In this presentation, we will discuss our recent result that perpendicular shocks are 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 η u_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 diffusive shock acceleration theory. These results provide a theoretical basis for the thirty-year-old conjecture that a supernova exploding into the wind of a Wolf-Rayet star may accelerate protons to an energy exceeding 10¹⁵ eV.

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