Supernova remnants as cosmic ray factories

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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.