Dispersion properties of electrostatic oscillations in quantum plasmas

TL;DR

This paper derives and analyzes the dispersion relation for electrostatic oscillations in zero-temperature quantum plasmas, highlighting effects like wave diffraction and Landau damping across various plasma conditions.

Contribution

It provides a comprehensive derivation of the dispersion relation for ESOs in quantum plasmas, incorporating quantum effects and comparing numerical solutions with approximate formulas.

Findings

Wave diffraction causes Landau damping at large wavenumbers.

Exact dispersion relations are numerically solved and compared with approximations.

The study covers parameters from semiconductor to dense astrophysical plasmas.

Abstract

We present a derivation of the dispersion relation for electrostatic oscillations (ESOs) in a zero temperature quantum plasma. In the latter, degenerate electrons are governed by the Wigner equation, while non-degenerate ions follow the classical fluid equations. The Poisson equation determines the electrostatic wave potential. We consider parameters ranging from semiconductor plasmas to metallic plasmas and electron densities of compressed matter such as in laser-compression schemes and dense astrophysical objects. Due to the wave diffraction caused by overlapping electron wave function due to the Heisenberg uncertainty principle in dense plasmas, we have possibility of Landau damping of the high-frequency electron plasma oscillations (EPOs) at large enough wavenumbers. The exact dispersion relations for the EPOs are solved numerically and compared to the ones obtained by using approximate formulas for the electron susceptibility in the high- and low-frequency cases.