plasma_geometry

Plasma geometry models and shape definitions for PROCESS.

PlasmaShapeModelType

Bases: IntEnum

Enum for plasma shape model types.

Source code in process/models/physics/plasma_geometry.py

class PlasmaShapeModelType(IntEnum):
    """Enum for plasma shape model types."""

    PROCESS_ORIGINAL = (0, "PROCESS Original Double Arc")
    SAUTER = (1, "Sauter")

    def __new__(cls, value: int, full_name: str):
        """Create a new PlasmaShapeModelType instance."""
        obj = int.__new__(cls, value)
        obj._value_ = value
        obj._full_name_ = full_name
        return obj

    @DynamicClassAttribute
    def full_name(self):
        """Get the full name of the plasma shape model."""
        return self._full_name_

PROCESS_ORIGINAL = (0, 'PROCESS Original Double Arc') class-attribute instance-attribute

SAUTER = (1, 'Sauter') class-attribute instance-attribute

full_name()

Get the full name of the plasma shape model.

Source code in process/models/physics/plasma_geometry.py

@DynamicClassAttribute
def full_name(self):
    """Get the full name of the plasma shape model."""
    return self._full_name_

PlasmaGeometryModels

Bases: IntEnum

Enum for plasma geometry model types.

Source code in process/models/physics/plasma_geometry.py

class PlasmaGeometryModels(IntEnum):
    """Enum for plasma geometry model types."""

    USER_INPUT = (0, "User Input")
    IPDG89 = (1, "IPDG89")
    STAR_CODE = (2, "STAR Code")
    ZOHM_ITER = (3, "Zohm ITER Scaling")
    MAST_DATA = (4, "Fit to MAST data")
    FIESTA_RUNS = (5, "Fiesta Runs")
    CREATE_DATA_EU_DEMO = (6, "CREATE Data EU DEMO")
    MENARD_2016 = (7, "Menard 2016 ST Scaling")
    UNKNOWN = (8, "Unknown")
    MENARD_1997 = (9, "Menard 1997 ST Scaling")

    def __new__(cls, value: int, description: str):
        """Create a new PlasmaGeometryModels instance."""
        obj = int.__new__(cls, value)
        obj._value_ = value
        obj._description_ = description
        return obj

    @DynamicClassAttribute
    def description(self):
        """Get the description of the plasma geometry model."""
        return self._description_

USER_INPUT = (0, 'User Input') class-attribute instance-attribute

IPDG89 = (1, 'IPDG89') class-attribute instance-attribute

STAR_CODE = (2, 'STAR Code') class-attribute instance-attribute

ZOHM_ITER = (3, 'Zohm ITER Scaling') class-attribute instance-attribute

MAST_DATA = (4, 'Fit to MAST data') class-attribute instance-attribute

FIESTA_RUNS = (5, 'Fiesta Runs') class-attribute instance-attribute

CREATE_DATA_EU_DEMO = (6, 'CREATE Data EU DEMO') class-attribute instance-attribute

MENARD_2016 = (7, 'Menard 2016 ST Scaling') class-attribute instance-attribute

UNKNOWN = (8, 'Unknown') class-attribute instance-attribute

MENARD_1997 = (9, 'Menard 1997 ST Scaling') class-attribute instance-attribute

description()

Get the description of the plasma geometry model.

Source code in process/models/physics/plasma_geometry.py

@DynamicClassAttribute
def description(self):
    """Get the description of the plasma geometry model."""
    return self._description_

PlasmaGeometryModelType

Bases: IntEnum

Enum for i_plasma_geometry plasma geometry model types.

Source code in process/models/physics/plasma_geometry.py

class PlasmaGeometryModelType(IntEnum):
    """Enum for i_plasma_geometry plasma geometry model types."""

    IPDG89_X_POINT = (
        0,
        PlasmaGeometryModels.USER_INPUT,
        PlasmaGeometryModels.USER_INPUT,
        PlasmaGeometryModels.IPDG89,
        PlasmaGeometryModels.IPDG89,
    )
    STAR_FIESTA = (
        1,
        PlasmaGeometryModels.STAR_CODE,
        PlasmaGeometryModels.STAR_CODE,
        PlasmaGeometryModels.FIESTA_RUNS,
        PlasmaGeometryModels.FIESTA_RUNS,
    )
    ZOHM_ITER_X_POINT = (
        2,
        PlasmaGeometryModels.ZOHM_ITER,
        PlasmaGeometryModels.USER_INPUT,
        PlasmaGeometryModels.IPDG89,
        PlasmaGeometryModels.IPDG89,
    )
    ZOHM_ITER_95 = (
        3,
        PlasmaGeometryModels.ZOHM_ITER,
        PlasmaGeometryModels.IPDG89,
        PlasmaGeometryModels.IPDG89,
        PlasmaGeometryModels.USER_INPUT,
    )
    IPDG89_95 = (
        4,
        PlasmaGeometryModels.IPDG89,
        PlasmaGeometryModels.IPDG89,
        PlasmaGeometryModels.USER_INPUT,
        PlasmaGeometryModels.USER_INPUT,
    )
    MAST_DATA_95 = (
        5,
        PlasmaGeometryModels.MAST_DATA,
        PlasmaGeometryModels.MAST_DATA,
        PlasmaGeometryModels.USER_INPUT,
        PlasmaGeometryModels.USER_INPUT,
    )
    MAST_DATA_X_POINT = (
        6,
        PlasmaGeometryModels.USER_INPUT,
        PlasmaGeometryModels.USER_INPUT,
        PlasmaGeometryModels.MAST_DATA,
        PlasmaGeometryModels.MAST_DATA,
    )
    FIESTA_RUNS_95 = (
        7,
        PlasmaGeometryModels.FIESTA_RUNS,
        PlasmaGeometryModels.FIESTA_RUNS,
        PlasmaGeometryModels.USER_INPUT,
        PlasmaGeometryModels.USER_INPUT,
    )
    FIESTA_RUNS_X_POINT = (
        8,
        PlasmaGeometryModels.USER_INPUT,
        PlasmaGeometryModels.USER_INPUT,
        PlasmaGeometryModels.FIESTA_RUNS,
        PlasmaGeometryModels.FIESTA_RUNS,
    )
    INDUCTANCE_SCALING_X_POINT = (
        9,
        PlasmaGeometryModels.UNKNOWN,
        PlasmaGeometryModels.USER_INPUT,
        PlasmaGeometryModels.IPDG89,
        PlasmaGeometryModels.IPDG89,
    )
    CREATE_DATA_EU_DEMO_X_POINT = (
        10,
        PlasmaGeometryModels.IPDG89,
        PlasmaGeometryModels.USER_INPUT,
        PlasmaGeometryModels.CREATE_DATA_EU_DEMO,
        PlasmaGeometryModels.IPDG89,
    )
    MENARD_2016_X_POINT = (
        11,
        PlasmaGeometryModels.MENARD_2016,
        PlasmaGeometryModels.USER_INPUT,
        PlasmaGeometryModels.IPDG89,
        PlasmaGeometryModels.IPDG89,
    )
    MENARD_1997_X_POINT = (
        12,
        PlasmaGeometryModels.MENARD_1997,
        PlasmaGeometryModels.USER_INPUT,
        PlasmaGeometryModels.IPDG89,
        PlasmaGeometryModels.IPDG89,
    )

    def __new__(
        cls,
        value: int,
        kappa_model: PlasmaGeometryModels,
        triang_model: PlasmaGeometryModels,
        kappa95_model: PlasmaGeometryModels,
        triang95_model: PlasmaGeometryModels,
    ):
        """Create a new PlasmaGeometryModelType instance."""
        obj = int.__new__(cls, value)
        obj._value_ = value
        obj._kappa_model_ = kappa_model
        obj._triang_model_ = triang_model
        obj._kappa95_model_ = kappa95_model
        obj._triang95_model_ = triang95_model
        return obj

    @DynamicClassAttribute
    def kappa_model(self):
        """Get the kappa model."""
        return self._kappa_model_

    @DynamicClassAttribute
    def triang_model(self):
        """Get the triangularity model."""
        return self._triang_model_

    @DynamicClassAttribute
    def kappa95_model(self):
        """Get the kappa95 model."""
        return self._kappa95_model_

    @DynamicClassAttribute
    def triang95_model(self):
        """Get the triangularity95 model."""
        return self._triang95_model_

IPDG89_X_POINT = (0, PlasmaGeometryModels.USER_INPUT, PlasmaGeometryModels.USER_INPUT, PlasmaGeometryModels.IPDG89, PlasmaGeometryModels.IPDG89) class-attribute instance-attribute

STAR_FIESTA = (1, PlasmaGeometryModels.STAR_CODE, PlasmaGeometryModels.STAR_CODE, PlasmaGeometryModels.FIESTA_RUNS, PlasmaGeometryModels.FIESTA_RUNS) class-attribute instance-attribute

ZOHM_ITER_X_POINT = (2, PlasmaGeometryModels.ZOHM_ITER, PlasmaGeometryModels.USER_INPUT, PlasmaGeometryModels.IPDG89, PlasmaGeometryModels.IPDG89) class-attribute instance-attribute

ZOHM_ITER_95 = (3, PlasmaGeometryModels.ZOHM_ITER, PlasmaGeometryModels.IPDG89, PlasmaGeometryModels.IPDG89, PlasmaGeometryModels.USER_INPUT) class-attribute instance-attribute

IPDG89_95 = (4, PlasmaGeometryModels.IPDG89, PlasmaGeometryModels.IPDG89, PlasmaGeometryModels.USER_INPUT, PlasmaGeometryModels.USER_INPUT) class-attribute instance-attribute

MAST_DATA_95 = (5, PlasmaGeometryModels.MAST_DATA, PlasmaGeometryModels.MAST_DATA, PlasmaGeometryModels.USER_INPUT, PlasmaGeometryModels.USER_INPUT) class-attribute instance-attribute

MAST_DATA_X_POINT = (6, PlasmaGeometryModels.USER_INPUT, PlasmaGeometryModels.USER_INPUT, PlasmaGeometryModels.MAST_DATA, PlasmaGeometryModels.MAST_DATA) class-attribute instance-attribute

