import logging
import sys
import warnings
import numpy as np
import pandas as pd
from scipy import interpolate
from tardis.plasma.exceptions import PlasmaIonizationError
from tardis.plasma.properties.base import ProcessingPlasmaProperty
from tardis.plasma.properties.continuum_processes import get_ion_multi_index
logger = logging.getLogger(__name__)
ION_ZERO_THRESHOLD = 1e-20
__all__ = [
"PhiSahaNebular",
"PhiSahaLTE",
"RadiationFieldCorrection",
"IonNumberDensity",
"IonNumberDensityHeNLTE",
"SahaFactor",
"ThermalPhiSahaLTE",
]
def calculate_block_ids_from_dataframe(dataframe):
block_start_id = (
np.where(np.diff(dataframe.index.get_level_values(0)) != 0.0)[0] + 1
)
return np.hstack(([0], block_start_id, [len(dataframe)]))
[docs]class PhiSahaLTE(ProcessingPlasmaProperty):
"""
Attributes
----------
phi : pandas.DataFrame, dtype float
Used for LTE ionization (at the radiation temperature).
Indexed by atomic number, ion number. Columns are zones.
"""
outputs = ("phi",)
latex_name = (r"\Phi",)
latex_formula = (
r"\dfrac{2Z_{i,j+1}}{Z_{i,j}}\big( \
\dfrac{2\pi m_{e}/\beta_{\textrm{rad}}}{h^2} \
\big)^{3/2}e^{\dfrac{-\chi_{i,j}}{kT_{\textrm{rad}}}}",
)
broadcast_ionization_energy = None
[docs] @staticmethod
def calculate(g_electron, beta_rad, partition_function, ionization_data):
phis = np.empty(
(
partition_function.shape[0]
- partition_function.index.get_level_values(0).unique().size,
partition_function.shape[1],
)
)
block_ids = calculate_block_ids_from_dataframe(partition_function)
for i, start_id in enumerate(block_ids[:-1]):
end_id = block_ids[i + 1]
current_block = partition_function.values[start_id:end_id]
current_phis = current_block[1:] / current_block[:-1]
phis[start_id - i : end_id - i - 1] = current_phis
broadcast_ionization_energy = ionization_data.reindex(
partition_function.index
).dropna()
phi_index = broadcast_ionization_energy.index
broadcast_ionization_energy = broadcast_ionization_energy.values
phi_coefficient = (
2
* g_electron
* np.exp(np.outer(broadcast_ionization_energy, -beta_rad))
)
return pd.DataFrame(phis * phi_coefficient, index=phi_index)
@staticmethod
def _calculate_block_ids(partition_function):
partition_function.index.get_level_values(0).unique()
[docs]class ThermalPhiSahaLTE(PhiSahaLTE):
"""
Attributes
----------
phi : pandas.DataFrame, dtype float
Used for LTE ionization (at the electron temperature).
Indexed by atomic number, ion number. Columns are zones.
"""
outputs = ("thermal_phi_lte",)
latex_name = (r"\Phi^{*}(T_\mathrm{e})",)
latex_formula = (
r"\dfrac{2Z_{i,j+1}}{Z_{i,j}}\big( \
\dfrac{2\pi m_{e}/\beta_{\textrm{electron}}}{h^2} \
\big)^{3/2}e^{\dfrac{-\chi_{i,j}}{kT_{\textrm{electron}}}}",
)
[docs] @staticmethod
def calculate(
thermal_g_electron,
beta_electron,
thermal_lte_partition_function,
ionization_data,
):
return super(ThermalPhiSahaLTE, ThermalPhiSahaLTE).calculate(
thermal_g_electron,
beta_electron,
thermal_lte_partition_function,
ionization_data,
)
[docs]class PhiSahaNebular(ProcessingPlasmaProperty):
"""
Attributes
----------
phi : pandas.DataFrame, dtype float
Used for nebular ionization. Indexed by atomic number, ion number.
Columns are zones.
