 2.0e0 * (
            r_tf_wp_inboard_inner * tan_theta_coil - dx_tf_side_case_min
        )

        # Averaged toroidal thickness of of winding pack [m]
        dx_tf_wp_toroidal_average = 0.5e0 * (
            dx_tf_wp_primary_toroidal + dx_tf_wp_secondary_toroidal
        )

        # Total cross-sectional area of winding pack [m²]
        # Including ground insulation and insertion gap
        a_tf_wp_with_insulation = (
            dr_tf_wp_with_insulation
            * 0.5
            * (dx_tf_wp_primary_toroidal + dx_tf_wp_secondary_toroidal)
        )

        # WP cross-section without insertion gap and ground insulation [m²]
        a_tf_wp_no_insulation = (
            (
                dr_tf_wp_with_insulation
                - 2.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
            )
            * (
                (
                    dx_tf_wp_secondary_toroidal
                    - 2.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
                )
                + (
                    dx_tf_wp_primary_toroidal
                    - 2.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
                )
            )
            / 2
        )

        # Cross-section area of the WP ground insulation [m²]
        a_tf_wp_ground_insulation = (
            dr_tf_wp_with_insulation - 2.0e0 * dx_tf_wp_insertion_gap
        ) * (
            (
                (dx_tf_wp_primary_toroidal - 2.0e0 * dx_tf_wp_insertion_gap)
                + (dx_tf_wp_secondary_toroidal - 2.0e0 * dx_tf_wp_insertion_gap)
            )
            / 2
        ) - a_tf_wp_no_insulation

    # --------------
    # Negative WP area error reporting
    if a_tf_wp_no_insulation <= 0.0e0 or a_tf_wp_with_insulation <= 0.0e0:
        logger.error(
            f"Winding pack cross-section problem... {a_tf_wp_no_insulation=} {a_tf_wp_with_insulation=}"
        )

    return (
        r_tf_wp_inboard_inner,
        r_tf_wp_inboard_outer,
        r_tf_wp_inboard_centre,
        dx_tf_wp_toroidal_min,
        dr_tf_wp_no_insulation,
        dx_tf_wp_primary_toroidal,
        dx_tf_wp_secondary_toroidal,
        dx_tf_wp_toroidal_average,
        a_tf_wp_with_insulation,
        a_tf_wp_no_insulation,
        a_tf_wp_ground_insulation,
    )

superconducting_tf_case_geometry(i_tf_wp_geom, i_tf_case_geom, a_tf_inboard_total, n_tf_coils, a_tf_wp_with_insulation, a_tf_leg_outboard, rad_tf_coil_inboard_toroidal_half, r_tf_inboard_out, tan_theta_coil, r_tf_wp_inboard_outer, dr_tf_plasma_case, r_tf_wp_inboard_inner, r_tf_inboard_in, dx_tf_side_case_min, dr_tf_wp_with_insulation)

Setting the case geometry and area for SC magnets

Parameters:

Name	Type	Description	Default
i_tf_wp_geom	int	Index specifying winding pack geometry (0: rectangular, 1: double rectangular, else: trapezoidal).	required
i_tf_case_geom	int	Index specifying case geometry (0: circular, else: straight).	required
a_tf_inboard_total	float	Total inboard area for TF coils [m²].	required
n_tf_coils	float	Number of TF coils.	required
a_tf_wp_with_insulation	float	Area of winding pack with insulation [m²].	required
a_tf_leg_outboard	float	Outboard leg cross-sectional area [m²].	required
rad_tf_coil_inboard_toroidal_half	float	Half toroidal radius of inboard coil [m].	required
r_tf_inboard_out	float	Outer radius of inboard TF coil [m].	required
tan_theta_coil	float	Tangent of coil angle theta.	required
r_tf_wp_inboard_outer	float	Outer radius of inboard winding pack [m].	required
dr_tf_plasma_case	float	Radial thickness of plasma case [m].	required
r_tf_wp_inboard_inner	float	Inner radius of inboard winding pack [m].	required
r_tf_inboard_in	float	Inner radius of inboard TF coil [m].	required
dx_tf_side_case_min	float	Minimum lateral casing thickness [m].	required
dr_tf_wp_with_insulation	float	Radial thickness of winding pack with insulation [m].	required

Returns:

Type	Description
tuple[float, float, float, float, float]	Tuple containing: - a_tf_coil_inboard_case (float): Inboard case area [m²]. - a_tf_coil_outboard_case (float): Outboard case area [m²]. - a_tf_plasma_case (float): Front casing area [m²]. - a_tf_coil_nose_case (float): Nose casing area [m²]. - dx_tf_side_case_average (float): Average lateral casing thickness [m]. - dx_tf_side_case_peak (float): Peak lateral casing thickness [m].

