A FOCUSED TRANSPORT APPROACH TO THE TIME-DEPENDENT SHOCK ACCELERATION OF SOLAR ENERGETIC PARTICLES AT A FAST TRAVELING SHOCK

Some of the most sophisticated models for solar energetic particle (SEP) acceleration at coronal mass ejection driven shocks are based on standard diffusive shock acceleration theory. However, this theory, which only applies when SEP pitch-angle anisotropies are small, might have difficulty in describing first-order Fermi acceleration or the shock pre-heating and injection of SEPs into first-order Fermi acceleration accurately at lower SEP speeds where SEP pitch-angle anisotropies upstream near the shock can be large. To avoid this problem, we use a time-dependent focused transport model to reinvestigate first-order Fermi acceleration at planar parallel and quasi-parallel spherical traveling shocks between the Sun and Earth with high shock speeds associated with rare extreme gradual SEP events. The focused transport model is also used to investigate and compare three different shock pre-heating mechanisms associated with different aspects of the nonuniform cross-shock solar wind flow, namely, the convergence of the flow (adiabatic compression), the shear tensor of the flow, and the acceleration of the flow, and a fourth shock pre-heating mechanism associated with the cross-shock electric field, to determine which pre-heating mechanism contributes the most to injecting shock pre-heated source particles into the first-order Fermi acceleration process. The effects of variations in traveling shock conditions, such as increasing shock obliquity and shock slowdown, and variations in the SEP source with increasing shock distance from the Sun on the coupled processes of shock pre-heating, injection, and first-order Fermi acceleration are analyzed. Besides the finding that the cross-shock acceleration of the solar wind flow yields the dominant shock pre-heating mechanism at high shock speeds, we find that first-order Fermi acceleration at fast traveling shocks differs in a number of respects from the predictions and assumptions of standard steady-state diffusive shock acceleration theory as is discussed below.