scrape_off_layer

Module for calculating plasma scrape off layer physics

ScrapeOffLayer

Bases: Model

Model for calculating plasma scrape off layer physics.

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

class ScrapeOffLayer(Model):
    """Model for calculating plasma scrape off layer physics."""

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

    def run(self):
        """Calculate the scrape off layer physics and update the physics variables."""
        self.data.physics.len_plasma_sol_eich13_power_decay = self.calculate_eich2013_sol_power_decay_length(  # noqa: E501
            p_plasma_separatrix_mw=self.data.physics.p_plasma_separatrix_mw,
            rmajor=self.data.physics.rmajor,
            b_plasma_surface_poloidal_average=self.data.physics.b_plasma_surface_poloidal_average,
            aspect=self.data.physics.aspect,
        )

        self.data.physics.len_plasma_sol_mast14_power_decay_1 = self.calculate_mast2014_sol_power_decay_length_1(  # noqa: E501
            p_plasma_separatrix_mw=self.data.physics.p_plasma_separatrix_mw,
            b_plasma_surface_poloidal_average=self.data.physics.b_plasma_surface_poloidal_average,
        )

        # NOTE: converting plasma_current from A to MA
        self.data.physics.len_plasma_sol_mast14_power_decay_2 = (
            self.calculate_mast2014_sol_power_decay_length_2(
                p_plasma_separatrix_mw=self.data.physics.p_plasma_separatrix_mw,
                cur_plasma_ma=self.data.physics.plasma_current / 1e6,
            )
        )

        self.data.physics.len_plasma_sol_eich11_jet_power_decay = (
            self.calculate_eich2011_jet_sol_power_decay_length(
                b_plasma_toroidal_on_axis=self.data.physics.b_plasma_toroidal_on_axis,
                q_cyl=self.data.physics.qstar,
                p_plasma_separatrix_mw=self.data.physics.p_plasma_separatrix_mw,
            )
        )

        self.data.physics.len_plasma_sol_eich11_jet_asdex_power_decay = (
            self.calculate_eich2011_jet_asdex_sol_power_decay_length(
                b_plasma_toroidal_on_axis=self.data.physics.b_plasma_toroidal_on_axis,
                q_cyl=self.data.physics.qstar,
                p_plasma_separatrix_mw=self.data.physics.p_plasma_separatrix_mw,
                rmajor=self.data.physics.rmajor,
            )
        )

        # Set to user input if OutbordSOLPowerDecayLengthModel = 1/USER_INUT
        match OutbordSOLPowerDecayLengthModel(
            self.data.physics.i_len_sol_outboard_power_decay
        ):
            case OutbordSOLPowerDecayLengthModel.EICH_2013:
                self.data.physics.len_sol_outboard_power_decay = (
                    self.data.physics.len_plasma_sol_eich13_power_decay
                )
            case OutbordSOLPowerDecayLengthModel.MAST_2014_1:
                self.data.physics.len_sol_outboard_power_decay = (
                    self.data.physics.len_plasma_sol_mast14_power_decay_1
                )
            case OutbordSOLPowerDecayLengthModel.MAST_2014_2:
                self.data.physics.len_sol_outboard_power_decay = (
                    self.data.physics.len_plasma_sol_mast14_power_decay_2
                )
            case OutbordSOLPowerDecayLengthModel.EICH_2011_JET:
                self.data.physics.len_sol_outboard_power_decay = (
                    self.data.physics.len_plasma_sol_eich11_jet_power_decay
                )
            case OutbordSOLPowerDecayLengthModel.EICH_2011_JET_ASDEX:
                self.data.physics.len_sol_outboard_power_decay = (
                    self.data.physics.len_plasma_sol_eich11_jet_asdex_power_decay
                )

        self.data.physics.len_sol_inboard_power_decay = (
            self.data.physics.f_len_sol_power_decay_inboard_outboard
            * self.data.physics.len_sol_outboard_power_decay
        )

        self.data.physics.a_plasma_outboard_sol_parallel = self.calculate_upstream_sol_outboard_parallel_area(  # noqa: E501
            rmajor=self.data.physics.rmajor,
            rminor=self.data.physics.rminor,
            len_plasma_sol_power_decay=self.data.physics.len_sol_outboard_power_decay,
            b_plasma_outboard_total=self.data.physics.b_plasma_outboard_total,
            b_plasma_surface_poloidal_average=self.data.physics.b_plasma_surface_poloidal_average,
        )

        self.data.physics.a_plasma_outboard_sol_eich13_parallel = self.calculate_upstream_sol_outboard_parallel_area(  # noqa: E501
            rmajor=self.data.physics.rmajor,
            rminor=self.data.physics.rminor,
            len_plasma_sol_power_decay=self.data.physics.len_plasma_sol_eich13_power_decay,
            b_plasma_outboard_total=self.data.physics.b_plasma_outboard_total,
            b_plasma_surface_poloidal_average=self.data.physics.b_plasma_surface_poloidal_average,
        )

        self.data.physics.pflux_plasma_outboard_sol_parallel_mw = (
            self.data.physics.p_plasma_separatrix_mw
            * self.data.physics.f_p_div_outboard_separatrix
            / self.data.physics.a_plasma_outboard_sol_parallel
        )

        self.data.physics.pflux_plasma_outboard_sol_eich13_parallel_mw = (
            self.data.physics.p_plasma_separatrix_mw
            / self.data.physics.a_plasma_outboard_sol_eich13_parallel
        )

        self.data.physics.len_div_outboard_lower_scarabosio15_power_spreading = self.calculate_scarabosio2015_power_spreading_factor(  # noqa: E501
            p_plasma_separatrix_mw=self.data.physics.p_plasma_separatrix_mw,
            b_plasma_surface_poloidal_average=self.data.physics.b_plasma_surface_poloidal_average,
            nd_plasma_separatrix_electron_19=self.data.physics.nd_plasma_separatrix_electron
            / 1e19,
            rmajor=self.data.physics.rmajor,
        )

        self.data.physics.len_div_outboard_lower_power_spreading = (
            self.data.physics.len_div_outboard_lower_scarabosio15_power_spreading
        )

    def output(self) -> None:
        """Output plasma scrape off layer physics information."""
        po.oheadr(self.outfile, "Plasma Scrape Off Layer")

        po.osubhd(self.outfile, "Power Decay Lengths (λ_q):")
        po.ovarre(
            self.outfile,
            "Outboard SOL power decay length model switch",
            "(i_len_sol_outboard_power_decay)",
            self.data.physics.i_len_sol_outboard_power_decay,
        )
        po.ocmmnt(
            self.outfile,
            "-> "
            + OutbordSOLPowerDecayLengthModel(
                self.data.physics.i_len_sol_outboard_power_decay
            ).description
            + " ",
        )
        po.ovarre(
            self.outfile,
            "Outboard SOL power decay length (λₒᵤₜ_q) [m]",
            "(len_sol_outboard_power_decay)",
            self.data.physics.len_sol_outboard_power_decay,
        )

        po.oblnkl(self.outfile)
        po.ovarre(
            self.outfile,
            "Inboard to outboard SOL power decay length ratio (λᵢₙ_q/λₒᵤₜ_q)",
            "(f_len_sol_power_decay_inboard_outboard)",
            self.data.physics.f_len_sol_power_decay_inboard_outboard,
        )
        po.ovarre(
            self.outfile,
            "Inboard SOL power decay length (λᵢₙ_q) [m]",
            "(len_sol_inboard_power_decay)",
            self.data.physics.len_sol_inboard_power_decay,
        )
        po.oblnkl(self.outfile)
        po.ovarre(
            self.outfile,
            "Eich 2013 SOL power decay length (λ_q) [m]",
            "(len_plasma_sol_eich13_power_decay)",
            self.data.physics.len_plasma_sol_eich13_power_decay,
        )
        po.ovarre(
            self.outfile,
            "MAST 2014 SOL power decay length 1 (λ_q) [m]",
            "(len_plasma_sol_mast14_power_decay_1)",
            self.data.physics.len_plasma_sol_mast14_power_decay_1,
        )
        po.ovarre(
            self.outfile,
            "MAST 2014 SOL power decay length 2 (λ_q) [m]",
            "(len_plasma_sol_mast14_power_decay_2)",
            self.data.physics.len_plasma_sol_mast14_power_decay_2,
        )
        po.ovarre(
            self.outfile,
            "Eich 2011 JET SOL power decay length (λ_q) [m]",
            "(len_plasma_sol_eich11_jet_power_decay)",
            self.data.physics.len_plasma_sol_eich11_jet_power_decay,
        )
        po.ovarre(
            self.outfile,
            "Eich 2011 JET + ASDEX Upgrade SOL power decay length (λ_q) [m]",
            "(len_plasma_sol_eich11_jet_asdex_power_decay)",
            self.data.physics.len_plasma_sol_eich11_jet_asdex_power_decay,
        )
        po.oblnkl(self.outfile)
        po.ocmmnt(self.outfile, "----------------------------")

