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reactivity

Reactivity calculations.

AllReactions = tokamak_neutron_source.reactions.Reactions | tokamak_neutron_source.reactions.AneutronicReactions module-attribute

Represent a PEP 604 union type

E.g. for int | str

ReactivityMethod

Bases: enum.Enum

Reactivity calculation method.

Source code in tokamak_neutron_source/reactivity.py 
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class ReactivityMethod(Enum):
    """Reactivity calculation method."""

    XS = auto()
    BOSCH_HALE = auto()
    AUTO = auto()

AUTO = <ReactivityMethod.AUTO: 3> class-attribute

Reactivity calculation method.

BOSCH_HALE = <ReactivityMethod.BOSCH_HALE: 2> class-attribute

Reactivity calculation method.

XS = <ReactivityMethod.XS: 1> class-attribute

Reactivity calculation method.

AneutronicReactions

Bases: tokamak_neutron_source.reactions.ReactionEnumMixin, enum.Enum

Aneutronic reaction channels.

Source code in tokamak_neutron_source/reactions.py 
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class AneutronicReactions(ReactionEnumMixin, Enum):
    """Aneutronic reaction channels."""

    D_D = ReactionData(
        label="D + D → T + p",
        total_energy=E_DD_TP_FUSION,
        num_neutrons=0,  # no neutrons in aneutronic branch
        cross_section=DD_TP_XS,
        bosch_hale_coefficients=BOSCH_HALE_DD_TP,
        ballabio_spectrum=None,
    )
    D_He3 = ReactionData(
        label="D + ³He → ⁴He + p",
        total_energy=E_DHE3_FUSION,
        num_neutrons=0,
        cross_section=DHE3_HEP_XS,
        bosch_hale_coefficients=None,
        ballabio_spectrum=None,
    )

D_D = <AneutronicReactions.D_D: ReactionData(label='D + D → T + p', total_energy=6.461016407480568e-13, num_neutrons=0, cross_section=<tokamak_neutron_source.reactivity_data.ReactionCrossSection object at 0x7ff2008b80d0>, bosch_hale_coefficients=BoschHaleCoefficients(name='D + D --> T + p', t_min=0.2, t_max=100.0, bg=31.397, mrc2=937814.0, c=array([5.65718e-12, 3.41267e-03, 1.99167e-03, 0.00000e+00, 1.05060e-05,0.00000e+00, 0.00000e+00])), ballabio_spectrum=None)> class-attribute

Aneutronic reaction channels.

D_He3 = <AneutronicReactions.D_He3: ReactionData(label='D + ³He → ⁴He + p', total_energy=2.940668400408501e-12, num_neutrons=0, cross_section=<tokamak_neutron_source.reactivity_data.ReactionCrossSection object at 0x7ff200901310>, bosch_hale_coefficients=None, ballabio_spectrum=None)> class-attribute

Aneutronic reaction channels.

BoschHaleCoefficients

Bosch-Hale parameterisation dataclass.

H.-S. Bosch and G.M. Hale 1992 Nucl. Fusion 32 611 DOI 10.1088/0029-5515/32/4/I07

Source code in tokamak_neutron_source/reactivity_data.py 
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@dataclass
class BoschHaleCoefficients:
    """
    Bosch-Hale parameterisation dataclass.

    H.-S. Bosch and G.M. Hale 1992 Nucl. Fusion 32 611
    DOI 10.1088/0029-5515/32/4/I07
    """

    name: str
    t_min: float  # [keV]
    t_max: float  # [keV]
    bg: float  # [keV**0.5]
    mrc2: float  # [keV]
    c: npt.NDArray

ReactionCrossSection

Fusion reaction cross-section.

