An efficient Monte Carlo scheme for relativistic shock acceleration

Obtaining good statistics for accelerated particle spectra, angular distributions and time distributions by simple Monte Carlo techniques is inefficient in relativistic shock acceleration because simulation of diffusion in the downstream region is very computer time-consuming. In this paper, I present Monte Carlo results for the angular and time distributions of particles returning to an ultrarelativistic shock after propagating downstream for the case of a random walk with isotropic scattering. These distributions have been parametrized and collectively represent an 'event generator' for simulating quickly and efficiently the downstream part of an acceleration cycle