FIESTA_RUNS_95 = (7, PlasmaGeometryModels.FIESTA_RUNS, PlasmaGeometryModels.FIESTA_RUNS, PlasmaGeometryModels.USER_INPUT, PlasmaGeometryModels.USER_INPUT) class-attribute instance-attribute

FIESTA_RUNS_X_POINT = (8, PlasmaGeometryModels.USER_INPUT, PlasmaGeometryModels.USER_INPUT, PlasmaGeometryModels.FIESTA_RUNS, PlasmaGeometryModels.FIESTA_RUNS) class-attribute instance-attribute

INDUCTANCE_SCALING_X_POINT = (9, PlasmaGeometryModels.UNKNOWN, PlasmaGeometryModels.USER_INPUT, PlasmaGeometryModels.IPDG89, PlasmaGeometryModels.IPDG89) class-attribute instance-attribute

CREATE_DATA_EU_DEMO_X_POINT = (10, PlasmaGeometryModels.IPDG89, PlasmaGeometryModels.USER_INPUT, PlasmaGeometryModels.CREATE_DATA_EU_DEMO, PlasmaGeometryModels.IPDG89) class-attribute instance-attribute

MENARD_2016_X_POINT = (11, PlasmaGeometryModels.MENARD_2016, PlasmaGeometryModels.USER_INPUT, PlasmaGeometryModels.IPDG89, PlasmaGeometryModels.IPDG89) class-attribute instance-attribute

MENARD_1997_X_POINT = (12, PlasmaGeometryModels.MENARD_1997, PlasmaGeometryModels.USER_INPUT, PlasmaGeometryModels.IPDG89, PlasmaGeometryModels.IPDG89) class-attribute instance-attribute

kappa_model()

Get the kappa model.

Source code in process/models/physics/plasma_geometry.py

@DynamicClassAttribute
def kappa_model(self):
    """Get the kappa model."""
    return self._kappa_model_

triang_model()

Get the triangularity model.

Source code in process/models/physics/plasma_geometry.py

@DynamicClassAttribute
def triang_model(self):
    """Get the triangularity model."""
    return self._triang_model_

kappa95_model()

Get the kappa95 model.

Source code in process/models/physics/plasma_geometry.py

@DynamicClassAttribute
def kappa95_model(self):
    """Get the kappa95 model."""
    return self._kappa95_model_

triang95_model()

Get the triangularity95 model.

Source code in process/models/physics/plasma_geometry.py

@DynamicClassAttribute
def triang95_model(self):
    """Get the triangularity95 model."""
    return self._triang95_model_

PlasmaGeom

Bases: Model

Class for calculating plasma geometry parameters.

Source code in process/models/physics/plasma_geometry.py

class PlasmaGeom(Model):
    """Class for calculating plasma geometry parameters."""

    def __init__(self):
        self.outfile = constants.NOUT

    def run(self):
        """Plasma geometry parameters

        This method calculates the plasma geometry parameters based on various shaping
        terms and input values. It updates the `physics_variables` with calculated
        values for kappa, triangularity, surface area, volume, etc.

        References
        ----------
            - J D Galambos, STAR Code : Spherical Tokamak Analysis and Reactor Code,
              unpublished internal Oak Ridge document
            - H. Zohm et al, On the Physics Guidelines for a Tokamak DEMO,
              FTP/3-3, Proc. IAEA Fusion Energy Conference, October 2012, San Diego
        """
        xsi = 0.0e0
        xso = 0.0e0
        thetai = 0.0e0
        thetao = 0.0e0
        xi = 0.0e0
        xo = 0.0e0

        # Define plasma minor radius from major radius and aspect ratio
        physics_variables.rminor = physics_variables.rmajor / physics_variables.aspect

        # Define the inverse aspect ratio
        physics_variables.eps = 1.0e0 / physics_variables.aspect

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

        if (
            physics_variables.i_plasma_geometry == PlasmaGeometryModelType.IPDG89_X_POINT
        ):  # Use input kappa, physics_variables.triang values
            #  Rough estimate of 95% values
            #  ITER Physics Design Guidlines: 1989 (Uckan et al. 1990)
            #  (close to previous estimate of (physics_variables.kappa - 0.04) / 1.1
            #  over a large physics_variables.kappa range)

            physics_variables.kappa95 = physics_variables.kappa / 1.12e0
            physics_variables.triang95 = physics_variables.triang / 1.50e0

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

        if (
            physics_variables.i_plasma_geometry == PlasmaGeometryModelType.STAR_FIESTA
        ):  # ST scaling with physics_variables.aspect ratio [STAR Code]
            physics_variables.q95_min = 3.0e0 * (
                1.0e0 + 2.6e0 * physics_variables.eps**2.8e0
            )

            physics_variables.kappa = 2.05e0 * (
                1.0e0 + 0.44e0 * physics_variables.eps**2.1e0
            )
            physics_variables.triang = 0.53e0 * (
                1.0e0 + 0.77e0 * physics_variables.eps**3
            )

            # SIM 10/09/2020: Switched to FIESTA ST scaling  from IPDG89
            physics_variables.kappa95 = (
                physics_variables.kappa - 0.39467e0
            ) / 0.90698e0  # Fit to FIESTA (Issue #1086)
            physics_variables.triang95 = (
                physics_variables.triang - 0.048306e0
            ) / 1.3799e0

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

        if (
            physics_variables.i_plasma_geometry
            == PlasmaGeometryModelType.ZOHM_ITER_X_POINT
        ):  # Zohm et al. ITER scaling for elongation, input physics_variables.triang
            physics_variables.kappa = physics_variables.fkzohm * min(
                2.0e0, 1.5e0 + 0.5e0 / (physics_variables.aspect - 1.0e0)
            )

            # ITER Physics Design Guidlines: 1989 (Uckan et al. 1990)
            physics_variables.kappa95 = physics_variables.kappa / 1.12e0
            physics_variables.triang95 = physics_variables.triang / 1.50e0

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

        if (
            physics_variables.i_plasma_geometry == PlasmaGeometryModelType.ZOHM_ITER_95
        ):  # Zohm et al. ITER scaling for elongation, input physics_variables.triang95
            physics_variables.kappa = physics_variables.fkzohm * min(
                2.0e0, 1.5e0 + 0.5e0 / (physics_variables.aspect - 1.0e0)
            )

            # ITER Physics Design Guidlines: 1989 (Uckan et al. 1990)
            physics_variables.triang = 1.5e0 * physics_variables.triang95

            physics_variables.kappa95 = physics_variables.kappa / 1.12e0

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

        if (
            physics_variables.i_plasma_geometry == PlasmaGeometryModelType.IPDG89_95
        ):  # Use input kappa95, physics_variables.triang95 values
            # ITER Physics Design Guidlines: 1989 (Uckan et al. 1990)
            physics_variables.kappa = 1.12e0 * physics_variables.kappa95
            physics_variables.triang = 1.5e0 * physics_variables.triang95

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

        if (
            physics_variables.i_plasma_geometry == PlasmaGeometryModelType.MAST_DATA_95
        ):  # Use input kappa95, physics_variables.triang95 values
            # Fit to MAST data (Issue #1086)
            physics_variables.kappa = 0.91300e0 * physics_variables.kappa95 + 0.38654e0
            physics_variables.triang = 0.77394e0 * physics_variables.triang95 + 0.18515e0

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

        if (
            physics_variables.i_plasma_geometry
            == PlasmaGeometryModelType.MAST_DATA_X_POINT
        ):  # Use input kappa, physics_variables.triang values
            # Fit to MAST data (Issue #1086)
            physics_variables.kappa95 = (physics_variables.kappa - 0.38654e0) / 0.91300e0
            physics_variables.triang95 = (
                physics_variables.triang - 0.18515e0
            ) / 0.77394e0

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

        if (
            physics_variables.i_plasma_geometry == PlasmaGeometryModelType.FIESTA_RUNS_95
        ):  # Use input kappa95, physics_variables.triang95 values
            # Fit to FIESTA (Issue #1086)
            physics_variables.kappa = 0.90698e0 * physics_variables.kappa95 + 0.39467e0
            physics_variables.triang = 1.3799e0 * physics_variables.triang95 + 0.048306e0

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

        if (
            physics_variables.i_plasma_geometry
            == PlasmaGeometryModelType.FIESTA_RUNS_X_POINT
        ):  # Use input kappa, physics_variables.triang values
            # Fit to FIESTA (Issue #1086)
            physics_variables.kappa95 = (physics_variables.kappa - 0.39467e0) / 0.90698e0
            physics_variables.triang95 = (
                physics_variables.triang - 0.048306e0
            ) / 1.3799e0

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

        if (
            physics_variables.i_plasma_geometry
            == PlasmaGeometryModelType.INDUCTANCE_SCALING_X_POINT
        ):  # Use input triang, physics_variables.ind_plasma_internal_norm values
            # physics_variables.kappa found from physics_variables.aspect ratio and
            # plasma internal inductance li(3)
            physics_variables.kappa = (
                1.09e0 + 0.26e0 / physics_variables.ind_plasma_internal_norm
            ) * (1.5e0 / physics_variables.aspect) ** 0.4e0

            physics_variables.kappa95 = physics_variables.kappa / 1.12e0
            physics_variables.triang95 = physics_variables.triang / 1.50e0

