Energy Spectra of Cosmic Rays Accelerated at Ultrarelativistic Shock Waves

Energy spectra of particles accelerated by the first-order Fermi mechanism are investigated at ultrarelativistic shock waves, outside the range of Lorentz factors considered previously. For particle transport near the shock a numerical method involving small amplitude pitch-angle scattering is applied for flows with Lorentz factors from 3 to 243. For large shocks a convergence of derived energy spectral indices up to the value _2. 2 is observed for all considered turbulence amplitudes and magnetic field configurations. Recently the same index was derived for -ray bursts by Waxman Astrophys. J. Lett. 485, L5 (1997).