Diffusive Shock Acceleration: the Fermi Mechanism

The mechanism of diffusive Fermi acceleration at collisionless plasma shock waves is widely invoked in astrophysics to explain the appearance of non-thermal particle populations in a variety of environments, including sites of cosmic ray production, and is observed to operate at several sites in the heliosphere. This review outlines the principal results from the theory of diffusive shock acceleration, focusing first on how it produces power-law distributions in test-particle regimes, where the shock dynamics are dominated by the thermal populations that provide the seed particles for the acceleration process. Then the importance of non-linear modifications to the shock hydrodynamics by the accelerated particles is addressed, emphasizing how these subsequently influence non-thermal spectral formation.