Diffusive shock acceleration - Acceleration rate, magnetic-field direction and the diffusion limit

This paper reviews the concept of diffusive shock acceleration, showing that the acceleration of charged particles at a collisionless shock is a straightforward consequence of the standard cosmic-ray transport equation, provided that one treats the discontinuity at the shock correctly. This is true for arbitrary direction of the upstream magnetic field. Within this framework, it is shown that acceleration at perpendicular or quasi-perpendicular shocks is generally much faster than for parallel shocks. Paradoxically, it follows also that, for a simple scattering law, the acceleration is faster for less scattering or larger mean free path. Obviously, the mean free path can not become too large or the diffusion limit becomes inapplicable. Gradient and curvature drifts caused by the magnetic-field change at the shock play a major role in the acceleration process in most cases. Recent observations of the charge state of the anomalous component are shown to require the faster acceleration at the quasi-perpendicular solar-wind termination shock.