Source code in process/models/tfcoil/superconducting.py

def superconducting_tf_case_geometry(
    self,
    i_tf_wp_geom: int,
    i_tf_case_geom: int,
    a_tf_inboard_total: float,
    n_tf_coils: float,
    a_tf_wp_with_insulation: float,
    a_tf_leg_outboard: float,
    rad_tf_coil_inboard_toroidal_half: float,
    r_tf_inboard_out: float,
    tan_theta_coil: float,
    r_tf_wp_inboard_outer: float,
    dr_tf_plasma_case: float,
    r_tf_wp_inboard_inner: float,
    r_tf_inboard_in: float,
    dx_tf_side_case_min: float,
    dr_tf_wp_with_insulation: float,
) -> tuple[float, float, float, float, float, float]:
    """Setting the case geometry and area for SC magnets

    Parameters
    ----------
    i_tf_wp_geom : int
        Index specifying winding pack geometry (0: rectangular, 1: double rectangular, else: trapezoidal).
    i_tf_case_geom : int
        Index specifying case geometry (0: circular, else: straight).
    a_tf_inboard_total : float
        Total inboard area for TF coils [m²].
    n_tf_coils : float
        Number of TF coils.
    a_tf_wp_with_insulation : float
        Area of winding pack with insulation [m²].
    a_tf_leg_outboard : float
        Outboard leg cross-sectional area [m²].
    rad_tf_coil_inboard_toroidal_half : float
        Half toroidal radius of inboard coil [m].
    r_tf_inboard_out : float
        Outer radius of inboard TF coil [m].
    tan_theta_coil : float
        Tangent of coil angle theta.
    r_tf_wp_inboard_outer : float
        Outer radius of inboard winding pack [m].
    dr_tf_plasma_case : float
        Radial thickness of plasma case [m].
    r_tf_wp_inboard_inner : float
        Inner radius of inboard winding pack [m].
    r_tf_inboard_in : float
        Inner radius of inboard TF coil [m].
    dx_tf_side_case_min : float
        Minimum lateral casing thickness [m].
    dr_tf_wp_with_insulation : float
        Radial thickness of winding pack with insulation [m].

    Returns
    -------
    tuple[float, float, float, float, float]
        Tuple containing:
        - a_tf_coil_inboard_case (float): Inboard case area [m²].
        - a_tf_coil_outboard_case (float): Outboard case area [m²].
        - a_tf_plasma_case (float): Front casing area [m²].
        - a_tf_coil_nose_case (float): Nose casing area [m²].
        - dx_tf_side_case_average (float): Average lateral casing thickness [m].
        - dx_tf_side_case_peak (float): Peak lateral casing thickness [m].
    """

    # Total area of inboard TF coil case [m²]
    a_tf_coil_inboard_case = (
        a_tf_inboard_total / n_tf_coils
    ) - a_tf_wp_with_insulation

    # Outboard leg cross-sectional area of surrounding case [m²]
    a_tf_coil_outboard_case = a_tf_leg_outboard - a_tf_wp_with_insulation

    # Front casing area [m²]
    if i_tf_case_geom == 0:
        # Circular front case
        a_tf_plasma_case = (
            rad_tf_coil_inboard_toroidal_half * r_tf_inboard_out**2
        ) - (tan_theta_coil * r_tf_wp_inboard_outer**2)
    else:
        # Straight front case [m²]
        a_tf_plasma_case = (
            (r_tf_wp_inboard_outer + dr_tf_plasma_case) ** 2
            - r_tf_wp_inboard_outer**2
        ) * tan_theta_coil

    # Nose casing area [m²]
    a_tf_coil_nose_case = (
        tan_theta_coil * r_tf_wp_inboard_inner**2
        - rad_tf_coil_inboard_toroidal_half * r_tf_inboard_in**2
    )

    # Report error if the casing area is negative
    if a_tf_coil_inboard_case <= 0.0e0 or a_tf_coil_outboard_case <= 0.0e0:
        logger.error(
            f"Winding pack cross-section problem... {a_tf_coil_inboard_case=} {a_tf_coil_outboard_case=}"
        )

    # Average lateral casing thickness [m]
    # --------------
    # Rectangular casing
    if i_tf_wp_geom == 0:
        dx_tf_side_case_average = (
            dx_tf_side_case_min + 0.5e0 * tan_theta_coil * dr_tf_wp_with_insulation
        )

    # Double rectangular WP
    elif i_tf_wp_geom == 1:
        dx_tf_side_case_average = (
            dx_tf_side_case_min + 0.25e0 * tan_theta_coil * dr_tf_wp_with_insulation
        )

    # Trapezoidal WP
    else:
        dx_tf_side_case_average = dx_tf_side_case_min

    # Peak lateral casing thickness [m]
    # --------------
    # Rectangular casing

    if i_tf_wp_geom == 0:
        dx_tf_side_case_peak = (
            dx_tf_side_case_min + tan_theta_coil * dr_tf_wp_with_insulation
        )
    # Double rectangular WP
    elif i_tf_wp_geom == 1:
        dx_tf_side_case_peak = (
            dx_tf_side_case_min + 0.5 * tan_theta_coil * dr_tf_wp_with_insulation
        )

    # Trapezoidal WP
    # Constant thickness so min = average
    else:
        dx_tf_side_case_peak = dx_tf_side_case_min

    return (
        a_tf_coil_inboard_case,
        a_tf_coil_outboard_case,
        a_tf_plasma_case,
        a_tf_coil_nose_case,
        dx_tf_side_case_average,
        dx_tf_side_case_peak,
    )

tf_cable_in_conduit_integer_turn_geometry(dr_tf_wp_with_insulation, dx_tf_wp_insulation, dx_tf_wp_insertion_gap, n_tf_wp_layers, dx_tf_wp_toroidal_min, n_tf_wp_pancakes, c_tf_coil, dx_tf_turn_steel, dx_tf_turn_insulation)

Set the TF WP turn geometry for superconducting magnets using the number of turn rows in the radial direction. The turns can have any rectangular shape.

This calculation checks if a turn can exist (positive cable space) and provides its dimensions, areas, and associated current.