Source code in tokamak_neutron_source/reactivity_data.py 
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class ReactionCrossSection:
    """Fusion reaction cross-section."""

    def __init__(self, file_name: str):
        """
        Parameters
        ----------
        file_name:
            Cross-sectional data file (ENDF format)

        Raises
        ------
        ReactivityError
            Data file path is not a file
        """
        path = get_tns_path("data/cross_sections")
        path = Path(path, file_name)
        if not path.is_file():
            raise ReactivityError(f"Cross-section data file {path} is not a file!")

        file = path.as_posix()
        # Read in the cross section (in barn) as a function of energy (MeV).
        energy, sigma = np.genfromtxt(file, comments="#", skip_footer=2, unpack=True)

        split = file_name.split(".", maxsplit=1)[0].split("_")
        collider, target = split[:2]
        self.name = f"{collider} + {target} -> {split[2]} + {split[3]}"

        mass_1, mass_2 = MOLAR_MASSES[collider], MOLAR_MASSES[target]

        self.reduced_mass = raw_uc(mass_1 * mass_2 / (mass_1 + mass_2), "amu", "kg")

        # Convert to center of mass frame
        # NOTE MC: Choice of target/collider thing makes Bosch-Hale line up...
        energy *= mass_2 / (mass_1 + mass_2)

        # Convert to kev / m^2
        self._cross_section = interp1d(energy * 1e3, sigma * 1e-28)

    def __call__(self, temp_kev: float | npt.NDArray) -> float | npt.NDArray:
        """Get cross section at a give temperature"""  # noqa: DOC201
        return self._cross_section(temp_kev)

Reactions

Bases: tokamak_neutron_source.reactions.ReactionEnumMixin, enum.Enum

Neutronic reaction channels.

Source code in tokamak_neutron_source/reactions.py 
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class Reactions(ReactionEnumMixin, Enum):
    """Neutronic reaction channels."""

    D_T = ReactionData(
        label="D + T → ⁴He + n",
        total_energy=E_DT_FUSION,
        num_neutrons=1,
        cross_section=DT_XS,
        bosch_hale_coefficients=BOSCH_HALE_DT_4HEN,
        ballabio_spectrum=BALLABIO_DT_NEUTRON,
    )
    D_D = ReactionData(
        label="D + D → ³He + n",
        total_energy=E_DD_HE3N_FUSION,
        num_neutrons=1,
        cross_section=DD_HE3N_XS,
        bosch_hale_coefficients=BOSCH_HALE_DD_3HEN,
        ballabio_spectrum=BALLABIO_DD_NEUTRON,
    )
    T_T = ReactionData(
        label="T + T → ⁴He + 2n",
        total_energy=E_TT_FUSION,
        num_neutrons=2,
        cross_section=TT_XS,
        bosch_hale_coefficients=None,
        ballabio_spectrum=None,
    )

D_D = <Reactions.D_D: ReactionData(label='D + D → ³He + n', total_energy=5.237367559215132e-13, num_neutrons=1, cross_section=<tokamak_neutron_source.reactivity_data.ReactionCrossSection object at 0x7ff2008dfb10>, bosch_hale_coefficients=BoschHaleCoefficients(name='D + D --> 3He + n', t_min=0.2, t_max=100.0, bg=31.397, mrc2=937814.0, c=array([ 5.43360e-12, 5.85778e-03, 7.68222e-03, 0.00000e+00,-2.96400e-06, 0.00000e+00, 0.00000e+00])), ballabio_spectrum=BallabioEnergySpectrum(energy_0=2449.5, omega_0=82.542, energy_shift_coeffs=BallabioCoefficients(a1=4.69515, a2=-0.040729, a3=0.47, a4=0.81844), width_correction_coeffs=BallabioCoefficients(a1=0.0017013, a2=0.16888, a3=0.49, a4=0.0007946)))> class-attribute

Neutronic reaction channels.

