Multi-messenger, multi-viewpoint, and time-resolved observations of solar flares are now providing unprecedented constraints on particle acceleration sites, energy conversion, and energy transport. The interpretation of current observations, including microwave imaging spectroscopy from EOVSA, hard x-ray (HXR) imaging from Solar Orbiter/STIX, gamma-ray diagnostics from Fermi, and in situ measurements from Parker Solar Probe and Solar Orbiter, collectively demands modeling frameworks that go beyond traditional spatially unresolved, one-zone models or single-mechanism descriptions. This review surveys multiscale and multidimensional modeling approaches, including kinetic, magnetohydrodynamic (MHD), and macroscopic particle models, that are being developed to meet the need. Kinetic simulations reveal that three-dimensional (3D) effects, including field-line chaos and self-generated turbulence, are essential for sustained power-law particle acceleration. MHD simulations now capture flux-rope eruptions, plasmoid-unstable current sheets, and turbulent flare regions in realistic magnetic topologies. Macroscopic models coupling MHD with energetic-particle models produce spatially resolved electron distributions and synthetic HXR and microwave emissions for direct comparison with observations. Despite these advances, outstanding challenges remain in bridging kinetic and global scales, improving MHD simulations and macroscopic particle models, and achieving quantitative model-observation closure.

The Space Weather Around Young Suns (SWAYS) program was introduced in I. Davis et al. as a multiwavelength monitoring program for studying the activity and particle environments of nearby, young solar-type stars. The SWAYS program currently includes the Owens Valley Radio Observatory Long Wavelength Array (OVRO-LWA) operating between 13 and 87 MHz to search for stellar equivalents of solar type II and III bursts, which are associated with bulk plasma motion in the corona and interplanetary medium. These observations are accompanied by simultaneous photometric data from the high-precision optical instrument Flarescope to identify associated flare events. These two instruments have collectively acquired nearly 900 hr of data with approximate to 70% overlap between 2023 November through 2024 June, dedicated to six stars. Here, we present the results of this first season of the SWAYS observing campaign, which include a superflare from the star EK Draconis with no accompanying low-frequency particle flux signal. The novelty of the coordination at these specific parts of the spectrum allow us to uniquely evaluate the conditions that may have inhibited a radio detection. We find that the exceptionally hot, dense coronae of incredibly active stars may not be conducive to the development of the instabilities required for type II and III bursts, or else inspire new expectations for when we should expect to observe a signal relative to the time of the flare. This may represent the plasma-density complement to the magnetospheric limitations to observing space-weather signatures at low frequencies.

We analyze the X7.1 flare on 2024 October 1 from NOAA AR 13842 using hard X-ray (HXR) imaging, microwave observations by the Expanded Owens Valley Solar Array (EOVSA), and a three-dimensional Magnetohydrodynamic (MHD) simulation. The flare was observed from two vantage points, with Solar Orbiter/Spectrometer Telescope for Imaging X-rays viewing the flare near the limb and Advanced Space-based Solar Observatory/Hard X-ray Imager and EOVSA observing it on the disk. We carried out a data-constrained MHD simulation using a nonlinear force-free field extrapolation as the initial condition and constrained the height of the non-thermal looptop source from stereoscopic HXR and microwave observations. The height is consistent between the stereoscopic analysis and the MHD simulation. A secondary non-thermal microwave source aligned with a southward plasma ejection corresponds to an elongated current sheet. Although the current sheet grows in multiple directions, the secondary microwave emission is observed only from the southern segment. This localization suggests reconnection in regions with different magnetic field strengths. Reconnection in strong-field regions produces flare arcades with dominant looptop emission, whereas reconnection in weaker southern regions gives rise to secondary microwave emission at higher altitudes. The height of the secondary source is consistent between the stereoscopic analysis and the MHD simulation. Microwave spectral fitting suggests a higher low-energy cutoff for non-thermal electrons in the secondary microwave source than in the main looptop source. This may reflect the transport of electrons pre-accelerated near the looptop source by the southward plasma ejection.

