Magnetically created instability in a collisionless plasma

In the Vlasov-Maxwell theory we prove that there are homogeneous equilibria that are monotone decreasing in every direction and are arbitrarily close to a Maxwellian. They are unstable under certain electromagnetic perturbati ons, but are stable under purely electric perturbations as well as under el ectromagnetic perturbations of sufficiently short period. These statements are valid both in the linear and nonlinear senses. (C) 2000 Editions scient ifiques et medicales Elsevier SAS.