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We investigate the diffusive shock acceleration in the presence of thenon-resonant streaming instability introduced by Bell (2004). The numerical MHDsimulations of the magnetic field amplification combined with the analyticaltreatment of cosmic ray acceleration permit us to calculate the maximum energyof particles accelerated by high-velocity supernova shocks. The estimates forCas A, Kepler, SN1006, and Tycho historical supernova remnants are given. Wealso found that the amplified magnetic field is preferentially orientedperpendicular to the shock front downstream of the fast shock. This explainsthe origin of the radial magnetic fields observed in young supernova remnants.

Diffusive Shock Acceleration with Magnetic Amplification by Non-resonant Streaming Instability in SNRs