  Particle acceleration at astrophysical shocks may be very efficient if
magnetic scattering is self-generated by the same particles. This nonlinear
process adds to the nonlinear modification of the shock due to the dynamical
reaction of the accelerated particles on the shock. Building on a previous
general solution of the problem of particle acceleration with arbitrary
diffusion coefficients (Amato & Blasi, 2005), we present here the first
semi-analytical calculation of particle acceleration with both effects taken
into account at the same time: charged particles are accelerated in the
background of Alfven waves that they generate due to the streaming instability,
and modify the dynamics of the plasma in the shock vicinity.
