Linear instability of Vlasov-Maxwell systems revisited-A Hamiltonian approach

TL;DR

This paper revisits the linear stability analysis of Vlasov-Maxwell systems in plasma physics using a Hamiltonian framework, providing sharp criteria and exponential estimates for both relativistic and nonrelativistic cases.

Contribution

It introduces a Hamiltonian approach to analyze linear stability, recovering known criteria and deriving exponential trichotomy estimates for the systems.

Findings

Recovered sharp linear stability criteria.

Established exponential trichotomy estimates.

Applied the theory to both relativistic and nonrelativistic systems.

Abstract

We consider linear stability of steady states of 1(1/2) and 3D Vlasov-Maxwell systems for collisionless plasmas. The linearized systems can be written as separable Hamiltonian systems with constraints. By using a general theory for separable Hamiltonian systems, we recover the sharp linear stability criteria obtained previously by different approaches. Moreover, we obtain the exponential trichotomy estimates for the linearized Vlasov-Maxwell systems in both relativistic and nonrelativistic cases.