Diffusive Shock Acceleration Theory Revisited

The theory of the acceleration of charged particles by shock waves predicts a power-law spectrum of accelerated particles, with the spectral index depending only on the compression ratio across the shock wave front. However, related observations in many cases demonstrate a dependence of the particle spectrum on other shock parameters as well. Here we account for the motion of Fermi's "scattering centers" with respect to the bulk plasma flow. The particle spectrum for the case of quasi-perpendicular shocks is proved to be harder than that for quasi-parallel shocks. The back-reaction of the accelerated particles, in the form of turbulence self-excitation, results in a reduction of the velocity differences of the "scattering centers" upstream and downstream, so that the spectrum of the accelerated particles softens. Depending on the upstream level of turbulence, the particle spectrum may be independent of the shock wave parameters over a wide range, yielding a universal particle spectrum of f ~ p^-4.3 to f ~ p^-5.