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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 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 Where and how flares efficiently accelerate charged particles remains an unresolved question. Recent studies revealed that a “magnetic bottle” structure, which forms near the bottom of a large-scale reconnection current sheet above the flare arcade, is an excellent candidate for confining and accelerating charged particles. However, further understanding its role requires linking the various observational signatures to the underlying coupled plasma and particle processes. Here we present the first study combining multiwavelength observations with data-informed macroscopic magnetohydrodynamics and particle modeling in a realistic eruptive flare geometry. The presence of an above-the-loop-top magnetic bottle structure is strongly supported by the observations, which feature not only a local minimum of magnetic field strength but also abruptly slowing plasma downflows. It also coincides with a compact above-the-loop-top hard X-ray source and an extended microwave source that bestrides the flare arcade. Spatially resolved spectral analysis suggests that nonthermal electrons are highly concentrated in this region. Our model returns synthetic emission signatures that are well matched to the observations. The results suggest that the energetic electrons are strongly trapped in the magnetic bottle region due to turbulence, with only a small fraction managing to escape. The electrons are primarily accelerated by plasma compression and facilitated by a fast-mode termination shock via the Fermi mechanism. Our results provide concrete support for the magnetic bottle as the primary electron acceleration site in eruptive solar flares. They also offer new insights into understanding the previously reported small population of flare-accelerated electrons entering interplanetary space. 

Abstract When and where the magnetic field energy is released and converted in eruptive solar flares remains an outstanding topic in solar physics. To shed light on this question, here we report multiwavelength observations of a C9.4-class eruptive limb flare that occurred on 2017 August 20. The flare, accompanied by a magnetic flux rope eruption and a white light coronal mass ejection, features three post-impulsive X-ray and microwave bursts immediately following its main impulsive phase. For each burst, both microwave and X-ray imaging suggest that the nonthermal electrons are located in the above-the-loop-top region. Interestingly, contrary to many other flares, the peak flux of the three post-impulsive microwave and X-ray bursts shows an increase for later bursts. Spectral analysis reveals that the sources have a hardening spectral index, suggesting a more efficient electron acceleration into the later post-impulsive bursts. We observe a positive correlation between the acceleration of the magnetic flux rope and the nonthermal energy release during the post-impulsive bursts in the same event. Intriguingly, different from some other eruptive events, this correlation does not hold for the main impulse phase of this event, which we interpret as energy release due to the tether-cutting reconnection before the primary flux rope acceleration occurs. In addition, using footpoint brightenings at conjugate flare ribbons, a weakening reconnection guide field is inferred, which may also contribute to the hardening of the nonthermal electrons during the post-impulsive phase. 

The standard flare model, despite its success, is limited in comprehensively explaining the various processes involving nonthermal particles. One such missing ingredient is a detailed understanding of the various processes involved during the transport of accelerated electrons from their site of acceleration to different parts of the flare region. Here we use simultaneous radio and X-ray observations from the Expanded Owens Valley Solar Array and the Spectrometer/Telescope for Imaging X-rays on board the Solar Orbiter, respectively, from two distinct viewing perspectives, to study the electron transport processes. Through detailed spectral modeling of the coronal source using radio data and footpoint sources using X-ray spectra, we compare the nonthermal electron distribution at the coronal and footpoint sources. We find that the flux of the nonthermal electrons precipitated at the footpoint is an order of magnitude greater than that trapped in the looptop, consistent with earlier works that primarily used X-ray for their studies. In addition, we find that the electron spectral indices obtained from X-ray footpoints are significantly softer than the spectral hardness of the nonthermal electron distribution in the corona. We interpret these differences based on transport effects and the difference in sensitivity of microwave and X-ray observations to different regimes of electron energies. Such an understanding is crucial for leveraging different diagnostic methods of nonthermal electrons simultaneously to achieve a more comprehensive understanding of the electron acceleration and transport processes of solar flares. 

Aims.The aim of this work is to identify the mechanism driving pulsations in hard X-ray (HXR) and microwave emission during solar flares. Using combined HXR and microwave observations from Solar Orbiter/STIX and EOVSA, we investigate an X1.3 GOES class flare, 2022-03-30T17:21:00, which displays pulsations on timescales evolving from ∼7 s in the impulsive phase to ∼35 s later in the flare. Methods.We analysed the temporal, spatial, and spectral evolution of the HXR and microwave pulsations during the impulsive phase of the flare. We reconstructed images for individual peaks in the impulsive phase and performed spectral fitting at high cadence throughout the first phase of pulsations. Results.Our imaging analysis demonstrates that the HXR and microwave emission originates from multiple sites along the flare ribbons. The brightest sources and the location of the emission change in time. Through HXR spectral analysis, the electron spectral index is found to be anti-correlated with the HXR flux, showing a “soft-hard-soft” spectral index evolution for each pulsation. The timing of the associated filament eruption coincides with the early impulsive phase. Conclusions.Our results indicate that periodic acceleration and/or injection of electrons from multiple sites along the flare arcade is responsible for the pulsations observed in HXR and microwave emission. The evolution of pulsation timescales is likely a result of changes in the 3D magnetic field configuration over time related to the associated filament eruption. 

Magnetic reconnection is the key mechanism for energy release in solar eruptions, where the high-temperature emission is the primary diagnostic for investigating the plasma properties during the reconnection process. Non-thermal broadening of high-temperature lines has been observed in both the reconnection current sheet (CS) and flare loop-top regions by UV spectrometers, but its origin remains unclear. In this work, we use a recently developed three-dimensional magnetohydrodynamic (MHD) simulation to model magnetic reconnection in the standard solar flare geometry and reveal highly dynamic plasma flows in the reconnection regions. We calculate the synthetic profiles of the Fe XXI 1354 Å line observed by the Interface Region Imaging Spectrograph (IRIS) spacecraft by using parameters of the MHD model, including plasma density, temperature, and velocity. Our model shows that the turbulent bulk plasma flows in the CS and flare loop-top regions are responsible for the non-thermal broadening of the Fe XXI emission line. The modeled non-thermal velocity ranges from tens of km s −1 to more than two hundred km s −1 , which is consistent with the IRIS observations. Simulated 2D spectral line maps around the reconnection region also reveal highly dynamic downwflow structures where the high non-thermal velocity is large, which is consistent with the observations as well. 

Abstract Quasi-periodic pulsations (QPPs) are frequently detected in solar and stellar flares, but the underlying physical mechanisms are still to be ascertained. Here, we show microwave QPPs during a solar flare originating from quasi-periodic magnetic reconnection at the flare current sheet. They appear as two vertically detached but closely related sources with the brighter ones located at flare loops and the weaker ones along the stretched current sheet. Although the brightness temperatures of the two microwave sources differ greatly, they vary in phase with periods of about 10–20 s and 30–60 s. The gyrosynchrotron-dominated microwave spectra also present a quasi-periodic soft-hard-soft evolution. These results suggest that relevant high-energy electrons are accelerated by quasi-periodic reconnection, likely arising from the modulation of magnetic islands within the current sheet as validated by a 2.5-dimensional magnetohydrodynamic simulation. 

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.