MONTE-CARLO SIMULATIONS OF ENERGETIC PARTICLE-TRANSPORT IN WEAKLY INHOMOGENEOUS MAGNETIC-FIELDS .1. PARTICLE-ACCELERATION IN RELATIVISTIC SHOCK-WAVES WITH OBLIQUE MAGNETIC-FIELDS

An extended form of the Kirk & Schneider method for simulation of energetic particle transport in weakly disturbed magnetic fields is presented. It is based on the 'mean field + perturbations' decomposition of magnetic field, i.e. a particle is considered to propagate in the mean field along its undisturbed 'adiabatic' trajectory, while the magnetic field inhomogeneities are allowed for by perturbing the trajectory parameters in finite time-steps. For the application of the method we have chosen a simulation of the particle shock acceleration in relativistic shock waves with oblique magnetic fields. We reproduced a number of previously obtained analytical results for parallel and oblique shocks and revealed a possibility for substantial excess of the energetic particle pressure in front of the oblique relativistic shock with respect to the pressure behind it. In such shocks the presence of increasing magnetic field perturbations produced non-monotone changes of the particle spectral index. An important finding was that there exists an amplitude range of perturbations leading to very steep particle spectra, even including ones steeper than those produced by strong non-relativistic shocks. The conditions leading to very flat particle spectra seem to be unstable due to the reaction effects of accelerated particles.