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

        if (
            physics_variables.i_plasma_geometry
            == PlasmaGeometryModelType.CREATE_DATA_EU_DEMO_X_POINT
        ):
            # physics_variables.kappa95 found from physics_variables.aspect ratio and
            # stability margin Based on fit to CREATE data. ref Issue #1399
            # valid for EU-DEMO like machine - physics_variables.aspect ratio 2.6 - 3.6
            # Model updated see Issue #1648
            a = 3.68436807e0
            b = -0.27706527e0
            c = 0.87040251e0
            d = -18.83740952e0
            e = -0.27267618e0
            f = 20.5141261e0

            physics_variables.kappa95 = (
                -d
                - c * physics_variables.aspect
                - np.sqrt(
                    (c**2.0e0 - 4.0e0 * a * b) * physics_variables.aspect**2.0e0
                    + (2.0e0 * d * c - 4.0e0 * a * e) * physics_variables.aspect
                    + d**2.0e0
                    - 4.0e0 * a * f
                    + 4.0e0 * a * physics_variables.m_s_limit
                )
            ) / (2.0e0 * a)

            if physics_variables.kappa95 > 1.77:
                ratio = 1.77 / physics_variables.kappa95
                corner_fudge = 0.3 * (physics_variables.kappa95 - 1.77) / ratio
                physics_variables.kappa95 = (
                    physics_variables.kappa95 ** (ratio) + corner_fudge
                )

            physics_variables.kappa = 1.12e0 * physics_variables.kappa95
            physics_variables.triang95 = physics_variables.triang / 1.50e0

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

        if (
            physics_variables.i_plasma_geometry
            == PlasmaGeometryModelType.MENARD_2016_X_POINT
        ):
            # See Issue #1439
            # physics_variables.triang is an input
            # physics_variables.kappa found from physics_variables.aspect ratio scaling
            # on p32 of Menard: Menard, et al. "Fusion Nuclear Science Facilities
            # and Pilot Plants Based on the Spherical Tokamak." Nucl. Fusion, 2016, 44.

            physics_variables.kappa = 0.95e0 * (
                1.9e0 + 1.9e0 / physics_variables.aspect**1.4e0
            )
            physics_variables.kappa95 = physics_variables.kappa / 1.12e0
            physics_variables.triang95 = physics_variables.triang / 1.50e0

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

        if (
            physics_variables.i_plasma_geometry
            == PlasmaGeometryModelType.MENARD_1997_X_POINT
        ):
            # physics_variables.triang is an input
            # physics_variables.kappa found from physics_variables.aspect ratio scaling from
            # J.E. Menard et al 1997 Nucl. Fusion 37 595 and assume max controllable kappa
            # and assume lᵢ(3) is held constant

            physics_variables.kappa = (
                2.93e0 * (1.8e0 / physics_variables.aspect) ** 0.4e0
            )

            physics_variables.kappa95 = physics_variables.kappa / 1.12e0
            physics_variables.triang95 = physics_variables.triang / 1.50e0

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

        #  Scrape-off layer thicknesses
        if physics_variables.i_plasma_wall_gap == 0:
            self.data.build.dr_fw_plasma_gap_outboard = 0.1e0 * physics_variables.rminor
            self.data.build.dr_fw_plasma_gap_inboard = 0.1e0 * physics_variables.rminor

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

        # Find parameters of arcs describing plasma surfaces
        xi, thetai, xo, thetao = self.plasma_angles_arcs(
            physics_variables.rminor,
            physics_variables.kappa,
            physics_variables.triang,
        )

        #  Surface area - inboard and outboard.  These are not given by Sauter but
        #  the outboard area is required by DCLL and divertor
        xsi, xso = self.plasma_surface_area(
            physics_variables.rmajor,
            physics_variables.rminor,
            xi,
            thetai,
            xo,
            thetao,
        )
        physics_variables.a_plasma_surface_outboard = xso

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

        # i_plasma_current = 8 specifies use of the Sauter geometry as well as plasma
        # current.
        if (
            physics_variables.i_plasma_current == 8
            or physics_variables.i_plasma_shape == PlasmaShapeModelType.SAUTER
        ):
            (
                physics_variables.len_plasma_poloidal,
                physics_variables.a_plasma_surface,
                physics_variables.a_plasma_poloidal,
                physics_variables.vol_plasma,
            ) = self.sauter_geometry(
                physics_variables.rminor,
                physics_variables.rmajor,
                physics_variables.kappa,
                physics_variables.triang,
                physics_variables.plasma_square,
            )

        else:
            #  Poloidal perimeter
            physics_variables.len_plasma_poloidal = self.plasma_poloidal_perimeter(
                xi, thetai, xo, thetao
            )

            #  Volume
            physics_variables.vol_plasma = (
                physics_variables.f_vol_plasma
                * self.plasma_volume(
                    physics_variables.rmajor,
                    physics_variables.rminor,
                    xi,
                    thetai,
                    xo,
                    thetao,
                )
            )

            #  Cross-sectional area
            physics_variables.a_plasma_poloidal = self.plasma_cross_section(
                xi, thetai, xo, thetao
            )

            #  Surface area - sum of inboard and outboard.
            physics_variables.a_plasma_surface = xsi + xso

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

    def output(self):
        """Output plasma geometry parameters to file.

        Raises
        ------
        ProcessValueError
            If `n_divertors` has an illegal value.
        """
        po.oheadr(self.outfile, "Plasma Geometry")

        if self.data.stellarator.istell == 0:
            if self.data.divertor.n_divertors == 0:
                po.ocmmnt(self.outfile, "Plasma configuration = limiter")
            elif self.data.divertor.n_divertors == 1:
                po.ocmmnt(self.outfile, "Plasma configuration = single null divertor")
            elif self.data.divertor.n_divertors == 2:
                po.ocmmnt(self.outfile, "Plasma configuration = double null divertor")
            else:
                raise ProcessValueError(
                    "Illegal value of n_divertors",
                    n_divertors=self.data.divertor.n_divertors,
                )
        else:
            po.ocmmnt(self.outfile, "Plasma configuration = stellarator")

        if self.data.stellarator.istell == 0:
            if physics_variables.itart == 0:
                physics_variables.itart_r = physics_variables.itart
                po.ovarin(
                    self.outfile,
                    "Tokamak aspect ratio = Conventional, itart = 0",
                    "(itart)",
                    physics_variables.itart_r,
                )
            elif physics_variables.itart == 1:
                physics_variables.itart_r = physics_variables.itart
                po.ovarin(
                    self.outfile,
                    "Tokamak aspect ratio = Spherical, itart = 1",
                    "(itart)",
                    physics_variables.itart_r,
                )

        po.ovarin(
            self.outfile,
            "Plasma shaping model",
            "(i_plasma_shape)",
            physics_variables.i_plasma_shape,
        )

        po.osubhd(
            self.outfile,
            f"{PlasmaShapeModelType(physics_variables.i_plasma_shape).full_name} "
            "plasma shape model is used :",
        )

        po.ovarrf(
            self.outfile, "Major radius (R₀) (m)", "(rmajor)", physics_variables.rmajor
        )
        po.ovarrf(
            self.outfile,
            "Minor radius (a) (m)",
            "(rminor)",
            physics_variables.rminor,
            "OP ",
        )
        po.ovarrf(self.outfile, "Aspect ratio (A)", "(aspect)", physics_variables.aspect)
        po.ovarrf(
            self.outfile,
            "Plasma squareness (ζ)",
            "(plasma_square)",
            physics_variables.plasma_square,
            "IP",
        )
        po.oblnkl(self.outfile)

        po.ovarin(
            self.outfile,
            "Plasma geometry model",
            "(i_plasma_geometry)",
            physics_variables.i_plasma_geometry,
        )
        po.oblnkl(self.outfile)
        po.ovarre(
            self.outfile,
            "ITER Physics Basis definition of elongation (κₐ)",
            "(kappa_ipb)",
            physics_variables.kappa_ipb,
            "OP ",
        )
        po.oblnkl(self.outfile)
        geom_type = PlasmaGeometryModelType(physics_variables.i_plasma_geometry)

        if self.data.stellarator.istell == 0:
            po.ocmmnt(
                self.outfile,
                f"X-Point Elongation set from: {geom_type.kappa_model.description}",
            )

            po.ovarrf(
                self.outfile,
                "Elongation, X-point (κₐ)",
                "(kappa)",
                physics_variables.kappa,
                "IP"
                if geom_type.kappa_model == PlasmaGeometryModels.USER_INPUT
                else "OP",
            )
            if geom_type.kappa_model == PlasmaGeometryModels.ZOHM_ITER:
                po.ovarrf(
                    self.outfile,
                    "Zohm scaling adjustment factor",
                    "(fkzohm)",
                    physics_variables.fkzohm,
                )

            po.oblnkl(self.outfile)

            po.ocmmnt(
                self.outfile,
                f"95% Elongation set from: {geom_type.kappa95_model.description}",
            )
            po.ovarrf(
                self.outfile,
                "Elongation, 95% surface (κ₉₅)",
                "(kappa95)",
                physics_variables.kappa95,
                "IP"
                if geom_type.kappa95_model == PlasmaGeometryModels.USER_INPUT
                else "OP",
            )

            po.oblnkl(self.outfile)

            po.ocmmnt(
                self.outfile,
                f"X-Point Triangularity set from: {geom_type.triang_model.description}",
            )

            po.ovarrf(
                self.outfile,
                "Triangularity, X-point (δ)",
                "(triang)",
                physics_variables.triang,
                "IP "
                if geom_type.triang_model == PlasmaGeometryModels.USER_INPUT
                else "OP",
            )
            po.oblnkl(self.outfile)
            po.ocmmnt(
                self.outfile,
                f"95% Triangularity set from: {geom_type.triang95_model.description}",
            )

            po.ovarrf(
                self.outfile,
                "Triangularity, 95% surface (δ₉₅)",
                "(triang95)",
                physics_variables.triang95,
                "IP "
                if geom_type.triang95_model == PlasmaGeometryModels.USER_INPUT
                else "OP",
            )

            po.oblnkl(self.outfile)

            po.ovarrf(
                self.outfile,
                "Plasma poloidal perimeter (m)",
                "(len_plasma_poloidal)",
                physics_variables.len_plasma_poloidal,
                "OP ",
            )

            po.ovarre(
                self.outfile,
                "Plasma cross-sectional area (m²)",
                "(a_plasma_poloidal)",
                physics_variables.a_plasma_poloidal,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Plasma surface area (m²)",
                "(a_plasma_surface)",
                physics_variables.a_plasma_surface,
                "OP ",
            )
            po.ovarre(
                self.outfile,
                "Plasma volume (m³)",
                "(vol_plasma)",
                physics_variables.vol_plasma,
                "OP ",
            )

        po.oblnkl(self.outfile)

    @staticmethod
    def plasma_angles_arcs(
        a: float, kappa: float, triang: float
    ) -> tuple[float, float, float, float]:
        """Routine to find parameters used for calculating geometrical
        properties for double-null plasmas.

