Landau Damping for Non-Maxwellian Distribution Functions

TL;DR

This paper investigates Landau damping in plasma physics by analyzing the roots of the dispersion relation for various non-Maxwellian velocity distributions, aiming to deepen understanding of the damping phenomenon.

Contribution

It extends the mathematical analysis of Landau damping to include non-Maxwellian distributions and explores the full set of solutions of the dispersion relation.

Findings

Analysis of roots for different distributions

Insights into damping mechanisms beyond Maxwellian cases

Potential implications for plasma stability studies

Abstract

Landau damping is one of the cornerstones of plasma physics. In the context of the mathematical framework developed by Landau in his original derivation of Landau damping, we examine the solutions of the linear Vlasov-Poisson system for different equilibrium velocity distribution functions, such as the Maxwellian distribution, kappa distributions, and cut-off distributions without and with energy diffusion. Specifically, we focus on the full set of roots that the dispersion relation of the linear Vlasov-Poisson system generally admits, and we wonder if the full structure of solutions might hint at a deeper understanding of the Landau damping phenomenon.