Dependence of Solar Energetic Particle Energy Spectra on the Fundamental Parameters of CME Shocks.

A significant fraction of the energy of extreme solar eruptive events is channeled into the energetic particles associated with gradual solar energetic particle (SEP) events, posing a significant radiation hazard to humans and technological assets in space.  The high-energy particles in gradual SEP events are known to be accelerated by coronal-mass-ejection-driven shocks, but how the resulting SEP energy spectra for different elements depend on the fundamental parameters that characterize the shock and ambient upstream medium remains an open question.  Here we present the predicted properties of SEP energy spectra using a Liouville mapping technique applied to the electromagnetic field structure of the shock transition generated by a suite of hybrid kinetic ion and fluid electron simulations of quasiperpendicular shocks.  We focus on how the predicted SEP energy spectra depend on the Mach number and shock-normal angle of a collisionless shock in the planar limit and on the suprathermal velocity distributions of protons and heavier elements in the upstream interplanetary medium.  For example, we find accelerated SEP energy spectra peak at higher energies for higher shock-normal angles, in qualitative agreement with previous numerical and observational findings.  We summarize our findings with a comparison of the fundamental parameter dependencies revealed here to those found in observations of CME shocks in the inner heliosphere.