# Copyright 2024 DeepMind Technologies Limited
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Fusion heat source for both ion and electron heat equations."""
import dataclasses
from typing import ClassVar, Literal
import chex
import jax
from jax import numpy as jnp
from torax import constants
from torax import jax_utils
from torax import state
from torax.config import runtime_params_slice
from torax.geometry import geometry
from torax.physics import collisions
from torax.sources import base
from torax.sources import runtime_params as runtime_params_lib
from torax.sources import source
from torax.sources import source_profiles
# Default value for the model function to be used for the fusion heat
# source. This is also used as an identifier for the model function in
# the default source config for Pydantic to "discriminate" against.
DEFAULT_MODEL_FUNCTION_NAME: str = 'fusion_heat_model_func'
[docs]
def calc_fusion(
geo: geometry.Geometry,
core_profiles: state.CoreProfiles,
static_runtime_params_slice: runtime_params_slice.StaticRuntimeParamsSlice,
dynamic_runtime_params_slice: runtime_params_slice.DynamicRuntimeParamsSlice,
) -> tuple[jax.Array, jax.Array, jax.Array]:
"""Computes DT fusion power with the Bosch-Hale parameterization NF 1992.
Args:
geo: Magnetic geometry.
core_profiles: Core plasma profiles.
static_runtime_params_slice: Static runtime params, used to determine the
existence of deuterium and tritium.
dynamic_runtime_params_slice: Dynamic runtime params, used to extract nref
and the D and T densities.
Returns:
Tuple of Ptot, Pfus_i, Pfus_e: total fusion power in MW, ion and electron
fusion power densities in W/m^3.
"""
# If both D and T not present in the main ion mixture, return zero fusion.
# Otherwise, calculate the fusion power.
if not {'D', 'T'}.issubset(static_runtime_params_slice.main_ion_names):
return (
jnp.array(0.0, dtype=jax_utils.get_dtype()),
jnp.zeros_like(core_profiles.temp_ion.value),
jnp.zeros_like(core_profiles.temp_ion.value),
)
else:
product = 1.0
for fraction, symbol in zip(
dynamic_runtime_params_slice.plasma_composition.main_ion.fractions,
static_runtime_params_slice.main_ion_names,
):
if symbol == 'D' or symbol == 'T':
product *= fraction
DT_fraction_product = product # pylint: disable=invalid-name
t_face = core_profiles.temp_ion.face_value()
# P [W/m^3] = Efus *1/4 * n^2 * <sigma*v>.
# <sigma*v> for DT calculated with the Bosch-Hale parameterization NF 1992.
# T is in keV for the formula
# pylint: disable=invalid-name
Efus = 17.6 * 1e3 * constants.CONSTANTS.keV2J
mrc2 = 1124656
BG = 34.3827
C1 = 1.17302e-9
C2 = 1.51361e-2
C3 = 7.51886e-2
C4 = 4.60643e-3
C5 = 1.35e-2
C6 = -1.0675e-4
C7 = 1.366e-5
theta = t_face / (
1.0
- (t_face * (C2 + t_face * (C4 + t_face * C6)))
/ (1.0 + t_face * (C3 + t_face * (C5 + t_face * C7)))
)
xi = (BG**2 / (4 * theta)) ** (1 / 3)
# sigmav = <cross section * velocity>, in m^3/s
# Calculate in log space to avoid overflow/underflow in f32
logsigmav = (
jnp.log(C1 * theta)
+ 0.5 * jnp.log(xi / (mrc2 * t_face**3))
- 3 * xi
- jnp.log(1e6)
)
logPfus = (
jnp.log(DT_fraction_product * Efus)
+ 2 * jnp.log(core_profiles.ni.face_value())
+ logsigmav
+ 2 * jnp.log(dynamic_runtime_params_slice.numerics.nref)
)
# [W/m^3]
Pfus_face = jnp.exp(logPfus)
Pfus_cell = 0.5 * (Pfus_face[:-1] + Pfus_face[1:])
# [MW]
Ptot = (
jax.scipy.integrate.trapezoid(Pfus_face * geo.vpr_face, geo.rho_face_norm)
/ 1e6
)
alpha_fraction = 3.5 / 17.6 # fusion power fraction to alpha particles
# Fractional fusion power ions/electrons.
birth_energy = 3520 # Birth energy of alpha particles is 3.52MeV.
alpha_mass = 4.002602
frac_i = collisions.fast_ion_fractional_heating_formula(
birth_energy,
core_profiles.temp_el.value,
alpha_mass,
)
frac_e = 1.0 - frac_i
Pfus_i = Pfus_cell * frac_i * alpha_fraction
Pfus_e = Pfus_cell * frac_e * alpha_fraction
return Ptot, Pfus_i, Pfus_e
[docs]
def fusion_heat_model_func(
static_runtime_params_slice: runtime_params_slice.StaticRuntimeParamsSlice,
dynamic_runtime_params_slice: runtime_params_slice.DynamicRuntimeParamsSlice,
geo: geometry.Geometry,
unused_source_name: str,
core_profiles: state.CoreProfiles,
unused_calculated_source_profiles: source_profiles.SourceProfiles | None,
) -> tuple[chex.Array, ...]:
"""Model function for fusion heating."""
# pylint: disable=invalid-name
_, Pfus_i, Pfus_e = calc_fusion(
geo,
core_profiles,
static_runtime_params_slice,
dynamic_runtime_params_slice,
)
return (Pfus_i, Pfus_e)
# pylint: enable=invalid-name
[docs]
@dataclasses.dataclass(kw_only=True, frozen=True, eq=True)
class FusionHeatSource(source.Source):
"""Fusion heat source for both ion and electron heat."""
SOURCE_NAME: ClassVar[str] = 'fusion_heat_source'
model_func: source.SourceProfileFunction = fusion_heat_model_func
@property
def source_name(self) -> str:
return self.SOURCE_NAME
@property
def affected_core_profiles(self) -> tuple[source.AffectedCoreProfile, ...]:
return (
source.AffectedCoreProfile.TEMP_ION,
source.AffectedCoreProfile.TEMP_EL,
)
[docs]
class FusionHeatSourceConfig(base.SourceModelBase):
"""Configuration for the FusionHeatSource."""
model_function_name: Literal['fusion_heat_model_func'] = (
'fusion_heat_model_func'
)
mode: runtime_params_lib.Mode = runtime_params_lib.Mode.MODEL_BASED
@property
def model_func(self) -> source.SourceProfileFunction:
return fusion_heat_model_func
[docs]
def build_dynamic_params(
self,
t: chex.Numeric,
) -> runtime_params_lib.DynamicRuntimeParams:
return runtime_params_lib.DynamicRuntimeParams(
prescribed_values=tuple(
[v.get_value(t) for v in self.prescribed_values]
),
)
[docs]
def build_source(self) -> FusionHeatSource:
return FusionHeatSource(model_func=self.model_func)