Particle acceleration is a fundamental astrophysical process occurring across diverse systems and scales, producing electromagnetic emission across all wavelengths. Radio bursts from astrophysical systems like active galaxy jets, solar flares, pulsars, etc., provide a probe into the emission mechanism and particle acceleration processes. Among all astrophysical phenomena, magnetically driven solar flares provide unique diagnostics of nonthermal particles due to the advantage of multiple spatial-temporal and spectral measurements. The subsequent emitted radiation spans various sections of the radio spectrum. Based on brightness temperature and spectrum, one can distinguish between bright plasma emission or 'nonthermal' emission. Nonthermal radio bursts in meter and microwave bands arise from suprathermal particles, while the surrounding plasma produces fainter thermal emission. High spatial-temporal studies along with polarimetry will enable tracking of electron beams in evolving magnetic fields and constrain coronal properties such as magnetic strength, density, and temperature. Fine spectral structures from gyrosynchrotron bursts allow mapping of magnetic fields along acceleration tracks. However, emissions from the more numerous, weaker particle populations remain difficult to observe. Particles in solar flares follow a power-law energy distribution, with weaker populations being more common. The Square Kilometre Array Observatory (SKAO) will provide high-fidelity data that will enable detailed characterisation of these populations, statistical studies of particle beams, and insights into their interaction with magnetic topologies. Its high-resolution (especially SKA-Mid) and multi-wavelength synergy (EUV, X-rays) will refine diagnostics of coronal and acceleration-region properties. This chapter reviews particle acceleration models and expected advances from SKAO.

Solar flares are among the most dramatic events in the solar system, releasing substantial magnetic energy and accelerating a large number of electrons to high energies. Notably, in certain events, the above-the-looptop region may contain a significant population of nonthermal electrons, both in number and energy. For the first time, we adopt a novel numerical method that combines magnetohydrodynamics with energetic particles incorporating feedback from nonthermal electrons to investigate electron acceleration and transport in solar flares. We find that a large fraction of energetic electrons are accelerated via the current sheet and termination shock regions. Most energetic electrons are concentrated in the above-the-looptop region, carrying a sizable amount of the released energy. We observe that greater feedback of nonthermal electrons leads to steeper energy spectra. The energy density of the nonthermal electrons oscillates due to the periodic impact of magnetic islands into the above-the-looptop region, which may help explain the observed quasiperiodic pulsations. Our simulations provide new insights into the origin of nonthermal electrons and associated emissions in the above-the-looptop region.

The electron density of the solar corona is a fundamental parameter in many areas of solar physics. Traditionally, routine estimates of coronal density have relied exclusively on white-light observations. However, these density estimates, obtained by inverting the white-light data, require simplifying assumptions, which may affect the robustness of the measurements. Hence, to improve the reliability of coronal density measurements, it is highly desirable to explore other complementary methods. In this study, we estimate the coronal electron densities in the middle corona, between approximately 1.7 and 3.5 R circle dot, using low-frequency radio observations from the recently commissioned Long Wavelength Array at the Owens Valley Radio Observatory (OVRO-LWA). The results demonstrate consistency with those derived from white-light coronagraph data and predictions from theoretical models. We also derive a density model valid between 1.7 and 3.5 r circle dot, given by rho(r ')=1.27r '-2+29.02r '-4+71.18r '-6 , where r '=r/R circle dot , with r the heliocentric distance. OVRO-LWA is a solar-dedicated radio interferometer that provides science-ready images with low latency, making it well suited for generating regular and independent estimates of coronal densities to complement existing white-light techniques.

