Linear Stability and instability of relativistic Vlasov-Maxwell systems

We consider the linear stability problem for a symmetric equilibrium of the relativistic Vlasov-Maxwell (RVM) system. For an equilibrium whose distribution function depends monotonically on the particle energy, we obtain a sharp linear stability criterion. The growing mode is proved to be purely growing and we get a sharp estimate of the maximal growth rate. In this paper we specifically treat the periodic 1 2 D case and the 3D whole-space case with cylindrical symmetry. We explicitly illustrate, using the linear stability criterion in the 1 2 D case, several stable and unstable examples. c © 2000 Wiley Periodicals, Inc.