"""
outputs = ("phi",)
latex_name = (r"\Phi",)
latex_formula = (
r"W(\delta\zeta_{i,j}+W(1-\zeta_{i,j}))\left( \
\dfrac{T_{\textrm{electron}}}{T_{\textrm{rad}}}\right)^{1/2}",
)
[docs] @staticmethod
def calculate(
t_rad,
w,
zeta_data,
t_electrons,
delta,
g_electron,
beta_rad,
partition_function,
ionization_data,
):
phi_lte = PhiSahaLTE.calculate(
g_electron, beta_rad, partition_function, ionization_data
)
zeta = PhiSahaNebular.get_zeta_values(zeta_data, phi_lte.index, t_rad)
phis = (
phi_lte
* w
* ((zeta * delta) + w * (1 - zeta))
* (t_electrons / t_rad) ** 0.5
)
return phis
[docs] @staticmethod
def get_zeta_values(zeta_data, ion_index, t_rad):
zeta_t_rad = zeta_data.columns.values.astype(np.float64)
zeta_values = zeta_data.loc[ion_index].values.astype(np.float64)
zeta = interpolate.interp1d(
zeta_t_rad, zeta_values, bounds_error=False, fill_value=np.nan
)(t_rad)
zeta = zeta.astype(float)
if np.any(np.isnan(zeta)):
warnings.warn(
f"t_rads outside of zeta factor interpolation"
f" zeta_min={zeta_data.columns.values.min():.2f} zeta_max={zeta_data.columns.values.max():.2f} "
f"- replacing with {t_rad}"
)
zeta[np.isnan(zeta)] = 1.0
return zeta
[docs]class RadiationFieldCorrection(ProcessingPlasmaProperty):
"""
Attributes
----------
delta : pandas.DataFrame, dtype float
Calculates the radiation field correction (see Mazzali & Lucy, 1993) if
not given as input in the config. file. The default chi_0_species is
Ca II, which is good for type Ia supernovae. For type II supernovae,
(1, 1) should be used. Indexed by atomic number, ion number. The columns are zones.
"""
outputs = ("delta",)
latex_name = (r"\delta",)
def __init__(
self,
plasma_parent=None,
departure_coefficient=None,
chi_0_species=(20, 2),
delta_treatment=None,
):
super(RadiationFieldCorrection, self).__init__(plasma_parent)
self.departure_coefficient = departure_coefficient
self.delta_treatment = delta_treatment
self.chi_0_species = chi_0_species
def _set_chi_0(self, ionization_data):
if self.chi_0_species == (20, 2):
self.chi_0 = 1.9020591570241798e-11
else:
self.chi_0 = ionization_data.loc[self.chi_0_species]
[docs] def calculate(
self, w, ionization_data, beta_rad, t_electrons, t_rad, beta_electron
):
if getattr(self, "chi_0", None) is None:
self._set_chi_0(ionization_data)
if self.delta_treatment is None:
if self.departure_coefficient is None:
departure_coefficient = 1.0 / w
else:
departure_coefficient = self.departure_coefficient
radiation_field_correction = -np.ones(
(len(ionization_data), len(beta_rad))
)
less_than_chi_0 = (ionization_data < self.chi_0).values
factor_a = t_electrons / (departure_coefficient * w * t_rad)
radiation_field_correction[~less_than_chi_0] = factor_a * np.exp(
np.outer(
ionization_data.values[~less_than_chi_0],
beta_rad - beta_electron,
)
)
radiation_field_correction[less_than_chi_0] = 1 - np.exp(
np.outer(ionization_data.values[less_than_chi_0], beta_rad)
- beta_rad * self.chi_0
)
radiation_field_correction[less_than_chi_0] += factor_a * np.exp(
np.outer(ionization_data.values[less_than_chi_0], beta_rad)
- self.chi_0 * beta_electron
)
else:
radiation_field_correction = (
np.ones((len(ionization_data), len(beta_rad)))
* self.delta_treatment
)
delta = pd.DataFrame(
radiation_field_correction,
columns=np.arange(len(t_rad)),
index=ionization_data.index,
)
return delta
[docs]class IonNumberDensity(ProcessingPlasmaProperty):
"""
Convergence process to find the correct solution. A trial value for
the electron density is initiated in a particular zone. The ion
number densities are then calculated using the Saha equation. The
electron density is then re-calculated by using the ion number
densities to sum over the number of free electrons. If the two values
for the electron densities are not similar to within the threshold
value, a new guess for the value of the electron density is chosen
and the process is repeated.
