Longitudinal dielectric permettivity of quantum Maxwell collisional plasmas

TL;DR

This paper derives an exact expression for the longitudinal dielectric permittivity of quantum collisional plasmas using a kinetic Wigner-Vlasov-Boltzmann approach, analyzing quantum-classical transition, damping, and comparing with classical models.

Contribution

It provides a new exact expression for dielectric permittivity in quantum collisional plasmas and compares it with classical and Mermin's models.

Findings

Dielectric permittivity reduces to classical form as Planck's constant approaches zero.

Dispersion relation solutions are obtained for small wave numbers.

Quantum and classical plasma dielectric parts are graphically compared.

Abstract

The kinetic equation of Wigner -- Vlasov -- Boltzmann with collision integral in relaxation BGK (Bhatnagar, Gross and Krook) form in coordinate space for quantum non--degenerate (Maxwellian) collisional plasma is used. Exact expression (within the limits of considered model) is found. The analysis of longitudinal dielectric permeability is done. It is shown that in the limit when Planck's constant tends to zero of expression for dielectric permettivity transforms into the classical case of dielectric permettivity. At small values of wave number it has been received the solution of the dispersion equation. Damping of plasma oscillations has been analized. The analytical comparison with the dielectric Mermin' function received with the use of the kinetic equation in momentum space is done. Graphic comparison of the real and imaginary parts of dielectric permettivity of quantum and classical plasma is done also.