Instability of Nonsymmetric Nonmonotone Equilibria of the Vlasov-Maxwell System

TL;DR

This paper presents a simple spectral instability criterion for a broad class of non-symmetric, non-monotone equilibria in the relativistic Vlasov-Maxwell system, expanding understanding of plasma stability without symmetry constraints.

Contribution

It introduces a new instability criterion based on spectral analysis of Schrödinger operators, applicable to non-homogeneous and non-symmetric plasma equilibria in the Vlasov-Maxwell system.

Findings

Identifies a spectral instability criterion for a wide class of equilibria.

Develops functional analytic tools for spectral analysis of related operators.

Extends potential applicability to higher-dimensional systems with finite or periodic domains.

Abstract

We consider the 1/2-dimensional relativistic Vlasov-Maxwell system that describes the time-evolution of a plasma. We find a relatively simple criterion for spectral instability of a wide class of equilibria. This class includes non-homogeneous equilibria that need not satisfy any additional symmetry properties (as was the case in previous results), nor should they be monotone in the particle energy. The criterion is given in terms of the spectral properties of two Schr\"{o}dinger operators that arise naturally from Maxwell's equations. The spectral analysis of these operators is quite delicate, and some general functional analytic tools are developed to treat them. These tools can be applied to similar systems in higher dimensions, as long as their domain is finite or periodic.