Attributes
----------
ion_number_density : pandas.DataFrame, dtype float
Index atom number, ion number. Columns zones.
electron_densities : numpy.ndarray, dtype float
"""
outputs = ("ion_number_density", "electron_densities")
latex_name = (
"N_{i,j}",
"n_{e}",
)
def __init__(
self,
plasma_parent,
ion_zero_threshold=ION_ZERO_THRESHOLD,
electron_densities=None,
):
super(IonNumberDensity, self).__init__(plasma_parent)
self.ion_zero_threshold = ion_zero_threshold
self.block_ids = None
self._electron_densities = electron_densities
[docs] @staticmethod
def calculate_with_n_electron(
phi,
partition_function,
number_density,
n_electron,
block_ids,
ion_zero_threshold,
):
if block_ids is None:
block_ids = IonNumberDensity._calculate_block_ids(phi)
ion_populations = np.empty_like(partition_function.values)
phi_electron = np.nan_to_num(phi.values / n_electron.values)
for i, start_id in enumerate(block_ids[:-1]):
end_id = block_ids[i + 1]
current_phis = phi_electron[start_id:end_id]
phis_product = np.cumprod(current_phis, 0)
tmp_ion_populations = np.empty(
(current_phis.shape[0] + 1, current_phis.shape[1])
)
tmp_ion_populations[0] = number_density.values[i] / (
1 + np.sum(phis_product, axis=0)
)
tmp_ion_populations[1:] = tmp_ion_populations[0] * phis_product
ion_populations[start_id + i : end_id + 1 + i] = tmp_ion_populations
ion_populations[ion_populations < ion_zero_threshold] = 0.0
return (
pd.DataFrame(data=ion_populations, index=partition_function.index),
block_ids,
)
@staticmethod
def _calculate_block_ids(phi):
return calculate_block_ids_from_dataframe(phi)
[docs] def calculate(self, phi, partition_function, number_density):
if self._electron_densities is None:
n_e_convergence_threshold = 0.05
n_electron = number_density.sum(axis=0)
n_electron_iterations = 0
while True:
(
ion_number_density,
self.block_ids,
) = self.calculate_with_n_electron(
phi,
partition_function,
number_density,
n_electron,
self.block_ids,
self.ion_zero_threshold,
)
ion_numbers = ion_number_density.index.get_level_values(
1
).values
ion_numbers = ion_numbers.reshape((ion_numbers.shape[0], 1))
new_n_electron = (ion_number_density.values * ion_numbers).sum(
axis=0
)
if np.any(np.isnan(new_n_electron)):
raise PlasmaIonizationError(
'n_electron just turned "nan" -' " aborting"
)
n_electron_iterations += 1
if n_electron_iterations > 100:
logger.warning(
f"n_electron iterations above 100 ({n_electron_iterations}) -"
f" something is probably wrong"
)
if np.all(
np.abs(new_n_electron - n_electron) / n_electron
< n_e_convergence_threshold
):
break
n_electron = 0.5 * (new_n_electron + n_electron)
else:
n_electron = self._electron_densities
ion_number_density, self.block_ids = self.calculate_with_n_electron(
phi,
partition_function,
number_density,
n_electron,
self.block_ids,
self.ion_zero_threshold,
)
return ion_number_density, n_electron
[docs]class IonNumberDensityHeNLTE(ProcessingPlasmaProperty):
"""
Convergence process to find the correct solution. A trial value for
the electron density is initiated in a particular zone. The ion
number densities are then calculated using the Saha equation. The
electron density is then re-calculated by using the ion number
densities to sum over the number of free electrons. If the two values
for the electron densities are not similar to within the threshold
value, a new guess for the value of the electron density is chosen
and the process is repeated.
Attributes
----------
ion_number_density : pandas.DataFrame, dtype float
Index atom number, ion number. Columns zones.
