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Abstract In astronomical environments, the high-temperature emission of plasma mainly depends on ion charge states, requiring accurate analysis of the ionization and recombination processes. For various phenomena involving energetic particles, non-Maxwellian distributions of electrons exhibiting high-energy tails can significantly enhance the ionization process. Therefore, accurately computing ionization and recombination rates with non-Maxwellian electron distributions is essential for emission diagnostic analysis. In this work, we report two methods for fitting various non-Maxwellian distributions by using the Maxwellian decomposition strategy. For standardκ-distributions, the calculated ionization and recombination rate coefficients show comparable accuracy to other public packages. Additionally, our methods support arbitrary electron distributions and can be easily extended to updated atomic databases. We apply the above methods to two specific non-Maxwellian distribution scenarios: (i) accelerated electron distributions due to magnetic reconnection revealed in a combined MHD–particle simulation; and (ii) the high-energy truncatedκ-distribution predicted by the exospheric model of the solar wind. During the electron acceleration process, we show that the ionization rates of high-temperature iron ions increase significantly compared to their initial Maxwellian distribution, while the recombination rates may decrease due to the electron distribution changes in low-energy ranges. This can potentially lead to an overestimation of the plasma temperature when analyzing the Fe emission lines under the Maxwellian distribution assumption. For the truncatedκ-distribution in the solar wind, our results show that the ionization rates are lower than those for the standardκ-distribution, while the recombination rates remain similar. This leads to an overestimation of the plasma temperature when assuming aκ-distribution. 

Abstract Recent observations and simulations indicate that solar flares undergo extremely complex 3D evolution, making 3D particle transport models essential for understanding electron acceleration and interpreting flare emissions. In this study, we investigate this problem by solving Parker’s transport equation with 3D MHD simulations of solar flares. By examining energy conversion in the 3D system, we evaluate the roles of different acceleration mechanisms, including reconnection current sheet (CS), termination shock (TS), and supra-arcade downflows (SADs). We find that large-amplitude turbulent fluctuations are generated and sustained in the 3D system. The model results demonstrate that a significant number of electrons are accelerated to hundreds of keV and even a few MeV, forming power-law energy spectra. These energetic particles are widely distributed, with concentrations at the TS and in the flare looptop region, consistent with results derived from recent hard X-ray (HXR) and microwave (MW) observations. By selectively turning particle acceleration on or off in specific regions, we find that the CS and SADs effectively accelerate electrons to several hundred keV, while the TS enables further acceleration to MeV. However, no single mechanism can independently account for the significant number of energetic electrons observed. Instead, the mechanisms work synergistically to produce a large population of accelerated electrons. Our model provides spatially and temporally resolved electron distributions in the whole flare region and at the flare footpoints, enabling synthetic HXR and MW emission modeling for comparison with observations. These results offer important insights into electron acceleration and transport in 3D solar flare regions. 

Abstract Determining the relative contribution of solar flares versus coronal mass ejections in large solar energetic particle (SEP) events is a long-standing problem. Flare-accelerated particles may travel through complex magnetic fields in the eruption region and escape into interplanetary space, thereby contributing to large SEP events. The process by which flare accelerated particles are released into the heliosphere is poorly understood and yet is critical to advancing our understanding of SEPs. In this work, we address the release problem by solving the focused transport equation in the context of a 2.5D ARMS magnetohydrodynamic simulation of a breakout coronal mass ejection (CME)/flare event. We find that particles accelerated by flare reconnection can be released into interplanetary space through interchange reconnection between closed and open field lines. These particles can contribute directly to SEP events and may become an important seed population for further acceleration by CME-driven shocks. Additionally, we find that the energetic particle fluxes in the inner heliosphere remain elevated for an extended period, allowing them to contribute to SEP acceleration by subsequent CMEs. This study represents the first direct particle modeling of how flare-accelerated particles can contribute to major SEP events. 

Abstract Solar flare above-the-loop-top (ALT) regions are vital for understanding solar eruptions and fundamental processes in plasma physics. Recent advances in three-dimensional (3D) magnetohydrodynamic (MHD) simulations have revealed unprecedented details on turbulent flows and MHD instabilities in flare ALT regions. Here, for the first time, we examine the observable anisotropic properties of turbulent flows in ALT by applying a flow-tracking algorithm on narrow-band extreme-ultraviolet images that are observed from the face-on viewing perspective. First, the results quantitatively confirm the previous observation that vertical motions dominate and that the anisotropic flows are widely distributed in the entire ALT region with the contribution from both upflows and downflows. Second, the anisotropy shows height-dependent features, with the most substantial anisotropy appearing at a certain middle height in ALT, which agrees well with the MHD modeling results where turbulent flows are caused by Rayleigh–Taylor-type instabilities in the ALT region. Finally, our finding suggests that supra-arcade downflows (SADs), the most prominently visible dynamical structures in ALT regions, are only one aspect of turbulent flows. Among these turbulent flows, we also report the antisunward-moving underdense flows that might develop due to MHD instabilities, as suggested by previous 3D flare models. Our results indicate that the entire flare fan displays group behavior of turbulent flows where the observational bright spikes and relatively dark SADs exhibit similar anisotropic characteristics. 