Coronal Mass Ejections (CMEs) are large expulsions of magnetized plasma from the Sun into interplanetary space and are the primary drivers of extreme space weather variations. The strength and topology of CME magnetic fields largely determine their impact on Earth. Although visible-light coronagraphs routinely observe CMEs and provide their geometric and kinematic properties, they cannot directly measure CME vector magnetic fields. These fields evolve from initiation through the inner heliosphere due to interactions with other CMEs, coronal structures, and the ambient solar wind, leading to significant structural deformation. Such evolution complicates predictions of the CME magnetic field at Earth. Accurate measurements of CME magnetic fields in the corona and heliosphere are therefore essential for advancing space weather forecasting. Radio observations spanning MHz to GHz frequencies provide a powerful remote-sensing approach for measuring CME magnetic fields from the ground. Recent observations with Square Kilometre Array (SKA) precursors and pathfinder instruments, as well as other new-generation facilities, have demonstrated the potential of these radio techniques for CME magnetic-field diagnostics. At the same time, these studies have highlighted several limitations of current instruments. The higher sensitivity, wider instantaneous bandwidth, and broader frequency coverage of the SKA will open a new observational window, enabling these techniques to be fully exploited for constraining SpWx models and improving predictive accuracy. However, such observations are non-standard and require special consideration in scheduling, calibration, and imaging. Developments achieved with SKA precursors and pathfinders are paving the way for robust CME magnetic-field measurements with the SKA.

Solar type II radio bursts are widely regarded as signatures of shock waves propagating in the solar corona and are of particular importance for understanding shock-driven particle acceleration processes. Type II radio bursts often exhibit complex multi-lane and split-band features. The detailed spectral, temporal, and spatial structures carry key information about the shock properties and evolution. However, the physical origin of the multi-lane and split-band features remains unclear, largely due to a lack of spatially resolved data and understanding of the concurrent shock morphology and its magnetic-field context. In this work, we combine radio imaging spectroscopy of a multi-lane, split-band type II burst event with a three-dimensional global magnetohydrodynamic simulation of the associated coronal mass ejection-driven shock using the Alfvén Wave Solar atmosphere Model-Realtime. In this event, the burst intensity evolves from fundamental-emission dominated to harmonic-emission dominated. Meanwhile, the preferential emission source region moves from the Earth-facing side to the limb or far side, coinciding with quasi-perpendicular shock regions with enhanced Mach numbers. The observed spatial offset between the fundamental and harmonic sources is generally aligned with the projected shock-surface magnetic field from the simulation, consistent with anisotropic scattering in a magnetized turbulent plasma. These results establish a physical connection between type II radio sources and coronal shock magnetic geometry, providing new insight into the origin of the multi-lane features and their diagnostics of coronal shocks.

The brief (10 nanoseconds) transient radio emission from cosmic ray air showers carries key information about the energy and mass composition of high energy cosmic rays, but anthropogenic radio frequency interference has historically prevented radio-based cosmic ray studies from being carried out independently from other types of detectors. We describe a cosmic ray detection system for the Owens Valley Radio Observatory Long Wavelength Array that searches for radio emission from cosmic ray air showers without relying on an external trigger, and runs alongside the other observing modes of the array. The OVRO-LWA, located in Eastern California, recently completed an expansion to 352 dual-polarization antennas and new signal processing infrastructure. In order to detect cosmic rays in the presence of radio frequency interference (RFI), initial event classification and RFI rejection is performed on Field Programmable Gate Array boards, which each process a sampled voltage timeseries from both polarizations of a subarray of 32 antennas. Each board uses dedicated RFI veto antennas outside the air shower radio footprint to reject RFI events. We present the trigger design, RFI flagging strategy, and candidate cosmic rays.

We report on a search for prompt, low-frequency radio emission from the gravitational-wave (GW) merger S250206dm using the Owens Valley Radio Observatory Long Wavelength Array (OVRO-LWA). Early alerts favored a neutron-star-containing merger, making this a compelling target. Motivated by theoretical predictions of coherent radio bursts from mergers involving a neutron star, we utilized the OVRO-LWA Time Machine system to analyze voltage data recorded around the time of the event. Time Machine is a two-stage voltage buffer and processing pipeline that continuously buffers raw data from all antennas across the array’s nearly full-hemisphere instantaneous field of view, enabling retrospective beamforming, dedispersion, and fast-transient candidate identification. For this event, we analyzed a 30 minute interval beginning 3.5 minutes after the merger, which included 2 minutes of pre-alert data recovered by the ring buffer. We searched the 50% localization probability region with millisecond time resolution in the 69–86 MHz frequency band. No radio counterpart was detected above a 7 σ fluence detection threshold of ∼150 Jy ms. Using Bayesian analysis, we place a 95% confidence upper limit on the source luminosity of L _95 = 4 × 10 ^41 erg s ^−1 . These constraints start to probe the bright end of the coherent-emission parameter space predicted by jet–interstellar medium shock processes, magnetar and blitzar-like mechanisms, and recent simulation-based scenarios for neutron-star-containing mergers. This study presents the first sensitive, large-area, millisecond-timescale search for prompt low-frequency radio emission from a GW merger with the OVRO-LWA, establishing a framework in which about 10 additional events will yield stringent population-level constraints.