        This function finds plasma geometrical parameters, using the
        revolution of two intersecting arcs around the device centreline.
        This calculation is appropriate for plasmas with a separatrix.


        Parameters
        ----------
        a : float
            Plasma minor radius (m)
        kappa : float
            Plasma separatrix elongation
        triang : float
            Plasma separatrix triangularity

        Returns
        -------
        tuple
            A tuple containing:
            - xi (float): Radius of arc describing inboard surface (m)
            - thetai (float): Half-angle of arc describing inboard surface
            - xo (float): Radius of arc describing outboard surface (m)
            - thetao (float): Half-angle of arc describing outboard surface


        References
        ----------
        - F/MI/PJK/LOGBOOK14, p.42
        - F/PL/PJK/PROCESS/CODE/047
        """
        t = 1.0e0 - triang
        denomi = (kappa**2 - t**2) / (2.0e0 * t)
        thetai = np.arctan(kappa / denomi)
        xi = a * (denomi + 1.0e0 - triang)

        #  Find radius and half-angle of outboard arc

        n = 1.0e0 + triang
        denomo = (kappa**2 - n**2) / (2.0e0 * n)
        thetao = np.arctan(kappa / denomo)
        xo = a * (denomo + 1.0e0 + triang)

        return xi, thetai, xo, thetao

    @staticmethod
    def plasma_poloidal_perimeter(
        xi: float, thetai: float, xo: float, thetao: float
    ) -> float:
        """Calculate the poloidal perimeter of the plasma.

        Parameters
        ----------
        xi : float
            Radius of arc describing inboard surface (m)
        thetai : float
            Half-angle of arc describing inboard surface
        xo : float
            Radius of arc describing outboard surface (m)
        thetao : float
            Half-angle of arc describing outboard surface

        Returns
        -------
        float
            Poloidal perimeter (m)
        """
        return 2.0e0 * (xo * thetao + xi * thetai)

    @staticmethod
    def plasma_surface_area(
        rmajor: float, rminor: float, xi: float, thetai: float, xo: float, thetao: float
    ) -> tuple[float, float]:
        """Plasma surface area calculation

        This function finds the plasma surface area, using the
        revolution of two intersecting arcs around the device centreline.
        This calculation is appropriate for plasmas with a separatrix.

        Parameters
        ----------
        rmajor : float
            Plasma major radius (m)
        rminor : float
            Plasma minor radius (m)
        xi : float
            Radius of arc describing inboard surface (m)
        thetai : float
            Half-angle of arc describing inboard surface
        xo : float
            Radius of arc describing outboard surface (m)
        thetao : float
            Half-angle of arc describing outboard surface

        Returns
        -------
        tuple
            A tuple containing:
            - xsi (float): Inboard surface area (m^2)
            - xso (float): Outboard surface area (m^2)


        References
        ----------
        - F/MI/PJK/LOGBOOK14, p.43
        """
        fourpi = 4.0e0 * np.pi

        rc = rmajor - rminor + xi
        xsi = fourpi * xi * (rc * thetai - xi * np.sin(thetai))

        rc = rmajor + rminor - xo
        xso = fourpi * xo * (rc * thetao + xo * np.sin(thetao))

        return xsi, xso

    @staticmethod
    def plasma_volume(
        rmajor: float, rminor: float, xi: float, thetai: float, xo: float, thetao: float
    ) -> float:
        """Plasma volume calculation
        This function finds the plasma volume, using the
        revolution of two intersecting arcs around the device centreline.
        This calculation is appropriate for plasmas with a separatrix.

        Parameters
        ----------
        rmajor : float
            Plasma major radius (m)
        rminor : float
            Plasma minor radius (m)
        xi : float
            Radius of arc describing inboard surface (m)
        thetai : float
            Half-angle of arc describing inboard surface
        xo : float
            Radius of arc describing outboard surface (m)
        thetao : float
            Half-angle of arc describing outboard surface

        Returns
        -------
        float
            Plasma volume (m^3)


        References
        ----------
        - F/MI/PJK/LOGBOOK14, p.43
        """
        third = 1.0e0 / 3.0e0

        rc = rmajor - rminor + xi
        vin = (
            2.0
            * np.pi
            * xi
            * (
                rc**2 * np.sin(thetai)
                - rc * xi * thetai
                - 0.5e0 * rc * xi * np.sin(2.0e0 * thetai)
                + xi * xi * np.sin(thetai)
                - third * xi * xi * (np.sin(thetai)) ** 3
            )
        )

        rc = rmajor + rminor - xo
        vout = (
            2.0
            * np.pi
            * xo
            * (
                rc**2 * np.sin(thetao)
                + rc * xo * thetao
                + 0.5e0 * rc * xo * np.sin(2.0e0 * thetao)
                + xo * xo * np.sin(thetao)
                - third * xo * xo * (np.sin(thetao)) ** 3
            )
        )

        return vout - vin

    @staticmethod
    def plasma_cross_section(
        xi: float, thetai: float, xo: float, thetao: float
    ) -> float:
        """Plasma cross-sectional area calculation

        This function finds the plasma cross-sectional area, using the
        revolution of two intersecting arcs around the device centreline.
        This calculation is appropriate for plasmas with a separatrix.

        Parameters
        ----------
        xi : float
            Radius of arc describing inboard surface (m)
        thetai : float
            Half-angle of arc describing inboard surface
        xo : float
            Radius of arc describing outboard surface (m)
        thetao : float
            Half-angle of arc describing outboard surface

        Returns
        -------
        float
            Plasma cross-sectional area (m^2)


        References
        ----------
        - F/MI/PJK/LOGBOOK14, p.41
        """
        return xo**2 * (thetao - np.cos(thetao) * np.sin(thetao)) + xi**2 * (
            thetai - np.cos(thetai) * np.sin(thetai)
        )

    @staticmethod
    def sauter_geometry(
        a: float, r0: float, kappa: float, triang: float, square: float
    ) -> tuple[float, float, float, float, float]:
        """Calculate the plasma geometry parameters using the Sauter geometry model.

        Parameters
        ----------
        a : float
            Plasma minor radius (m)
        r0 : float
            Plasma major radius (m)
        kappa : float
            Plasma separatrix elongation
        triang : float
            Plasma separatrix triangularity
        square : float
            Plasma squareness

        Returns
        -------
        tuple
            A tuple containing:
            - len_plasma_poloidal (float): Poloidal perimeter
            - a_plasma_surface (float): Surface area
            - a_plasma_poloidal (float): Cross-section area
            - vol_plasma (float): Plasma volume


        References
        ----------
            - O. Sauter, “Geometric formulas for system codes including the effect of
              negative triangularity,” Fusion Engineering and Design, vol. 112,
              pp. 633-645, Nov. 2016,
              doi: https://doi.org/10.1016/j.fusengdes.2016.04.033.
        """
        # Calculate w07 parameter from paper from squareness assuming top-down symmetry
        w07 = square + 1

        # Inverse aspect ratio
        eps = a / r0

        # Poloidal perimeter (named Lp in Sauter)
        len_plasma_poloidal = (
            2.0e0
            * np.pi
            * a
            * (1 + 0.55 * (kappa - 1))
            * (1 + 0.08 * triang**2)
            * (1 + 0.2 * (w07 - 1))
        )

        # Surface area (named Ap in Sauter)
        a_plasma_surface = (
            2.0e0 * np.pi * r0 * (1 - 0.32 * triang * eps) * len_plasma_poloidal
        )

        # Cross-section area (named S_phi in Sauter)
        a_plasma_poloidal = np.pi * a**2 * kappa * (1 + 0.52 * (w07 - 1))

        # Volume
        vol_plasma = 2.0e0 * np.pi * r0 * (1 - 0.25 * triang * eps) * a_plasma_poloidal

        return (
            len_plasma_poloidal,
            a_plasma_surface,
            a_plasma_poloidal,
            vol_plasma,
        )

    @staticmethod
    def calculate_iter_physics_basis_elongation(
        vol_plasma: float, rmajor: float, rminor: float
    ) -> float:
        """Calculate the ITER physics basis elongation.

        This method calculates the ITER physics basis elongation (κₐ) based on the
        aspect ratio and a scaling factor.

        Parameters
        ----------
        vol_plasma :
            Plasma volume (m³)
        rmajor :
            Plasma major radius (m)
        rminor :
            Plasma minor radius (m)

        Returns
        -------
        kappa_ipb:
            The calculated ITER physics basis elongation.

        References
        ----------
            - Otto Kardaun, N. K. Thomsen, and Alexander Chudnovskiy,
              “Corrections to a sequence of papers in Nuclear Fusion,” Nuclear Fusion,
              vol. 48, no. 9, pp. 099801099801, Aug. 2008, doi: https://doi.org/10.1088/0029-5515/48/9/099801.
        """
        return (vol_plasma / (2.0 * np.pi * rmajor)) / (np.pi * rminor**2)

outfile = constants.NOUT instance-attribute

run()

Plasma geometry parameters

This method calculates the plasma geometry parameters based on various shaping terms and input values. It updates the physics_variables with calculated values for kappa, triangularity, surface area, volume, etc.

References

- J D Galambos, STAR Code : Spherical Tokamak Analysis and Reactor Code,
  unpublished internal Oak Ridge document
- H. Zohm et al, On the Physics Guidelines for a Tokamak DEMO,
  FTP/3-3, Proc. IAEA Fusion Energy Conference, October 2012, San Diego

Source code in process/models/physics/plasma_geometry.py

def run(self):
    """Plasma geometry parameters

    This method calculates the plasma geometry parameters based on various shaping
    terms and input values. It updates the `physics_variables` with calculated
    values for kappa, triangularity, surface area, volume, etc.

