  Diffusive shock acceleration in the environs of a remnant's expanding shell
is a popular candidate for the origin of SNR gamma-rays. In this paper, results
from our study of non-linear effects in shock acceleration theory and their
impact on the gamma-ray spectra of SNRs are presented. These effects describe
the dynamical influence of the accelerated cosmic rays on the shocked plasma at
the same time as addressing how the non-uniformities in the fluid flow force
the distribution of the cosmic rays to deviate from pure power-laws. Such
deviations are crucial to gamma-ray spectral determination. Our self-consistent
Monte Carlo approach to shock acceleration is used to predict ion and electron
distributions that spawn neutral pion decay, bremsstrahlung and inverse Compton
emission components for SNRs. We demonstrate how the spatial and temporal
limitations imposed by the expanding SNR shell quench acceleration above
critical energies in the 500 GeV - 10 TeV range, thereby spawning gamma-ray
spectral cutoffs that are quite consistent with Whipple's TeV upper limits to
the EGRET unidentified sources that have SNR associations. We also discuss the
role of electron injection in shocks and its impact on the significance of
electromagnetic components to GeV--TeV spectral formation.

Astrophysics