The effect of losses on acceleration of energetic particles by diffusive scattering through shock waves

A discussion of the effect of local losses on the acceleration of energetic particles by shocks is presented, which considers the energy losses of individual particles and the damping processes for the scattering hydromagnetic waves by means of time asymptotic and steady-state calculations. For acceleration to be a local effect within the Galaxy, the local scattering mean free path must be small by comparison with the effective overall galactic mean free path deduced from the cosmic-ray escape time. Given the spatial extent of the layer for strong shocks propagating into neutral interstellar clouds, the possibility of localized diffusive acceleration is investigated. The estimated strength and extent of the scattering region is not large enough to confine acceleration within the layer, which will instead extend across the entire cloud. The integrated losses of the cloud will then determine the efficiency.