ENERGY-SPECTRA OF COSMIC-RAYS ACCELERATED AT ULTRARELATIVISTIC SHOCK-WAVES

Energy spectra of particles accelerated by the first-order Fermi mecha nism are investigated at ultrarelativistic shock waves, outside the ra nge of Lorentz factors considered previously. For particle transport n ear the shock a numerical method involving small amplitude pitch angle scattering is applied for flows with Lorentz factors gamma from 3 to 243. For large gamma shocks a convergence of derived energy spectral i ndices up to the value sigma(infinity) approximate to 2.2 is observed for all considered turbulence amplitudes and magnetic field configurat ions. Recently the same index was derived for gamma-ray bursts by Waxm an [Astrophys. J. Lett. 485, L5 (1997)].