Intrinsic energy cut-off in diffusive shock acceleration: possible reason for non-detection of TeV-protons in SNRs

The linear theory of shock acceleration predicts the maximum particle energy to be limited only by the acceleration time and the size of the shock. We study the combined effect of acceleration nonlinearity (shock modification by accelerated particles, that must be present in strong astrophysical shocks) and propagation of Alfven waves that are responsible for particle confinement to the shock front. We show that wave refraction to larger wave numbers in the nonlinearly modified flow causes enhanced losses of particles in the momentum range pmax/R < p < pmax, where R > 1 is the nonlinear pre-compression of the flow and pmax is a conventional maximum momentum, that could be reached if there was no refraction.