Source code for pyMETHES.utils

#  Copyright (c) 2020-2021 ETH Zurich

Module with some utility methods.

from typing import Union
import numpy as np
import scipy.constants as sc

num = Union[int, float, np.ndarray]

[docs]def velocity_from_energy(energy: num) -> num: """ Calculate the velocity norm of electrons, based on their kinetic energy. Args: energy: Energy of the electron (eV) Returns: Velocity norm of the electrons (m.s-1) """ return np.sqrt(2 * energy * sc.elementary_charge / sc.electron_mass)
[docs]def energy_from_velocity(velocity: num) -> num: """ Calculate the kinetic energy of electrons, based on the norm of their velocity. Args: velocity: velocity norm of the electrons (m.s-1) Returns: Energy of the electrons (eV) """ return 0.5 * sc.electron_mass * velocity ** 2 / sc.elementary_charge
[docs]def acceleration_from_electric_field(electric_field: num) -> num: """ Calculates the acceleration of electrons, based on the local electric field. Args: electric_field: local electric field strength (V.m-1) Returns: acceleration (m.s-2) """ return electric_field * (sc.elementary_charge / sc.electron_mass)
[docs]def maxwell_boltzmann_eedf(points: num, temperature: Union[int, float]) -> num: """ Calculates the Maxwell-Boltzmann EEDF of the given points or point Args: points (Union[int, float, np.ndarray]): Scalar or vector of energies in eV temperature (Union[int, float]): Temperature at which to calculate the distribution """ kB = sc.k me = sc.m_e q0 = sc.e T = temperature v = np.sqrt(2 * points * q0 / me) mb = np.sqrt(2/np.pi) * (me/(kB*T))**(3/2) * v**2 * np.exp(-me * v**2 / (kB*T)) return mb * np.sqrt(points)
[docs]def maxwell_boltzmann_random(num: int, temperature: Union[float, int]) -> list: """ Returns a list of `num` Maxwell Boltzmann distributed values (in eV) at temperature `temperature` Args: num (int): Number of electrons temperature (float): Temperature """ d = False i = 0 last = -1 di = 0.0001 # determine the range for values while not d or not np.isclose(last, 0): now = maxwell_boltzmann_eedf(i, temperature) if now < last: d = True last = now i += di # divide the range into subintervals bins = np.arange(0, i, di) vals = [] # for each subinterval associate a probability (the mean of the eedf value # at the right and left side of the subinterval) for b in bins: left = maxwell_boltzmann_eedf(b, temperature) right = maxwell_boltzmann_eedf(b+di, temperature) m = left + right / 2 vals.append(m) # sum all probabilities together (imagine putting them all on a line) total = sum(vals) e = [] # generate num values by choosing a random point the line and select a # random energy in the corresponding energy interval. Both random numbers # are chosen uniformly. for i in range(0, num): u = np.random.uniform(0, total) s = 0 for b, v in zip(bins, vals): s += v if u <= s: e.append(np.random.uniform(b, b + di)) break return e