Fokker-Planck theory for cosmic ray diffusion in the presence of Alfvén waves 1. Theory

Abstract

Using the standard quasi-linear Fokker-Planck approach and an expansion of the cosmic ray distribution function in Legendre polynomials, we derive a complete set of Fokker-Planck coefficients and expressions for the complete cosmic ray diffusion tensor due to linearly polarized planar Alfven waves propagating at an angle to the average magnetic field. We find that although an off-diagonal term formally appears in the diffusion tensor, it is identically zero. In addition, the cross-field diffusion coefficient is identically the same as that found for wave propagation exactly parallel to the average magnetic field.