sarkas.utilities.fdints.invfd1h

sarkas.utilities.fdints.invfd1h(u)

Approximate the inverse of the Fermi-Dirac integral \(I_{-1/2}(\eta)\) using the fits provided by Fukushima. Function translated from Fukushima’s code, see [Fukushima, 2015].

Parameters

u (float) – Normalized electron density \(=\Lambda_{\rm deB}^3 n_e \sqrt{\pi}/4\),

where \(\Lambda_{\rm deB}\) is the de Broglie wavelength of the electron gas.

Examples

>>> import numpy as np
>>> # Values taken from Tutorial Notebooks
>>> ne = 1.62e32 # [N/m^3]
>>> lambda_deB = 1.957093e-11 # [m]
>>> u = lambda_deB**3 * ne * np.sqrt(np.pi)/4.0
>>> eta = invfd1h(u)
>>> f"{eta:.4f}"
'-0.2860'

Return type

float

Returns

difdih (float) – Scaled chemical potential.