        po.osubhd(self.outfile, "Upstream Outboard SOL Parallel Area and Power Flux:")

        po.ovarre(
            self.outfile,
            "Plasma outboard midplane SOL parallel area (Aₗₗ,ᵤ) [m²]",
            "(a_plasma_outboard_sol_parallel)",
            self.data.physics.a_plasma_outboard_sol_parallel,
        )
        po.oblnkl(self.outfile)

        po.ovarre(
            self.outfile,
            "Plasma outboard midplane Eich 2013 SOL parallel area (Aₗₗ,ᵤ) [m²]",
            "(a_plasma_outboard_sol_eich13_parallel)",
            self.data.physics.a_plasma_outboard_sol_eich13_parallel,
        )
        po.oblnkl(self.outfile)
        po.ovarre(
            self.outfile,
            "Plasma outboard midplane SOL parallel power flux (qₗₗ,ᵤ) [MW/m²]",
            "(pflux_plasma_outboard_sol_parallel_mw)",
            self.data.physics.pflux_plasma_outboard_sol_parallel_mw,
        )
        po.oblnkl(self.outfile)
        po.ovarre(
            self.outfile,
            "Plasma outboard midplane Eich 2013 SOL parallel power flux (qₗₗ,ᵤ) [MW/m²]",
            "(pflux_plasma_outboard_sol_eich13_parallel_mw)",
            self.data.physics.pflux_plasma_outboard_sol_eich13_parallel_mw,
        )
        po.oblnkl(self.outfile)
        po.ocmmnt(self.outfile, "----------------------------")
        po.osubhd(self.outfile, "Power Spreading Factors (S):")

        po.ovarre(
            self.outfile,
            "Outboard lower divertor power spreading factor (S) [m]",
            "(len_div_outboard_lower_power_spreading)",
            self.data.physics.len_div_outboard_lower_power_spreading,
        )
        po.ovarre(
            self.outfile,
            "Scarabosio 2015 H-mode power spreading factor (S) [m]",
            "(len_div_outboard_lower_scarabosio15_power_spreading)",
            self.data.physics.len_div_outboard_lower_scarabosio15_power_spreading,
        )
        po.oblnkl(self.outfile)
        po.ocmmnt(self.outfile, "----------------------------")
        po.oblnkl(self.outfile)
        po.ovarre(
            self.outfile,
            "Outboard lower divertor flux expansion factor for the divertor targets "
            "(fₓ)",
            "(f_b_div_outboard_lower_flux_expansion)",
            self.data.physics.f_b_div_outboard_lower_flux_expansion,
        )

    @staticmethod
    def calculate_eich2013_sol_power_decay_length(
        p_plasma_separatrix_mw: float,
        rmajor: float,
        b_plasma_surface_poloidal_average: float,
        aspect: float,
    ) -> float:
        """Calculate the Eich 2013 SOL power decay length (λ_q).

        Parameters
        ----------
        p_plasma_separatrix_mw : float
            Power crossing the separatrix (Pₛₑₚ) [MW]
        rmajor : float
            Major radius of the plasma (R₀) [m]
        b_plasma_surface_poloidal_average : float
            Poloidal magnetic field at the plasma surface (⟨Bₚₒₗ(a)⟩) [T]
        aspect : float
            Aspect ratio of the plasma (A)

        Returns
        -------
        float
            Eich 2013 SOL power decay length (λ_q) [m]

        Notes
        -----
        - The paper states that the poloidal field terms is for the outer midplane
        Bₚₒₗ(a), we are using the outer surface average

        References
        ----------
        [1] T. Eich et al., “Scaling of the tokamak near the scrape-off layer H-mode
        power width and implications for ITER,” Nuclear Fusion, vol. 53, no. 9,
        p. 093031, Aug. 2013, doi: 10.1088/0029-5515/53/9/093031.

        """
        return (
            1.35e-3
            * p_plasma_separatrix_mw**-0.02
            * rmajor**0.04
            * b_plasma_surface_poloidal_average**-0.92
            * aspect**-0.42
        )

    @staticmethod
    def calculate_mast2014_sol_power_decay_length_1(
        p_plasma_separatrix_mw: float,
        b_plasma_surface_poloidal_average: float,
    ) -> float:
        """Calculate the MAST 2014 SOL power decay length (λ_q).

        Parameters
        ----------
        p_plasma_separatrix_mw : float
            Power crossing the separatrix (Pₛₑₚ) [MW]
        b_plasma_surface_poloidal_average : float
            Poloidal magnetic field at the plasma surface (⟨Bₚₒₗ(a)⟩) [T]

        Returns
        -------
        float
            MAST 2014 SOL power decay length (λ_q) [m]

        Notes
        -----
        - The paper states that the poloidal field terms is for the outer midplane
        Bₚₒₗ(a), we are using the outer surface average

        References
        ----------
        [1] A. J. Thornton and A. Kirk, “Scaling of the scrape-off layer width during
        inter-ELM H modes on MAST as measured by infrared thermography,”
        Plasma Physics and Controlled Fusion, vol. 56, no. 5, p. 055008, Apr. 2014,
        doi: 10.1088/0741-3335/56/5/055008.

        """
        return (
            1.84e-3
            * p_plasma_separatrix_mw**0.18
            * b_plasma_surface_poloidal_average**-0.68
        )

    @staticmethod
    def calculate_mast2014_sol_power_decay_length_2(
        p_plasma_separatrix_mw: float,
        cur_plasma_ma: float,
    ) -> float:
        """Calculate the MAST 2014 SOL power decay length (λ_q).

        Parameters
        ----------
        p_plasma_separatrix_mw : float
            Power crossing the separatrix (Pₛₑₚ) [MW]
        cur_plasma_ma : float
            Plasma current (Iₚ) [MA]

        Returns
        -------
        float
            MAST 2014 SOL power decay length (λ_q) [m]


        References
        ----------
        [1] A. J. Thornton and A. Kirk, “Scaling of the scrape-off layer width during
        inter-ELM H modes on MAST as measured by infrared thermography,”
        Plasma Physics and Controlled Fusion, vol. 56, no. 5, p. 055008, Apr. 2014,
        doi: 10.1088/0741-3335/56/5/055008.

        """
        return 4.57e-3 * p_plasma_separatrix_mw**0.22 * cur_plasma_ma**-0.64

    @staticmethod
    def calculate_eich2011_jet_sol_power_decay_length(
        b_plasma_toroidal_on_axis: float,
        q_cyl: float,
        p_plasma_separatrix_mw: float,
    ) -> float:
        """Calculate the Eich 2011 JET SOL power decay length (λ_q).

        Parameters
        ----------
        b_plasma_toroidal_on_axis : float
            Toroidal magnetic field at the plasma axis (Bᴛ(R₀)) [T]
        q_cyl : float
            Cylindrical safety factor (q_cyl) [-]
        p_plasma_separatrix_mw : float
            Power crossing the separatrix (Pₛₑₚ) [MW]

        Returns
        -------
        float
            Eich 2011 JET SOL power decay length (λ_q) [m]

        Notes
        -----
        - The fit values can be found in Table 2 of [1].
        - The scaling is done for type-I ELMy H-mode plasmas

        References
        ----------
        [1] T. Eich, B. Sieglin, A. Scarabosio, W. Fundamenski, Robert James Goldston,
        and A. Herrmann, “Inter-ELM Power Decay Length for JET and ASDEX Upgrade:
        Measurement and Comparison with Heuristic Drift-Based Model,”
        Physical Review Letters, vol. 107, no. 21, Nov. 2011,
        doi: https://doi.org/10.1103/PhysRevLett.107.215001.