Analysis of γ-rays in solar flares has suggested a distinct continuum component dominating at MeV energies, which differs from the well-studied X-ray continuum produced by flare-accelerated electrons with spectra steeply falling with energy. The origin, precise spatial location, and extent of this mysterious MeV component have been unknown up to now. If it is produced by bremsstrahlung, such a γ-ray component requires an unusual population of electrons peaked at a few MeV. Here we report a joint study of this MeV-peaked electron population in the 2017-Sep-10 solar flare with Fermi MeV γ-ray data and EOVSA spatially resolved microwave imaging spectroscopy data. We demonstrate that the microwave spectrum from the MeV-peaked distribution has a distinctly different shape from that produced by the electrons with falling energy spectrum. We inspected microwave maps of the flare and identified an evolving area where the measured microwave spectra matched the theoretically expected one for the MeV-peaked population, thus pinpointing the site where this MeV component resides. The locations are in a coronal volume adjacent to the region where prominent release of magnetic energy and bulk electron acceleration were detected, which implies that transport effects play a key role in forming this population.

We investigated the three-dimensional (3D) magnetic structures and dynamics responsible for particle acceleration in an X7.1-class flare that occurred on 2024 October 1, in NOAA active region 13842. We combined stereoscopic hard X-ray (HXR) observations from the Advanced Space-based Solar Observatory/Hard X-ray Imager and the Solar Orbiter/Spectrometer Telescope for Imaging X-rays (STIX) with a 3D magnetohydrodynamic (MHD) simulation constrained by observed photospheric magnetic fields. During the two main peaks of the impulsive phase, HXR footpoints appeared at different locations, indicating a migration of the primary reconnection site in the corona. Our data-constrained MHD simulation successfully reproduced the reconnected field lines linking the observed conjugate HXR footpoints. Furthermore, the simulation shows that these primary reconnections occur along a single quasi-separatrix layer (QSL) system. Therefore, the two main peaks of HXR can be interpreted as episodic energy release within the single QSL system. This study demonstrates that the data-constrained MHD model provides a realistic 3D magnetic context for interpreting HXR emission. Notably, STIX observations revealed a vertically distributed thermal HXR source, extending from the footpoints to the looptop, with its centroid migrating between the two peaks. This marks a first step toward understanding the particle acceleration processes in solar flares.

Analysis of γ-rays in solar flares has suggested a distinct continuum component dominating at megaelectronvolt energies, which differs from the well-studied X-ray continuum produced by flare-accelerated electrons, with spectra steeply falling with energy. The origin, precise spatial location and extent of this mysterious megaelectronvolt component have been unknown up to now. If it is produced by bremsstrahlung, such a γ-ray component requires an unusual population of electrons peaked at a few million electron volts. Here we report a joint study of this megaelectronvolt-peaked electron population in the 2017 September 10 solar flare with Fermi megaelectronvolt γ-ray data and spatially resolved microwave imaging spectroscopy data obtained by the Expanded Owens Valley Solar Array. We demonstrate that the microwave spectrum from the megaelectronvolt-peaked distribution has a distinctly different shape from that produced by the electrons with a falling energy spectrum. We inspected microwave maps of the flare and identified an evolving area where the measured microwave spectra matched the theoretically expected ones for the megaelectronvolt-peaked population, thus pinpointing the site where this megaelectronvolt component resides. The locations are in a coronal volume adjacent to the region where prominent release of magnetic energy and bulk electron acceleration were detected. The results imply that transport effects play a key role in forming this population of high-energy particles, which is crucial for building a complete picture of the multifaceted solar flare phenomena. A group of extremely energetic electrons peaking at a few million electron volts is revealed in a large solar flare observed in microwaves. This megaelectronvolt-peaked population appears to originate near a coronal source where bulk electron acceleration occurs.

