Numerical simulation of charged particle interactions with interplanetary shock waves

Significant intensity enhancements of low energy (0.10 to 10.0 MeV) solar ions are sometimes observed several hours prior to the passage of solar flare generated shock waves by satellites located in interplanetary space. The intimate temporal association between these energetic storm particle (ESP) events and the propagating shock strongly suggests that ambient particles are accelerated locally at the shock front. A computer model has been developed to numerically simulate the combined effects of a charged particle's energization at the shock and propagation to a satellite-borne particle detector at the observation point. A charged particle's adiabatic motion is assumed to be scatter-free along the laminar spiral interplanetary magnetic field (IMF). The interplanetary shock wave is taken as a suncentered spherical surface that expands radially outward. The plasma and field changes across the shock obey the jump conditions for a fast mode MHD shock wave. For a chosen shock model, a particle of specified observed kinetic energy and pitch angle at a given observation time and fixed observation point is followed numerically backward in time through the IMF and shock wave. The shock interaction is treated by solving the particle's exact orbit equations through the locally planar MHD shock discontinuity. The resultant trajectory relates the particle's phase space coordinates at the time of observation to those at a time immediately before shock interaction. The application of Liouville's theorem of the constancy of the single-particle distribution function along a dynamical phase space trajectory enables one to construct particle fluxes at the observation point by using an ensemble of numerically generated trajectories and a model of the ambient particle distribution