Consequences of Soliton Acceleration: Statistical Model

Mathematics – Probability

Scientific paper

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2104 Cosmic Rays, 7807 Charged Particle Motion And Acceleration, 7839 Nonlinear Phenomena, 7859 Transport Processes, 7867 Wave/Particle Interactions

Scientific paper

In magnetohydrodynamic (MHD) turbulence, correlation of wave phases may naturally arise due to nonlinear coupling between wave modes and nonlinear interaction between the waves and particles. As a result, spatially localized structures such as SLAMS and shocklets are generated. In a presence of such waves, charged particles can be efficiently Fermi-accelerated as they successively interact with oppositely propagating wave packets. This process, which we will refer to as the soliton acceleration, is quite different from the well-known quasi-linear energy diffusion process. Some of the distinct features of the soliton acceleration are the formation of multiple peaks in the velocity distribution function, and the development of spatial density inhomogeneities. The latter point is in contrast with the random wave phase case, in which the field fluctuations are random and the diffusion is Markovian. By introducing the interaction probability between a particle and the wave packet, we construct a Fokker-Planck-type model equation to describe the statistics of the soliton acceleration, and argue temporal as well as spatial dependence of distribution function of accelerated particles.

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