        """
        return (
            0.7e-3
            * b_plasma_toroidal_on_axis**-0.84
            * q_cyl**1.23
            * p_plasma_separatrix_mw**0.14
        )

    @staticmethod
    def calculate_eich2011_jet_asdex_sol_power_decay_length(
        b_plasma_toroidal_on_axis: float,
        q_cyl: float,
        p_plasma_separatrix_mw: float,
        rmajor: float,
    ) -> float:
        """Calculate the Eich 2011 JET + ASDEX Upgrade SOL power decay length (λ_q).

        Parameters
        ----------
        b_plasma_toroidal_on_axis : float
            Toroidal magnetic field at the plasma axis (Bᴛ(R₀)) [T]
        q_cyl : float
            Cylindrical safety factor (q_cyl) [-]
        p_plasma_separatrix_mw : float
            Power crossing the separatrix (Pₛₑₚ) [MW]
        rmajor : float
            Major radius of the plasma (R₀) [m]

        Returns
        -------
        float
            Eich 2011 JET + ASDEX Upgrade SOL power decay length (λ_q) [m]

        Notes
        -----
        - The fit values can be found in Table 2 of [1].
        - The scaling is done for type-I ELMy H-mode plasmas

        References
        ----------
        [1] T. Eich, B. Sieglin, A. Scarabosio, W. Fundamenski, Robert James Goldston,
        and A. Herrmann, “Inter-ELM Power Decay Length for JET and ASDEX Upgrade:
        Measurement and Comparison with Heuristic Drift-Based Model,”
        Physical Review Letters, vol. 107, no. 21, Nov. 2011,
        doi: https://doi.org/10.1103/PhysRevLett.107.215001.

        """
        return (
            0.73e-3
            * b_plasma_toroidal_on_axis**-0.78
            * q_cyl**1.2
            * p_plasma_separatrix_mw**0.1
            * rmajor**0.02
        )

    @staticmethod
    def calculate_upstream_sol_outboard_parallel_area(
        rmajor: float,
        rminor: float,
        len_plasma_sol_power_decay: float,
        b_plasma_outboard_total: float,
        b_plasma_surface_poloidal_average: float,
    ) -> float:
        """Calculate the outboard SOL upstream parallel area (Aₗₗ,ᵤ) [m²].

        Parameters
        ----------
        rmajor : float
            Major radius of the plasma (R₀) [m]
        rminor : float
            Minor radius of the plasma (a) [m]
        len_plasma_sol_power_decay : float
            Power decay length (λ_q) [m]
        b_plasma_outboard_total : float
            Total magnetic field at the plasma outboard (Bₜₒₜ(R₀+a)) [T]
        b_plasma_surface_poloidal_average : float
            Poloidal magnetic field at the plasma surface (⟨Bₚₒₗ(a)⟩) [T]

        Returns
        -------
        float
            Upstream outboard SOL parallel area (Aₗₗ,ᵤ) [m²]

        References
        ----------
        [1] P. C. Stangeby, “The Plasma Boundary of Magnetic Fusion Devices,” Jan. 2000,
        doi: 10.1201/9780367801489.

        [2] S. S. Henderson et al., “An overview of the STEP divertor design and the
        simple models driving the plasma exhaust scenario,” Nuclear Fusion, vol. 65,
        no. 1, pp. 016033-016033, Nov. 2024, doi: 10.1088/1741-4326/ad93e7.

        """
        return (
            (2 * np.pi * (rmajor + rminor))
            * len_plasma_sol_power_decay
            * (b_plasma_surface_poloidal_average / b_plasma_outboard_total)
        )

    @staticmethod
    def calculate_outboard_midplane_near_sol_radial_profile(
        rmajor: float,
        rminor: float,
        len_plasma_sol_power_decay: float,
        pflux_plasma_outboard_sol_parallel_mw: float,
        r: float | np.ndarray,
    ) -> float | np.ndarray:
        """Calculate the outboard midplane near SOL radial profile (qₗₗ(r)) [MW/m²].

        Parameters
        ----------
        rmajor : float
            Major radius of the plasma (R₀) [m]
        rminor : float
            Minor radius of the plasma (a) [m]
        len_plasma_sol_power_decay : float
            Power decay length (λ_q) [m]
        pflux_plasma_outboard_sol_parallel_mw : float
            Parallel power flux at the outboard midplane (qₗₗ,ᵤ) [MW/m²]
        r : float|np.ndarray
            Radial position(s) at which to calculate the SOL profile [m]

        Returns
        -------
        float|np.ndarray
            Outboard midplane SOL radial profile (qₗₗ(r)) [MW/m²]

        Raises
        ------
        ValueError
            If any radial position r is inside the plasma edge (r < rmajor + rminor)

        Notes
        -----
        - The exponential model is highly valid in the "near-SOL" (typically the first
        few millimeters to a centimeter outside the separatrix). In this region, parallel
        heat transport is dominated by classical electron heat conduction
        (Spitzer-Härm conductivity), which is vastly faster than perpendicular diffusion.
        This competition between fast parallel conduction and slow perpendicular
        diffusion naturally produces an exponential radial profile.

        - The midplane exponential assumes steady-state H-mode conditions without the
        massive, transient convective bursts caused by ELMs, which momentarily
        flatten the entire midplane profile.

        References
        ----------
        [1] T. Eich et al., “Scaling of the tokamak near the scrape-off layer H-mode
        power width and implications for ITER,” Nuclear Fusion, vol. 53, no. 9,
        p. 093031, Aug. 2013, doi: 10.1088/0029-5515/53/9/093031.

        """
        if np.any(r < (rmajor + rminor)):
            raise ValueError(
                f"Radial position {r=} must be greater than or equal to the plasma "
                f"edge {(rmajor + rminor)=}."
            )

        return pflux_plasma_outboard_sol_parallel_mw * np.exp(
            -(r - (rmajor + rminor)) / len_plasma_sol_power_decay
        )

    @staticmethod
    def calculate_eich_target_heat_flux_profile(
        rmajor: float,
        rminor: float,
        pflux_plasma_sol_parallel_mw: float,
        len_plasma_sol_power_decay: float,
        f_b_div_flux_expansion: float,
        len_plasma_sol_power_spreading: float,
        pflux_target_background_heat_flux_mw: float,
        r: float | np.ndarray,
    ) -> float | np.ndarray:
        """Calculate the Eich parallel target heat flux profile (qₗₗ,ₜ(r)) [MW/m²].

        Parameters
        ----------
        rmajor : float
            Major radius of the plasma (R₀) [m]
        rminor : float
            Minor radius of the plasma (a) [m]
        pflux_plasma_sol_parallel_mw : float
            Parallel power flux at the outboard midplane (qₗₗ,ᵤ) [MW/m²]
        len_plasma_sol_power_decay : float
            Power decay length (λ_q) [m]
        f_b_div_flux_expansion : float
            Divertor flux expansion factor (fₓ) [-]
        len_plasma_sol_power_spreading : float
            Power spreading length in the divertor (S) [m]
        pflux_target_background_heat_flux_mw : float
            Background heat flux at the divertor target [MW/m²]
        r : float|np.ndarray
            Radial position(s) at which to calculate the target heat flux profile [m]

        Returns
        -------
        float|np.ndarray
            Eich parallel target heat flux profile (qₗₗ,ₜ(r)) [MW/m²]

        Notes
        -----
        - The Eich parallel target heat flux profile is derived from the midplane
        exponential profile, taking into account the magnetic geometry and flux expansion
        between the midplane and the divertor target. The profile is typically
        characterized by a combination of an exponential decay and a Gaussian spreading
        due to cross-field transport in the divertor leg.

        References
        ----------
        [1] T. Eich, B. Sieglin, A. Scarabosio, W. Fundamenski, R. J. Goldston, and
        A. Herrmann, “Inter-ELM Power Decay Length for JET and ASDEX Upgrade: Measurement
        and Comparison with Heuristic Drift-Based Model,” Physical Review Letters,
        vol. 107, no. 21, Nov. 2011, doi: https://doi.org/10.1103/PhysRevLett.107.215001

        [2] T. Eich et al., “Scaling of the tokamak near the scrape-off layer H-mode
        power width and implications for ITER,” Nuclear Fusion, vol. 53, no. 9,
        p. 093031, Aug. 2013, doi: 10.1088/0029-5515/53/9/093031.

