Velocity space diffusion of charged particles in weak magnetostatic fields: Nonlinear effects, model constraints, and implications for simulations

Abstract

The velocity space diffusion of charged test particles in random magnetostatic fields is re-investigated from a semi-dynamical point of view. The dynamics of charged particles in resonance with parallel propagating electromagnetic waves is investigated numerically and compared with analytical results for the trapping width in velocity space, Δv∥, and the bounce frequency, ωb. It is demonstrated how an understanding of the basic resonance phenomenon can lead to a better understanding of the validity regions of the quasi-linear theory and their implications for numerical simulations. It is shown, using established analytical expressions for Δv∥ and ωb, that the quasi-linear diffusion coefficient can be written in a new physically illuminating form. The concept of an effective trapping width in velocity space for the turbulence modified resonance structure is introduced. It is shown how this effective resonance width implies a condition on the density of wave modes in Fourier space, in the vicinity of the resonant wave number. The implications of this condition for simulations utilizing discrete fields are discussed in detail and examples of simulations violating this condition are presented. Other issues pertinent to the simulation of velocity diffusion in turbulent electromagnetic fields are discussed, paying attention to the discretization of the fields and the temporal discretization of the dynamical equations.