Landau Damping of Electrostatic Waves in Arbitrarily Degenerate Quantum Plasmas

TL;DR

This paper systematically analyzes the dispersion relation of electrostatic waves in degenerate quantum plasmas, revealing how frequency and damping depend on wave number and degeneracy level, with implications for plasma stability.

Contribution

It provides a comprehensive solution for the complex frequency spectrum of electrostatic waves across various degeneracy levels and wave numbers, highlighting new scaling behaviors.

Findings

Real part of frequency scales linearly with wave number at high degeneracy and large wave numbers.

Landau damping rate becomes independent of wave number and inversely proportional to degeneracy level.

Damping remains weak but finite at moderate degeneracy for short wavelengths.

Abstract

We carry out a systematic study of the dispersion relation for linear electrostatic waves in an arbitrarily degenerate quantum electron plasma. We solve for the complex frequency spectrum for arbitrary values of wavenumber $k$ and level of degeneracy $\mu$. Our finding is that for large $k$ and high $\mu$ the real part of the frequency $\omega_{r}$ grows linearly with $k$ and scales with $\mu$ only because of the scaling of the Fermi energy. In this regime the relative Landau damping rate $\gamma/\omega_{r}$ becomes independent of $k$ and varies inversly with $\mu$. Thus, damping is weak but finite at moderate levels of degeneracy for short wavelengths.