        """
        return (pflux_plasma_sol_parallel_mw / 2) * np.exp(
            (
                (len_plasma_sol_power_spreading)
                / (2 * len_plasma_sol_power_decay * f_b_div_flux_expansion)
            )
            ** 2
            - (
                (r - (rmajor + rminor))
                / (len_plasma_sol_power_decay * f_b_div_flux_expansion)
            )
        ) * scipy.special.erfc(
            (
                len_plasma_sol_power_spreading
                / (2 * len_plasma_sol_power_decay * f_b_div_flux_expansion)
            )
            - ((r - (rmajor + rminor)) / (len_plasma_sol_power_spreading))
        ) + pflux_target_background_heat_flux_mw

    @staticmethod
    def calculate_scarabosio2015_power_spreading_factor(
        p_plasma_separatrix_mw: float,
        b_plasma_surface_poloidal_average: float,
        nd_plasma_separatrix_electron_19: float,
        rmajor: float,
    ) -> float:
        """Calculate the Scarabosio 2015 H-mode power spreading factor (S).

        Parameters
        ----------
        p_plasma_separatrix_mw : float
            Power crossing the separatrix (Pₛₑₚ) [MW]
        b_plasma_surface_poloidal_average : float
            Poloidal magnetic field at the plasma surface (Bₚₒₗ(a))  [T]
        nd_plasma_separatrix_electron_19 : float
            Electron density at the separatrix (nₑ,ₛₑₚ) [10¹⁹ m⁻³]
        rmajor : float
            Major radius of the plasma (R₀) [m]

        Returns
        -------
        float
            Scarabosio 2015 H-mode power spreading factor (S) [m]

        Notes
        -----
        - The R² for the fit is 0.65

        References
        ----------
        [1] A. Scarabosio et al., “Scaling of the divertor power spreading (S-factor) in
        open and closed divertor operation in JET and ASDEX Upgrade,”
        Journal of Nuclear Materials, vol. 463, pp. 49-54, Aug. 2015,
        doi: 10.1016/j.jnucmat.2014.11.076.

        """
        return (
            0.12e-3
            * p_plasma_separatrix_mw**0.21
            * b_plasma_surface_poloidal_average**-0.82
            * nd_plasma_separatrix_electron_19**-0.02
            * rmajor**0.71
        )

outfile = constants.NOUT instance-attribute

mfile = constants.MFILE instance-attribute

run()

Calculate the scrape off layer physics and update the physics variables.

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

def run(self):
    """Calculate the scrape off layer physics and update the physics variables."""
    self.data.physics.len_plasma_sol_eich13_power_decay = self.calculate_eich2013_sol_power_decay_length(  # noqa: E501
        p_plasma_separatrix_mw=self.data.physics.p_plasma_separatrix_mw,
        rmajor=self.data.physics.rmajor,
        b_plasma_surface_poloidal_average=self.data.physics.b_plasma_surface_poloidal_average,
        aspect=self.data.physics.aspect,
    )

    self.data.physics.len_plasma_sol_mast14_power_decay_1 = self.calculate_mast2014_sol_power_decay_length_1(  # noqa: E501
        p_plasma_separatrix_mw=self.data.physics.p_plasma_separatrix_mw,
        b_plasma_surface_poloidal_average=self.data.physics.b_plasma_surface_poloidal_average,
    )

    # NOTE: converting plasma_current from A to MA
    self.data.physics.len_plasma_sol_mast14_power_decay_2 = (
        self.calculate_mast2014_sol_power_decay_length_2(
            p_plasma_separatrix_mw=self.data.physics.p_plasma_separatrix_mw,
            cur_plasma_ma=self.data.physics.plasma_current / 1e6,
        )
    )

    self.data.physics.len_plasma_sol_eich11_jet_power_decay = (
        self.calculate_eich2011_jet_sol_power_decay_length(
            b_plasma_toroidal_on_axis=self.data.physics.b_plasma_toroidal_on_axis,
            q_cyl=self.data.physics.qstar,
            p_plasma_separatrix_mw=self.data.physics.p_plasma_separatrix_mw,
        )
    )

    self.data.physics.len_plasma_sol_eich11_jet_asdex_power_decay = (
        self.calculate_eich2011_jet_asdex_sol_power_decay_length(
            b_plasma_toroidal_on_axis=self.data.physics.b_plasma_toroidal_on_axis,
            q_cyl=self.data.physics.qstar,
            p_plasma_separatrix_mw=self.data.physics.p_plasma_separatrix_mw,
            rmajor=self.data.physics.rmajor,
        )
    )

    # Set to user input if OutbordSOLPowerDecayLengthModel = 1/USER_INUT
    match OutbordSOLPowerDecayLengthModel(
        self.data.physics.i_len_sol_outboard_power_decay
    ):
        case OutbordSOLPowerDecayLengthModel.EICH_2013:
            self.data.physics.len_sol_outboard_power_decay = (
                self.data.physics.len_plasma_sol_eich13_power_decay
            )
        case OutbordSOLPowerDecayLengthModel.MAST_2014_1:
            self.data.physics.len_sol_outboard_power_decay = (
                self.data.physics.len_plasma_sol_mast14_power_decay_1
            )
        case OutbordSOLPowerDecayLengthModel.MAST_2014_2:
            self.data.physics.len_sol_outboard_power_decay = (
                self.data.physics.len_plasma_sol_mast14_power_decay_2
            )
        case OutbordSOLPowerDecayLengthModel.EICH_2011_JET:
            self.data.physics.len_sol_outboard_power_decay = (
                self.data.physics.len_plasma_sol_eich11_jet_power_decay
            )
        case OutbordSOLPowerDecayLengthModel.EICH_2011_JET_ASDEX:
            self.data.physics.len_sol_outboard_power_decay = (
                self.data.physics.len_plasma_sol_eich11_jet_asdex_power_decay
            )

    self.data.physics.len_sol_inboard_power_decay = (
        self.data.physics.f_len_sol_power_decay_inboard_outboard
        * self.data.physics.len_sol_outboard_power_decay
    )

    self.data.physics.a_plasma_outboard_sol_parallel = self.calculate_upstream_sol_outboard_parallel_area(  # noqa: E501
        rmajor=self.data.physics.rmajor,
        rminor=self.data.physics.rminor,
        len_plasma_sol_power_decay=self.data.physics.len_sol_outboard_power_decay,
        b_plasma_outboard_total=self.data.physics.b_plasma_outboard_total,
        b_plasma_surface_poloidal_average=self.data.physics.b_plasma_surface_poloidal_average,
    )

    self.data.physics.a_plasma_outboard_sol_eich13_parallel = self.calculate_upstream_sol_outboard_parallel_area(  # noqa: E501
        rmajor=self.data.physics.rmajor,
        rminor=self.data.physics.rminor,
        len_plasma_sol_power_decay=self.data.physics.len_plasma_sol_eich13_power_decay,
        b_plasma_outboard_total=self.data.physics.b_plasma_outboard_total,
        b_plasma_surface_poloidal_average=self.data.physics.b_plasma_surface_poloidal_average,
    )

    self.data.physics.pflux_plasma_outboard_sol_parallel_mw = (
        self.data.physics.p_plasma_separatrix_mw
        * self.data.physics.f_p_div_outboard_separatrix
        / self.data.physics.a_plasma_outboard_sol_parallel
    )

    self.data.physics.pflux_plasma_outboard_sol_eich13_parallel_mw = (
        self.data.physics.p_plasma_separatrix_mw
        / self.data.physics.a_plasma_outboard_sol_eich13_parallel
    )

    self.data.physics.len_div_outboard_lower_scarabosio15_power_spreading = self.calculate_scarabosio2015_power_spreading_factor(  # noqa: E501
        p_plasma_separatrix_mw=self.data.physics.p_plasma_separatrix_mw,
        b_plasma_surface_poloidal_average=self.data.physics.b_plasma_surface_poloidal_average,
        nd_plasma_separatrix_electron_19=self.data.physics.nd_plasma_separatrix_electron
        / 1e19,
        rmajor=self.data.physics.rmajor,
    )

    self.data.physics.len_div_outboard_lower_power_spreading = (
        self.data.physics.len_div_outboard_lower_scarabosio15_power_spreading
    )

output()

Output plasma scrape off layer physics information.

