Energy spectrum and pitch angle distribution of particles reflected by MHD shock waves of fast mode

Abstract

To study the macroscopic acceleration process for non-thermal particles at the front of MHD shock waves, two limiting treatments, namely the “adiabatic” and the “kink” treatments have been developed. They correspond to cases of (particle gyroradius)/(width of shock transition region) ⪡ 1 and ⪢ 1, respectively. The effects of the acceleration process on energy and pitch angle distributions of reflected particles are examined by using each of these treatments and results are compared. It is shown that these two treatments give almost the same energy and pitch angle distribution in the case of nearly-perpendicular shock waves. In the case of nearly-parallel shock waves, the pitch angle distributions differ significantly, there being reflected particles in the adiabatic loss cone when the kink treatment is employed, while the ranges of the energy distribution for these two treatments do not differ greatly. Analytic representation for the acceleration in the adiabatic treatment is given for the later usage.