Acceleration of energetic particles by compressible plasma waves of arbitrary scale sizes

Abstract

This paper presents a calculation of energetic particle acceleration by a train of compressible plasma waves of arbitrary scale sizes. It is an extension of the work by Zhang (1). The compressible plasma waves can broaden the momentum distribution of particles significantly only when the particle diffusion scale κ/V is greater than the size of each compression zone but is smaller than the spatial extent of wave presence. The accelerated particles downstream of the compressible waves will typically have a power-law distribution at momenta far away from the source injection momentum with a slope only slightly steeper than the diffusive shock acceleration with the same plasma compression ratio. If the source particles are continuously injected in the entire wave span, after enough wave cycles, the summed distribution of accelerated particles can approach to an asymptotic p −3 distribution which does not seem to depend on any model parameters. This distribution of particles contains divergent amount of pressure. A nonlinear interaction between the wave and accelerated particles must be considered in order to produce a p −5 distribution.