Shock acceleration of cosmic rays - a critical review

Motivated by recent unsuccessful efforts to detect the predicted flux of TeV gamma-rays from supernova remnants, we present a critical examination of the theory on which these predictions are based. Three crucial problems are identified: injection, maximum achievable particle energy and spectral index. In each case significant new advances in understanding have been achieved, which cast doubt on prevailing paradigms such as Bohm diffusion and single-fluid magneto-hydrodynamics. This indicates that more realistic analytical models, backed by more sophisticated numerical techniques, should be employed to obtain reliable predictions. Preliminary work on incorporating the effects of anomalous transport suggest that the resulting spectrum should be significantly softer than that predicted by conventional theory. (author)