Parameters:

Name	Type	Description	Default
dr_tf_wp_with_insulation	float	Radial thickness of winding pack with insulation [m].	required
dx_tf_wp_insulation	float	Thickness of winding pack insulation [m].	required
dx_tf_wp_insertion_gap	float	Thickness of winding pack insertion gap [m].	required
n_tf_wp_layers	int	Number of winding pack layers (radial direction).	required
dx_tf_wp_toroidal_min	float	Minimum toroidal thickness of winding pack [m].	required
n_tf_wp_pancakes	int	Number of winding pack pancakes (toroidal direction).	required
c_tf_coil	float	Total TF coil current [A].	required
dx_tf_turn_steel	float	Thickness of turn steel [m].	required
dx_tf_turn_insulation	float	Thickness of turn insulation [m].	required

Returns:

Type	Description
type	tuple containing: - radius_tf_turn_cable_space_corners - dr_tf_turn - dx_tf_turn - a_tf_turn_cable_space_no_void - a_tf_turn_steel - a_tf_turn_insulation - c_tf_turn - n_tf_coil_turns - t_conductor_radial - t_conductor_toroidal - t_conductor - dr_tf_turn_cable_space - dx_tf_turn_cable_space - dx_tf_turn_cable_space_average

Source code in process/models/tfcoil/superconducting.py

def tf_cable_in_conduit_integer_turn_geometry(
    self,
    dr_tf_wp_with_insulation: float,
    dx_tf_wp_insulation: float,
    dx_tf_wp_insertion_gap: float,
    n_tf_wp_layers: int,
    dx_tf_wp_toroidal_min: float,
    n_tf_wp_pancakes: int,
    c_tf_coil: float,
    dx_tf_turn_steel: float,
    dx_tf_turn_insulation: float,
) -> tuple[
    float,  # radius_tf_turn_cable_space_corners
    float,  # dr_tf_turn
    float,  # dx_tf_turn
    float,  # a_tf_turn_cable_space_no_void
    float,  # a_tf_turn_steel
    float,  # a_tf_turn_insulation
    float,  # c_tf_turn
    float,  # n_tf_coil_turns
    float,  # t_conductor_radial
    float,  # t_conductor_toroidal
    float,  # t_conductor
    float,  # dr_tf_turn_cable_space
    float,  # dx_tf_turn_cable_space
    float,  # dx_tf_turn_cable_space_average
]:
    """Set the TF WP turn geometry for superconducting magnets using the number of turn rows in the radial direction.
    The turns can have any rectangular shape.

    This calculation checks if a turn can exist (positive cable space) and provides its dimensions, areas, and associated current.

    Parameters
    ----------
    dr_tf_wp_with_insulation : float
        Radial thickness of winding pack with insulation [m].
    dx_tf_wp_insulation : float
        Thickness of winding pack insulation [m].
    dx_tf_wp_insertion_gap : float
        Thickness of winding pack insertion gap [m].
    n_tf_wp_layers : int
        Number of winding pack layers (radial direction).
    dx_tf_wp_toroidal_min : float
        Minimum toroidal thickness of winding pack [m].
    n_tf_wp_pancakes : int
        Number of winding pack pancakes (toroidal direction).
    c_tf_coil : float
        Total TF coil current [A].
    dx_tf_turn_steel : float
        Thickness of turn steel [m].
    dx_tf_turn_insulation : float
        Thickness of turn insulation [m].

    Returns
    -------
    type
        tuple containing:
        - radius_tf_turn_cable_space_corners
        - dr_tf_turn
        - dx_tf_turn
        - a_tf_turn_cable_space_no_void
        - a_tf_turn_steel
        - a_tf_turn_insulation
        - c_tf_turn
        - n_tf_coil_turns
        - t_conductor_radial
        - t_conductor_toroidal
        - t_conductor
        - dr_tf_turn_cable_space
        - dx_tf_turn_cable_space
        - dx_tf_turn_cable_space_average
    """

    # Radius of rounded corners in the cable space [m]
    radius_tf_turn_cable_space_corners = dx_tf_turn_steel * 0.75e0

    # Radial turn dimension [m]
    dr_tf_turn = (
        dr_tf_wp_with_insulation
        - 2.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
    ) / n_tf_wp_layers

    if dr_tf_turn <= (2.0e0 * dx_tf_turn_insulation + 2.0e0 * dx_tf_turn_steel):
        logger.error(
            "Negative cable space dimension; reduce conduit thicknesses or raise c_tf_turn. "
            f"{dr_tf_turn=} {dx_tf_turn_insulation=} {dx_tf_turn_steel=}"
        )

    # Toroidal turn dimension [m]
    dx_tf_turn = (
        dx_tf_wp_toroidal_min
        - 2.0e0 * (dx_tf_wp_insulation + dx_tf_wp_insertion_gap)
    ) / n_tf_wp_pancakes

    if dx_tf_turn <= (2.0e0 * dx_tf_turn_insulation + 2.0e0 * dx_tf_turn_steel):
        logger.error(
            "Negative cable space dimension; reduce conduit thicknesses or raise c_tf_turn. "
            f"{dx_tf_turn=} {dx_tf_turn_insulation=} {dx_tf_turn_steel=}"
        )

    # Average turn dimension [m]
    tfcoil_variables.dx_tf_turn_general = np.sqrt(dr_tf_turn * dx_tf_turn)

    # Number of TF turns
    n_tf_coil_turns = np.double(n_tf_wp_layers * n_tf_wp_pancakes)

    # Current per turn [A/turn]
    c_tf_turn = c_tf_coil / n_tf_coil_turns

    # Radial and toroidal dimension of conductor [m]
    t_conductor_radial = dr_tf_turn - 2.0e0 * dx_tf_turn_insulation
    t_conductor_toroidal = dx_tf_turn - 2.0e0 * dx_tf_turn_insulation
    t_conductor = np.sqrt(t_conductor_radial * t_conductor_toroidal)

