Cut-offs and pile-ups in shock acceleration spectra
  We have examined cutoffs and pile-ups due to various processes in the spectra of particles produced by shock acceleration, and found that, even in the absence of energy losses, the shape of the spectrum of accelerated particles at energies well below the nominal maximum energy depends strongly on the energy dependence of the diffusion coefficient. This has implications in many areas, for example, in fitting the observed cosmic ray spectrum with models based on power-law source spectra and rigidity dependent diffusive escape from the galaxy. With continuous energy losses, prominent pile-ups may arise, and these should be included when modelling synchrotron X-ray and inverse Compton gamma-ray spectra from a shock-accelerated electron population.   We have developed a Monte Carlo/numerical technique to model the shape of the spectrum for the case of non-continuous energy losses such as inverse Compton scattering in the Klein-Nishina regime. We find that the shapes of the resulting cut-offs differ substantially from those arising from continuous processes, and we suggest that such differences could be observable through their effect on the spectrum of radiation emitted by a population of recently accelerated electrons as, for example, may exist in young supernova remnants. 
R.J. Protheroe and Todor Stanev