Particle acceleration around SNR shocks

We review the basic features of particle acceleration theory around collisionless shocks in supernova remnants (SNRs). We show how non-linear effects induced by the back reaction of accelerated particles onto the shock dynamics are of paramount importance to support the hipotesys that SNRs are the factories of Galactic cosmic rays. Recent developments in the modeling of the mechanism of diffusive shock acceleration are discussed, with emphasis on the role of magnetic field amplification and the presence of neutrals in the circumstellar environment. Special attention will be devoted to observational consequences of non-linear effects on the multi-wavelength spectrum of SNRs, with emphasis on X-ray and gamma-ray emission. Finally we also discuss how Balmer lines, detected from several young SNRs, can be used to estimate the shock dynamical properties and the efficiency of CR acceleration.