  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 p_max/R < p < p_max, where R>1 is the nonlinear pre-compression of the
flow and p_max is a conventional maximum momentum, that could be reached if
there was no refraction.
