Transmission and damping of hydromagnetic waves behind a strong shock front: implications for cosmic ray acceleration

Abstract

The transmission of hydromagnetic wave modes by a strong shock front is analyzed. The character and damping rates of the low frequency modes in the high beta plasma behind the shock are described. These results are applied to the theory of Fermi acceleration by shock waves. It is shown that for a sufficiently large angle between the shock normal and the incident magnetic field, wave modes in the post-shock region are subject to linear transit time damping thus impairing the particle acceleration. Short-wavelength modes propagating along the field are subject to non-linear transit time damping (taking account of the saturation associated with particle trapping). Long-wavelength modes, responsible for scattering extremely relativistic ions, should not be damped and should thus mediate particle acceleration. If low-energy cosmic rays are to be accelerated by the Fermi process at a shock front, then either the wave turbulence ahead of the shock must have large amplitude (possibly invalidating the perturbation expansion upon which the calculations described in this paper are based) or hydromagnetic turbulence must be generated behind the shock front. The role of firehose instabilities in generating such post-shock turbulence is briefly discussed.