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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 
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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.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_eich13_parallel_mw = (
            self.data.physics.p_plasma_separatrix_mw
            / self.data.physics.a_plasma_outboard_sol_eich13_parallel
        )

    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,
            "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.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 Eich 2013 SOL parallel area (Aₗₗ,ᵤ) [m²]",
            "(a_plasma_outboard_sol_eich13_parallel)",
            self.data.physics.a_plasma_outboard_sol_eich13_parallel,
        )
        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,
        )

    @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_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)
        )

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 
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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.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_eich13_parallel_mw = (
        self.data.physics.p_plasma_separatrix_mw
        / self.data.physics.a_plasma_outboard_sol_eich13_parallel
    )

output()

Output plasma scrape off layer physics information.

Source code in process/models/physics/scrape_off_layer.py 
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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,
        "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.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 Eich 2013 SOL parallel area (Aₗₗ,ᵤ) [m²]",
        "(a_plasma_outboard_sol_eich13_parallel)",
        self.data.physics.a_plasma_outboard_sol_eich13_parallel,
    )
    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,
    )

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 
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@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 
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@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 
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@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_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 
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@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)
    )