Particle acceleration in shocks: the effect of finite cosmic-ray pressure on the energy distribution

The spectrum of Fermi-accelerated cosmic rays in shock fronts is discussed in a perturbation expansion, to take account of the effect of the cosmic-ray pressure on the shock structure and acceleration. The perturbation to the steady-state test-particle distribution is calculated when the cosmic-ray pressure is small compared with the ram pressure of the incoming gas. The method can be used for any diffusion coefficient, as the perturbation to the energy distribution does not depend, to first order, on the perturbation to the diffusion coefficient. (author)