    # Dimension of square cable space inside conduit [m]
    dr_tf_turn_cable_space = t_conductor_radial - 2.0e0 * dx_tf_turn_steel
    dx_tf_turn_cable_space = t_conductor_toroidal - 2.0e0 * dx_tf_turn_steel
    dx_tf_turn_cable_space_average = np.sqrt(
        dr_tf_turn_cable_space * dx_tf_turn_cable_space
    )

    # Cross-sectional area of cable space per turn
    # taking account of rounded inside corners [m²]
    a_tf_turn_cable_space_no_void = (
        dr_tf_turn_cable_space * dx_tf_turn_cable_space
    ) - (4.0e0 - np.pi) * radius_tf_turn_cable_space_corners**2

    # Calculate the true effective cable space by taking away the cooling
    # channel and the extra void fraction
    superconducting_tf_coil_variables.a_tf_turn_cable_space_effective = (
        a_tf_turn_cable_space_no_void
        -
        # Coolant channel area
        (
            (np.pi / 4.0e0)
            * tfcoil_variables.dia_tf_turn_coolant_channel
            * tfcoil_variables.dia_tf_turn_coolant_channel
        )
        # Additional void area deduction
        - (
            a_tf_turn_cable_space_no_void
            * tfcoil_variables.f_a_tf_turn_cable_space_extra_void
        )
    )

    superconducting_tf_coil_variables.f_a_tf_turn_cable_space_cooling = 1 - (
        superconducting_tf_coil_variables.a_tf_turn_cable_space_effective
        / a_tf_turn_cable_space_no_void
    )

    if a_tf_turn_cable_space_no_void <= 0.0e0:
        if (dr_tf_turn_cable_space < 0.0e0) or (dx_tf_turn_cable_space < 0.0e0):
            logger.error(
                f"Negative cable space dimension. {a_tf_turn_cable_space_no_void=} "
                f"{dr_tf_turn_cable_space=} {dx_tf_turn_cable_space=}"
            )
        else:
            logger.error(
                "Cable space area problem; artificially set rounded corner radius to 0. "
                f"{a_tf_turn_cable_space_no_void=} {dr_tf_turn_cable_space=}"
                f" {dx_tf_turn_cable_space=}"
            )
            radius_tf_turn_cable_space_corners = 0.0e0
            a_tf_turn_cable_space_no_void = (
                dr_tf_turn_cable_space * dx_tf_turn_cable_space
            )

    # Cross-sectional area of conduit jacket per turn [m²]
    a_tf_turn_steel = (
        t_conductor_radial * t_conductor_toroidal - a_tf_turn_cable_space_no_void
    )

    # Area of inter-turn insulation: single turn [m²]
    a_tf_turn_insulation = (
        dr_tf_turn * dx_tf_turn - a_tf_turn_steel - a_tf_turn_cable_space_no_void
    )
    return (
        radius_tf_turn_cable_space_corners,
        dr_tf_turn,
        dx_tf_turn,
        a_tf_turn_cable_space_no_void,
        a_tf_turn_steel,
        a_tf_turn_insulation,
        c_tf_turn,
        n_tf_coil_turns,
        t_conductor_radial,
        t_conductor_toroidal,
        t_conductor,
        dr_tf_turn_cable_space,
        dx_tf_turn_cable_space,
        dx_tf_turn_cable_space_average,
    )

tf_wp_currents()

Turn engineering turn currents/densities

Source code in process/models/tfcoil/superconducting.py

def tf_wp_currents(self):
    """
    Turn engineering turn currents/densities
    """
    tfcoil_variables.j_tf_wp = max(
        1.0e0,
        tfcoil_variables.c_tf_total
        / (
            tfcoil_variables.n_tf_coils
            * superconducting_tf_coil_variables.a_tf_wp_no_insulation
        ),
    )

tf_cable_in_conduit_averaged_turn_geometry(j_tf_wp, dx_tf_turn_steel, dx_tf_turn_insulation, i_tf_sc_mat, dx_tf_turn_general, c_tf_turn, i_dx_tf_turn_general_input, i_dx_tf_turn_cable_space_general_input, dx_tf_turn_cable_space_general, layer_ins, a_tf_wp_no_insulation, dia_tf_turn_coolant_channel, f_a_tf_turn_cable_space_extra_void)

subroutine straight from Python, see comments in tf_averaged_turn_geom_wrapper Setting the TF WP turn geometry for SC magnets from the number the current per turn. This calculation has two purposes, first to check if a turn can exist (positive cable space) and the second to provide its dimensions, areas and the (float) number of turns

Parameters:

Name	Type	Description	Default
j_tf_wp			required
dx_tf_turn_steel			required
dx_tf_turn_insulation			required
i_tf_sc_mat			required
dx_tf_turn_general			required
c_tf_turn			required
i_dx_tf_turn_general_input			required
i_dx_tf_turn_cable_space_general_input			required
dx_tf_turn_cable_space_general			required
layer_ins			required
a_tf_wp_no_insulation			required
dia_tf_turn_coolant_channel			required
f_a_tf_turn_cable_space_extra_void			required