Solar eruptions are sudden ejections of coronal mass and magnetic fields accompanied by intense energy release. The eruptive structure does not always erupt successfully: it sometimes fails to escape the Sun after initiation. The failure of an eruption, however, provides an invaluable opportunity for improving our understanding of the intricate mechanism of eruptions. Here we present a comprehensive set of observations of a failed prominence eruption on the Sun that takes advantage of multi-viewpoint and multi-messenger imaging. Simultaneous off-limb and on-disk observations provides evidence of magnetic reconnection processes occurring at different sites during the flare. In addition to the standard flare reconnection behind the eruption, strong external reconnection occurs on the erupting flux rope, as evidenced by a wealth of signatures via multi-wavelength imaging and spectroscopy. The two reconnection processes may play contrasting roles in the acceleration of the flux rope and compete in altering the magnetic flux in the rope. As the high rate of external reconnection proceeds, the flux rope and embedded prominence decelerate noticeably and fail to erupt into the heliosphere, under strong magnetic confinement of overlying fields. Our results illustrate a well-defined physical picture for solar eruptive activities and provide insight into the lack of coronal mass ejections seen in other solar-type stars.

How the solar wind is heated to over a million degrees and accelerated to supersonic speeds remains an unresolved problem. One promising mechanism invokes numerous nanoflare-like energy release events driven by interchange reconnection between open and closed magnetic field lines in the solar corona, yet direct evidence for their ubiquity and particle-acceleration nature has been elusive. Using ultra-sensitive radio imaging spectroscopy, we detect extremely frequent and faint type III radio bursts originating from regions near open–closed magnetic boundaries in the low solar corona. These bursts trace energetic electrons produced by prevalent interchange reconnection events, injecting energy, momentum, and particles into the solar wind. Direct in situ measurements from the Parker Solar Probe reveal suprathermal electrons and ions in the near-Sun solar wind consistent with particle injections from these regions. Together, these observations uncover a previously inaccessible spectrum of particle-accelerating, small-scale interchange reconnection events and provide new insight into the long-standing problem of coronal heating and solar wind acceleration.

When in situ solar energetic electron (SEE) events are closely associated with nonthermal flares, the escaping electron population is frequently observed to be much smaller than the nonthermal-radiation-emitting population near the solar surface. If a single accelerated population drives both signatures, the physical mechanism causing this severe deficit of upward-propagating electrons remains poorly understood. Focusing on one of the 2022 November 10-12 SEE events associated with recurrent solar jets and interplanetary type III radio bursts, we present a new, combined microwave-X-ray analysis using the Expanded Owens Valley Solar Array and the Spectrometer/Telescope for Imaging X-rays on board Solar Orbiter. For the first time for such an event, this synergy enables spatially resolved diagnostics over a broad energy spectrum of the near-Sun energetic electrons, complemented by in situ measurements made by spacecraft at multiple heliocentric longitudes and distances. Consistent with earlier results based on in situ and X-ray data, our results show that only 0.1%-1% of energetic electrons escape into interplanetary space. Crucially, the new microwave spectral imaging analysis suggests that energetic electrons are strongly concentrated in a compact region just above a miniflare arcade at the base of the jet spire and that their number density decreases by at least 2 orders of magnitude in the direction of the jet spire away from this region. This steep gradient, revealed by the microwave diagnostics, points to efficient local acceleration and trapping in the region analogous to the above-the-loop-top "magnetic bottle" region in major eruptive flares, allowing only a small fraction of electrons to access open magnetic field lines and enter interplanetary space.

