More uniform perturbation theory of the Vlasov equation

Abstract

The Vlasov—Poisson equations are reformulated by applying an arbitrary transformation to the velocity variable in such a way that perturbation theory of the transformed equations does not exhibit the customary secularity in time (or space) in second or higher order. The lowest order approximation of the new formulation is discussed and compared with conventional results. The source of the non-uniformity appears to be the divergence of Particle trajectories as calculated by perturbation methods, from the exact ones after long times. The transformation which allows one to follow the particle trajectories is a transformation to a frame of reference moving with a plasma test particle in the self-consistent field.