  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 (2004, 2006) has been augmented here by a
large-amplitude short-wave downstream component, imitating that generated by
plasma instabilities at the shock front. Following Niemiec & Ostrowski (2006),
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
wavevector 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. AGN and GRBs, is likely generated by particles
accelerated in processes other than the widely invoked first-order Fermi
mechanism.
