COSMIC-RAY ACCELERATION AT RELATIVISTIC SHOCK-WAVES IN THE PRESENCE OF OBLIQUE MAGNETIC-FIELDS WITH FINITE-AMPLITUDE PERTURBATIONS

The process of first-order Fermi acceleration at relativistic shock waves is investigated by means of Monte Carlo particle simulations. The simulations are based on numerical integration of the equations of motion of the particles in a perturbed magnetic field. We consider finite-amplitude field perturbations to be a superposition of sinusoidal static waves. The downstream magnetic field structure is obtained from the upstream one by assuming simple plasma compression at the shock for the frozen magnetic field. For shock waves with oblique mean magnetic fields, we confirm our previous finding of non-monotonic change of spectral index with increasing field perturbation amplitude. It is thus possible to have steep spectra with synchrotron spectral indices below -0.5 in relativistic shocks also. In the case of quasi-perpendicular (superluminal) shocks, the acceleration is reduced to a simple compression for small-amplitude magnetic field perturbations. At larger amplitudes, power-law spectra can be produced, which flatten with growing field perturbations. We present results for a number of shock velocities: 0.5, 0.7, 0.9 and 0.98 times the velocity of light.