Abstract

For a collisionless plasma that is modeled by the relativistic Vlasov-Maxwell system, many equilibria are stable but many others are unstable. In this talk, presenting joint work with Zhiwu Lin, I will consider axisymmetric equilibria of the form f(e, p) that are decreasing in the particle energy e and also depend on the particle angular momentum p. Then a necessary and sufficient condition for linear stability is the positivity of a certain linear operator L^{0. This operator L}0 is much less complicated than the generator of the full linearized system. It has an interesting non-local term that can definitely affect its positivity. There is a similar reduction in the simpler case of 1.5 dimensional symmetry. For the important example of a purely magnetic equilibrium, explicit conditions for the linear/nonlinear stability/instability are obtained.