Acceleration of cosmic ray electrons by ion-excited waves at quasi-perpendicular shocks

The standard model of cosmic ray electron acceleration requires electrons to be preaccelerated to mildly relativistic energies. It has been suggested that energy transfer from waves, generated by gyrotropic ions reflected from quasi-perpendicular shocks, could provide the necessary pre-acceleration. The distribution of shock-reflected ions at any upstream point is more likely to consist of two beams rather than a gyrotropic ring. Wave excitation in the presence of both types of ion distribution is Studied. It is shown that gyrotropic or beam ions, reflected from shocks associated with supernova remnants, can excite waves capable of accelerating electrons to beyond the required injection energies. The wave group velocity along the shock normal can be approximately equal to the shock velocity: such waves are not rapidly convected away from the shock, and can thus grow to a high level. Moreover, waves satisfying this condition which also have phase velocities parallel to the magnetic field ranging from the electron thermal speed to relativistic speeds are excited in high Mach number shocks with a low ratio of electron plasma frequency to cyclotron frequency. Bulk electrons can then be accelerated to the required energies within the region in which shock-reflected ions are present. This is consistent with a suggestion, based on a comparison between Wolf-Rayet stars and radio supernovae, that there exists a threshold perpendicular shock speed (between 1 and 3 per cent of the speed of light) above which the efficiency of electron injection increases by several orders of magnitude.