Nonlinear perturbation theory for cosmic ray propagation in random magnetic fields

A nonlinear perturbation theory is applied to the problem of pitch angle diffusion of energetic particles in random magnetic fields. To keep the analysis simple, the discussion is restricted to fluctuation fields, consisting of Alfvén waves. It is shown that the failure of quasilinear theory at small particle velocities parallel to the average field can be overcome by a statistically exact treatment of the particle orbits in the first order fields. In fact, for spherical power spectra which, in addition, do not fall off too steeply with increasing frequency, the conventional perturbation theory also leads to formally convergent expressions for the scattering mean free path. These results are shown to be quite satisfactory, even in a quantitative sense. For more general physically realistic power spectra, however, a divergence-free diffusion theory is indispensible. A simple representation for the resulting pitch-angle diffusion coefficient is suggested.