Small-Angle Scattering and Diffusion: Application to Relativistic Shock Acceleration

We investigate ways of accurately simulating the propagation of energetic charged particles over small times where the standard Monte Carlo approximation to diffusive transport breaks down. We find that a small-angle scattering procedure with appropriately chosen step-lengths and scattering angles gives accurate results, and we apply this to the simulation of propagation upstream in relativistic shock acceleration.