    References
    ----------
        - J D Galambos, STAR Code : Spherical Tokamak Analysis and Reactor Code,
          unpublished internal Oak Ridge document
        - H. Zohm et al, On the Physics Guidelines for a Tokamak DEMO,
          FTP/3-3, Proc. IAEA Fusion Energy Conference, October 2012, San Diego
    """
    xsi = 0.0e0
    xso = 0.0e0
    thetai = 0.0e0
    thetao = 0.0e0
    xi = 0.0e0
    xo = 0.0e0

    # Define plasma minor radius from major radius and aspect ratio
    physics_variables.rminor = physics_variables.rmajor / physics_variables.aspect

    # Define the inverse aspect ratio
    physics_variables.eps = 1.0e0 / physics_variables.aspect

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

    if (
        physics_variables.i_plasma_geometry == PlasmaGeometryModelType.IPDG89_X_POINT
    ):  # Use input kappa, physics_variables.triang values
        #  Rough estimate of 95% values
        #  ITER Physics Design Guidlines: 1989 (Uckan et al. 1990)
        #  (close to previous estimate of (physics_variables.kappa - 0.04) / 1.1
        #  over a large physics_variables.kappa range)

        physics_variables.kappa95 = physics_variables.kappa / 1.12e0
        physics_variables.triang95 = physics_variables.triang / 1.50e0

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

    if (
        physics_variables.i_plasma_geometry == PlasmaGeometryModelType.STAR_FIESTA
    ):  # ST scaling with physics_variables.aspect ratio [STAR Code]
        physics_variables.q95_min = 3.0e0 * (
            1.0e0 + 2.6e0 * physics_variables.eps**2.8e0
        )

        physics_variables.kappa = 2.05e0 * (
            1.0e0 + 0.44e0 * physics_variables.eps**2.1e0
        )
        physics_variables.triang = 0.53e0 * (
            1.0e0 + 0.77e0 * physics_variables.eps**3
        )

        # SIM 10/09/2020: Switched to FIESTA ST scaling  from IPDG89
        physics_variables.kappa95 = (
            physics_variables.kappa - 0.39467e0
        ) / 0.90698e0  # Fit to FIESTA (Issue #1086)
        physics_variables.triang95 = (
            physics_variables.triang - 0.048306e0
        ) / 1.3799e0

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

    if (
        physics_variables.i_plasma_geometry
        == PlasmaGeometryModelType.ZOHM_ITER_X_POINT
    ):  # Zohm et al. ITER scaling for elongation, input physics_variables.triang
        physics_variables.kappa = physics_variables.fkzohm * min(
            2.0e0, 1.5e0 + 0.5e0 / (physics_variables.aspect - 1.0e0)
        )

        # ITER Physics Design Guidlines: 1989 (Uckan et al. 1990)
        physics_variables.kappa95 = physics_variables.kappa / 1.12e0
        physics_variables.triang95 = physics_variables.triang / 1.50e0

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

    if (
        physics_variables.i_plasma_geometry == PlasmaGeometryModelType.ZOHM_ITER_95
    ):  # Zohm et al. ITER scaling for elongation, input physics_variables.triang95
        physics_variables.kappa = physics_variables.fkzohm * min(
            2.0e0, 1.5e0 + 0.5e0 / (physics_variables.aspect - 1.0e0)
        )

        # ITER Physics Design Guidlines: 1989 (Uckan et al. 1990)
        physics_variables.triang = 1.5e0 * physics_variables.triang95

        physics_variables.kappa95 = physics_variables.kappa / 1.12e0

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

    if (
        physics_variables.i_plasma_geometry == PlasmaGeometryModelType.IPDG89_95
    ):  # Use input kappa95, physics_variables.triang95 values
        # ITER Physics Design Guidlines: 1989 (Uckan et al. 1990)
        physics_variables.kappa = 1.12e0 * physics_variables.kappa95
        physics_variables.triang = 1.5e0 * physics_variables.triang95

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

    if (
        physics_variables.i_plasma_geometry == PlasmaGeometryModelType.MAST_DATA_95
    ):  # Use input kappa95, physics_variables.triang95 values
        # Fit to MAST data (Issue #1086)
        physics_variables.kappa = 0.91300e0 * physics_variables.kappa95 + 0.38654e0
        physics_variables.triang = 0.77394e0 * physics_variables.triang95 + 0.18515e0

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

    if (
        physics_variables.i_plasma_geometry
        == PlasmaGeometryModelType.MAST_DATA_X_POINT
    ):  # Use input kappa, physics_variables.triang values
        # Fit to MAST data (Issue #1086)
        physics_variables.kappa95 = (physics_variables.kappa - 0.38654e0) / 0.91300e0
        physics_variables.triang95 = (
            physics_variables.triang - 0.18515e0
        ) / 0.77394e0

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

    if (
        physics_variables.i_plasma_geometry == PlasmaGeometryModelType.FIESTA_RUNS_95
    ):  # Use input kappa95, physics_variables.triang95 values
        # Fit to FIESTA (Issue #1086)
        physics_variables.kappa = 0.90698e0 * physics_variables.kappa95 + 0.39467e0
        physics_variables.triang = 1.3799e0 * physics_variables.triang95 + 0.048306e0

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

    if (
        physics_variables.i_plasma_geometry
        == PlasmaGeometryModelType.FIESTA_RUNS_X_POINT
    ):  # Use input kappa, physics_variables.triang values
        # Fit to FIESTA (Issue #1086)
        physics_variables.kappa95 = (physics_variables.kappa - 0.39467e0) / 0.90698e0
        physics_variables.triang95 = (
            physics_variables.triang - 0.048306e0
        ) / 1.3799e0

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

    if (
        physics_variables.i_plasma_geometry
        == PlasmaGeometryModelType.INDUCTANCE_SCALING_X_POINT
    ):  # Use input triang, physics_variables.ind_plasma_internal_norm values
        # physics_variables.kappa found from physics_variables.aspect ratio and
        # plasma internal inductance li(3)
        physics_variables.kappa = (
            1.09e0 + 0.26e0 / physics_variables.ind_plasma_internal_norm
        ) * (1.5e0 / physics_variables.aspect) ** 0.4e0

        physics_variables.kappa95 = physics_variables.kappa / 1.12e0
        physics_variables.triang95 = physics_variables.triang / 1.50e0

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

    if (
        physics_variables.i_plasma_geometry
        == PlasmaGeometryModelType.CREATE_DATA_EU_DEMO_X_POINT
    ):
        # physics_variables.kappa95 found from physics_variables.aspect ratio and
        # stability margin Based on fit to CREATE data. ref Issue #1399
        # valid for EU-DEMO like machine - physics_variables.aspect ratio 2.6 - 3.6
        # Model updated see Issue #1648
        a = 3.68436807e0
        b = -0.27706527e0
        c = 0.87040251e0
        d = -18.83740952e0
        e = -0.27267618e0
        f = 20.5141261e0

        physics_variables.kappa95 = (
            -d
            - c * physics_variables.aspect
            - np.sqrt(
                (c**2.0e0 - 4.0e0 * a * b) * physics_variables.aspect**2.0e0
                + (2.0e0 * d * c - 4.0e0 * a * e) * physics_variables.aspect
                + d**2.0e0
                - 4.0e0 * a * f
                + 4.0e0 * a * physics_variables.m_s_limit
            )
        ) / (2.0e0 * a)

        if physics_variables.kappa95 > 1.77:
            ratio = 1.77 / physics_variables.kappa95
            corner_fudge = 0.3 * (physics_variables.kappa95 - 1.77) / ratio
            physics_variables.kappa95 = (
                physics_variables.kappa95 ** (ratio) + corner_fudge
            )

        physics_variables.kappa = 1.12e0 * physics_variables.kappa95
        physics_variables.triang95 = physics_variables.triang / 1.50e0

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

    if (
        physics_variables.i_plasma_geometry
        == PlasmaGeometryModelType.MENARD_2016_X_POINT
    ):
        # See Issue #1439
        # physics_variables.triang is an input
        # physics_variables.kappa found from physics_variables.aspect ratio scaling
        # on p32 of Menard: Menard, et al. "Fusion Nuclear Science Facilities
        # and Pilot Plants Based on the Spherical Tokamak." Nucl. Fusion, 2016, 44.

        physics_variables.kappa = 0.95e0 * (
            1.9e0 + 1.9e0 / physics_variables.aspect**1.4e0
        )
        physics_variables.kappa95 = physics_variables.kappa / 1.12e0
        physics_variables.triang95 = physics_variables.triang / 1.50e0

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

    if (
        physics_variables.i_plasma_geometry
        == PlasmaGeometryModelType.MENARD_1997_X_POINT
    ):
        # physics_variables.triang is an input
        # physics_variables.kappa found from physics_variables.aspect ratio scaling from
        # J.E. Menard et al 1997 Nucl. Fusion 37 595 and assume max controllable kappa
        # and assume lᵢ(3) is held constant

        physics_variables.kappa = (
            2.93e0 * (1.8e0 / physics_variables.aspect) ** 0.4e0
        )

        physics_variables.kappa95 = physics_variables.kappa / 1.12e0
        physics_variables.triang95 = physics_variables.triang / 1.50e0

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

    #  Scrape-off layer thicknesses
    if physics_variables.i_plasma_wall_gap == 0:
        self.data.build.dr_fw_plasma_gap_outboard = 0.1e0 * physics_variables.rminor
        self.data.build.dr_fw_plasma_gap_inboard = 0.1e0 * physics_variables.rminor

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

    # Find parameters of arcs describing plasma surfaces
    xi, thetai, xo, thetao = self.plasma_angles_arcs(
        physics_variables.rminor,
        physics_variables.kappa,
        physics_variables.triang,
    )

    #  Surface area - inboard and outboard.  These are not given by Sauter but
    #  the outboard area is required by DCLL and divertor
    xsi, xso = self.plasma_surface_area(
        physics_variables.rmajor,
        physics_variables.rminor,
        xi,
        thetai,
        xo,
        thetao,
    )
    physics_variables.a_plasma_surface_outboard = xso

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

    # i_plasma_current = 8 specifies use of the Sauter geometry as well as plasma
    # current.
    if (
        physics_variables.i_plasma_current == 8
        or physics_variables.i_plasma_shape == PlasmaShapeModelType.SAUTER
    ):
        (
            physics_variables.len_plasma_poloidal,
            physics_variables.a_plasma_surface,
            physics_variables.a_plasma_poloidal,
            physics_variables.vol_plasma,
        ) = self.sauter_geometry(
            physics_variables.rminor,
            physics_variables.rmajor,
            physics_variables.kappa,
            physics_variables.triang,
            physics_variables.plasma_square,
        )

    else:
        #  Poloidal perimeter
        physics_variables.len_plasma_poloidal = self.plasma_poloidal_perimeter(
            xi, thetai, xo, thetao
        )

        #  Volume
        physics_variables.vol_plasma = (
            physics_variables.f_vol_plasma
            * self.plasma_volume(
                physics_variables.rmajor,
                physics_variables.rminor,
                xi,
                thetai,
                xo,
                thetao,
            )
        )

        #  Cross-sectional area
        physics_variables.a_plasma_poloidal = self.plasma_cross_section(
            xi, thetai, xo, thetao
        )

        #  Surface area - sum of inboard and outboard.
        physics_variables.a_plasma_surface = xsi + xso

output()

Output plasma geometry parameters to file.

