Stochastic Particle Acceleration in Parallel Relativistic Shocks

We present results of test-particle simulations on both the first- and the second-order Fermi acceleration for relativistic parallel shock waves. Our studies suggest that the role of the second-order mechanism in the turbulent downstream of a relativistic shock may have been underestimated in the past, and that the stochastic mechanism may have significant effects on the form of the particle spectra and its time evolution.