Particle Spectra Of Ultra-Relativistic Shock Waves

Numerical Monte Carlo simulations of the diffusive shock acceleration in the test particle limit are investigated. We simulate high relativistic flow astrophysical plasmas for upstream $\gamma$ $\sim5$ and up to $\gamma$ $\sim1000$. These gamma values are relevant to the diffusive shock acceleration models of Active Galactic Nuclei (AGN) and Gamma Ray Bursts (GRBs). The spectral shape for the above high relativistic processes will be calculated. This work presents distinctive spectral shapes with plateau-like characteristics due to the relativistic effects and the spectral indexes are found to be as flat as the flow becomes relativistic; the latter is in a very good agreement with previous theoretical and numerical works concerning relativistic plasma flows.