Raises:

Type	Description
ProcessValueError	If n_divertors has an illegal value.

Source code in process/models/physics/plasma_geometry.py

def output(self):
    """Output plasma geometry parameters to file.

    Raises
    ------
    ProcessValueError
        If `n_divertors` has an illegal value.
    """
    po.oheadr(self.outfile, "Plasma Geometry")

    if self.data.stellarator.istell == 0:
        if self.data.divertor.n_divertors == 0:
            po.ocmmnt(self.outfile, "Plasma configuration = limiter")
        elif self.data.divertor.n_divertors == 1:
            po.ocmmnt(self.outfile, "Plasma configuration = single null divertor")
        elif self.data.divertor.n_divertors == 2:
            po.ocmmnt(self.outfile, "Plasma configuration = double null divertor")
        else:
            raise ProcessValueError(
                "Illegal value of n_divertors",
                n_divertors=self.data.divertor.n_divertors,
            )
    else:
        po.ocmmnt(self.outfile, "Plasma configuration = stellarator")

    if self.data.stellarator.istell == 0:
        if physics_variables.itart == 0:
            physics_variables.itart_r = physics_variables.itart
            po.ovarin(
                self.outfile,
                "Tokamak aspect ratio = Conventional, itart = 0",
                "(itart)",
                physics_variables.itart_r,
            )
        elif physics_variables.itart == 1:
            physics_variables.itart_r = physics_variables.itart
            po.ovarin(
                self.outfile,
                "Tokamak aspect ratio = Spherical, itart = 1",
                "(itart)",
                physics_variables.itart_r,
            )

    po.ovarin(
        self.outfile,
        "Plasma shaping model",
        "(i_plasma_shape)",
        physics_variables.i_plasma_shape,
    )

    po.osubhd(
        self.outfile,
        f"{PlasmaShapeModelType(physics_variables.i_plasma_shape).full_name} "
        "plasma shape model is used :",
    )

    po.ovarrf(
        self.outfile, "Major radius (R₀) (m)", "(rmajor)", physics_variables.rmajor
    )
    po.ovarrf(
        self.outfile,
        "Minor radius (a) (m)",
        "(rminor)",
        physics_variables.rminor,
        "OP ",
    )
    po.ovarrf(self.outfile, "Aspect ratio (A)", "(aspect)", physics_variables.aspect)
    po.ovarrf(
        self.outfile,
        "Plasma squareness (ζ)",
        "(plasma_square)",
        physics_variables.plasma_square,
        "IP",
    )
    po.oblnkl(self.outfile)

    po.ovarin(
        self.outfile,
        "Plasma geometry model",
        "(i_plasma_geometry)",
        physics_variables.i_plasma_geometry,
    )
    po.oblnkl(self.outfile)
    po.ovarre(
        self.outfile,
        "ITER Physics Basis definition of elongation (κₐ)",
        "(kappa_ipb)",
        physics_variables.kappa_ipb,
        "OP ",
    )
    po.oblnkl(self.outfile)
    geom_type = PlasmaGeometryModelType(physics_variables.i_plasma_geometry)

    if self.data.stellarator.istell == 0:
        po.ocmmnt(
            self.outfile,
            f"X-Point Elongation set from: {geom_type.kappa_model.description}",
        )

        po.ovarrf(
            self.outfile,
            "Elongation, X-point (κₐ)",
            "(kappa)",
            physics_variables.kappa,
            "IP"
            if geom_type.kappa_model == PlasmaGeometryModels.USER_INPUT
            else "OP",
        )
        if geom_type.kappa_model == PlasmaGeometryModels.ZOHM_ITER:
            po.ovarrf(
                self.outfile,
                "Zohm scaling adjustment factor",
                "(fkzohm)",
                physics_variables.fkzohm,
            )

        po.oblnkl(self.outfile)

        po.ocmmnt(
            self.outfile,
            f"95% Elongation set from: {geom_type.kappa95_model.description}",
        )
        po.ovarrf(
            self.outfile,
            "Elongation, 95% surface (κ₉₅)",
            "(kappa95)",
            physics_variables.kappa95,
            "IP"
            if geom_type.kappa95_model == PlasmaGeometryModels.USER_INPUT
            else "OP",
        )

        po.oblnkl(self.outfile)

        po.ocmmnt(
            self.outfile,
            f"X-Point Triangularity set from: {geom_type.triang_model.description}",
        )

        po.ovarrf(
            self.outfile,
            "Triangularity, X-point (δ)",
            "(triang)",
            physics_variables.triang,
            "IP "
            if geom_type.triang_model == PlasmaGeometryModels.USER_INPUT
            else "OP",
        )
        po.oblnkl(self.outfile)
        po.ocmmnt(
            self.outfile,
            f"95% Triangularity set from: {geom_type.triang95_model.description}",
        )

        po.ovarrf(
            self.outfile,
            "Triangularity, 95% surface (δ₉₅)",
            "(triang95)",
            physics_variables.triang95,
            "IP "
            if geom_type.triang95_model == PlasmaGeometryModels.USER_INPUT
            else "OP",
        )

        po.oblnkl(self.outfile)

        po.ovarrf(
            self.outfile,
            "Plasma poloidal perimeter (m)",
            "(len_plasma_poloidal)",
            physics_variables.len_plasma_poloidal,
            "OP ",
        )

        po.ovarre(
            self.outfile,
            "Plasma cross-sectional area (m²)",
            "(a_plasma_poloidal)",
            physics_variables.a_plasma_poloidal,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Plasma surface area (m²)",
            "(a_plasma_surface)",
            physics_variables.a_plasma_surface,
            "OP ",
        )
        po.ovarre(
            self.outfile,
            "Plasma volume (m³)",
            "(vol_plasma)",
            physics_variables.vol_plasma,
            "OP ",
        )

    po.oblnkl(self.outfile)

plasma_angles_arcs(a, kappa, triang) staticmethod

Routine to find parameters used for calculating geometrical properties for double-null plasmas.

This function finds plasma geometrical parameters, using the revolution of two intersecting arcs around the device centreline. This calculation is appropriate for plasmas with a separatrix.

Parameters:

Name	Type	Description	Default
a	float	Plasma minor radius (m)	required
kappa	float	Plasma separatrix elongation	required
triang	float	Plasma separatrix triangularity	required

Returns:

Type	Description
tuple	A tuple containing: - xi (float): Radius of arc describing inboard surface (m) - thetai (float): Half-angle of arc describing inboard surface - xo (float): Radius of arc describing outboard surface (m) - thetao (float): Half-angle of arc describing outboard surface

References

• F/MI/PJK/LOGBOOK14, p.42
• F/PL/PJK/PROCESS/CODE/047

Source code in process/models/physics/plasma_geometry.py

@staticmethod
def plasma_angles_arcs(
    a: float, kappa: float, triang: float
) -> tuple[float, float, float, float]:
    """Routine to find parameters used for calculating geometrical
    properties for double-null plasmas.

    This function finds plasma geometrical parameters, using the
    revolution of two intersecting arcs around the device centreline.
    This calculation is appropriate for plasmas with a separatrix.


    Parameters
    ----------
    a : float
        Plasma minor radius (m)
    kappa : float
        Plasma separatrix elongation
    triang : float
        Plasma separatrix triangularity

    Returns
    -------
    tuple
        A tuple containing:
        - xi (float): Radius of arc describing inboard surface (m)
        - thetai (float): Half-angle of arc describing inboard surface
        - xo (float): Radius of arc describing outboard surface (m)
        - thetao (float): Half-angle of arc describing outboard surface


    References
    ----------
    - F/MI/PJK/LOGBOOK14, p.42
    - F/PL/PJK/PROCESS/CODE/047
    """
    t = 1.0e0 - triang
    denomi = (kappa**2 - t**2) / (2.0e0 * t)
    thetai = np.arctan(kappa / denomi)
    xi = a * (denomi + 1.0e0 - triang)

    #  Find radius and half-angle of outboard arc

    n = 1.0e0 + triang
    denomo = (kappa**2 - n**2) / (2.0e0 * n)
    thetao = np.arctan(kappa / denomo)
    xo = a * (denomo + 1.0e0 + triang)

    return xi, thetai, xo, thetao

plasma_poloidal_perimeter(xi, thetai, xo, thetao) staticmethod

Calculate the poloidal perimeter of the plasma.

Parameters:

Name	Type	Description	Default
xi	float	Radius of arc describing inboard surface (m)	required
thetai	float	Half-angle of arc describing inboard surface	required
xo	float	Radius of arc describing outboard surface (m)	required
thetao	float	Half-angle of arc describing outboard surface	required

Returns:

Type	Description
float	Poloidal perimeter (m)

Source code in process/models/physics/plasma_geometry.py

@staticmethod
def plasma_poloidal_perimeter(
    xi: float, thetai: float, xo: float, thetao: float
) -> float:
    """Calculate the poloidal perimeter of the plasma.