Abstract Relativistic magnetic turbulence has been proposed as a process for producing nonthermal particles in high-energy astrophysics. The particle energization may be contributed by both magnetic reconnection and turbulent fluctuations, but their interplay is poorly understood. It has been suggested that during magnetic reconnection the parallel electric field dominates the particle acceleration up to the lower bound of the power-law particle spectrum, but recent studies show that electric fields perpendicular to the magnetic field can play an important, if not dominant role. In this study, we carry out two-dimensional fully kinetic particle-in-cell simulations of magnetically dominated decaying turbulence in a relativistic pair plasma. For a fixed magnetization parameterσ₀ = 20, we find that the injection energyε_injconverges with increasing domain size toε_inj ≃ 10m_ec². In contrast, the power-law index, the cut-off energy, and the power-law extent increase steadily with domain size. We trace a large number of particles and evaluate the contributions of the work done by the parallel (W_∥) and perpendicular (W_⊥) electric fields during both the injection phase and the postinjection phase. We find that during the injection phase, theW_⊥contribution increases with domain size, suggesting that it may eventually dominate injection for a sufficiently large domain. In contrast, on average, both components contribute equally during the postinjection phase, insensitive to the domain size. For high energy (ε ≫ ε_inj) particles,W_⊥dominates the subsequent energization. These findings may improve our understanding of nonthermal particles and their emissions in astrophysical plasmas. 

Abstract Magnetic reconnection regions in space and astrophysics are known as active particle acceleration sites. There is ample evidence showing that energetic particles can take a substantial amount of converted energy during magnetic reconnection. However, there has been a lack of studies understanding the backreaction of energetic particles at magnetohydrodynamical scales in magnetic reconnection. To address this, we have developed a new computational method to explore the feedback by nonthermal energetic particles. This approach considers the backreaction from these energetic particles by incorporating their pressure into magnetohydrodynamics (MHD) equations. The pressure of the energetic particles is evaluated from their distribution evolved through Parker’s transport equation, solved using stochastic differential equations (SDEs), so we coin the name MHD-SDE. Applying this method to low-βmagnetic reconnection simulations, we find that reconnection is capable of accelerating a large fraction of energetic particles that contain a substantial amount of energy. When the feedback from these particles is included, their pressure suppresses the compression structures generated by magnetic reconnection, thereby mediating particle energization. Consequently, the feedback from energetic particles results in a steeper power-law energy spectrum. These findings suggest that feedback from nonthermal energetic particles plays a crucial role in magnetic reconnection and particle acceleration. 

Abstract Understanding plasma dynamics and nonthermal particle acceleration in 3D magnetic reconnection has been a long-standing challenge. In this paper, we explore these problems by performing large-scale fully kinetic simulations of multi-X-line plasmoid reconnection with various parameters in both the weak- and strong-guide-field regimes. In each regime, we have identified its unique 3D dynamics that lead to field-line chaos and efficient acceleration, and we have achieved nonthermal acceleration of both electrons and protons into power-law spectra. The spectral indices agree well with a simple Fermi acceleration theory that includes guide-field dependence. In the low-guide-field regime, the flux rope kink instability governs the 3D dynamics for efficient acceleration. The weak dependence of the spectra on the ion-to-electron mass ratio andβ(≪1) implies that the particles are sufficiently magnetized for Fermi acceleration in our simulations. While both electrons and protons are injected at reconnection exhausts, protons are primarily injected by perpendicular electric fields through Fermi reflections and electrons are injected by a combination of perpendicular and parallel electric fields. The magnetic power spectra agree with in situ magnetotail observations, and the spectral index may reflect a reconnection-driven size distribution of plasmoids instead of the Goldreich–Sridhar vortex cascade. As the guide field becomes stronger, the oblique flux ropes of large sizes capture the main 3D dynamics for efficient acceleration. Intriguingly, the oblique flux ropes can also experience flux rope kink instability, to drive extra 3D dynamics. This work has broad implications for 3D reconnection dynamics and particle acceleration in heliophysics and astrophysics. 

Abstract Recent observations by the Parker Solar Probe (PSP) suggest that protons and heavier ions are accelerated to high energies by magnetic reconnection at the heliospheric current sheet (HCS). By solving the energetic particle transport equation in large-scale MHD simulations, we study the compression acceleration of protons and heavier ions in the reconnecting HCS. We find that the acceleration of multispecies ions results in nonthermal power-law distributions with a spectral index consistent with the PSP observations. Our study shows that the high-energy cutoff of protons can reach $E_{\max }\sim 0.1$–1 MeV depending on the particle diffusion coefficients. We also study how the high-energy cutoff of different ion species scales with the charge-to-mass ratio $E_{\max }\propto {\left(Q/M\right)}^{\alpha }$. When determining the diffusion coefficients from the quasi-linear theory with a Kolmogorov magnetic power spectrum, we find thatα∼ 0.4, which is somewhat smaller thanα∼ 0.7 observed by PSP. 

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 Magnetic reconnection occurs ubiquitously in the universe and is often invoked to explain fast energy release and particle acceleration in high-energy astrophysics. The study of relativistic magnetic reconnection in the magnetically dominated regime has surged over the past two decades, revealing the physics of fast magnetic reconnection and nonthermal particle acceleration. Here we review these recent progresses, including the magnetohydrodynamic and collisionless reconnection dynamics as well as particle energization. The insights in astrophysical reconnection strongly connect to the development of magnetic reconnection in other areas, and further communication is greatly desired. We also provide a summary and discussion of key physics processes and frontier problems, toward a better understanding of the roles of magnetic reconnection in high-energy astrophysics.