Diffusive Acceleration of Ions at Interplanetary Shocks
  Heliospheric shocks are excellent systems for testing theories of particle acceleration in their environs. These generally fall into two classes: (1) interplanetary shocks that are linear in their ion acceleration characteristics, with the non-thermal ions serving as test particles, and (2) non-linear systems such as the Earth's bow shock and the solar wind termination shock, where the accelerated ions strongly influence the magnetohydrodynamic structure of the shock. This paper explores the modelling of diffusive acceleration at a particular interplanetary shock, with an emphasis on explaining in situ measurements of ion distribution functions. The observational data for this event was acquired on day 292 of 1991 by the Ulysses mission. The modeling is performed using a well-known kinetic Monte Carlo simulation, which has yielded good agreement with observations at several heliospheric shocks, as have other theoretical techniques, namely hybrid plasma simulations, and numerical solution of the diffusion-convection equation. In this theory/data comparison, it is demonstrated that diffusive acceleration theory can, to first order, successfully account for both the proton distribution data near the shock, and the observation of energetic protons farther upstream of this interplanetary shock than lower energy pick-up protons, using a single turbulence parameter. The principal conclusion is that diffusive acceleration of inflowing upstream ions can model this pick-up ion-rich event without the invoking any seed pre-acceleration mechanism, though this investigation does not rule out the action of such pre-acceleration. 
Matthew G. Baring and Errol J. Summerlin