    Parameters
    ----------
    xi : float
        Radius of arc describing inboard surface (m)
    thetai : float
        Half-angle of arc describing inboard surface
    xo : float
        Radius of arc describing outboard surface (m)
    thetao : float
        Half-angle of arc describing outboard surface

    Returns
    -------
    float
        Poloidal perimeter (m)
    """
    return 2.0e0 * (xo * thetao + xi * thetai)

plasma_surface_area(rmajor, rminor, xi, thetai, xo, thetao) staticmethod

Plasma surface area calculation

This function finds the plasma surface area, using the revolution of two intersecting arcs around the device centreline. This calculation is appropriate for plasmas with a separatrix.

Parameters:

Name	Type	Description	Default
rmajor	float	Plasma major radius (m)	required
rminor	float	Plasma minor radius (m)	required
xi	float	Radius of arc describing inboard surface (m)	required
thetai	float	Half-angle of arc describing inboard surface	required
xo	float	Radius of arc describing outboard surface (m)	required
thetao	float	Half-angle of arc describing outboard surface	required

Returns:

Type	Description
tuple	A tuple containing: - xsi (float): Inboard surface area (m^2) - xso (float): Outboard surface area (m^2)

References

• F/MI/PJK/LOGBOOK14, p.43

Source code in process/models/physics/plasma_geometry.py

@staticmethod
def plasma_surface_area(
    rmajor: float, rminor: float, xi: float, thetai: float, xo: float, thetao: float
) -> tuple[float, float]:
    """Plasma surface area calculation

    This function finds the plasma surface area, using the
    revolution of two intersecting arcs around the device centreline.
    This calculation is appropriate for plasmas with a separatrix.

    Parameters
    ----------
    rmajor : float
        Plasma major radius (m)
    rminor : float
        Plasma minor radius (m)
    xi : float
        Radius of arc describing inboard surface (m)
    thetai : float
        Half-angle of arc describing inboard surface
    xo : float
        Radius of arc describing outboard surface (m)
    thetao : float
        Half-angle of arc describing outboard surface

    Returns
    -------
    tuple
        A tuple containing:
        - xsi (float): Inboard surface area (m^2)
        - xso (float): Outboard surface area (m^2)


    References
    ----------
    - F/MI/PJK/LOGBOOK14, p.43
    """
    fourpi = 4.0e0 * np.pi

    rc = rmajor - rminor + xi
    xsi = fourpi * xi * (rc * thetai - xi * np.sin(thetai))

    rc = rmajor + rminor - xo
    xso = fourpi * xo * (rc * thetao + xo * np.sin(thetao))

    return xsi, xso

plasma_volume(rmajor, rminor, xi, thetai, xo, thetao) staticmethod

Plasma volume calculation This function finds the plasma volume, using the revolution of two intersecting arcs around the device centreline. This calculation is appropriate for plasmas with a separatrix.

Parameters:

Name	Type	Description	Default
rmajor	float	Plasma major radius (m)	required
rminor	float	Plasma minor radius (m)	required
xi	float	Radius of arc describing inboard surface (m)	required
thetai	float	Half-angle of arc describing inboard surface	required
xo	float	Radius of arc describing outboard surface (m)	required
thetao	float	Half-angle of arc describing outboard surface	required

Returns:

Type	Description
float	Plasma volume (m^3)

References

• F/MI/PJK/LOGBOOK14, p.43

Source code in process/models/physics/plasma_geometry.py

@staticmethod
def plasma_volume(
    rmajor: float, rminor: float, xi: float, thetai: float, xo: float, thetao: float
) -> float:
    """Plasma volume calculation
    This function finds the plasma volume, using the
    revolution of two intersecting arcs around the device centreline.
    This calculation is appropriate for plasmas with a separatrix.

    Parameters
    ----------
    rmajor : float
        Plasma major radius (m)
    rminor : float
        Plasma minor radius (m)
    xi : float
        Radius of arc describing inboard surface (m)
    thetai : float
        Half-angle of arc describing inboard surface
    xo : float
        Radius of arc describing outboard surface (m)
    thetao : float
        Half-angle of arc describing outboard surface

    Returns
    -------
    float
        Plasma volume (m^3)


    References
    ----------
    - F/MI/PJK/LOGBOOK14, p.43
    """
    third = 1.0e0 / 3.0e0

    rc = rmajor - rminor + xi
    vin = (
        2.0
        * np.pi
        * xi
        * (
            rc**2 * np.sin(thetai)
            - rc * xi * thetai
            - 0.5e0 * rc * xi * np.sin(2.0e0 * thetai)
            + xi * xi * np.sin(thetai)
            - third * xi * xi * (np.sin(thetai)) ** 3
        )
    )

    rc = rmajor + rminor - xo
    vout = (
        2.0
        * np.pi
        * xo
        * (
            rc**2 * np.sin(thetao)
            + rc * xo * thetao
            + 0.5e0 * rc * xo * np.sin(2.0e0 * thetao)
            + xo * xo * np.sin(thetao)
            - third * xo * xo * (np.sin(thetao)) ** 3
        )
    )

    return vout - vin

plasma_cross_section(xi, thetai, xo, thetao) staticmethod

Plasma cross-sectional area calculation

This function finds the plasma cross-sectional area, using the revolution of two intersecting arcs around the device centreline. This calculation is appropriate for plasmas with a separatrix.

Parameters:

Name	Type	Description	Default
xi	float	Radius of arc describing inboard surface (m)	required
thetai	float	Half-angle of arc describing inboard surface	required
xo	float	Radius of arc describing outboard surface (m)	required
thetao	float	Half-angle of arc describing outboard surface	required

Returns:

Type	Description
float	Plasma cross-sectional area (m^2)

References

• F/MI/PJK/LOGBOOK14, p.41

Source code in process/models/physics/plasma_geometry.py

@staticmethod
def plasma_cross_section(
    xi: float, thetai: float, xo: float, thetao: float
) -> float:
    """Plasma cross-sectional area calculation

    This function finds the plasma cross-sectional area, using the
    revolution of two intersecting arcs around the device centreline.
    This calculation is appropriate for plasmas with a separatrix.

    Parameters
    ----------
    xi : float
        Radius of arc describing inboard surface (m)
    thetai : float
        Half-angle of arc describing inboard surface
    xo : float
        Radius of arc describing outboard surface (m)
    thetao : float
        Half-angle of arc describing outboard surface

    Returns
    -------
    float
        Plasma cross-sectional area (m^2)


    References
    ----------
    - F/MI/PJK/LOGBOOK14, p.41
    """
    return xo**2 * (thetao - np.cos(thetao) * np.sin(thetao)) + xi**2 * (
        thetai - np.cos(thetai) * np.sin(thetai)
    )

sauter_geometry(a, r0, kappa, triang, square) staticmethod

Calculate the plasma geometry parameters using the Sauter geometry model.

Parameters:

Name	Type	Description	Default
a	float	Plasma minor radius (m)	required
r0	float	Plasma major radius (m)	required
kappa	float	Plasma separatrix elongation	required
triang	float	Plasma separatrix triangularity	required
square	float	Plasma squareness	required

Returns:

Type	Description
tuple	A tuple containing: - len_plasma_poloidal (float): Poloidal perimeter - a_plasma_surface (float): Surface area - a_plasma_poloidal (float): Cross-section area - vol_plasma (float): Plasma volume

References

- O. Sauter, “Geometric formulas for system codes including the effect of
  negative triangularity,” Fusion Engineering and Design, vol. 112,
  pp. 633-645, Nov. 2016,
  doi: https://doi.org/10.1016/j.fusengdes.2016.04.033.

Source code in process/models/physics/plasma_geometry.py

@staticmethod
def sauter_geometry(
    a: float, r0: float, kappa: float, triang: float, square: float
) -> tuple[float, float, float, float, float]:
    """Calculate the plasma geometry parameters using the Sauter geometry model.

    Parameters
    ----------
    a : float
        Plasma minor radius (m)
    r0 : float
        Plasma major radius (m)
    kappa : float
        Plasma separatrix elongation
    triang : float
        Plasma separatrix triangularity
    square : float
        Plasma squareness

    Returns
    -------
    tuple
        A tuple containing:
        - len_plasma_poloidal (float): Poloidal perimeter
        - a_plasma_surface (float): Surface area
        - a_plasma_poloidal (float): Cross-section area
        - vol_plasma (float): Plasma volume


    References
    ----------
        - O. Sauter, “Geometric formulas for system codes including the effect of
          negative triangularity,” Fusion Engineering and Design, vol. 112,
          pp. 633-645, Nov. 2016,
          doi: https://doi.org/10.1016/j.fusengdes.2016.04.033.
    """
    # Calculate w07 parameter from paper from squareness assuming top-down symmetry
    w07 = square + 1

    # Inverse aspect ratio
    eps = a / r0

    # Poloidal perimeter (named Lp in Sauter)
    len_plasma_poloidal = (
        2.0e0
        * np.pi
        * a
        * (1 + 0.55 * (kappa - 1))
        * (1 + 0.08 * triang**2)
        * (1 + 0.2 * (w07 - 1))
    )

    # Surface area (named Ap in Sauter)
    a_plasma_surface = (
        2.0e0 * np.pi * r0 * (1 - 0.32 * triang * eps) * len_plasma_poloidal
    )

    # Cross-section area (named S_phi in Sauter)
    a_plasma_poloidal = np.pi * a**2 * kappa * (1 + 0.52 * (w07 - 1))

    # Volume
    vol_plasma = 2.0e0 * np.pi * r0 * (1 - 0.25 * triang * eps) * a_plasma_poloidal

    return (
        len_plasma_poloidal,
        a_plasma_surface,
        a_plasma_poloidal,
        vol_plasma,
    )

calculate_iter_physics_basis_elongation(vol_plasma, rmajor, rminor) staticmethod

Calculate the ITER physics basis elongation.

This method calculates the ITER physics basis elongation (κₐ) based on the aspect ratio and a scaling factor.

