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

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Abstract
The authors derive the three Fokker-Planck coefficients Dmu mu , Dmu p, Dpp 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 Dmu mu and Dmu p are simplified by expanding the general expressions to zeroth and first order in omega j/kc<mu mu and Dmu 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.