Relativistic Cosmic-Ray Spectra in the Fully Nonlinear Theory of Shock Acceleration

Abstract
Cosmic-ray spectra are calculated within the fully nonlinear theory of shock acceleration including the finite phase velocity of the scattering Alfvén waves. The spectra are weakly dependent on shock parameters over the range typical of supernova remnants, and in good agreement with the observations. Nevertheless, the very hard spectra indicated by ultrahigh-energy observations of compact binary sources can be accounted for with extremely strong shocks.