Instabilities of the relativistic Vlasov-Maxwell system on unbounded domains

TL;DR

This paper investigates the linear instability of the relativistic Vlasov-Maxwell system in unbounded domains, providing spectral conditions for instability that do not rely on domain boundedness or monotonicity of equilibria.

Contribution

It introduces new spectral criteria for instability applicable to unbounded domains without requiring boundedness or monotonicity assumptions.

Findings

Derived spectral conditions for instability in unbounded domains.

Applicable to both 1.5D and 3D cylindrical symmetric cases.

Conditions do not depend on domain boundedness or equilibrium monotonicity.

Abstract

The relativistic Vlasov-Maxwell system describes the evolution of a collisionless plasma. The problem of linear instability of this system is considered in two physical settings: the so-called "one and one-half" dimensional case, and the three dimensional case with cylindrical symmetry. Sufficient conditions for instability are obtained in terms of the spectral properties of certain Schr\"odinger operators that act on the spatial variable alone (and not in full phase space). An important aspect of these conditions is that they do not require any boundedness assumptions on the domains, nor do they require monotonicity of the equilibrium.