  In this work we investigate particle acceleration in supernova remnant shocks
within a semi-analytical formalism which self-consistently accounts for
particle acceleration, amplification of the magnetic field via streaming
instability and back-reaction of both accelerated particles and magnetic
turbulence on the shock dynamics. In particular, we study the interplay between
particle injection and magnetic field amplification, showing how a
phenomenological but reasonable saturation of the standard streaming
instability may lead to quite steep spectra for the accelerated particles. We
comment on the implications that such a scenario may have on the comprehension
of the diffuse spectrum of Galactic cosmic rays and of gamma-ray observations
of single remnants.
