"""Shared functions used for computing the separatrix operational space."""
import numpy as np
from ....algorithm_class import Algorithm
from ....unit_handling import Quantity, Unitfull, ureg, wraps_ufunc
from ...metrics.larmor_radius import calc_larmor_radius
def calc_ideal_MHD_wavenumber(beta_e: Unitfull, epsilon_hat: Unitfull, omega_B: Unitfull, tau_i: Unitfull, alpha_t: Unitfull) -> Unitfull:
"""Calculate k_ideal, which gives the spatial scale of ideal MHD modes.
Equation G.3 from :cite:`Eich_2021`.
N.b. G.3 is written in terms of beta_hat = beta_e * epsilon_hat
where epsilon_hat = (q R / electron_pressure_decay_length)**2
"""
return np.sqrt(beta_e * epsilon_hat * omega_B**1.5 * (1.0 + tau_i) / alpha_t)
def calc_resistive_ballooning_wavenumber(critical_alpha_MHD: Unitfull, alpha_t: Unitfull, omega_B: Unitfull) -> Unitfull:
"""Calculate k_RBM, which gives the spatial scale of resistive ballooning modes.
This is the square root of the right-hand-side of equation 4 from :cite:`Eich_2021`.
From equation D.3 we see that the left-hand-side of equation 4 is k_EM^2.
In G.3 this is related to k_ideal. Equation 4 is given as equation 3 (k_ideal = k_RBM),
so if the left-hand-side is ~k_ideal^2, the right-hand-side is ~k_RBM^2. N.b. this isn't
entirely clear from the paper, but it does reproduce the results from the paper.
N.b. There is an extra factor of Lambda_pe multiplied on omega_B compared to
table 1. In Appendix A it is noted that Lambda_pe = perpendicular_decay_length / electron_pressure_decay_length = 1.
"""
return np.sqrt(critical_alpha_MHD / alpha_t * np.sqrt(omega_B))
def calc_electromagnetic_wavenumber(beta_e: Unitfull, mu: Unitfull) -> Unitfull:
"""Calculate k_EM, which gives the spatial scale of electromagnetic effects.
Equation D.3 from :cite:`Eich_2021`, but without a factor of 2 since we are
using the electron beta and not the electron dynamical beta.
"""
return np.sqrt(beta_e / mu)
def calc_electron_beta(electron_density: Unitfull, electron_temp: Unitfull, magnetic_field_strength: Unitfull) -> Unitfull:
"""Calculate the electron beta (beta_e).
N.b. this is NOT the electron dynamical beta, which does not have the factor of 2.
Row 5, table 2 from :cite:`Eich_2021`, corrected for factor of 2
"""
return 2.0 * ureg.mu_0 * electron_density * electron_temp / magnetic_field_strength**2
def calc_electron_to_ion_mass_ratio(average_ion_mass: Unitfull) -> Unitfull:
"""Calculate the electron-to-ion mass ratio.
Row 3, table 2 from :cite:`Eich_2021`
"""
return Quantity(1, ureg.electron_mass) / average_ion_mass
def calc_curvature_drive(perpendicular_decay_length: Unitfull, major_radius: Unitfull) -> Unitfull:
"""Calculate the curvature (interchange) drive term.
Row 6, table 2 from :cite:`Eich_2021`
N.b. equation 7 from :cite:`Eich_2020` has an extra factor of (1 + Z)
where Z = ne / ni where ni is summed over all charge states
"""
return 2.0 * perpendicular_decay_length / major_radius
def calc_squared_scale_ratio(safety_factor: Unitfull, major_radius: Unitfull, perpendicular_decay_length: Unitfull) -> Unitfull:
"""Calculate the squared ratio of the parallel to perpendicular length scales.
From text at top of right column on page 12 of :cite:`Eich_2021`
"""
return (safety_factor * major_radius / perpendicular_decay_length) ** 2
[docs]
@Algorithm.register_algorithm(return_keys=["critical_alpha_MHD"])
def calc_critical_alpha_MHD(elongation_psi95: Unitfull, triangularity_psi95: Unitfull) -> Unitfull:
"""Calculate the critical value of alpha_MHD.
Equation K.5 from :cite:`Eich_2021`
"""
return elongation_psi95**1.2 * (1 + 1.5 * triangularity_psi95)
[docs]
@Algorithm.register_algorithm(return_keys=["poloidal_sound_larmor_radius"])
def calc_poloidal_sound_larmor_radius(
minor_radius: Unitfull,
elongation_psi95: Unitfull,
triangularity_psi95: Unitfull,
plasma_current: Unitfull,
separatrix_electron_temp: Unitfull,
average_ion_mass: Unitfull,
) -> Unitfull:
"""Calculate the poloidally-averaged sound Larmor radius (rho_s_pol).
Equation K.4 from :cite:`Eich_2021`, using B_pol from equations K.6 and K.7.
Args:
minor_radius: :term:`glossary link<minor_radius>`
elongation_psi95: :term:`glossary link<elongation_psi95>`
triangularity_psi95: :term:`glossary link<triangularity_psi95>`
plasma_current: :term:`glossary link<plasma_current>`
separatrix_electron_temp: :term:`glossary link<separatrix_electron_temp>`
average_ion_mass: :term:`glossary link<average_ion_mass>`
Returns:
:term:`poloidal_sound_larmor_radius`
"""
poloidal_circumference = 2.0 * np.pi * minor_radius * (1 + 0.55 * (elongation_psi95 - 1)) * (1 + 0.08 * triangularity_psi95**2)
B_pol_avg = ureg.mu_0 * plasma_current / poloidal_circumference
return calc_larmor_radius(
species_temperature=separatrix_electron_temp,
magnetic_field_strength=B_pol_avg,
species_mass=average_ion_mass,
)
def calc_electron_pressure_decay_length_Eich2021H(
alpha_t: Unitfull, poloidal_sound_larmor_radius: Unitfull, factor: float = 3.6
) -> Unitfull:
"""Calculate the H-mode electron pressure decay length.
Equation K.1 from :cite:`Eich_2021`
"""
return 1.2 * (1 + factor * alpha_t**1.9) * poloidal_sound_larmor_radius
@wraps_ufunc(input_units=dict(alpha_t=ureg.dimensionless), return_units=dict(electron_pressure_decay_length=ureg.mm))
def calc_electron_pressure_decay_length_Manz2023L(alpha_t: float) -> float:
"""Calculate the L-mode electron pressure decay length.
Equation B.1 from :cite:`Manz_2023`
"""
return 17.3 * alpha_t**0.298 # type:ignore[no-any-return]
def calc_lambda_q_Eich2020H(alpha_t: Unitfull, poloidal_sound_larmor_radius: Unitfull) -> Unitfull:
"""Calculate the H-mode heat flux decay length.
Equation 22 from :cite:`Eich_2020`, then using lambda_q = 2/7 lambda_Te (equation A1)
"""
lambda_Te = 2.1 * (1 + 2.1 * alpha_t**1.7) * poloidal_sound_larmor_radius
return 2.0 / 7.0 * lambda_Te