The Fokker-Planck coefficients of cosmic ray transport in random electromagnetic fields

The authors derive the three Fokker-Planck coefficients D mu mu , D mu p , D pp of cosmic ray particle transport in a uniform magnetic field with superposed small-amplitude electromagnetic plasma waves in the weak interaction approximation by calculating first-order corrections to the particle's orbit. The calculations are done in the full electromagnetic case avoiding the magnetostatic approximation and any restriction on the waves' propagation direction and the waves' dispersion relation. Special attention is given to low-frequency magnetohydrodynamic waves because of their importance in space physics and astrophysics, and the Fokker-Planck coefficients D mu mu and D mu p are simplified by expanding the general expressions to zeroth and first order in omega j /kc<<1, respectively. Then the concept of slab and isotropic turbulence is critically re-examined leading to the introduction of the cone model in which waves can propagate with an angle psi < chi with respect to the background magnetic field. The Fokker-Planck coefficients D mu mu and D mu p for this cone model can be further simplified and results depend critically on the value of delta = mod tan chi mod . For transverse Alfven waves, results are given for small cone opening values delta <<1.