Cosmic-Ray Transport and Acceleration. I. Derivation of the Kinetic Equation and Application to Cosmic Rays in Static Cold Media

The propagation of energetic charged particles in a zero electric field and an ordered uniform magnetic field (B0) in a cold background medium is investigated theoretically, with a focus on the case where Alfven waves propagating parallel or antiparallel to B0 are superposed. The derivations of the governing equations of a quasi-linear theory for pitch-angle and momentum diffusion and for its applications to cosmic-ray protons in a cold medium at rest or in nonrelativistic motion parallel to B0 are given in great detail; numerical predictions are presented in tables and graphs and discussed with reference to published observational data.