MONTE-CARLO SIMULATION OF DIFFUSIVE PARTICLE-ACCELERATION IN SHOCK-WAVES WITH OBLIQUE MAGNETIC-FIELDS

Using Monte Carlo simulation, the phase-space distribution function of diffusively accelerated particles in shock waves with oblique magnetic fields is calculated. We adopt test particle approximation and adiabaticity at the shock crossing. Both large-angle scattering and pitch-angle scattering are examined as possible diffusion processes. We calculate the distribution function for a shock speed of 0.1c, a compression ratio of 4.0, and various values of cos Phi up, where Phi(up) is the angle between the magnetic field and shock normal in the upstream rest frame. From the calculated distribution function, we obtain the spectral index and the acceleration time-scale. The spectral index lies in the range 1.5 less than or equal to alpha less than or equal to 2.1 in the case of the large-angle scattering for a reasonable obliqueness, and becomes large for extremely oblique shocks. For the pitch angle scattering it lies in the range 1.0 less than or equal to alpha less than or equal to 2.1, which is quite similar to the earlier result of Kirk and Heavens. The resultant acceleration time becomes short as cos Phi(up) up decreases, and for cos Phi(up)less than or equal to 0.5 it is much shorter than the estimate based on the diffusion convection equation. It is one or two orders of magnitude shorter than that for the parallel shock. In general, pitch-angle scattering gives a flatter spectrum and a shorter acceleration time than large-angle scattering.