electron_densities : numpy.ndarray, dtype float
"""
outputs = (
"ion_number_density",
"electron_densities",
"helium_population_updated",
)
latex_name = (
"N_{i,j}",
"n_{e}",
)
def __init__(
self, plasma_parent, ion_zero_threshold=1e-20, electron_densities=None
):
super(IonNumberDensityHeNLTE, self).__init__(plasma_parent)
self.ion_zero_threshold = ion_zero_threshold
self.block_ids = None
self._electron_densities = electron_densities
[docs] def update_he_population(
self, helium_population, n_electron, number_density
):
helium_population_updated = helium_population.copy()
he_one_population = helium_population_updated.loc[0].mul(n_electron)
he_three_population = helium_population_updated.loc[2].mul(
1.0 / n_electron
)
helium_population_updated.loc[0].update(he_one_population)
helium_population_updated.loc[2].update(he_three_population)
unnormalised = helium_population_updated.sum()
normalised = helium_population_updated.mul(
number_density.loc[2] / unnormalised
)
helium_population_updated.update(normalised)
return helium_population_updated
[docs] def calculate(
self, phi, partition_function, number_density, helium_population
):
if self._electron_densities is None:
n_e_convergence_threshold = 0.05
n_electron = number_density.sum(axis=0)
n_electron_iterations = 0
while True:
(
ion_number_density,
self.block_ids,
) = IonNumberDensity.calculate_with_n_electron(
phi,
partition_function,
number_density,
n_electron,
self.block_ids,
self.ion_zero_threshold,
)
helium_population_updated = self.update_he_population(
helium_population, n_electron, number_density
)
ion_number_density.loc[2, 0].update(
helium_population_updated.loc[0].sum(axis=0)
)
ion_number_density.loc[2, 1].update(
helium_population_updated.loc[1].sum(axis=0)
)
ion_number_density.loc[2, 2].update(
helium_population_updated.loc[2, 0]
)
ion_numbers = ion_number_density.index.get_level_values(
1
).values
ion_numbers = ion_numbers.reshape((ion_numbers.shape[0], 1))
new_n_electron = (ion_number_density.values * ion_numbers).sum(
axis=0
)
if np.any(np.isnan(new_n_electron)):
raise PlasmaIonizationError(
'n_electron just turned "nan" -' " aborting"
)
n_electron_iterations += 1
if n_electron_iterations > 100:
logger.warning(
f"n_electron iterations above 100 ({n_electron_iterations}) -"
f" something is probably wrong"
)
if np.all(
np.abs(new_n_electron - n_electron) / n_electron
< n_e_convergence_threshold
):
break
n_electron = 0.5 * (new_n_electron + n_electron)
else:
n_electron = self._electron_densities
(
ion_number_density,
self.block_ids,
) = IonNumberDensity.calculate_with_n_electron(
phi,
partition_function,
number_density,
n_electron,
self.block_ids,
self.ion_zero_threshold,
)
helium_population_updated = self.update_he_population(
helium_population, n_electron, number_density
)
ion_number_density.loc[2, 0].update(
helium_population_updated.loc[0].sum(axis=0)
)
ion_number_density.loc[2, 1].update(
helium_population_updated.loc[1].sum(axis=0)
)
ion_number_density.loc[2, 2].update(
helium_population_updated.loc[2, 0]
)
return ion_number_density, n_electron, helium_population_updated
[docs]class SahaFactor(ProcessingPlasmaProperty):
"""
Calculates the 'Saha factor' Phi_ik = n_i* / (n_k* n_e), i.e.,
the ratio of the LTE level population n_i*, and the product of
the LTE ion density n_k* and the actual electron density n_e.
Attributes
----------
phi_ik : pandas.DataFrame, dtype float
Indexed by atom number, ion number, level number.
Columns are zones.
"""
outputs = ("phi_ik",)
latex_name = (r"\Phi_{i,\kappa}",)
[docs] def calculate(
self,
thermal_phi_lte,
thermal_lte_level_boltzmann_factor,
thermal_lte_partition_function,
):
boltzmann_factor = self._prepare_boltzmann_factor(
thermal_lte_level_boltzmann_factor
)
phi_saha_index = get_ion_multi_index(boltzmann_factor.index)
partition_function_index = get_ion_multi_index(
boltzmann_factor.index, next_higher=False
)
phi_saha = thermal_phi_lte.loc[phi_saha_index].values
# Replace zero values in phi_saha to avoid zero division in Saha factor
phi_saha[phi_saha == 0.0] = sys.float_info.min
partition_function = thermal_lte_partition_function.loc[
partition_function_index
].values
return boltzmann_factor / (phi_saha * partition_function)
@staticmethod
def _prepare_boltzmann_factor(boltzmann_factor):
atomic_number = boltzmann_factor.index.get_level_values(0)
ion_number = boltzmann_factor.index.get_level_values(1)
selected_ions_mask = atomic_number != ion_number
return boltzmann_factor[selected_ions_mask]