First-order Fermi acceleration processes at ultrarelativistic ( \gamma \sim 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- \gamma 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 \gamma .
We also study the influence of strong short-wave perturbations , generated downstream of the shock , on the particle acceleration processes at high- \gamma shocks .
The spectral indices obtained do not converge to the “ universal ” value \alpha \approx 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 .