Source code in process/models/tfcoil/superconducting.py

def tf_cable_in_conduit_averaged_turn_geometry(
    self,
    j_tf_wp,
    dx_tf_turn_steel,
    dx_tf_turn_insulation,
    i_tf_sc_mat,
    dx_tf_turn_general,
    c_tf_turn,
    i_dx_tf_turn_general_input,
    i_dx_tf_turn_cable_space_general_input,
    dx_tf_turn_cable_space_general,
    layer_ins,
    a_tf_wp_no_insulation,
    dia_tf_turn_coolant_channel,
    f_a_tf_turn_cable_space_extra_void,
):
    """subroutine straight from Python, see comments in tf_averaged_turn_geom_wrapper
    Setting the TF WP turn geometry for SC magnets from the number
    the current per turn.
    This calculation has two purposes, first to check if a turn can exist
    (positive cable space) and the second to provide its dimensions,
    areas and the (float) number of turns

    Parameters
    ----------
    j_tf_wp :

    dx_tf_turn_steel :

    dx_tf_turn_insulation :

    i_tf_sc_mat :

    dx_tf_turn_general :

    c_tf_turn :

    i_dx_tf_turn_general_input :

    i_dx_tf_turn_cable_space_general_input :

    dx_tf_turn_cable_space_general :

    layer_ins :

    a_tf_wp_no_insulation :

    dia_tf_turn_coolant_channel :

    f_a_tf_turn_cable_space_extra_void :

    """

    # Turn dimension is a an input
    if i_dx_tf_turn_general_input:
        # Turn area [m2]
        a_tf_turn = dx_tf_turn_general**2

        # Current per turn [A]
        c_tf_turn = a_tf_turn * j_tf_wp

    # Turn cable dimension is an input
    elif i_dx_tf_turn_cable_space_general_input:
        # Turn squared dimension [m]
        dx_tf_turn_general = dx_tf_turn_cable_space_general + 2.0e0 * (
            dx_tf_turn_insulation + dx_tf_turn_steel
        )

        # Turn area [m2]
        a_tf_turn = dx_tf_turn_general**2

        # Current per turn [A]
        c_tf_turn = a_tf_turn * j_tf_wp

    # Current per turn is an input
    else:
        # Turn area [m2]
        # Allow for additional inter-layer insulation MDK 13/11/18
        # Area of turn including conduit and inter-layer insulation
        a_tf_turn = c_tf_turn / j_tf_wp

        # Dimension of square cross-section of each turn including inter-turn insulation [m]
        dx_tf_turn_general = np.sqrt(a_tf_turn)

    # Square turn assumption
    dr_tf_turn = dx_tf_turn_general
    dx_tf_turn = dx_tf_turn_general

    # See derivation in the following document
    # k:\power plant physics and technology\process\hts\hts coil module for process.docx
    t_conductor = (
        -layer_ins + np.sqrt(layer_ins**2 + 4.0e00 * a_tf_turn)
    ) / 2 - 2.0e0 * dx_tf_turn_insulation

    # Total number of turns per TF coil (not required to be an integer)
    n_tf_coil_turns = a_tf_wp_no_insulation / a_tf_turn

    # Area of inter-turn insulation: single turn [m2]
    a_tf_turn_insulation = a_tf_turn - t_conductor**2

    # NOTE: Fortran has a_tf_turn_cable_space_no_void as an intent(out) variable that was outputting
    # into tfcoil_variables.a_tf_turn_cable_space_no_void. The local variable, however, appears to
    # initially hold the value of tfcoil_variables.a_tf_turn_cable_space_no_void despite not being
    # intent(in). I have replicated this behaviour in Python for now.
    a_tf_turn_cable_space_no_void = copy.copy(
        tfcoil_variables.a_tf_turn_cable_space_no_void
    )

    # ITER like turn structure
    if i_tf_sc_mat != 6:
        # Radius of rounded corners of cable space inside conduit [m]
        radius_tf_turn_cable_space_corners = dx_tf_turn_steel * 0.75e0

        # Dimension of square cable space inside conduit [m]
        dx_tf_turn_cable_space_average = t_conductor - 2.0e0 * dx_tf_turn_steel

        # Cross-sectional area of cable space per turn
        # taking account of rounded inside corners [m2]
        a_tf_turn_cable_space_no_void = (
            dx_tf_turn_cable_space_average**2
            - (4.0e0 - np.pi) * radius_tf_turn_cable_space_corners**2
        )

        # Calculate the true effective cable space by taking away the cooling
        # channel and the extra void fraction

        a_tf_turn_cable_space_effective = (
            a_tf_turn_cable_space_no_void
            -
            # Coolant channel area
            (
                (np.pi / 4.0e0)
                * dia_tf_turn_coolant_channel
                * dia_tf_turn_coolant_channel
            )
            # Additional void area deduction
            - (a_tf_turn_cable_space_no_void * f_a_tf_turn_cable_space_extra_void)
        )

        f_a_tf_turn_cable_space_cooling = 1 - (
            a_tf_turn_cable_space_effective / a_tf_turn_cable_space_no_void
        )

        if a_tf_turn_cable_space_no_void <= 0.0e0:
            if t_conductor < 0.0e0:
                logger.error(
                    f"Negative cable space dimension. {a_tf_turn_cable_space_no_void=} "
                    f"{dx_tf_turn_cable_space_average=}"
                )
            else:
                logger.error(
                    "Cable space area problem; artificially set rounded corner radius to 0. "
                    f"{a_tf_turn_cable_space_no_void=} {dx_tf_turn_cable_space_average=}"
                )
                radius_tf_turn_cable_space_corners = 0.0e0
                a_tf_turn_cable_space_no_void = dx_tf_turn_cable_space_average**2

