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The shock waves produce relativistic particles via the diffusive shockacceleration (DSA) mechanism. Among various circumstances, fast accelerationhas been expected for perpendicular shocks. We investigate the accelerationtime and the energy spectrum of particles accelerated at a perpendicular shock.In our model, the upstream perpendicular magnetic field has no fluctuation, andthe downstream region is highly turbulent. Then, the particle motion is thegyration in the upstream region and Bohm-like diffusion downstream. Under thissituation, we derive an analytical form of the acceleration time. Using testparticle simulations, the validity of our formula is verified. In addition, theenergy spectrum of particles is the same as those predicted by standard DSA.Therefore, presently proposed mechanism simultaneously realizes the rapidacceleration and the canonical spectrum, $dN/dp \propto p^{-2}$, even if thereis no upstream magnetic amplification.

Fast Particle Acceleration at Perpendicular Shocks with Uniform Upstream Magnetic Field and Strong Downstream Turbulence