A Focused Transport Model for the Shock Pre-Heating, Injection and First Order Fermi Acceleration of Solar Wind Source Particles at a Fast Traveling Shock

We plan to present solutions of a time-dependent focused transport model for the shock-pre-heating, injection, and first order Fermi acceleration of solar energetic particles (SEPs) at a fast traveling shock propagating between the Sun and Earth. The results were first calculated for a planar parallel shock to act as a benchmark for the more complicated simulations for a quasi-parallel spherical shock propagating in a spherically expanding solar wind with a spiral magnetic field. First, we will discuss whether first-time adiabatic compression, the cross-shock electric field, or the noninertial force due to deceleration of the solar wind flow across the shock contributes the most in forming a pre-heated population of solar wind source particles that can be injected across the threshold for first order Fermi acceleration of SEPs. Second, the first order Fermi acceleration process of SEPs at a fast traveling shock will be analyzed to see to what extent it agrees with the predictions and assumptions of standard diffusive shock acceleration (DSA) theory. For clues we will present results of SEP pitch-angle distributions upstream at different energies, variations of the pitch-angle averaged SEP distributions across the traveling shock at different SEP energies, and results of how shock slowdown and increasing shock obliquity affect the injection and the first order Fermi acceleration of SEPs with increasing shock distance. Preliminary results suggest a strong role for the noninertial force in shock pre-heating and injection of solar wind source particles at fast traveling shocks. Significant deviations of the first order Fermi acceleration SEP spectra from the predictions and assumptions of standard DSA theory were detected at fast traveling shocks due to the important roles of the noninertial force, shock slowdown, and increasing shock obliquity.