Particle Acceleration at High-γ Shock Waves

First-order Fermi acceleration processes at ultrarelativistic (γ ∼ 5-30) shocks are studied with the method of Monte Carlo simulations. The accelerated particle spectra are obtained by integrating the exact particle trajectories in a turbulent magnetic field near the shock. The magnetic field model assumes finite-amplitude perturbations within a wide wavevector range and with a predefined wave power spectrum, which are imposed on the mean field component inclined at some angle to the shock normal. The downstream field structure is obtained as the compressed upstream field. We show that the main acceleration process at oblique shocks is the particle compression at the shock. Formation of energetic spectral tails is possible in a limited energy range for highly perturbed magnetic fields. Cut-offs in the spectra occur at low energies in the resonance range considered. We relate this feature to the structure of the magnetic field downstream of the shock, where field compression produces effectively 2D turbulence in which cross-field diffusion is very small. Because of the field compression downstream, the acceleration process is inefficient also in parallel high-γ shocks for larger turbulence amplitudes, and features observed in oblique shocks are recovered. For small-amplitude perturbations, particle spectra are formed in a wide energy range and modifications of the acceleration process due to the existence of long-wave perturbations are observed. The critical turbulence amplitude for efficient acceleration at parallel shocks decreases with γ . We also study the influence of strong short-wave perturbations, generated downstream of the shock, on the particle acceleration processes at high-γ shocks. The spectral indices obtained do not converge to the “universal” value α ≈ 4.2. Our results indicate inefficiency of the first-order Fermi process to generate high-energy cosmic rays at ultrarelativistic shocks with the perturbed magnetic field structures considered in the present work.