A sharp stability criterion for the Vlasov-Maxwell system

Details A sharp stability criterion for the Vlasov-Maxwell system A sharp stability criterion for the Vlasov-Maxwell system

2007-02-02

arxiv.org/abs/physics/0702023v1

Physics

Plasma Physics

Scientific paper

10.1007/s00222-008-0122-1

We consider the linear stability problem for a 3D cylindrically symmetric equilibrium of the relativistic Vlasov-Maxwell system that describes a collisionless plasma. For an equilibrium whose distribution function decreases monotonically with the particle energy, we obtained a linear stability criterion in our previous paper. Here we prove that this criterion is sharp; that is, there would otherwise be an exponentially growing solution to the linearized system. Therefore for the class of symmetric Vlasov-Maxwell equilibria, we establish an energy principle for linear stability. We also treat the considerably simpler periodic 1.5D case. The new formulation introduced here is applicable as well to the nonrelativistic case, to other symmetries, and to general equilibria.

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