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Abstract We revisit previous hybrid simulations of the heating and acceleration of interstellar pickup ions (PUIs) at the solar wind termination shock. In previous simulations, a relatively cold initial distribution of PUIs was assumed; and while the resulting shock-heated distribution was consistent with Voyager 2 LECP measurements at about 30 keV, the intensity of the distribution downstream of the shock in the ~1–10 keV energy range was lower than predictions based on analysis of energetic neutral atoms (ENAs) from the Interstellar Boundary Explorer-Hi and Cassini's Ion and Neutral Camera. Here we perform new simulations with more realistic initial PUI distributions. We assume the distribution is a partially filled spherical shell in velocity space with a radius that varies from 320 to 640 km s⁻¹. We then use the distributions downstream of the shock from these new simulations to estimate the ENA flux spectrum and compare with observations. We find that the predicted ENA spectrum from the new simulations much better matches the observations over a broad range of energies. We conclude that the hybrid simulations provide reasonable predictions for the distribution of charged particles in the energy range from ~0.5 to 50 keV. 

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, extendingupstream of the shockfor up to seven fluxe-folds before submerging into the background spectrum. Remarkably, at and downstream of the shock we have studied in detail, the flux falls off in energy asϵ⁻¹, consistent with the DSA prediction for a strong shock. The upstream plateau suggests a particle transport mechanism different from 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 diffusivityκon the particle fluxF(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^3/2that simultaneously decreases with the particle flux as 1/F. The combination of these two trends results in the flat spectrum upstream. We speculate that nonmonotonic spatial variations of the upstream spectrum, apart from being time-dependent, may also result from non-DSA acceleration mechanisms at work upstream, such as stochastic Fermi or magnetic pumping acceleration. 

Abstract The acceleration and transport of energetic electrons during solar flares is one of the outstanding topics in solar physics. Recent X-ray and radio imaging and spectroscopy observations have provided diagnostics of the distribution of nonthermal electrons and suggested that, in certain flare events, electrons are primarily accelerated in the loop top and likely experience trapping and/or scattering effects. By combining the focused particle transport equation with magnetohydrodynamic (MHD) simulations of solar flares, we present a macroscopic particle model that naturally incorporates electron acceleration and transport. Our simulation results indicate that physical processes such as turbulent pitch-angle scattering can have important impacts on both electron acceleration in the loop top and transport in the flare loop, and their influences are highly energy-dependent. A spatial-dependent turbulent scattering with enhancement in the loop top can enable both efficient electron acceleration to high energies and transport of abundant electrons to the footpoints. We further generate spatially resolved synthetic hard X-ray (HXR) emission images and spectra, revealing both the loop-top and footpoint HXR sources. Similar to the observations, we show that the footpoint HXR sources are brighter and harder than the loop-top HXR source. We suggest that the macroscopic particle model provides new insights into understanding the connection between the observed loop-top and footpoint nonthermal emission sources by combining the particle model with dynamically evolving MHD simulations of solar flares. 

Abstract A number of double coronal X-ray sources have been observed during solar flares by RHESSI, where the two sources reside at different sides of the inferred reconnection site. However, where and how these X-ray-emitting electrons are accelerated remains unclear. Here we present the first model of the double coronal hard X-ray (HXR) sources, where electrons are accelerated by a pair of termination shocks driven by bidirectional fast reconnection outflows. We model the acceleration and transport of electrons in the flare region by numerically solving the Parker transport equation using velocity and magnetic fields from the macroscopic magnetohydrodynamic simulation of a flux rope eruption. We show that electrons can be efficiently accelerated by the termination shocks and high-energy electrons mainly concentrate around the two shocks. The synthetic HXR emission images display two distinct sources extending to >100 keV below and above the reconnection region, with the upper source much fainter than the lower one. The HXR energy spectra of the two coronal sources show similar spectral slopes, consistent with the observations. Our simulation results suggest that the flare termination shock can be a promising particle acceleration mechanism in explaining the double-source nonthermal emissions in solar flares. 

Abstract The acceleration of charged particles by interplanetary shocks (IPs) can drain a nonnegligible fraction of the plasma pressure. In this study, we have selected 17 IPs observed in situ at 1 au by the Advanced Composition Explorer and the Wind spacecraft, and 1 shock at 0.8 au observed by Parker Solar Probe. We have calculated the time-dependent partial pressure of suprathermal and energetic particles (smaller and greater than 50 keV for protons and 30 keV for electrons, respectively) in both the upstream and downstream regions. The particle fluxes were averaged for 1 hr before and 1 hr after the shock time to remove short timescale effects. Using the MHD Rankine–Hugoniot jump conditions, we find that the fraction of the total upstream energy flux transferred to suprathermal and energetic downstream particles is typically ≲16%, in agreement with previous observations and simulations. Notably, by accounting for errors on all measured shock parameters, we have found that for any given fast magnetosonic Mach number,M_f< 7, the angle between the shock normal and average upstream magnetic field,θ_Bn, is not correlated with the energetic particle pressure; in particular, the partial pressure of energized particles does not decrease forθ_Bn≳ 45°. The downstream electron-to-proton energy ratio in the range ≳ 140 eV for electrons and ≳ 70 keV for protons exceeds the expected ∼1% and nears equipartition (>0.1) for the Wind events.