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

def output(self) -> None:
    """Output plasma scrape off layer physics information."""
    po.oheadr(self.outfile, "Plasma Scrape Off Layer")

    po.osubhd(self.outfile, "Power Decay Lengths (λ_q):")
    po.ovarre(
        self.outfile,
        "Outboard SOL power decay length model switch",
        "(i_len_sol_outboard_power_decay)",
        self.data.physics.i_len_sol_outboard_power_decay,
    )
    po.ocmmnt(
        self.outfile,
        "-> "
        + OutbordSOLPowerDecayLengthModel(
            self.data.physics.i_len_sol_outboard_power_decay
        ).description
        + " ",
    )
    po.ovarre(
        self.outfile,
        "Outboard SOL power decay length (λₒᵤₜ_q) [m]",
        "(len_sol_outboard_power_decay)",
        self.data.physics.len_sol_outboard_power_decay,
    )

    po.oblnkl(self.outfile)
    po.ovarre(
        self.outfile,
        "Inboard to outboard SOL power decay length ratio (λᵢₙ_q/λₒᵤₜ_q)",
        "(f_len_sol_power_decay_inboard_outboard)",
        self.data.physics.f_len_sol_power_decay_inboard_outboard,
    )
    po.ovarre(
        self.outfile,
        "Inboard SOL power decay length (λᵢₙ_q) [m]",
        "(len_sol_inboard_power_decay)",
        self.data.physics.len_sol_inboard_power_decay,
    )
    po.oblnkl(self.outfile)
    po.ovarre(
        self.outfile,
        "Eich 2013 SOL power decay length (λ_q) [m]",
        "(len_plasma_sol_eich13_power_decay)",
        self.data.physics.len_plasma_sol_eich13_power_decay,
    )
    po.ovarre(
        self.outfile,
        "MAST 2014 SOL power decay length 1 (λ_q) [m]",
        "(len_plasma_sol_mast14_power_decay_1)",
        self.data.physics.len_plasma_sol_mast14_power_decay_1,
    )
    po.ovarre(
        self.outfile,
        "MAST 2014 SOL power decay length 2 (λ_q) [m]",
        "(len_plasma_sol_mast14_power_decay_2)",
        self.data.physics.len_plasma_sol_mast14_power_decay_2,
    )
    po.ovarre(
        self.outfile,
        "Eich 2011 JET SOL power decay length (λ_q) [m]",
        "(len_plasma_sol_eich11_jet_power_decay)",
        self.data.physics.len_plasma_sol_eich11_jet_power_decay,
    )
    po.ovarre(
        self.outfile,
        "Eich 2011 JET + ASDEX Upgrade SOL power decay length (λ_q) [m]",
        "(len_plasma_sol_eich11_jet_asdex_power_decay)",
        self.data.physics.len_plasma_sol_eich11_jet_asdex_power_decay,
    )
    po.oblnkl(self.outfile)
    po.ocmmnt(self.outfile, "----------------------------")

    po.osubhd(self.outfile, "Upstream Outboard SOL Parallel Area and Power Flux:")

    po.ovarre(
        self.outfile,
        "Plasma outboard midplane SOL parallel area (Aₗₗ,ᵤ) [m²]",
        "(a_plasma_outboard_sol_parallel)",
        self.data.physics.a_plasma_outboard_sol_parallel,
    )
    po.oblnkl(self.outfile)

    po.ovarre(
        self.outfile,
        "Plasma outboard midplane Eich 2013 SOL parallel area (Aₗₗ,ᵤ) [m²]",
        "(a_plasma_outboard_sol_eich13_parallel)",
        self.data.physics.a_plasma_outboard_sol_eich13_parallel,
    )
    po.oblnkl(self.outfile)
    po.ovarre(
        self.outfile,
        "Plasma outboard midplane SOL parallel power flux (qₗₗ,ᵤ) [MW/m²]",
        "(pflux_plasma_outboard_sol_parallel_mw)",
        self.data.physics.pflux_plasma_outboard_sol_parallel_mw,
    )
    po.oblnkl(self.outfile)
    po.ovarre(
        self.outfile,
        "Plasma outboard midplane Eich 2013 SOL parallel power flux (qₗₗ,ᵤ) [MW/m²]",
        "(pflux_plasma_outboard_sol_eich13_parallel_mw)",
        self.data.physics.pflux_plasma_outboard_sol_eich13_parallel_mw,
    )
    po.oblnkl(self.outfile)
    po.ocmmnt(self.outfile, "----------------------------")
    po.osubhd(self.outfile, "Power Spreading Factors (S):")

    po.ovarre(
        self.outfile,
        "Outboard lower divertor power spreading factor (S) [m]",
        "(len_div_outboard_lower_power_spreading)",
        self.data.physics.len_div_outboard_lower_power_spreading,
    )
    po.ovarre(
        self.outfile,
        "Scarabosio 2015 H-mode power spreading factor (S) [m]",
        "(len_div_outboard_lower_scarabosio15_power_spreading)",
        self.data.physics.len_div_outboard_lower_scarabosio15_power_spreading,
    )
    po.oblnkl(self.outfile)
    po.ocmmnt(self.outfile, "----------------------------")
    po.oblnkl(self.outfile)
    po.ovarre(
        self.outfile,
        "Outboard lower divertor flux expansion factor for the divertor targets "
        "(fₓ)",
        "(f_b_div_outboard_lower_flux_expansion)",
        self.data.physics.f_b_div_outboard_lower_flux_expansion,
    )

calculate_eich2013_sol_power_decay_length(p_plasma_separatrix_mw, rmajor, b_plasma_surface_poloidal_average, aspect) staticmethod

Calculate the Eich 2013 SOL power decay length (λ_q).

Parameters:

Name	Type	Description	Default
p_plasma_separatrix_mw	float	Power crossing the separatrix (Pₛₑₚ) [MW]	required
rmajor	float	Major radius of the plasma (R₀) [m]	required
b_plasma_surface_poloidal_average	float	Poloidal magnetic field at the plasma surface (⟨Bₚₒₗ(a)⟩) [T]	required
aspect	float	Aspect ratio of the plasma (A)	required

Returns:

Type	Description
float	Eich 2013 SOL power decay length (λ_q) [m]

Notes

• The paper states that the poloidal field terms is for the outer midplane Bₚₒₗ(a), we are using the outer surface average

References

[1] T. Eich et al., “Scaling of the tokamak near the scrape-off layer H-mode power width and implications for ITER,” Nuclear Fusion, vol. 53, no. 9, p. 093031, Aug. 2013, doi: 10.1088/0029-5515/53/9/093031.

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

@staticmethod
def calculate_eich2013_sol_power_decay_length(
    p_plasma_separatrix_mw: float,
    rmajor: float,
    b_plasma_surface_poloidal_average: float,
    aspect: float,
) -> float:
    """Calculate the Eich 2013 SOL power decay length (λ_q).

    Parameters
    ----------
    p_plasma_separatrix_mw : float
        Power crossing the separatrix (Pₛₑₚ) [MW]
    rmajor : float
        Major radius of the plasma (R₀) [m]
    b_plasma_surface_poloidal_average : float
        Poloidal magnetic field at the plasma surface (⟨Bₚₒₗ(a)⟩) [T]
    aspect : float
        Aspect ratio of the plasma (A)

    Returns
    -------
    float
        Eich 2013 SOL power decay length (λ_q) [m]

    Notes
    -----
    - The paper states that the poloidal field terms is for the outer midplane
    Bₚₒₗ(a), we are using the outer surface average

    References
    ----------
    [1] T. Eich et al., “Scaling of the tokamak near the scrape-off layer H-mode
    power width and implications for ITER,” Nuclear Fusion, vol. 53, no. 9,
    p. 093031, Aug. 2013, doi: 10.1088/0029-5515/53/9/093031.

    """
    return (
        1.35e-3
        * p_plasma_separatrix_mw**-0.02
        * rmajor**0.04
        * b_plasma_surface_poloidal_average**-0.92
        * aspect**-0.42
    )

calculate_mast2014_sol_power_decay_length_1(p_plasma_separatrix_mw, b_plasma_surface_poloidal_average) staticmethod

Calculate the MAST 2014 SOL power decay length (λ_q).