D_T = <Reactions.D_T: ReactionData(label='D + T → ⁴He + n', total_energy=2.8183035155819573e-12, num_neutrons=1, cross_section=<tokamak_neutron_source.reactivity_data.ReactionCrossSection object at 0x7ff2008d4c50>, bosch_hale_coefficients=BoschHaleCoefficients(name='D + T --> 4He + n', t_min=0.2, t_max=100.0, bg=34.3827, mrc2=1124656.0, c=array([ 1.17302e-09, 1.51361e-02, 7.51886e-02, 4.60643e-03,1.35000e-02, -1.06750e-04, 1.36600e-05])), ballabio_spectrum=BallabioEnergySpectrum(energy_0=14021.0, omega_0=177.259, energy_shift_coeffs=BallabioCoefficients(a1=5.30509, a2=0.0024736, a3=1.84, a4=1.3818), width_correction_coeffs=BallabioCoefficients(a1=0.00051068, a2=0.0076223, a3=1.78, a4=8.7691e-05)))> class-attribute

Neutronic reaction channels.

T_T = <Reactions.T_T: ReactionData(label='T + T → ⁴He + 2n', total_energy=1.8157845541890245e-12, num_neutrons=2, cross_section=<tokamak_neutron_source.reactivity_data.ReactionCrossSection object at 0x7ff20ad03850>, bosch_hale_coefficients=None, ballabio_spectrum=None)> class-attribute

Neutronic reaction channels.

ReactivityError

Bases: tokamak_neutron_source.error.TNSError

Reactivity error class

Source code in tokamak_neutron_source/error.py 
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class ReactivityError(TNSError):
    """Reactivity error class"""

density_weighted_reactivity(temp_kev, density_d, density_t, density_he3, reaction=<Reactions.D_T: ReactionData(label='D + T → ⁴He + n', total_energy=2.8183035155819573e-12, num_neutrons=1, cross_section=<tokamak_neutron_source.reactivity_data.ReactionCrossSection object at 0x7ff2008d4c50>, bosch_hale_coefficients=BoschHaleCoefficients(name='D + T --> 4He + n', t_min=0.2, t_max=100.0, bg=34.3827, mrc2=1124656.0, c=array([ 1.17302e-09, 1.51361e-02, 7.51886e-02, 4.60643e-03,1.35000e-02, -1.06750e-04, 1.36600e-05])), ballabio_spectrum=BallabioEnergySpectrum(energy_0=14021.0, omega_0=177.259, energy_shift_coeffs=BallabioCoefficients(a1=5.30509, a2=0.0024736, a3=1.84, a4=1.3818), width_correction_coeffs=BallabioCoefficients(a1=0.00051068, a2=0.0076223, a3=1.78, a4=8.7691e-05)))>, method=<ReactivityMethod.AUTO: 3>)

Calculate the density-weighted thermal reactivity of a fusion reaction in Maxwellian plasmas, \t:math:n_1 n_2 <\sigma v>.

Parameters:

Name Type Description Default
temp_kev float | ndarray[tuple[Any, ...], dtype[~_ScalarT]]

Temperature [keV]

 required
density_d float | ndarray[tuple[Any, ...], dtype[~_ScalarT]]

Deuterium density [m^-3]

 required
density_t float | ndarray[tuple[Any, ...], dtype[~_ScalarT]]

Tritium density [m^-3]

 required
density_he3 float | ndarray[tuple[Any, ...], dtype[~_ScalarT]]

Helium-3 density [m^-3]

 required
reaction str | Reactions | AneutronicReactions

The fusion reaction

 <Reactions.D_T: ReactionData(label='D + T → ⁴He + n', total_energy=2.8183035155819573e-12, num_neutrons=1, cross_section=<tokamak_neutron_source.reactivity_data.ReactionCrossSection object at 0x7ff2008d4c50>, bosch_hale_coefficients=BoschHaleCoefficients(name='D + T --> 4He + n', t_min=0.2, t_max=100.0, bg=34.3827, mrc2=1124656.0, c=array([ 1.17302e-09, 1.51361e-02, 7.51886e-02, 4.60643e-03, 1.35000e-02, -1.06750e-04, 1.36600e-05])), ballabio_spectrum=BallabioEnergySpectrum(energy_0=14021.0, omega_0=177.259, energy_shift_coeffs=BallabioCoefficients(a1=5.30509, a2=0.0024736, a3=1.84, a4=1.3818), width_correction_coeffs=BallabioCoefficients(a1=0.00051068, a2=0.0076223, a3=1.78, a4=8.7691e-05)))>
method ReactivityMethod

