Diffusive Shock Acceleration with Magnetic Amplification by Nonresonant Streaming Instability in Supernova Remnants

We investigate the diffusive shock acceleration in the presence of the nonresonant streaming instability introduced by Bell. The numerical MHD simulations of the magnetic field amplification combined with the analytical treatment of cosmic-ray acceleration permit us to calculate the maximum energy of particles accelerated by high-velocity supernova shocks. The estimates for the Cas A, Kepler, SN 1006, and Tycho historical supernova remnants are given. We also found that the amplified magnetic field is preferentially oriented perpendicular to the shock front downstream of the fast shock. This explains the origin of the radial magnetic fields observed in young supernova remnants.