Flat Particle Fluxes Upstream of Interplanetary Shocks

The observed energy spectra of accelerated particles at interplanetary shocks often do not match the diffusive shock acceleration (DSA) theory predictions. In some cases, the particle flux forms a plateau over a wide range of energies, extending upstream of the shock for up to seven e-folds before submerging into the background spectrum. Remarkably, at and behind the shock, the flux falls off in energy as ε^-1, consistent with the DSA. The upstream plateau suggests a change in the particle transport mechanism. A standard (linear) DSA solution based on a widely-accepted resonant wave-particle interaction cannot explain it. To explain the plateau, we modify the DSA theory in two ways. First, we include a dependence of the particle diffusivity κ on the particle flux F (nonlinear particle transport). Second, we invoke short-scale magnetic perturbations that are self-consistently generated by, but not resonant with, accelerated particles. In this solution, the particle diffusivity increases with energy as ∝ε^3/2, simultaneously decaying with the particle flux as 1/F almost everywhere in the shock precursor.