The method to use when calculating the reactivity

 <ReactivityMethod.AUTO: 3>

Returns:

Type Description
float | ndarray[tuple[Any, ...], dtype[~_ScalarT]]

Density-weighted reactivity of the reaction at the specified temperature(s) [1/m^3/s]
Source code in tokamak_neutron_source/reactivity.py 
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def density_weighted_reactivity(
    temp_kev: float | npt.NDArray,
    density_d: float | npt.NDArray,
    density_t: float | npt.NDArray,
    density_he3: float | npt.NDArray,
    reaction: str | AllReactions = Reactions.D_T,
    method: ReactivityMethod = ReactivityMethod.AUTO,
) -> float | npt.NDArray:
    """
    Calculate the density-weighted thermal reactivity of a fusion reaction in
    Maxwellian plasmas, \\t:math:`n_1 n_2 <\\sigma v>`.

    Parameters
    ----------
    temp_kev:
        Temperature [keV]
    density_d:
        Deuterium density [m^-3]
    density_t:
        Tritium density [m^-3]
    density_he3:
        Helium-3 density [m^-3]
    reaction:
        The fusion reaction
    method:
        The method to use when calculating the reactivity

    Returns
    -------
    :
        Density-weighted reactivity of the reaction at the specified temperature(s)
        [1/m^3/s]
    """
    reaction = _parse_reaction(reaction)

    match reaction:
        case Reactions.D_D | AneutronicReactions.D_D:
            n1_n2 = density_d * density_d / 2
        case Reactions.D_T:
            n1_n2 = density_d * density_t
        case Reactions.T_T:
            n1_n2 = density_t * density_t / 2
        case AneutronicReactions.D_He3:
            n1_n2 = density_d * density_he3
        case _:
            raise NotImplementedError(f"Reaction {reaction} not implemented.")

    return n1_n2 * reactivity(temp_kev, reaction, method)

reactivity(temp_kev, reaction=<Reactions.D_T: ReactionData(label='D + T → ⁴He + n', total_energy=2.8183035155819573e-12, num_neutrons=1, cross_section=<tokamak_neutron_source.reactivity_data.ReactionCrossSection object at 0x7ff2008d4c50>, bosch_hale_coefficients=BoschHaleCoefficients(name='D + T --> 4He + n', t_min=0.2, t_max=100.0, bg=34.3827, mrc2=1124656.0, c=array([ 1.17302e-09, 1.51361e-02, 7.51886e-02, 4.60643e-03,1.35000e-02, -1.06750e-04, 1.36600e-05])), ballabio_spectrum=BallabioEnergySpectrum(energy_0=14021.0, omega_0=177.259, energy_shift_coeffs=BallabioCoefficients(a1=5.30509, a2=0.0024736, a3=1.84, a4=1.3818), width_correction_coeffs=BallabioCoefficients(a1=0.00051068, a2=0.0076223, a3=1.78, a4=8.7691e-05)))>, method=<ReactivityMethod.AUTO: 3>)

Calculate the thermal reactivity of a fusion reaction in Maxwellian plasmas, \t:math:<\sigma v>.

