Flat Spectra of Energetic Particles in Interplanetary Shock Precursors
arxiv(2024)
Abstract
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 flux's e-folds before
submerging into the background spectrum. Remarkably, at and behind the shock
that we have studied in detail, the flux falls off in energy as
ϵ^-1, consistent with the DSA prediction for a strong shock. The
upstream plateau suggests a different particle transport mechanism than those
traditionally employed in DSA models. We show that a standard (linear) DSA
solution based on a widely accepted diffusive particle transport with an
underlying resonant wave-particle interaction is inconsistent with the plateau
in the particle flux. To resolve this contradiction, 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. They lead to the particle
diffusivity increasing with the particle energy as ∝ϵ^3/2 that
simultaneously decreases with the particle flux as 1/F. The combination of
these two trends results in the flat spectrum upstream.
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