Parameters:

Name	Type	Description	Default
p_plasma_separatrix_mw	float	Power crossing the separatrix (Pₛₑₚ) [MW]	required
b_plasma_surface_poloidal_average	float	Poloidal magnetic field at the plasma surface (⟨Bₚₒₗ(a)⟩) [T]	required

Returns:

Type	Description
float	MAST 2014 SOL power decay length (λ_q) [m]

Notes

• The paper states that the poloidal field terms is for the outer midplane Bₚₒₗ(a), we are using the outer surface average

References

[1] A. J. Thornton and A. Kirk, “Scaling of the scrape-off layer width during inter-ELM H modes on MAST as measured by infrared thermography,” Plasma Physics and Controlled Fusion, vol. 56, no. 5, p. 055008, Apr. 2014, doi: 10.1088/0741-3335/56/5/055008.

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

@staticmethod
def calculate_mast2014_sol_power_decay_length_1(
    p_plasma_separatrix_mw: float,
    b_plasma_surface_poloidal_average: float,
) -> float:
    """Calculate the MAST 2014 SOL power decay length (λ_q).

    Parameters
    ----------
    p_plasma_separatrix_mw : float
        Power crossing the separatrix (Pₛₑₚ) [MW]
    b_plasma_surface_poloidal_average : float
        Poloidal magnetic field at the plasma surface (⟨Bₚₒₗ(a)⟩) [T]

    Returns
    -------
    float
        MAST 2014 SOL power decay length (λ_q) [m]

    Notes
    -----
    - The paper states that the poloidal field terms is for the outer midplane
    Bₚₒₗ(a), we are using the outer surface average

    References
    ----------
    [1] A. J. Thornton and A. Kirk, “Scaling of the scrape-off layer width during
    inter-ELM H modes on MAST as measured by infrared thermography,”
    Plasma Physics and Controlled Fusion, vol. 56, no. 5, p. 055008, Apr. 2014,
    doi: 10.1088/0741-3335/56/5/055008.

    """
    return (
        1.84e-3
        * p_plasma_separatrix_mw**0.18
        * b_plasma_surface_poloidal_average**-0.68
    )

calculate_mast2014_sol_power_decay_length_2(p_plasma_separatrix_mw, cur_plasma_ma) staticmethod

Calculate the MAST 2014 SOL power decay length (λ_q).

Parameters:

Name	Type	Description	Default
p_plasma_separatrix_mw	float	Power crossing the separatrix (Pₛₑₚ) [MW]	required
cur_plasma_ma	float	Plasma current (Iₚ) [MA]	required

Returns:

Type	Description
float	MAST 2014 SOL power decay length (λ_q) [m]

References

[1] A. J. Thornton and A. Kirk, “Scaling of the scrape-off layer width during inter-ELM H modes on MAST as measured by infrared thermography,” Plasma Physics and Controlled Fusion, vol. 56, no. 5, p. 055008, Apr. 2014, doi: 10.1088/0741-3335/56/5/055008.

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

@staticmethod
def calculate_mast2014_sol_power_decay_length_2(
    p_plasma_separatrix_mw: float,
    cur_plasma_ma: float,
) -> float:
    """Calculate the MAST 2014 SOL power decay length (λ_q).

    Parameters
    ----------
    p_plasma_separatrix_mw : float
        Power crossing the separatrix (Pₛₑₚ) [MW]
    cur_plasma_ma : float
        Plasma current (Iₚ) [MA]

    Returns
    -------
    float
        MAST 2014 SOL power decay length (λ_q) [m]


    References
    ----------
    [1] A. J. Thornton and A. Kirk, “Scaling of the scrape-off layer width during
    inter-ELM H modes on MAST as measured by infrared thermography,”
    Plasma Physics and Controlled Fusion, vol. 56, no. 5, p. 055008, Apr. 2014,
    doi: 10.1088/0741-3335/56/5/055008.

    """
    return 4.57e-3 * p_plasma_separatrix_mw**0.22 * cur_plasma_ma**-0.64

calculate_eich2011_jet_sol_power_decay_length(b_plasma_toroidal_on_axis, q_cyl, p_plasma_separatrix_mw) staticmethod

Calculate the Eich 2011 JET SOL power decay length (λ_q).

Parameters:

Name	Type	Description	Default
b_plasma_toroidal_on_axis	float	Toroidal magnetic field at the plasma axis (Bᴛ(R₀)) [T]	required
q_cyl	float	Cylindrical safety factor (q_cyl) [-]	required
p_plasma_separatrix_mw	float	Power crossing the separatrix (Pₛₑₚ) [MW]	required

Returns:

Type	Description
float	Eich 2011 JET SOL power decay length (λ_q) [m]

Notes

• The fit values can be found in Table 2 of [1].
• The scaling is done for type-I ELMy H-mode plasmas

References

[1] T. Eich, B. Sieglin, A. Scarabosio, W. Fundamenski, Robert James Goldston, and A. Herrmann, “Inter-ELM Power Decay Length for JET and ASDEX Upgrade: Measurement and Comparison with Heuristic Drift-Based Model,” Physical Review Letters, vol. 107, no. 21, Nov. 2011, doi: https://doi.org/10.1103/PhysRevLett.107.215001.

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

@staticmethod
def calculate_eich2011_jet_sol_power_decay_length(
    b_plasma_toroidal_on_axis: float,
    q_cyl: float,
    p_plasma_separatrix_mw: float,
) -> float:
    """Calculate the Eich 2011 JET SOL power decay length (λ_q).

    Parameters
    ----------
    b_plasma_toroidal_on_axis : float
        Toroidal magnetic field at the plasma axis (Bᴛ(R₀)) [T]
    q_cyl : float
        Cylindrical safety factor (q_cyl) [-]
    p_plasma_separatrix_mw : float
        Power crossing the separatrix (Pₛₑₚ) [MW]

    Returns
    -------
    float
        Eich 2011 JET SOL power decay length (λ_q) [m]

    Notes
    -----
    - The fit values can be found in Table 2 of [1].
    - The scaling is done for type-I ELMy H-mode plasmas

    References
    ----------
    [1] T. Eich, B. Sieglin, A. Scarabosio, W. Fundamenski, Robert James Goldston,
    and A. Herrmann, “Inter-ELM Power Decay Length for JET and ASDEX Upgrade:
    Measurement and Comparison with Heuristic Drift-Based Model,”
    Physical Review Letters, vol. 107, no. 21, Nov. 2011,
    doi: https://doi.org/10.1103/PhysRevLett.107.215001.

    """
    return (
        0.7e-3
        * b_plasma_toroidal_on_axis**-0.84
        * q_cyl**1.23
        * p_plasma_separatrix_mw**0.14
    )

calculate_eich2011_jet_asdex_sol_power_decay_length(b_plasma_toroidal_on_axis, q_cyl, p_plasma_separatrix_mw, rmajor) staticmethod

Calculate the Eich 2011 JET + ASDEX Upgrade SOL power decay length (λ_q).

Parameters:

Name	Type	Description	Default
b_plasma_toroidal_on_axis	float	Toroidal magnetic field at the plasma axis (Bᴛ(R₀)) [T]	required
q_cyl	float	Cylindrical safety factor (q_cyl) [-]	required
p_plasma_separatrix_mw	float	Power crossing the separatrix (Pₛₑₚ) [MW]	required
rmajor	float	Major radius of the plasma (R₀) [m]	required

Returns:

Type	Description
float	Eich 2011 JET + ASDEX Upgrade SOL power decay length (λ_q) [m]

Notes

• The fit values can be found in Table 2 of [1].
• The scaling is done for type-I ELMy H-mode plasmas

References

[1] T. Eich, B. Sieglin, A. Scarabosio, W. Fundamenski, Robert James Goldston, and A. Herrmann, “Inter-ELM Power Decay Length for JET and ASDEX Upgrade: Measurement and Comparison with Heuristic Drift-Based Model,” Physical Review Letters, vol. 107, no. 21, Nov. 2011, doi: https://doi.org/10.1103/PhysRevLett.107.215001.

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

@staticmethod
def calculate_eich2011_jet_asdex_sol_power_decay_length(
    b_plasma_toroidal_on_axis: float,
    q_cyl: float,
    p_plasma_separatrix_mw: float,
    rmajor: float,
) -> float:
    """Calculate the Eich 2011 JET + ASDEX Upgrade SOL power decay length (λ_q).