Parameters:

Name	Type	Description	Default
vol_plasma	float	Plasma volume (m³)	required
rmajor	float	Plasma major radius (m)	required
rminor	float	Plasma minor radius (m)	required

Returns:

Name	Type	Description
kappa_ipb	float	The calculated ITER physics basis elongation.

References

- Otto Kardaun, N. K. Thomsen, and Alexander Chudnovskiy,
  “Corrections to a sequence of papers in Nuclear Fusion,” Nuclear Fusion,
  vol. 48, no. 9, pp. 099801099801, Aug. 2008, doi: https://doi.org/10.1088/0029-5515/48/9/099801.

Source code in process/models/physics/plasma_geometry.py

@staticmethod
def calculate_iter_physics_basis_elongation(
    vol_plasma: float, rmajor: float, rminor: float
) -> float:
    """Calculate the ITER physics basis elongation.

    This method calculates the ITER physics basis elongation (κₐ) based on the
    aspect ratio and a scaling factor.

    Parameters
    ----------
    vol_plasma :
        Plasma volume (m³)
    rmajor :
        Plasma major radius (m)
    rminor :
        Plasma minor radius (m)

    Returns
    -------
    kappa_ipb:
        The calculated ITER physics basis elongation.

    References
    ----------
        - Otto Kardaun, N. K. Thomsen, and Alexander Chudnovskiy,
          “Corrections to a sequence of papers in Nuclear Fusion,” Nuclear Fusion,
          vol. 48, no. 9, pp. 099801099801, Aug. 2008, doi: https://doi.org/10.1088/0029-5515/48/9/099801.
    """
    return (vol_plasma / (2.0 * np.pi * rmajor)) / (np.pi * rminor**2)

surfa(a, r, k, d)

Plasma surface area calculation

This function finds the plasma surface area, using the revolution of two intersecting arcs around the device centreline. This calculation is appropriate for plasmas with a separatrix. It was the original method in PROCESS.

Parameters:

Name	Type	Description	Default
a	float	Plasma minor radius (m)	required
r	float	Plasma major radius (m)	required
k	float	Plasma separatrix elongation	required
d	float	Plasma separatrix triangularity	required

Returns:

Type	Description
tuple	A tuple containing: - sa (float): Plasma total surface area (m^2) - so (float): Plasma outboard surface area (m^2)

References

• J D Galambos, STAR Code : Spherical Tokamak Analysis and Reactor Code, unpublished internal Oak Ridge document

Source code in process/models/physics/plasma_geometry.py

def surfa(a: float, r: float, k: float, d: float) -> tuple[float, float]:
    """Plasma surface area calculation

    This function finds the plasma surface area, using the
    revolution of two intersecting arcs around the device centreline.
    This calculation is appropriate for plasmas with a separatrix.
    It was the original method in PROCESS.

    Parameters
    ----------
    a : float
        Plasma minor radius (m)
    r : float
        Plasma major radius (m)
    k : float
        Plasma separatrix elongation
    d : float
        Plasma separatrix triangularity

    Returns
    -------
    tuple
        A tuple containing:
        - sa (float): Plasma total surface area (m^2)
        - so (float): Plasma outboard surface area (m^2)


    References
    ----------
    - J D Galambos, STAR Code : Spherical Tokamak Analysis and Reactor Code,
    unpublished internal Oak Ridge document
    """
    radco = a * (1.0e0 + (k**2 + d**2 - 1.0e0) / (2.0e0 * (1.0e0 + d)))
    b = k * a
    thto = np.arcsin(b / radco)
    so = 4.0e0 * np.pi * radco * ((r + a - radco) * thto + b)

    #  Inboard side

    radci = a * (1.0e0 + (k**2 + d**2 - 1.0e0) / (2.0e0 * (1.0e0 - d)))
    thti = np.arcsin(b / radci)
    si = 4.0e0 * np.pi * radci * ((r - a + radci) * thti - b)

    sa = so + si

    return sa, so

perim(a, kap, tri)

Plasma poloidal perimeter calculation

This function finds the plasma poloidal perimeter, using the revolution of two intersecting arcs around the device centreline. This calculation is appropriate for plasmas with a separatrix.

Parameters:

Name	Type	Description	Default
a	float	Plasma minor radius (m)	required
kap	float	Plasma separatrix elongation	required
tri	float	Plasma separatrix triangularity	required

Returns:

Type	Description
float	Plasma poloidal perimeter (m)

References

• F/PL/PJK/PROCESS/CODE/047

Source code in process/models/physics/plasma_geometry.py

def perim(a: float, kap: float, tri: float) -> float:
    """Plasma poloidal perimeter calculation

    This function finds the plasma poloidal perimeter, using the
    revolution of two intersecting arcs around the device centreline.
    This calculation is appropriate for plasmas with a separatrix.

    Parameters
    ----------
    a : float
        Plasma minor radius (m)
    kap : float
        Plasma separatrix elongation
    tri : float
        Plasma separatrix triangularity

    Returns
    -------
    float
        Plasma poloidal perimeter (m)


    References
    ----------
    - F/PL/PJK/PROCESS/CODE/047
    """
    #  Inboard arc

    denomi = (tri**2 + kap**2 - 1.0e0) / (2.0e0 * (1.0e0 - tri)) + tri
    thetai = np.arctan(kap / denomi)
    xli = a * (denomi + 1.0e0 - tri)

    #  Outboard arc

    denomo = (tri**2 + kap**2 - 1.0e0) / (2.0e0 * (1.0e0 + tri)) - tri
    thetao = np.arctan(kap / denomo)
    xlo = a * (denomo + 1.0e0 + tri)

    return 2.0e0 * (xlo * thetao + xli * thetai)

fvol(r, a, kap, tri)

Plasma volume calculation

This function finds the plasma volume, using the revolution of two intersecting arcs around the device centreline. This calculation is appropriate for plasmas with a separatrix.

Parameters:

Name	Type	Description	Default
r	float	Plasma major radius (m)	required
a	float	Plasma minor radius (m)	required
kap	float	Plasma separatrix elongation	required
tri	float	Plasma separatrix triangularity	required

Returns:

Type	Description
float	Plasma volume (m^3)

References

• F/MI/PJK/LOGBOOK14, p.41
• F/PL/PJK/PROCESS/CODE/047

Source code in process/models/physics/plasma_geometry.py

def fvol(r: float, a: float, kap: float, tri: float) -> float:
    """Plasma volume calculation

    This function finds the plasma volume, using the
    revolution of two intersecting arcs around the device centreline.
    This calculation is appropriate for plasmas with a separatrix.

    Parameters
    ----------
    r : float
        Plasma major radius (m)
    a : float
        Plasma minor radius (m)
    kap : float
        Plasma separatrix elongation
    tri : float
        Plasma separatrix triangularity

    Returns
    -------
    float
        Plasma volume (m^3)


    References
    ----------
    - F/MI/PJK/LOGBOOK14, p.41
    - F/PL/PJK/PROCESS/CODE/047
    """
    zn = kap * a

    c1 = ((r + a) ** 2 - (r - tri * a) ** 2 - zn**2) / (2.0e0 * (1.0e0 + tri) * a)
    rc1 = r + a - c1
    vout = (
        -0.66666666e0 * np.pi * zn**3
        + 2.0e0 * np.pi * zn * (c1**2 + rc1**2)
        + 2.0e0
        * np.pi
        * c1
        * (zn * np.sqrt(rc1**2 - zn**2) + rc1**2 * np.arcsin(zn / rc1))
    )

    c2 = (-((r - a) ** 2) + (r - tri * a) ** 2 + zn**2) / (2.0e0 * (1.0e0 - tri) * a)
    rc2 = c2 - r + a
    vin = (
        -0.66666e0 * np.pi * zn**3
        + 2.0e0 * np.pi * zn * (rc2**2 + c2**2)
        - 2.0e0
        * np.pi
        * c2
        * (zn * np.sqrt(rc2**2 - zn**2) + rc2**2 * np.arcsin(zn / rc2))
    )

    return vout - vin

xsect0(a, kap, tri)

Plasma cross-sectional area calculation

This function finds the plasma cross-sectional area, using the revolution of two intersecting arcs around the device centreline. This calculation is appropriate for plasmas with a separatrix.

Parameters:

Name	Type	Description	Default
a	float	Plasma minor radius (m)	required
kap	float	Plasma separatrix elongation	required
tri	float	Plasma separatrix triangularity	required

Returns:

Type	Description
float	Plasma cross-sectional area (m^2)

References

• F/MI/PJK/LOGBOOK14, p.41
• F/PL/PJK/PROCESS/CODE/047

Source code in process/models/physics/plasma_geometry.py

def xsect0(a: float, kap: float, tri: float) -> float:
    """Plasma cross-sectional area calculation

    This function finds the plasma cross-sectional area, using the
    revolution of two intersecting arcs around the device centreline.
    This calculation is appropriate for plasmas with a separatrix.

    Parameters
    ----------
    a : float
        Plasma minor radius (m)
    kap : float
        Plasma separatrix elongation
    tri : float
        Plasma separatrix triangularity

    Returns
    -------
    float
        Plasma cross-sectional area (m^2)

    References
    ----------
    - F/MI/PJK/LOGBOOK14, p.41
    - F/PL/PJK/PROCESS/CODE/047
    """
    denomi = (tri**2 + kap**2 - 1.0e0) / (2.0e0 * (1.0e0 - tri)) + tri
    thetai = np.arctan(kap / denomi)
    xli = a * (denomi + 1.0e0 - tri)

    cti = np.cos(thetai)
    sti = np.sin(thetai)

    #  Find radius and half-angle of outboard arc

    denomo = (tri**2 + kap**2 - 1.0e0) / (2.0e0 * (1.0e0 + tri)) - tri
    thetao = np.arctan(kap / denomo)
    xlo = a * (denomo + 1.0e0 + tri)

    cto = np.cos(thetao)
    sto = np.sin(thetao)

    #  Find cross-sectional area

    return xlo**2 * (thetao - cto * sto) + xli**2 * (thetai - cti * sti)