Monte Carlo Modeling of Nonlinear Particle Acceleration by a Collisionless Shock Wave for Different Laws of Scattering

A nonlinear Monte Carlo model is presented in which the spectra of accelerated particles and magnetic fluctuations are calculated self-consistently, allowing for nonlinear effects and plasma instabilities in the vicinity of a strong shock wave. Different model modes of particle scattering are considered. It is shown that the spectrum of accelerated particles is smoothed considerably when using the generalized mode of small-scale scattering instead of Bohm’s law of scattering.