Diffusive Shock Acceleration in Astrophysics

Diffusive shock acceleration is invoked to explain non-thermal particle acceleration at the Bow shock, in the Interplanetary Medium and Solar Flares, in Supernova Remnants, the Interstellar Medium, Active Galactic Nuclei Jets and in large-scale cosmic structures. The basic test particle mechanism to describe the spectrum and acceleration time is detailed for non-relativistic flows, and the non-linear regime where the accelerated particles react back on the flow is mentioned. Extension of the acceleration mechanism to relativistic flows is outlined, with emphasis on Monte Carlo results. The importance of explaining the time constant for achieving the highest observed energies in a given situation is a recurring theme. Current problems range from predicting the high energy output of Gamma-Ray Bursts to establishing the injection mechanism in all situations.