We report simulations of diffusive particle acceleration in oblique magnetohydrodynamical (MHD) shocks. These calculations are based on extension to oblique shocks of a numerical model for "thermal leakage" injection of particles at low energy into the cosmic-ray population. That technique, incorporated into a fully dynamical diffusion-convection formalism, was recently introduced for parallel shocks by Kang & Jones. Here, we have compared results of time-dependent numerical simulations using our technique with Monte Carlo simulations by Ellison, Baring, & Jones and with in situ observations from the Ulysses spacecraft of oblique interplanetary shocks discussed by Baring et al. Through the success of these comparisons, we have demonstrated that our diffusion-convection method and injection techniques provide a practical tool to capture essential physics of the injection process and particle acceleration at oblique MHD shocks. In addition to the diffusion-convection simulations, we have included time-dependent two-fluid simulations for a couple of the shocks to demonstrate the basic validity of that formalism in the oblique shock context. Using simple models for the two-fluid closure parameters based on test particle considerations, we find good agreement with the dynamical properties of the more detailed diffusion-convection results. We emphasize, however, that such two-fluid results can be sensitive to the properties of these closure parameters when the flows are not truly steady. Furthermore, we emphasize through example how the validity of the two-fluid formalism does not necessarily mean that steady state two-fluid models provide a reliable tool for predicting the efficiency of particle acceleration in real shocks.
- Acceleration of particles
- Shock waves