Cosmic-ray acceleration at ultrarelativistic shock waves: Effects of downstream short-wave turbulence

The present paper is the last of a series studying the first-order Fermi acceleration processes at relativistic shock waves with the method of Monte Carlo simulations applied to shocks propagating in realistically modeled turbulent magnetic fields. The model of the background magnetic field structure of Niemiec & Ostrowski has been augmented here by a large-amplitude short-wave downstream component, imitating that generated by plasma instabilities at the shock front. Following the recent work of Niemiec & Ostrowski, we have considered ultrarelativistic shocks with the mean magnetic field oriented both oblique and parallel to the shock normal. For both cases, simulations have been performed for different choices of magnetic field perturbations, represented by various wave power spectra within a wide wave-vector range. The results show that the introduction of the short-wave component downstream of the shock is not sufficient to produce power-law particle spectra with the universal'' spectral index 4.2. On the contrary, concave spectra with cutoffs are preferentially formed, the curvature and cutoff energy being dependent on the properties of turbulence. Our results suggest that the electromagnetic emission observed from astrophysical sites with relativistic jets, e.g., active galactic nuclei and gamma-ray bursts, is likely generated by particles accelerated in processes other than the widely invoked first-order Fermi mechanism.