    Parameters
    ----------
    b_plasma_toroidal_on_axis : float
        Toroidal magnetic field at the plasma axis (Bᴛ(R₀)) [T]
    q_cyl : float
        Cylindrical safety factor (q_cyl) [-]
    p_plasma_separatrix_mw : float
        Power crossing the separatrix (Pₛₑₚ) [MW]
    rmajor : float
        Major radius of the plasma (R₀) [m]

    Returns
    -------
    float
        Eich 2011 JET + ASDEX Upgrade SOL power decay length (λ_q) [m]

    Notes
    -----
    - The fit values can be found in Table 2 of [1].
    - The scaling is done for type-I ELMy H-mode plasmas

    References
    ----------
    [1] T. Eich, B. Sieglin, A. Scarabosio, W. Fundamenski, Robert James Goldston,
    and A. Herrmann, “Inter-ELM Power Decay Length for JET and ASDEX Upgrade:
    Measurement and Comparison with Heuristic Drift-Based Model,”
    Physical Review Letters, vol. 107, no. 21, Nov. 2011,
    doi: https://doi.org/10.1103/PhysRevLett.107.215001.

    """
    return (
        0.73e-3
        * b_plasma_toroidal_on_axis**-0.78
        * q_cyl**1.2
        * p_plasma_separatrix_mw**0.1
        * rmajor**0.02
    )

calculate_upstream_sol_outboard_parallel_area(rmajor, rminor, len_plasma_sol_power_decay, b_plasma_outboard_total, b_plasma_surface_poloidal_average) staticmethod

Calculate the outboard SOL upstream parallel area (Aₗₗ,ᵤ) [m²].

Parameters:

Name	Type	Description	Default
rmajor	float	Major radius of the plasma (R₀) [m]	required
rminor	float	Minor radius of the plasma (a) [m]	required
len_plasma_sol_power_decay	float	Power decay length (λ_q) [m]	required
b_plasma_outboard_total	float	Total magnetic field at the plasma outboard (Bₜₒₜ(R₀+a)) [T]	required
b_plasma_surface_poloidal_average	float	Poloidal magnetic field at the plasma surface (⟨Bₚₒₗ(a)⟩) [T]	required

Returns:

Type	Description
float	Upstream outboard SOL parallel area (Aₗₗ,ᵤ) [m²]

References

[1] P. C. Stangeby, “The Plasma Boundary of Magnetic Fusion Devices,” Jan. 2000, doi: 10.1201/9780367801489.

[2] S. S. Henderson et al., “An overview of the STEP divertor design and the simple models driving the plasma exhaust scenario,” Nuclear Fusion, vol. 65, no. 1, pp. 016033-016033, Nov. 2024, doi: 10.1088/1741-4326/ad93e7.

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

@staticmethod
def calculate_upstream_sol_outboard_parallel_area(
    rmajor: float,
    rminor: float,
    len_plasma_sol_power_decay: float,
    b_plasma_outboard_total: float,
    b_plasma_surface_poloidal_average: float,
) -> float:
    """Calculate the outboard SOL upstream parallel area (Aₗₗ,ᵤ) [m²].

    Parameters
    ----------
    rmajor : float
        Major radius of the plasma (R₀) [m]
    rminor : float
        Minor radius of the plasma (a) [m]
    len_plasma_sol_power_decay : float
        Power decay length (λ_q) [m]
    b_plasma_outboard_total : float
        Total magnetic field at the plasma outboard (Bₜₒₜ(R₀+a)) [T]
    b_plasma_surface_poloidal_average : float
        Poloidal magnetic field at the plasma surface (⟨Bₚₒₗ(a)⟩) [T]

    Returns
    -------
    float
        Upstream outboard SOL parallel area (Aₗₗ,ᵤ) [m²]

    References
    ----------
    [1] P. C. Stangeby, “The Plasma Boundary of Magnetic Fusion Devices,” Jan. 2000,
    doi: 10.1201/9780367801489.

    [2] S. S. Henderson et al., “An overview of the STEP divertor design and the
    simple models driving the plasma exhaust scenario,” Nuclear Fusion, vol. 65,
    no. 1, pp. 016033-016033, Nov. 2024, doi: 10.1088/1741-4326/ad93e7.

    """
    return (
        (2 * np.pi * (rmajor + rminor))
        * len_plasma_sol_power_decay
        * (b_plasma_surface_poloidal_average / b_plasma_outboard_total)
    )

calculate_outboard_midplane_near_sol_radial_profile(rmajor, rminor, len_plasma_sol_power_decay, pflux_plasma_outboard_sol_parallel_mw, r) staticmethod

Calculate the outboard midplane near SOL radial profile (qₗₗ®) [MW/m²].

Parameters:

Name	Type	Description	Default
rmajor	float	Major radius of the plasma (R₀) [m]	required
rminor	float	Minor radius of the plasma (a) [m]	required
len_plasma_sol_power_decay	float	Power decay length (λ_q) [m]	required
pflux_plasma_outboard_sol_parallel_mw	float	Parallel power flux at the outboard midplane (qₗₗ,ᵤ) [MW/m²]	required
r	float | ndarray	Radial position(s) at which to calculate the SOL profile [m]	required

Returns:

Type	Description
float | ndarray	Outboard midplane SOL radial profile (qₗₗ®) [MW/m²]

Raises:

Type	Description
ValueError	If any radial position r is inside the plasma edge (r < rmajor + rminor)

Notes

• The exponential model is highly valid in the "near-SOL" (typically the first few millimeters to a centimeter outside the separatrix). In this region, parallel heat transport is dominated by classical electron heat conduction (Spitzer-Härm conductivity), which is vastly faster than perpendicular diffusion. This competition between fast parallel conduction and slow perpendicular diffusion naturally produces an exponential radial profile.

• The midplane exponential assumes steady-state H-mode conditions without the massive, transient convective bursts caused by ELMs, which momentarily flatten the entire midplane profile.

References

[1] T. Eich et al., “Scaling of the tokamak near the scrape-off layer H-mode power width and implications for ITER,” Nuclear Fusion, vol. 53, no. 9, p. 093031, Aug. 2013, doi: 10.1088/0029-5515/53/9/093031.

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

@staticmethod
def calculate_outboard_midplane_near_sol_radial_profile(
    rmajor: float,
    rminor: float,
    len_plasma_sol_power_decay: float,
    pflux_plasma_outboard_sol_parallel_mw: float,
    r: float | np.ndarray,
) -> float | np.ndarray:
    """Calculate the outboard midplane near SOL radial profile (qₗₗ(r)) [MW/m²].

    Parameters
    ----------
    rmajor : float
        Major radius of the plasma (R₀) [m]
    rminor : float
        Minor radius of the plasma (a) [m]
    len_plasma_sol_power_decay : float
        Power decay length (λ_q) [m]
    pflux_plasma_outboard_sol_parallel_mw : float
        Parallel power flux at the outboard midplane (qₗₗ,ᵤ) [MW/m²]
    r : float|np.ndarray
        Radial position(s) at which to calculate the SOL profile [m]

    Returns
    -------
    float|np.ndarray
        Outboard midplane SOL radial profile (qₗₗ(r)) [MW/m²]

    Raises
    ------
    ValueError
        If any radial position r is inside the plasma edge (r < rmajor + rminor)

    Notes
    -----
    - The exponential model is highly valid in the "near-SOL" (typically the first
    few millimeters to a centimeter outside the separatrix). In this region, parallel
    heat transport is dominated by classical electron heat conduction
    (Spitzer-Härm conductivity), which is vastly faster than perpendicular diffusion.
    This competition between fast parallel conduction and slow perpendicular
    diffusion naturally produces an exponential radial profile.

    - The midplane exponential assumes steady-state H-mode conditions without the
    massive, transient convective bursts caused by ELMs, which momentarily
    flatten the entire midplane profile.

    References
    ----------
    [1] T. Eich et al., “Scaling of the tokamak near the scrape-off layer H-mode
    power width and implications for ITER,” Nuclear Fusion, vol. 53, no. 9,
    p. 093031, Aug. 2013, doi: 10.1088/0029-5515/53/9/093031.

