TP-26

An eigenfunction method for particle acceleration at ultra-relativistic shocks

A. Guthmann, J.G. Kirk (MPI Kernphysik, Heidelberg, Germany), Y.A. Gallant (DIAS, Dublin, Ireland), and A. Achterberg (Sterrenkundig Instituut, Utrecht, Netherlands)

We adapt the eigenfunction method of computing the power-law spectrum of particles accelerated at a relativistic shock front (Kirk & Schneider 1987) to apply to shocks of arbitrarily high Lorentz factor. The power-law index of accelerated particles undergoing isotropic small-angle scattering at an ultrarelativistic, unmagnetized shock is found to be s=4.23 (where $s=- d[\ln(f)]/d[\ln(p)]$ with f the Lorentz-invariant phase-space density and p the momentum), in agreement with the results of Monte-Carlo simulations. We present results for shocks in plasmas with different equations of state and for Lorentz factors ranging from 5 to infinity.