Phase mixing importance for both Landau instability and damping

TL;DR

This paper explores how phase mixing influences Landau instability and damping in plasmas, using a Hamiltonian approach to connect microscopic dynamics with the Vlasov model, revealing that phase mixing underpins both growth and damping phenomena.

Contribution

It introduces a Hamiltonian formalism for plasma dynamics that clarifies the role of phase mixing in both wave growth and damping, bridging microscopic and Vlasov descriptions.

Findings

Phase mixing causes both wave growth and damping.

Eigenfrequencies are computed for many degrees of freedom.

Stable and unstable regimes share underlying phase mixing mechanisms.

Abstract

We discuss the self-consistent dynamics of plasmas by means of hamiltonian formalism for a system of $N$ near-resonant electrons interacting with a single Langmuir wave. The connection with the Vlasov description is revisited through the numerical calculation of the van Kampen-like eigenfrequencies of the linearized dynamics for many degrees of freedom. Both the exponential-like growth as well as damping of the Langmuir wave are shown to emerge from a phase mixing effect among beam modes, revealing unexpected similarities between the stable and unstable regimes.