Acceleration of Solar Wind Ions by Nearby Interplanetary Shocks:   Comparison of Monte Carlo Simulations with Ulysses Observations
  The most stringent test of theoretical models of the first-order Fermi mechanism at collisionless astrophysical shocks is a comparison of the theoretical predictions with observational data on particle populations. Such comparisons have yielded good agreement between observations at the quasi-parallel portion of the Earth's bow shock and three theoretical approaches, including Monte Carlo kinetic simulations. This paper extends such model testing to the realm of oblique interplanetary shocks: here observations of proton and alpha particle distributions made by the SWICS ion mass spectrometer on Ulysses at nearby interplanetary shocks are compared with test particle Monte Carlo simulation predictions of accelerated populations. The plasma parameters used in the simulation are obtained from measurements of solar wind particles and the magnetic field upstream of individual shocks. Good agreement between downstream spectral measurements and the simulation predictions are obtained for two shocks by allowing the the ratio of the mean-free scattering length to the ionic gyroradius, to vary in an optimization of the fit to the data. Generally small values of this ratio are obtained, corresponding to the case of strong scattering. The acceleration process appears to be roughly independent of the mass or charge of the species. 
Matthew G. Baring, Keith Ogilvie, Donald Ellison and Robert Forsyth