Source code for pyMETHES.rate_coefficients

#  Copyright (c) 2020-2021 ETH Zurich

Module for the CountedRates and ConvolutedRates classes.

Both classes are based on the RateCoefficients abstract class. They implement two
different methods for calculating ionization/attachment rate coefficients. The
CountedRates class calculates the rate coefficients by averaging over time the number
of ionization and attachment collisions. The ConvolutedRates class calculates the
rate coefficients by calculating the convolution product of the cross section with the
time-averaged electron energy distribution of the electrons.

# Import Packages
from abc import ABC
import numpy as np
import scipy.constants as csts

# Import modules
from pyMETHES.energy_distribution import TimeAveragedEnergyDistribution
from pyMETHES.gas_mixture import GasMixture
from pyMETHES.temporal_evolution import TimeSeries


[docs]class RateCoefficients(ABC): """ Ionization, attachment and effective ionization rate coefficients Attributes: ionization: ionization reaction rate coefficient (m3.s-1) attachment: attachment reaction rate coefficient (m3.s-1) effective: effective ionization reaction rate coefficient (m3.s-1) """ def __init__(self): self.ionization = None self.attachment = None self.effective = None
[docs]class ConvolutedRates(RateCoefficients): """ Ionization, attachment and effective ionization rate coefficients calculated by convolution product of eedf and cross section. """
[docs] def calculate_data(self, mix: GasMixture, distri: TimeAveragedEnergyDistribution) -> None: """ Calculates the effective, ionization and attachment rate coefficients. Args: mix (GasMixture): GasMixture object containing the cross section data distri (TimeAveragedEnergyDistribution): electron energy distribution (eV-1) """ self.ionization = np.sum([self.calculate_convolution(x, distri) for x in mix.cross_sections[mix.is_ionization]]) self.attachment = np.sum([self.calculate_convolution(x, distri) for x in mix.cross_sections[mix.is_attachment]]) self.effective = self.ionization - self.attachment
[docs] @staticmethod def calculate_convolution(interp, distri: TimeAveragedEnergyDistribution) -> float: """ Calculates the reaction rate of a collision type by calculating the convolution product of the eedf and the corresponding cross sections. Args: interp: linear interpolation of the cross section (m2) distri (TimeAveragedEnergyDistribution): energy distribution of the electrons (eV-1) Returns: reaction rate coefficient (m3.s-1) """ cross_section = interp(distri.energy_bin_centers) A = distri.eedf * distri.energy_bin_centers ** 0.5 * np.diff(distri.energy_bins) rrate = np.sqrt( 2 * csts.elementary_charge / csts.electron_mass) *, cross_section) return rrate
[docs]class CountedRates(RateCoefficients): """ Ionization, attachment and effective ionization rate coefficients, calculated by counting ionization and attachment collisions. Attributes: gas_number_density (float): gas number density (m-3) conserve (bool): conservation of the electron number """
[docs] def __init__(self, gas_number_density: float, conserve: bool): """ Instantiation of CountedRates. Args: gas_number_density (float): gas number density (m-3) for normalization conserve (bool): bool indicating conservation of the electron number (affects the statistics when counting the collisions) """ super().__init__() self.gas_number_density = gas_number_density self.conserve = conserve self.ionization_err = None self.attachment_err = None self.effective_err = None
[docs] def calculate_data(self, time_series: TimeSeries) -> None: """ Calculates the ionization, attachment and effective ionization rate coefficients values by counting collision events. Args: time_series (TimeSeries): temporal evolution of some quantities """ steps_since_sst = time_series.time.size - 1 - time_series.ind_equ x = time_series.time[time_series.ind_equ:] \ - time_series.time[time_series.ind_equ] if not self.conserve: # Ne(t-t_SST) = Ne(t_SST) * exp(nu_eff * (t-t_SST)) # log(Ne(t-t_SST)) - log(Ne(t_SST)) = nu_eff * (t-t_SST) y = np.log(time_series.num_electrons[time_series.ind_equ:]) \ - np.log(time_series.num_electrons[time_series.ind_equ]) d = y[1:] / x[1:] nu_eff = np.mean(d) if nu_eff != 0: x = (np.exp(nu_eff * x) - 1) / nu_eff \ * time_series.num_electrons[time_series.ind_equ] else: y = time_series.num_electrons[time_series.ind_equ:] \ - time_series.num_electrons[time_series.ind_equ] d = y[1:] / x[1:] # effective ionization self.effective = np.mean(d) / self.gas_number_density self.effective_err = np.std(d) / np.sqrt(steps_since_sst) \ / self.gas_number_density # ionization (cations, positively charged) y = time_series.num_cations[time_series.ind_equ:] \ - time_series.num_cations[time_series.ind_equ] d = y[1:] / x[1:] self.ionization = np.mean(d) / self.gas_number_density self.ionization_err = \ np.std(d) / np.sqrt(steps_since_sst) / self.gas_number_density # attachment (anions, negatively charged) y = time_series.num_anions[time_series.ind_equ:] \ - time_series.num_anions[time_series.ind_equ] d = y[1:] / x[1:] self.attachment = np.mean(d) / self.gas_number_density self.attachment_err = \ np.std(d) / np.sqrt(steps_since_sst) / self.gas_number_density