Fermi acceleration at supernova remnant shocks

We investigate the physics of particle acceleration at non-relativistic shocks exploiting two different and complementary approaches, namely a semi-analytic modeling of cosmic-ray modified shocks and large hybrid (kinetic protons/fluid electrons) simulations. The former technique allows us to extract some information from the multi-wavelength observations of supernova remnants, especially in the gamma-ray band, while the latter returns fundamental insights into the details of particle injection and magnetic field amplification via plasma instabilities. In particular, we present the results of large hybrid simulations of non-relativistic shocks, discussing the properties of the transition from the thermal to the non-thermal component, the spectrum of which turns out to be the power-law predicted by first-order Fermi acceleration. Along with a rather effective magnetic field amplification, we find that more than 20% of the bulk energy is converted in non-thermal particles, altering significantly the dynamics of the shock and leading to the formation of a precursor.