Dispersion of Waves in Relativistic Plasmas with Isotropic Particle Distributions

TL;DR

This paper calculates wave dispersion laws in relativistic plasmas with various isotropic particle distributions, revealing differences in damping and mode behavior, including the existence of a maximum wavenumber and stronger Landau damping in non-thermal cases.

Contribution

It provides new analytical and numerical results for wave dispersion in relativistic plasmas with multiple isotropic distributions, including thermal, power-law, Lorentzian, and hybrid types.

Findings

Identification of superluminal undamped and damped modes for Langmuir waves

Discovery of a maximum wavenumber above which longitudinal modes do not exist

Stronger Landau damping observed in non-thermal distributions

Abstract

The dispersion laws of Langmuir and transverse waves are calculated in the relativistic non-magnetized formalism for several isotropic particle distributions: thermal, power-law, relativistic Lorentzian $\kappa,$ and hybrid $\beta$. For Langmuir waves the parameters of superluminal undamped, subluminal damped principal and higher modes are determined for a range of distribution parameters. The undamped and principal damped modes are found to match smoothly. Principal damped and second damped modes are found not to match smoothly. The presence of maximum wavenumber is discovered above that no longitudinal modes formally exist. The higher damped modes are discovered to be qualitatively different for thermal and certain non-thermal distributions. Consistently with the known results, the Landau damping is calculated to be stronger for non-thermal power-law-like distributions. The dispersion law is obtained for the single undamped transverse mode. The analytic results for the simplest distributions are provided.