    """
    if np.any(r < (rmajor + rminor)):
        raise ValueError(
            f"Radial position {r=} must be greater than or equal to the plasma "
            f"edge {(rmajor + rminor)=}."
        )

    return pflux_plasma_outboard_sol_parallel_mw * np.exp(
        -(r - (rmajor + rminor)) / len_plasma_sol_power_decay
    )

calculate_eich_target_heat_flux_profile(rmajor, rminor, pflux_plasma_sol_parallel_mw, len_plasma_sol_power_decay, f_b_div_flux_expansion, len_plasma_sol_power_spreading, pflux_target_background_heat_flux_mw, r) staticmethod

Calculate the Eich parallel target heat flux profile (qₗₗ,ₜ®) [MW/m²].

Parameters:

Name	Type	Description	Default
rmajor	float	Major radius of the plasma (R₀) [m]	required
rminor	float	Minor radius of the plasma (a) [m]	required
pflux_plasma_sol_parallel_mw	float	Parallel power flux at the outboard midplane (qₗₗ,ᵤ) [MW/m²]	required
len_plasma_sol_power_decay	float	Power decay length (λ_q) [m]	required
f_b_div_flux_expansion	float	Divertor flux expansion factor (fₓ) [-]	required
len_plasma_sol_power_spreading	float	Power spreading length in the divertor (S) [m]	required
pflux_target_background_heat_flux_mw	float	Background heat flux at the divertor target [MW/m²]	required
r	float | ndarray	Radial position(s) at which to calculate the target heat flux profile [m]	required

Returns:

Type	Description
float | ndarray	Eich parallel target heat flux profile (qₗₗ,ₜ®) [MW/m²]

Notes

• The Eich parallel target heat flux profile is derived from the midplane exponential profile, taking into account the magnetic geometry and flux expansion between the midplane and the divertor target. The profile is typically characterized by a combination of an exponential decay and a Gaussian spreading due to cross-field transport in the divertor leg.

References

[1] T. Eich, B. Sieglin, A. Scarabosio, W. Fundamenski, R. J. Goldston, and A. Herrmann, “Inter-ELM Power Decay Length for JET and ASDEX Upgrade: Measurement and Comparison with Heuristic Drift-Based Model,” Physical Review Letters, vol. 107, no. 21, Nov. 2011, doi: https://doi.org/10.1103/PhysRevLett.107.215001

[2] T. Eich et al., “Scaling of the tokamak near the scrape-off layer H-mode power width and implications for ITER,” Nuclear Fusion, vol. 53, no. 9, p. 093031, Aug. 2013, doi: 10.1088/0029-5515/53/9/093031.

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

@staticmethod
def calculate_eich_target_heat_flux_profile(
    rmajor: float,
    rminor: float,
    pflux_plasma_sol_parallel_mw: float,
    len_plasma_sol_power_decay: float,
    f_b_div_flux_expansion: float,
    len_plasma_sol_power_spreading: float,
    pflux_target_background_heat_flux_mw: float,
    r: float | np.ndarray,
) -> float | np.ndarray:
    """Calculate the Eich parallel target heat flux profile (qₗₗ,ₜ(r)) [MW/m²].

    Parameters
    ----------
    rmajor : float
        Major radius of the plasma (R₀) [m]
    rminor : float
        Minor radius of the plasma (a) [m]
    pflux_plasma_sol_parallel_mw : float
        Parallel power flux at the outboard midplane (qₗₗ,ᵤ) [MW/m²]
    len_plasma_sol_power_decay : float
        Power decay length (λ_q) [m]
    f_b_div_flux_expansion : float
        Divertor flux expansion factor (fₓ) [-]
    len_plasma_sol_power_spreading : float
        Power spreading length in the divertor (S) [m]
    pflux_target_background_heat_flux_mw : float
        Background heat flux at the divertor target [MW/m²]
    r : float|np.ndarray
        Radial position(s) at which to calculate the target heat flux profile [m]

    Returns
    -------
    float|np.ndarray
        Eich parallel target heat flux profile (qₗₗ,ₜ(r)) [MW/m²]

    Notes
    -----
    - The Eich parallel target heat flux profile is derived from the midplane
    exponential profile, taking into account the magnetic geometry and flux expansion
    between the midplane and the divertor target. The profile is typically
    characterized by a combination of an exponential decay and a Gaussian spreading
    due to cross-field transport in the divertor leg.

    References
    ----------
    [1] T. Eich, B. Sieglin, A. Scarabosio, W. Fundamenski, R. J. Goldston, and
    A. Herrmann, “Inter-ELM Power Decay Length for JET and ASDEX Upgrade: Measurement
    and Comparison with Heuristic Drift-Based Model,” Physical Review Letters,
    vol. 107, no. 21, Nov. 2011, doi: https://doi.org/10.1103/PhysRevLett.107.215001

    [2] T. Eich et al., “Scaling of the tokamak near the scrape-off layer H-mode
    power width and implications for ITER,” Nuclear Fusion, vol. 53, no. 9,
    p. 093031, Aug. 2013, doi: 10.1088/0029-5515/53/9/093031.

    """
    return (pflux_plasma_sol_parallel_mw / 2) * np.exp(
        (
            (len_plasma_sol_power_spreading)
            / (2 * len_plasma_sol_power_decay * f_b_div_flux_expansion)
        )
        ** 2
        - (
            (r - (rmajor + rminor))
            / (len_plasma_sol_power_decay * f_b_div_flux_expansion)
        )
    ) * scipy.special.erfc(
        (
            len_plasma_sol_power_spreading
            / (2 * len_plasma_sol_power_decay * f_b_div_flux_expansion)
        )
        - ((r - (rmajor + rminor)) / (len_plasma_sol_power_spreading))
    ) + pflux_target_background_heat_flux_mw

calculate_scarabosio2015_power_spreading_factor(p_plasma_separatrix_mw, b_plasma_surface_poloidal_average, nd_plasma_separatrix_electron_19, rmajor) staticmethod

Calculate the Scarabosio 2015 H-mode power spreading factor (S).

Parameters:

Name	Type	Description	Default
p_plasma_separatrix_mw	float	Power crossing the separatrix (Pₛₑₚ) [MW]	required
b_plasma_surface_poloidal_average	float	Poloidal magnetic field at the plasma surface (Bₚₒₗ(a)) [T]	required
nd_plasma_separatrix_electron_19	float	Electron density at the separatrix (nₑ,ₛₑₚ) [10¹⁹ m⁻³]	required
rmajor	float	Major radius of the plasma (R₀) [m]	required

Returns:

Type	Description
float	Scarabosio 2015 H-mode power spreading factor (S) [m]

Notes

• The R² for the fit is 0.65

References

[1] A. Scarabosio et al., “Scaling of the divertor power spreading (S-factor) in open and closed divertor operation in JET and ASDEX Upgrade,” Journal of Nuclear Materials, vol. 463, pp. 49-54, Aug. 2015, doi: 10.1016/j.jnucmat.2014.11.076.

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

@staticmethod
def calculate_scarabosio2015_power_spreading_factor(
    p_plasma_separatrix_mw: float,
    b_plasma_surface_poloidal_average: float,
    nd_plasma_separatrix_electron_19: float,
    rmajor: float,
) -> float:
    """Calculate the Scarabosio 2015 H-mode power spreading factor (S).

    Parameters
    ----------
    p_plasma_separatrix_mw : float
        Power crossing the separatrix (Pₛₑₚ) [MW]
    b_plasma_surface_poloidal_average : float
        Poloidal magnetic field at the plasma surface (Bₚₒₗ(a))  [T]
    nd_plasma_separatrix_electron_19 : float
        Electron density at the separatrix (nₑ,ₛₑₚ) [10¹⁹ m⁻³]
    rmajor : float
        Major radius of the plasma (R₀) [m]

    Returns
    -------
    float
        Scarabosio 2015 H-mode power spreading factor (S) [m]

    Notes
    -----
    - The R² for the fit is 0.65

    References
    ----------
    [1] A. Scarabosio et al., “Scaling of the divertor power spreading (S-factor) in
    open and closed divertor operation in JET and ASDEX Upgrade,”
    Journal of Nuclear Materials, vol. 463, pp. 49-54, Aug. 2015,
    doi: 10.1016/j.jnucmat.2014.11.076.

    """
    return (
        0.12e-3
        * p_plasma_separatrix_mw**0.21
        * b_plasma_surface_poloidal_average**-0.82
        * nd_plasma_separatrix_electron_19**-0.02
        * rmajor**0.71
    )