        # Cross-sectional area of conduit jacket per turn [m2]
        a_tf_turn_steel = t_conductor**2 - a_tf_turn_cable_space_no_void

    # REBCO turn structure
    elif i_tf_sc_mat == 6:
        # Diameter of circular cable space inside conduit [m]
        dx_tf_turn_cable_space_average = t_conductor - 2.0e0 * dx_tf_turn_steel

        # Cross-sectional area of conduit jacket per turn [m2]
        a_tf_turn_steel = t_conductor**2 - a_tf_turn_cable_space_no_void

    return (
        a_tf_turn_cable_space_no_void,
        a_tf_turn_steel,
        a_tf_turn_insulation,
        n_tf_coil_turns,
        dx_tf_turn_general,
        c_tf_turn,
        dx_tf_turn_general,
        dr_tf_turn,
        dx_tf_turn,
        t_conductor,
        radius_tf_turn_cable_space_corners,
        dx_tf_turn_cable_space_average,
        a_tf_turn_cable_space_effective,
        f_a_tf_turn_cable_space_cooling,
    )

superconducting_tf_coil_areas_and_masses()

Source code in process/models/tfcoil/superconducting.py

def superconducting_tf_coil_areas_and_masses(self):
    # Mass of case [kg]
    # ***

    # Mass of ground-wall insulation [kg]
    # (assumed to be same density/material as turn insulation)
    tfcoil_variables.m_tf_coil_wp_insulation = (
        tfcoil_variables.len_tf_coil
        * (
            superconducting_tf_coil_variables.a_tf_wp_with_insulation
            - superconducting_tf_coil_variables.a_tf_wp_no_insulation
        )
        * tfcoil_variables.den_tf_wp_turn_insulation
    )

    # The length of the vertical section is that of the first (inboard) segment
    # = height of TF coil inner edge + (2 * coil thickness)
    tfcoil_variables.cplen = (2.0e0 * build_variables.z_tf_inside_half) + (
        2.0e0 * build_variables.dr_tf_inboard
    )

    # The 2.2 factor is used as a scaling factor to fit
    # to the ITER-FDR value of 450 tonnes; see CCFE note T&M/PKNIGHT/PROCESS/026
    if physics_variables.itart == 1:
        # tfcoil_variables.len_tf_coil does not include inboard leg ('centrepost') length in TART
        tfcoil_variables.m_tf_coil_case = (
            2.2e0
            * tfcoil_variables.den_tf_coil_case
            * (
                tfcoil_variables.cplen * tfcoil_variables.a_tf_coil_inboard_case
                + tfcoil_variables.len_tf_coil
                * tfcoil_variables.a_tf_coil_outboard_case
            )
        )
    else:
        tfcoil_variables.m_tf_coil_case = (
            2.2e0
            * tfcoil_variables.den_tf_coil_case
            * (
                tfcoil_variables.cplen * tfcoil_variables.a_tf_coil_inboard_case
                + (tfcoil_variables.len_tf_coil - tfcoil_variables.cplen)
                * tfcoil_variables.a_tf_coil_outboard_case
            )
        )

    # ***

    # Masses of conductor constituents
    # ---------------------------------
    # Superconductor mass [kg]
    # Includes space allowance for central helium channel, area tfcoil_variables.a_tf_wp_coolant_channels
    tfcoil_variables.m_tf_coil_superconductor = (
        tfcoil_variables.len_tf_coil
        * tfcoil_variables.n_tf_coil_turns
        * tfcoil_variables.a_tf_turn_cable_space_no_void
        * (1.0e0 - tfcoil_variables.f_a_tf_turn_cable_space_extra_void)
        * (1.0e0 - tfcoil_variables.f_a_tf_turn_cable_copper)
        - tfcoil_variables.len_tf_coil * tfcoil_variables.a_tf_wp_coolant_channels
    ) * tfcoil_variables.dcond[tfcoil_variables.i_tf_sc_mat - 1]

    # Copper mass [kg]
    tfcoil_variables.m_tf_coil_copper = (
        tfcoil_variables.len_tf_coil
        * tfcoil_variables.n_tf_coil_turns
        * tfcoil_variables.a_tf_turn_cable_space_no_void
        * (1.0e0 - tfcoil_variables.f_a_tf_turn_cable_space_extra_void)
        * tfcoil_variables.f_a_tf_turn_cable_copper
        - tfcoil_variables.len_tf_coil * tfcoil_variables.a_tf_wp_coolant_channels
    ) * constants.den_copper
    if tfcoil_variables.m_tf_coil_copper <= 0.0e0:
        tfcoil_variables.m_tf_coil_copper = 0.0e0

    # Steel conduit (sheath) mass [kg]
    tfcoil_variables.m_tf_wp_steel_conduit = (
        tfcoil_variables.len_tf_coil
        * tfcoil_variables.n_tf_coil_turns
        * tfcoil_variables.a_tf_turn_steel
        * fwbs_variables.den_steel
    )

    # Conduit insulation mass [kg]
    # (tfcoil_variables.a_tf_coil_wp_turn_insulation already contains tfcoil_variables.n_tf_coil_turns)
    tfcoil_variables.m_tf_coil_wp_turn_insulation = (
        tfcoil_variables.len_tf_coil
        * tfcoil_variables.a_tf_coil_wp_turn_insulation
        * tfcoil_variables.den_tf_wp_turn_insulation
    )

