# 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.
"""bootstrap current source profile."""
import dataclasses
from typing import ClassVar
import chex
import jax
from jax import numpy as jnp
from torax import constants
from torax import jax_utils
from torax import math_utils
from torax import state
from torax.config import runtime_params_slice
from torax.fvm import cell_variable
from torax.geometry import geometry
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
[docs]
@chex.dataclass(frozen=True)
class DynamicRuntimeParams(runtime_params_lib.DynamicRuntimeParams):
bootstrap_mult: float
[docs]
@dataclasses.dataclass(kw_only=True, frozen=True, eq=True)
class BootstrapCurrentSource(source.Source):
"""Bootstrap current density source profile.
Unlike other sources within TORAX, the BootstrapCurrentSource provides more
than just the bootstrap current. It uses a neoclassical physics model to
also determine the neoclassical conductivity. Outputs are as follows:
- sigmaneo: neoclassical conductivity
- bootstrap current (on cell and face grids)
- total integrated bootstrap current
"""
SOURCE_NAME: ClassVar[str] = 'j_bootstrap'
@property
def source_name(self) -> str:
return self.SOURCE_NAME
@property
def affected_core_profiles(self) -> tuple[source.AffectedCoreProfile, ...]:
return (source.AffectedCoreProfile.PSI,)
def get_bootstrap(
self,
dynamic_runtime_params_slice: runtime_params_slice.DynamicRuntimeParamsSlice,
static_runtime_params_slice: runtime_params_slice.StaticRuntimeParamsSlice,
geo: geometry.Geometry,
core_profiles: state.CoreProfiles,
) -> source_profiles.BootstrapCurrentProfile:
static_source_runtime_params = static_runtime_params_slice.sources[
self.source_name
]
dynamic_source_runtime_params = dynamic_runtime_params_slice.sources[
self.source_name
]
# Make sure the input params are the correct type.
if not isinstance(dynamic_source_runtime_params, DynamicRuntimeParams):
raise TypeError(
'Expected DynamicRuntimeParams, got '
f'{type(dynamic_source_runtime_params)}.'
)
if (
static_source_runtime_params.mode
== runtime_params_lib.Mode.PRESCRIBED.value
):
raise NotImplementedError(
'Prescribed mode not supported for bootstrap current.'
)
bootstrap_current = calc_sauter_model(
bootstrap_multiplier=dynamic_source_runtime_params.bootstrap_mult,
nref=dynamic_runtime_params_slice.numerics.nref,
Zeff_face=dynamic_runtime_params_slice.plasma_composition.Zeff_face,
Zi_face=core_profiles.Zi_face,
ne=core_profiles.ne,
ni=core_profiles.ni,
temp_el=core_profiles.temp_el,
temp_ion=core_profiles.temp_ion,
psi=core_profiles.psi,
q_face=core_profiles.q_face,
geo=geo,
)
if static_source_runtime_params.mode == runtime_params_lib.Mode.ZERO.value:
bootstrap_current = source_profiles.BootstrapCurrentProfile(
sigma=bootstrap_current.sigma,
sigma_face=bootstrap_current.sigma_face,
j_bootstrap=jnp.zeros_like(bootstrap_current.j_bootstrap),
j_bootstrap_face=jnp.zeros_like(bootstrap_current.j_bootstrap_face),
I_bootstrap=jnp.zeros_like(bootstrap_current.I_bootstrap),
)
return bootstrap_current
[docs]
def get_value(
self,
static_runtime_params_slice: runtime_params_slice.StaticRuntimeParamsSlice,
dynamic_runtime_params_slice: runtime_params_slice.DynamicRuntimeParamsSlice,
geo: geometry.Geometry,
core_profiles: state.CoreProfiles,
calculated_source_profiles: source_profiles.SourceProfiles | None,
) -> tuple[chex.Array, ...]:
raise NotImplementedError('Call `get_bootstrap` instead.')
def get_source_profile_for_affected_core_profile(
self,
profile: chex.ArrayTree,
affected_core_profile: int,
geo: geometry.Geometry,
) -> jax.Array:
raise NotImplementedError('Call `get_bootstrap` instead.')
[docs]
class BootstrapCurrentSourceConfig(base.SourceModelBase):
"""Bootstrap current density source profile.