Certain solar flares exhibit a distinctive candle-flame or cusp-shaped feature above the bright flare arcade visible in extreme ultraviolet (EUV) and X-ray channels sensitive to high-temperature plasma. The presence of a cusp-like structure is generally regarded as a key piece of morphological evidence for magnetic reconnection to power explosive energy release in solar flares. In addition, downward-propagating plasma flows above the flare arcade have often been interpreted as outflows driven by magnetic reconnection. However, the relationship between the observed candle-flame-shaped morphology and the underlying magnetic field geometry for reconnection remains unclear. Likewise, the observed speed of the plasma downflows has been found to be too low compared to the upstream Alfv & eacute;n speed predicted by reconnection theories. With the help of a recently developed three-dimensional magnetohydrodynamics model, we examine the locations where magnetic topology changes from antiparallel to closed (Y-points) in a candle-flame-shaped flare, compare the observational emission features with synthetic EUV images generated from the model, and analyze their time evolutions. We also investigate the role of projection effects and line-of-sight integration in the measurements of plasma downflow speeds. Our analysis reveals that the Y-points do not necessarily coincide with the apparent cusp tip. Also, the apparent speeds of the supra-arcade downflows, as derived from tracks in the time-distance plots, underestimate the true Alfv & eacute;n speeds in the reconnection inflow region by at least a factor of 2 up to an order of magnitude.

Incoherent radio emission at meter--decimeter wavelengths provides a key diagnostic of the coronal thermal plasma, but at frequencies below $\sim$\,1\,GHz coronal refraction can substantially bend ray paths and modify the apparent source size and brightness distribution. We develop a forward-modeling framework that combines refractive ray tracing through a global 3D coronal model with radiative transfer along each ray. The method tracks the ray-tube cross-sectional area $S(s)$ using a step-wise perturbation retracing approach and incorporates a geometric magnification term proportional to $d\ln S/ds$ to enforce flux conservation under focusing/defocusing. Thermal free--free emission and absorption are then computed with the \texttt{GRFF} radiative transfer code to produce synthetic radio maps over 40--800\,MHz. Applying the framework to Carrington rotation 2298, we find that including propagation effects allows the quiet-Sun background spectrum to be well reproduced. However, active region brightness is less accurately modeled, suggesting that additional physical factors should be considered in future work. These results establish a physics-based method for generating low-frequency quiet-Sun synthetic images suitable for quantitative comparison with interferometric observations and for assessing how propagation effects shape the observed morphology.

Strong solar activities are often accompanied by a variety of radio bursts. These radio bursts not only serve as valuable diagnostics of coronal and heliospheric processes but also as potential tools in space weather monitoring and forecasting. However, space weather applications call for the capability for low-latency and high-sensitivity radio burst recording and reporting, which has remained lacking. In this work, we present the development of a near-real-time radio burst recording and reporting system with the Owens Valley Radio Observatory's Long Wavelength Array. The system directly clips data from the real-time buffer and streams it as a live real-time radio dynamic spectrogram. The spectrograms are then fed to a deep learning-based burst identification module for type III radio bursts. The identifier is built on a You Only Look Once architecture, trained by synthetic type III radio bursts generated by using a physics-based model to achieve accurate and robust detection. This system enables continuous real-time radio spectrum streaming and the automatic reporting of type III radio bursts within similar to 10 s of their occurrence.

We perform a detailed study of the energetics for a well-observed solar eruption and flare that occurred on 2021 October 28. This event included a GOES class X1.0 flare, a global extreme-UV (EUV) wave, and a coronal mass ejection (CME) that reached speeds of >2000 km s(-1). The event was observed from a variety of spacecraft in NASA's Heliophysics System Observatory, including multiple missions near Earth, STEREO-A off the Sun-Earth line, and Solar Orbiter, near the Sun-Earth line at about 0.8 au. Using remote sensing, in situ observations, and in some cases scaling laws based on previous observations, we characterize the following quantities: free magnetic energy, energy in nonthermal electrons, energy in nonthermal ions, bolometric energy, energy deposited in the chromosphere, thermal energy radiated in the flare loops, energy dissipated by the EUV wave, CME kinetic and gravitational potential energy, CME energy flux in the heliosphere, and the energy partition in the CME shock. We find that the total energy released during the event is consistent with estimates of the pre-event stored magnetic energy, and the CME kinetic + potential energy dominates the energy partition.