  First-order Fermi acceleration process at a relativistic shock wave is
investigated by means of Monte Carlo simulations involving numerical
integration of particle equations of motion in a turbulent magnetic field near
the shock. In comparison to earlier studies a few 'realistic' features of the
magnetic field structure are included. The upstream field consists of a mean
field component inclined at some angle to the shock normal and finite-amplitude
perturbations imposed upon it. The perturbations are assumed to be static in
the local plasma rest frame. We apply an analytic model for the turbulence with
a flat or a Kolmogorov spectrum within a finite (wide) wave vector range. The
magnetic field is continuous across the shock -- the downstream field structure
is derived from the upstream one from the hydrodynamical shock jump conditions.
We present and discuss the obtained particle spectra and angular distributions
at mildly relativistic sub- and superluminal shocks. We show that particle
spectra diverge from a simple power-law, an exact shape of the spectrum depends
on both an amplitude of the magnetic field perturbations and the considered
wave power spectrum.
