A Revised Theory of Diffusive Shock Acceleration

Diffusive shock acceleration (DSA) is an efficient mechanism that produces power-law distributions of nonthermal particles and is responsible for the acceleration of Galactic cosmic rays (CRs) at the forward shocks of supernova remnants (SNRs). However, observations of nonthermal SNR emission imply CR energy distributions that are generally steeper than E^-2, the standard DSA prediction. Recent results from kinetic hybrid simulations suggest that such steep spectra may arise from the drift of magnetic structures with respect to the thermal plasma downstream of the shock. Using a semi-analytic model of non-linear DSA, we generalize this result to a wide range of shocks. By accounting for the motion of magnetic structures in the downstream, we produce CR energy distributions that are substantially steeper than E^-2 and consistent with observations. Our revised theory of DSA reproduces both modestly steep spectra of Galactic supernova remnants (∝E^-2.2) and the very steep spectra of young radio supernovae (∝E^-3).