The efficiency of shock acceleration Original Research Article

The most popular acceleration mechanism for cosmic rays (at least up to energy 1015 eV/nucleon) is shock acceleration. Its efficiency had been discussed mostly in the context of injection. In this article we address the efficiency from the point of view of comparing the acceleration of cosmic rays in plasma flows with and without discontinuity (subshock). We adopt a nonlinear test particle picture, which comprises cosmic rays and two oppositely propagating Alfvén waves. The plasma flow is considered as a heat bath. We find that there is no increase in cosmic ray energy flux, and the efficiency has to be defined in terms of cosmic ray energy density or pressure. Depending on the compression ratio and the location of the subshock, the efficiency can be negative, i.e., the shock decelerates cosmic rays in some parameter regime.