On Particle Acceleration around Shocks. III. Shock Waves Moving at Arbitrary Speed. The Case of Large-Scale Magnetic Field and Anisotropic Scattering

A mathematical approach to investigate particle acceleration at shock waves moving at arbitrary speed in a medium with arbitrary scattering properties was first discussed in work by Vietri and Blasi. We use this method and somewhat extend it in order to include the effect of a large-scale magnetic field in the upstream plasma, with arbitrary orientation with respect to the direction of motion of the shock. We also use this approach to investigate the effects of anisotropic scattering on spectra and anisotropies of the distribution function of the accelerated particles.