Partially averaged field approach to cosmic ray diffusion

Abstract

The kinetic equation for particles interacting with turbulent fluctuations is derived by a new nonlinear technique which successfully corrects the difficulties associated with quasi-linear theory. In this new method the effects of the fluctuations are evaluated along particle orbits which themselves include the effects of a statistically averaged subset of the possible configurations of the turbulence. The new method is illustrated by calculating the pitch angle diffusion coefficient Dμμ for particles interacting with ’’slab model’’ magnetic turbulence, i.e., magnetic fluctuations linearly polarized transverse to a mean magnetic field 〈B〉. Results are compared with those of quasi-linear theory and also with those of Monte Carlo calculations reported in a companion paper. The major effect of the nonlinear treatment in this illustration is the determination of Dμμ in the vicinity of 90° pitch angles where quasi-linear theory breaks down. The spatial diffusion coefficient κ∥ parallel to 〈B〉 is evaluated using Dμμ as calculated by our technique. It is argued that the partially averaged field method is not limited to small amplitude fluctuating fields and hence is not a perturbation theory.