Parameters:

Name Type Description Default
temp_kev float | ndarray[tuple[Any, ...], dtype[~_ScalarT]]

Temperature [keV]

 required
reaction str | Reactions | AneutronicReactions

The fusion reaction

 <Reactions.D_T: ReactionData(label='D + T → ⁴He + n', total_energy=2.8183035155819573e-12, num_neutrons=1, cross_section=<tokamak_neutron_source.reactivity_data.ReactionCrossSection object at 0x7ff2008d4c50>, bosch_hale_coefficients=BoschHaleCoefficients(name='D + T --> 4He + n', t_min=0.2, t_max=100.0, bg=34.3827, mrc2=1124656.0, c=array([ 1.17302e-09, 1.51361e-02, 7.51886e-02, 4.60643e-03, 1.35000e-02, -1.06750e-04, 1.36600e-05])), ballabio_spectrum=BallabioEnergySpectrum(energy_0=14021.0, omega_0=177.259, energy_shift_coeffs=BallabioCoefficients(a1=5.30509, a2=0.0024736, a3=1.84, a4=1.3818), width_correction_coeffs=BallabioCoefficients(a1=0.00051068, a2=0.0076223, a3=1.78, a4=8.7691e-05)))>
method ReactivityMethod

The method to use when calculating the reactivity

 <ReactivityMethod.AUTO: 3>

Returns:

Type Description
float | ndarray[tuple[Any, ...], dtype[~_ScalarT]]

Reactivity of the reaction at the specified temperature(s) [m^3/s]
Source code in tokamak_neutron_source/reactivity.py 
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def reactivity(
    temp_kev: float | npt.NDArray,
    reaction: str | AllReactions = Reactions.D_T,
    method: ReactivityMethod = ReactivityMethod.AUTO,
) -> float | npt.NDArray:
    """
    Calculate the thermal reactivity of a fusion reaction in Maxwellian plasmas,
    \\t:math:`<\\sigma v>`.

    Parameters
    ----------
    temp_kev:
        Temperature [keV]
    reaction:
        The fusion reaction
    method:
        The method to use when calculating the reactivity

    Returns
    -------
    :
        Reactivity of the reaction at the specified temperature(s) [m^3/s]
    """
    reaction = _parse_reaction(reaction)

    match method:
        case ReactivityMethod.AUTO:
            if reaction.bosch_hale_coefficients is not None:
                return _reactivity_bosch_hale(temp_kev, reaction)
            return _reactivity_from_xs(temp_kev, reaction.cross_section)
        case ReactivityMethod.BOSCH_HALE:
            if reaction.bosch_hale_coefficients is not None:
                return _reactivity_bosch_hale(temp_kev, reaction)

            logger.warning(
                f"There is no Bosch-Hale parameterisation for reaction {reaction.name}, "
                "returning reactivity calculated by cross-section."
            )
            return _reactivity_from_xs(temp_kev, reaction.cross_section)
        case ReactivityMethod.XS:
            return _reactivity_from_xs(temp_kev, reaction.cross_section)

raw_uc(value, unit_from, unit_to)

Raw unit converter Converts a value from one unit to another

Parameters:

Name Type Description Default
value ValueLikeT

value to convert

 required
unit_from str | Unit

unit to convert from

 required
unit_to str | Unit

unit to convert to

 required

Returns:

Type Description
ValueLikeT

converted value
Source code in tokamak_neutron_source/constants.py 
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def raw_uc(
    value: ValueLikeT,
    unit_from: str | ureg.Unit,
    unit_to: str | ureg.Unit,
) -> ValueLikeT:
    """
    Raw unit converter
    Converts a value from one unit to another

    Parameters
    ----------
    value:
        value to convert
    unit_from:
        unit to convert from
    unit_to:
        unit to convert to

    Returns
    -------
    :
        converted value
    """
    try:
        return (
            ureg.Quantity(value, ureg.Unit(unit_from)).to(ureg.Unit(unit_to)).magnitude
        )
    except ValueError:
        # Catch scales on units eg the ridculousness of this unit: 10^19/m^3
        unit_from_q = ureg.Quantity(unit_from)
        unit_to_q = ureg.Quantity(unit_to)
        return (
            ureg.Quantity(value * unit_from_q).to(unit_to_q.units).magnitude
            / unit_to_q.magnitude
        )