    # Total conductor mass [kg]
    tfcoil_variables.m_tf_coil_conductor = (
        tfcoil_variables.m_tf_coil_superconductor
        + tfcoil_variables.m_tf_coil_copper
        + tfcoil_variables.m_tf_wp_steel_conduit
        + tfcoil_variables.m_tf_coil_wp_turn_insulation
    )
    # ---------------------------------

    # Total TF coil mass [kg] (all coils)
    tfcoil_variables.m_tf_coils_total = (
        tfcoil_variables.m_tf_coil_case
        + tfcoil_variables.m_tf_coil_conductor
        + tfcoil_variables.m_tf_coil_wp_insulation
    ) * tfcoil_variables.n_tf_coils

    # If spherical tokamak, distribute between centrepost and outboard legs
    # (in this case, total TF coil length = inboard `cplen` + outboard `len_tf_coil`)
    if physics_variables.itart == 1:
        tfleng_sph = tfcoil_variables.cplen + tfcoil_variables.len_tf_coil
        tfcoil_variables.whtcp = tfcoil_variables.m_tf_coils_total * (
            tfcoil_variables.cplen / tfleng_sph
        )
        tfcoil_variables.whttflgs = tfcoil_variables.m_tf_coils_total * (
            tfcoil_variables.len_tf_coil / tfleng_sph
        )

lambda_term(tau, omega) staticmethod

The lambda function used inegral in inductance calcuation found in Y. Itoh et al. The full form of the functions are given in appendix A.

Parameters:

Name	Type	Description	Default
tau	float	tau_{s,k} = (R_{s,k} - R_{c,k}) / R_k	required
omega	float	omega_k = R_{c,k}/R_k	required

Returns:

Type	Description
float	integral

Source code in process/models/tfcoil/superconducting.py

@staticmethod
def lambda_term(tau: float, omega: float) -> float:
    """The lambda function used inegral in inductance calcuation found
    in Y. Itoh et al. The full form of the functions are given in appendix A.

    Parameters
    ----------
    tau :
        tau_{s,k} = (R_{s,k} - R_{c,k}) / R_k
    omega :
        omega_k = R_{c,k}/R_k

    Returns
    -------
    :
        integral
    """
    p = 1.0 - omega**2.0

    if p < 0:
        integral = (1.0 / np.sqrt(np.abs(p))) * np.arcsin(
            (1.0 + omega * tau) / (tau + omega)
        )
    else:
        integral = (1.0 / np.sqrt(np.abs(p))) * np.log(
            (2.0 * (1.0 + tau * omega - np.sqrt(p * (1 - tau**2.0)))) / (tau + omega)
        )

    return integral

vv_stress_on_quench(H_coil, ri_coil, ro_coil, rm_coil, ccl_length_coil, theta1_coil, H_vv, ri_vv, ro_vv, rm_vv, theta1_vv, n_tf_coils, n_tf_coil_turns, s_rp, s_cc, taud, i_op, d_vv)

Generic model to calculate the Tresca stress of the Vacuum Vessel (VV), experienced when the TF coil quenches.

The current center line (CCL) of a structure is an appoximation of where the poloidal current of a structure acts. This model considers how the current (self-)induced in the following structures affects the Tresca stress on the VV (corresponding to the structure index used in [1]):

1. the TF coil conductors
2. the TF coil steel structure
3. the VV

Parameters:

Name	Type	Description	Default
H_coil	float	the maximum height of the TF coil CCL	required
ri_coil	float	the radius of the inboard edge of the TF coil CCL	required
ro_coil	float	the radius of the outboard edge of the TF coil CCL	required
rm_coil	float	the radius where the maximum height of the TF coil CCL occurs	required
ccl_length_coil	float	the length of the TF coil CCL	required
theta1_coil	float	the polar angle of the point at which one circular arc is joined to another circular arc in the approximation to the coil CCL, using an arbitrary origin of coordinates (Rc2, Zc2).	required
H_vv	float	the maximum height of the VV CCL	required
ri_vv	float	the radius of the inboard edge of the VV CCL	required
ro_vv	float	the radius of the outboard edge of the VV CCL	required
rm_vv	float	the radius where the maximum height of the VV CCL occurs	required
theta1_vv	float	the polar angle of the point at which one circular arc is joined to another circular arc in the approximation to the VV CCL, using an arbitrary origin of coordinates (Rc2, Zc2).	required
n_tf_coils	float	the number of TF coils	required
n_tf_coil_turns	float	the number of turns per TF coil	required
s_rp	float	the cross-sectional area of the radial plates of the TF coil	required
s_cc	float	the cross-sectional area of the TF coil case	required
taud	float	the discharge time of the TF coil when quench occurs	required
i_op	float	the 'normal' operating current of the TF coil	required
d_vv	float	the thickness of the vacuum vessel shell	required

Returns:

Type	Description
float	the maximum stress experienced by the vacuum vessel

Notes

The theta1 quantity for the TF coil and VV is not very meaningful. The impact of it of the inductance is rather small. Generally, the paper seems to suggest the TF coil is between 40 and 60, as this is the range they calculate the surrogates over. The thickness of the VV considers an ITER like design and only the outer and inner shells that which act of conductuve structural material.

References

1. ITOH, Yasuyuki & Utoh, Hiroyasu & SAKAMOTO, Yoshiteru & Hiwatari, Ryoji. (2020). Empirical Formulas for Estimating Self and Mutual Inductances of Toroidal Field Coils and Structures. Plasma and Fusion Research. 15. 1405078-1405078. 10.1585/pfr.15.1405078.

