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

Abstract

We consider linear stability of steady states of 1\begin{document}$ \frac{1}{2} $\end{document} and 3DVlasov-Maxwell systems for collisionless plasmas. The linearized systems canbe written as separable Hamiltonian systems with constraints. By using ageneral theory for separable Hamiltonian systems, we recover the sharp linearstability criteria obtained previously by different approaches. Moreover, weobtain the exponential trichotomy estimates for the linearized Vlasov-Maxwellsystems in both relativistic and nonrelativistic cases.