On the possible reason for nondetection of TeV protons in supernova remnants

The theory of shock acceleration predicts the maximum particle energy to be limited only by the acceleration time and the size (geometry) of the shock. This led to optimistic estimates for the galactic cosmic-ray energy achievable in supernova remnant (SNR) shocks. The estimates imply that the accelerated particles, while making no strong impact on the shock structure (test-particle approach), are nevertheless scattered by the strong self-generated Alfvén waves (turbulent boost) needed to accelerate them quickly. We demonstrate that these two assumptions are in conflict when applied to SNRs of the age required for cosmic-ray acceleration to the "knee" energy. We study the combined effect of acceleration nonlinearity (shock modification by accelerated particles) and wave generation on the acceleration process. We show that the refraction of self-generated waves resulting from the deceleration of the plasma flow by the pressure of energetic particles causes enhanced losses of these particles. This effect slows down the acceleration and changes the shape of the particle spectrum near the cutoff. The implications for observations of TeV emission from SNRs are also discussed.