Attributes:
bootstrap_mult: Multiplication factor for bootstrap current.
"""
bootstrap_mult: float = 1.0
mode: runtime_params_lib.Mode = runtime_params_lib.Mode.MODEL_BASED
[docs]
def model_func(self):
raise NotImplementedError(
'Bootstrap current source is not meant to be used as a model.'
)
[docs]
def build_source(self) -> BootstrapCurrentSource:
return BootstrapCurrentSource()
[docs]
def build_dynamic_params(
self,
t: chex.Numeric,
) -> DynamicRuntimeParams:
return DynamicRuntimeParams(
prescribed_values=tuple(
[v.get_value(t) for v in self.prescribed_values]
),
bootstrap_mult=self.bootstrap_mult,
)
[docs]
@jax_utils.jit
def calc_sauter_model(
*,
bootstrap_multiplier: float,
nref: float,
Zeff_face: chex.Array,
Zi_face: chex.Array,
ne: cell_variable.CellVariable,
ni: cell_variable.CellVariable,
temp_el: cell_variable.CellVariable,
temp_ion: cell_variable.CellVariable,
psi: cell_variable.CellVariable,
q_face: chex.Array,
geo: geometry.Geometry,
) -> source_profiles.BootstrapCurrentProfile:
"""Calculates sigmaneo, j_bootstrap, and I_bootstrap."""
# pylint: disable=invalid-name
# Formulas from Sauter PoP 1999. Future work can include Redl PoP 2021
# corrections.
true_ne_face = ne.face_value() * nref
true_ni_face = ni.face_value() * nref
# # local r/R0 on face grid
epsilon = (geo.Rout_face - geo.Rin_face) / (geo.Rout_face + geo.Rin_face)
epseff = (
0.67 * (1.0 - 1.4 * jnp.abs(geo.delta_face) * geo.delta_face) * epsilon
)
aa = (1.0 - epsilon) / (1.0 + epsilon)
ftrap = 1.0 - jnp.sqrt(aa) * (1.0 - epseff) / (1.0 + 2.0 * jnp.sqrt(epseff))
# Spitzer conductivity
NZ = 0.58 + 0.74 / (0.76 + Zeff_face)
lnLame = (
31.3 - 0.5 * jnp.log(true_ne_face) + jnp.log(temp_el.face_value() * 1e3)
)
lnLami = (
30
- 3 * jnp.log(Zi_face)
- 0.5 * jnp.log(true_ni_face)
+ 1.5 * jnp.log(temp_ion.face_value() * 1e3)
)
sigsptz = (
1.9012e04 * (temp_el.face_value() * 1e3) ** 1.5 / Zeff_face / NZ / lnLame
)
nuestar = (
6.921e-18
* q_face
* geo.Rmaj
* true_ne_face
* Zeff_face
* lnLame
/ (
((temp_el.face_value() * 1e3) ** 2)
* (epsilon + constants.CONSTANTS.eps) ** 1.5
)
)
nuistar = (
4.9e-18
* q_face
* geo.Rmaj
* true_ni_face
* Zeff_face**4
* lnLami
/ (
((temp_ion.face_value() * 1e3) ** 2)
* (epsilon + constants.CONSTANTS.eps) ** 1.5
)
)
# Neoclassical correction to spitzer conductivity
ft33 = ftrap / (
1.0
+ (0.55 - 0.1 * ftrap) * jnp.sqrt(nuestar)
+ 0.45 * (1.0 - ftrap) * nuestar / (Zeff_face**1.5)
)
signeo_face = 1.0 - ft33 * (
1.0
+ 0.36 / Zeff_face
- ft33 * (0.59 / Zeff_face - 0.23 / Zeff_face * ft33)
)
sigmaneo = sigsptz * signeo_face
# Calculate terms needed for bootstrap current
denom = (
1.0
+ (1 - 0.1 * ftrap) * jnp.sqrt(nuestar)
+ 0.5 * (1.0 - ftrap) * nuestar / Zeff_face
)
