Acceleration time scale in an ultrarelativistic shock

Abstract

The acceleration mechanism at ultrarelativistic shocks is investigated using the Monte Carlo simulations. We apply a method of discrete small amplitude particle momentum scattering to reproduce highly anisotropic conditions at the shock and carefully describe the acceleration mechanism. The obtained acceleration times equal $1.0 r_{g}/c$ if the spectral index reach the value of 2.2, independent of physical conditions in the shock. Some other parameters of the acceleration process are also provided.