Relativistic Shock Acceleration: A Hartree-Fock Approach

Abstract

We examine the problem of particle acceleration at a relativistic shocks assuming pitch-angle scattering and using a Hartree-Fock method to approximate the associated eigenfunctions. This leads to a simple transcendental equation determining the power-law index, $s$, given the up and downstream velocities. We compare our results with accurate numerical solutions obtained using the eigenfunction method. In addition to the power-law index this method yields the angular and spatial distributions upstream of the shock.

4 pages, 2 figures, proceedings of the "4th Heidelberg International Symposium on High Energy Gamma-Ray Astronomy" July 7-11, 2008, Heidelberg, Germany