Fermi acceleration by relativistic shock waves

Abstract

This paper discusses the acceleration of charged particles by astrophysical shock waves of arbitrary strength. As in the non-relativistic case, an energy spectrum of power-law form is produced, the slope of which varies according to the type of shock being considered. General solutions for the propagation of relativistic shock waves in a variety of physical conditions are presented, and the energy spectra for the resulting cosmic rays are derived. For strong shocks, a synchrotron spectral index in the range 0.3-0.5 is produced for propagation velocities less than 0.9 c; higher spectral indices can be produced only be weak shocks. The application of this acceleration mechanism to extragalactic radio sources is discussed briefly.