Source code in process/models/tfcoil/superconducting.py

def vv_stress_on_quench(
    # TF shape
    H_coil: float,
    ri_coil: float,
    ro_coil: float,
    rm_coil: float,
    ccl_length_coil: float,
    theta1_coil: float,
    # VV shape
    H_vv: float,
    ri_vv: float,
    ro_vv: float,
    rm_vv: float,
    theta1_vv: float,
    # TF properties
    n_tf_coils: float,
    n_tf_coil_turns: float,
    s_rp: float,
    s_cc: float,
    taud: float,
    i_op: float,
    # VV properties
    d_vv: float,
) -> float:
    """Generic model to calculate the Tresca stress of the
    Vacuum Vessel (VV), experienced when the TF coil quenches.

    The current center line (CCL) of a structure is an appoximation
    of where the poloidal current of a structure acts. This model
    considers how the current (self-)induced in the following structures
    affects the Tresca stress on the VV (corresponding to the structure
    index used in [1]):

    0. the TF coil conductors
    1. the TF coil steel structure
    2. the VV

    Parameters
    ----------
    H_coil :
        the maximum height of the TF coil CCL
    ri_coil :
        the radius of the inboard edge of the TF coil CCL
    ro_coil :
        the radius of the outboard edge of the TF coil CCL
    rm_coil :
        the radius where the maximum height of the TF coil CCL occurs
    ccl_length_coil :
        the length of the TF coil CCL
    theta1_coil :
        the polar angle of the point at which one circular arc is
        joined to another circular arc in the approximation to the coil CCL,
        using an arbitrary origin of coordinates (Rc2, Zc2).
    H_vv :
        the maximum height of the VV CCL
    ri_vv :
        the radius of the inboard edge of the VV CCL
    ro_vv :
        the radius of the outboard edge of the VV CCL
    rm_vv :
        the radius where the maximum height of the VV CCL occurs
    theta1_vv :
        the polar angle of the point at which one circular arc is
        joined to another circular arc in the approximation to the VV CCL,
        using an arbitrary origin of coordinates (Rc2, Zc2).
    n_tf_coils :
        the number of TF coils
    n_tf_coil_turns :
        the number of turns per TF coil
    s_rp :
        the cross-sectional area of the radial plates of the TF coil
    s_cc :
        the cross-sectional area of the TF coil case
    taud :
        the discharge time of the TF coil when quench occurs
    i_op :
        the 'normal' operating current of the TF coil
    d_vv :
        the thickness of the vacuum vessel shell

    Returns
    -------
    :
        the maximum stress experienced by the vacuum vessel

    Notes
    -----
    The theta1 quantity for the TF coil and VV is not very meaningful. The
    impact of it of the inductance is rather small. Generally, the paper seems to
    suggest the TF coil is between 40 and 60, as this is the range they calculate
    the surrogates over. The thickness of the VV considers an ITER like design and
    only the outer and inner shells that which act of conductuve structural material.

    References
    ----------
    1. ITOH, Yasuyuki & Utoh, Hiroyasu & SAKAMOTO, Yoshiteru & Hiwatari, Ryoji. (2020).
    Empirical Formulas for Estimating Self and Mutual Inductances of Toroidal Field Coils and Structures.
    Plasma and Fusion Research. 15. 1405078-1405078. 10.1585/pfr.15.1405078.
    """
    # Convert angles into radians
    theta1_vv_rad = np.pi * (theta1_vv / 180.0)

    # Poloidal loop resistance (PLR) in ohms
    theta_vv = _theta_factor_integral(ro_vv, ri_vv, rm_vv, H_vv, theta1_vv_rad)
    plr_coil = ((0.5 * ccl_length_coil) / (n_tf_coils * (s_cc + s_rp))) * 1e-6
    plr_vv = ((0.84 / d_vv) * theta_vv) * 1e-6

    # relevant self-inductances in henry (H)
    coil_structure_self_inductance = (
        (constants.RMU0 / np.pi)
        * H_coil
        * _inductance_factor(H_coil, ri_coil, ro_coil, rm_coil, theta1_coil)
    )
    vv_self_inductance = (
        (constants.RMU0 / np.pi)
        * H_vv
        * _inductance_factor(H_vv, ri_vv, ro_vv, rm_vv, theta1_vv)
    )

    # s^-1
    lambda0 = 1 / taud
    lambda1 = (plr_coil) / coil_structure_self_inductance
    lambda2 = (plr_vv) / vv_self_inductance

    # approximate time at which the maximum force (and stress) will occur on the VV
    tmaxforce = np.log((lambda0 + lambda1) / (2 * lambda0)) / (lambda1 - lambda0)

    i0 = i_op * np.exp(-lambda0 * tmaxforce)
    i1 = (
        lambda0
        * n_tf_coils
        * n_tf_coil_turns
        * i_op
        * (
            (np.exp(-lambda1 * tmaxforce) - np.exp(-lambda0 * tmaxforce))
            / (lambda0 - lambda1)
        )
    )
    i2 = (lambda1 / lambda2) * i1

    a_vv = (ro_vv + ri_vv) / (ro_vv - ri_vv)
    b_vvi = (constants.RMU0 * (n_tf_coils * n_tf_coil_turns * i0 + i1 + (i2 / 2))) / (
        2 * np.pi * ri_vv
    )
    j_vvi = i2 / (2 * np.pi * d_vv * ri_vv)

    zeta = 1 + ((a_vv - 1) * np.log((a_vv + 1) / (a_vv - 1)) / (2 * a_vv))

    return zeta * b_vvi * j_vvi * ri_vv