Shock Acceleration of High-Energy Cosmic Rays: The Importance of the Magnetic-Field Angle

The physics of particle acceleration by collisionless shocks is addressed using analytic theory and numerical simulations. In this paper we focus on the importance of the angle between the shock normal and upstream mean magnetic field, 〈θBn〉, in determining the energy spectrum of the accelerated particles. We show that the acceleration rate is strongly dependent on θBn and is a maximum at perpendicular shocks. Moreover, we demonstrate that for a wide range of reasonable parameters, the acceleration efficiency is weakly dependent on the shock normal angle. When applied to acceleration at supernovae blast waves, we find, therefore, for any given time interval, the highest-energy cosmic rays originate from regions in which the shock moves normal to the mean magnetic field. We also find that maximum energy is larger than that obtained using the well-known Bohm-limit.