Longitudinal permeability of collisional plasmas under arbitrary degree of degeneration of electron gas

TL;DR

This paper derives the electric conductivity and dielectric permeability of collisional plasmas with arbitrary electron degeneracy, using kinetic equations and comparing quantum and classical limits.

Contribution

It provides new formulas for dielectric permeability in collisional plasmas considering arbitrary electron degeneracy, extending previous models.

Findings

Derived dielectric permeability using Wigner-Vlasov-Boltzmann equation.

Compared quantum and classical limits of dielectric permeability.

Validated formulas against Mermin's results.

Abstract

Electric conductivity and dielectric permeability of the non-degenerate electronic gas for the collisional plasmas under arbitrary degree of degeneration of electron gas is found. The kinetic equation of Wigner - Vlasov - Boltzmann with collision integral in relaxation form BGK (Bhatnagar, Gross and Krook) in coordinate space is used. Dielectric permeability with using of the relaxation equation in the momentum space has been received by Mermin. Comparison with Mermin's formula has been realized. It is shown, that in the limit when Planck's constant tends to zero expression for dielectric permeability passes in the classical.