ft31 = ftrap / denom
ft32ee = ftrap / (
1
+ 0.26 * (1 - ftrap) * jnp.sqrt(nuestar)
+ 0.18 * (1 - 0.37 * ftrap) * nuestar / jnp.sqrt(Zeff_face)
)
ft32ei = ftrap / (
1
+ (1 + 0.6 * ftrap) * jnp.sqrt(nuestar)
+ 0.85 * (1 - 0.37 * ftrap) * nuestar * (1 + Zeff_face)
)
ft34 = ftrap / (
1.0
+ (1 - 0.1 * ftrap) * jnp.sqrt(nuestar)
+ 0.5 * (1.0 - 0.5 * ftrap) * nuestar / Zeff_face
)
F32ee = (
(0.05 + 0.62 * Zeff_face)
/ (Zeff_face * (1 + 0.44 * Zeff_face))
* (ft32ee - ft32ee**4)
+ 1
/ (1 + 0.22 * Zeff_face)
* (ft32ee**2 - ft32ee**4 - 1.2 * (ft32ee**3 - ft32ee**4))
+ 1.2 / (1 + 0.5 * Zeff_face) * ft32ee**4
)
F32ei = (
-(0.56 + 1.93 * Zeff_face)
/ (Zeff_face * (1 + 0.44 * Zeff_face))
* (ft32ei - ft32ei**4)
+ 4.95
/ (1 + 2.48 * Zeff_face)
* (ft32ei**2 - ft32ei**4 - 0.55 * (ft32ei**3 - ft32ei**4))
- 1.2 / (1 + 0.5 * Zeff_face) * ft32ei**4
)
term_0 = (1 + 1.4 / (Zeff_face + 1)) * ft31
term_1 = -1.9 / (Zeff_face + 1) * ft31**2
term_2 = 0.3 / (Zeff_face + 1) * ft31**3
term_3 = 0.2 / (Zeff_face + 1) * ft31**4
L31 = term_0 + term_1 + term_2 + term_3
L32 = F32ee + F32ei
L34 = (
(1 + 1.4 / (Zeff_face + 1)) * ft34
- 1.9 / (Zeff_face + 1) * ft34**2
+ 0.3 / (Zeff_face + 1) * ft34**3
+ 0.2 / (Zeff_face + 1) * ft34**4
)
alpha0 = -1.17 * (1 - ftrap) / (1 - 0.22 * ftrap - 0.19 * ftrap**2)
alpha = (
alpha0
+ 0.25
* (1 - ftrap**2)
* jnp.sqrt(nuistar)
/ (1 + 0.5 * jnp.sqrt(nuistar))
+ 0.315 * nuistar**2 * ftrap**6
) / (1 + 0.15 * nuistar**2 * ftrap**6)
# calculate bootstrap current
prefactor = -geo.F_face * bootstrap_multiplier * 2 * jnp.pi / geo.B0
pe = true_ne_face * (temp_el.face_value()) * 1e3 * 1.6e-19
pi = true_ni_face * (temp_ion.face_value()) * 1e3 * 1.6e-19
dpsi_drnorm = psi.face_grad()
dlnne_drnorm = ne.face_grad() / ne.face_value()
dlnni_drnorm = ni.face_grad() / ni.face_value()
dlnte_drnorm = temp_el.face_grad() / temp_el.face_value()
dlnti_drnorm = temp_ion.face_grad() / temp_ion.face_value()
global_coeff = prefactor[1:] / dpsi_drnorm[1:]
global_coeff = jnp.concatenate([jnp.zeros(1), global_coeff])
necoeff = L31 * pe
nicoeff = L31 * pi
tecoeff = (L31 + L32) * pe
ticoeff = (L31 + alpha * L34) * pi
j_bootstrap_face = global_coeff * (
necoeff * dlnne_drnorm
+ nicoeff * dlnni_drnorm
+ tecoeff * dlnte_drnorm
+ ticoeff * dlnti_drnorm
)
# j_bootstrap_face = jnp.concatenate([jnp.zeros(1), j_bootstrap_face])
j_bootstrap_face = jnp.array(j_bootstrap_face)
j_bootstrap = geometry.face_to_cell(j_bootstrap_face)
sigmaneo_cell = geometry.face_to_cell(sigmaneo)
I_bootstrap = math_utils.area_integration(j_bootstrap, geo)
return source_profiles.BootstrapCurrentProfile(
sigma=sigmaneo_cell,
sigma_face=sigmaneo,
j_bootstrap=j_bootstrap,
j_bootstrap_face=j_bootstrap_face,
I_bootstrap=I_bootstrap,
)