59 lines
1.8 KiB
Python
59 lines
1.8 KiB
Python
import numpy as np
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from pynam.baskets import CalculationConstants, CalculationParams
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LINDHARD_SERIES_THRESHOLD = 1e4
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class LindhardDielectric(object):
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def __init__(self,
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params: CalculationParams,
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constants: CalculationConstants = CalculationConstants(),
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thres=LINDHARD_SERIES_THRESHOLD):
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self.series_threshold = thres
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self.omega = params.omega
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self.v_f = params.v_f
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self.omega_p = params.omega_p
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self.tau = params.tau
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self.c_light = constants.c_light
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self.s = 1 / (self.tau * self.omega)
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self.prefactor = 3 * (self.omega_p ** 2) / (self.omega ** 2)
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def get_eps(self):
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def eps_lindhard(u_inverse_wavelength: float) -> complex:
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""" the lindhard dielectric function
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:param u_inverse_wavelength: u is in units of the reciprocal vacuum wavelength (omega / c_light)
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:return: returns the value of epsilon, dimensionless
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"""
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# converts u from inverse vacuum wavelength to inverse mean free path
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u = u_inverse_wavelength * self.v_f / self.c_light
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if u < LINDHARD_SERIES_THRESHOLD * self.v_f / self.omega:
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return eps_series(u)
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else:
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return eps_full_lindhard(u)
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def eps_series(u: float) -> complex:
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rel_value = (
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(1j / (3 * (self.s - 1j))) + u ** 2 * ((-9j + 5 * self.s) / (45 * (-1j + self.s) ** 3))
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)
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return 1 + (self.prefactor * rel_value)
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def eps_full_lindhard(u: float) -> complex:
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log_value = np.log((1 - u + (self.s * 1j)) / (1 + u + (self.s * 1j)))
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rel_value = (1 + ((1 + (self.s * 1j)) / (2 * u)) * log_value) / (1 + ((self.s * 1j) / (2 * u)) * log_value)
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return 1 + (self.prefactor / (u ** 2)) * rel_value
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return eps_lindhard
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def get_lindhard_dielectric(params: CalculationParams,
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constants: CalculationConstants = CalculationConstants()):
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return LindhardDielectric(params, constants).get_eps()
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