Rapid Cosmic-Ray Acceleration at Perpendicular Shocks in Supernova Remnants

Perpendicular shocks are shown to be rapid particle accelerators that perform optimally when the ratio u s of the shock speed to the particle speed roughly equals the ratio 1/ η of the scattering rate to the gyro frequency. We use analytical methods and Monte-Carlo simulations to solve the kinetic equation that governs the anisotropy generated at these shocks, and find, for ηu s ≈ 1, that the spectral index softens by unity and the acceleration time increases by a factor of two compared to the standard result of the diffusive shock acceleration theory. These results provide a theoretical basis for the 30 year old conjecture that a supernova exploding into the wind of a Wolf–Rayet star may accelerate protons to an energy exceeding 10 15 eV.