Nonthermal Electron Acceleration Research Articles

Nonthermal Observations of a Flare Loop-top Using IRIS Fe xxi: Implications for Turbulence and Electron Acceleration

The excess broadening of high-temperature spectral lines, long observed near the tops of flare arcades, is widely considered to result from magnetohydrodynamic turbulence. According to different theories, plasma turbulence is also believed to be a candidate mechanism for particle acceleration during solar flares. However, the degree to which this broadening is connected to the acceleration of nonthermal electrons remains largely unexplored outside of recent work, and many observations have been limited by limited spatial resolution and cadence. Using the Interface Region Imaging Spectrometer, we present spatially resolved observations of loop-top (LT) broadenings using hot (≈11 MK) Fe xxi 1354.1 Å line emission at ≈9 s cadence during the 2022 March 30 X1.3 flare. We find nonthermal velocities upward of 65 km s−1 that decay linearly with time, indicating the presence and subsequent dissipation of plasma turbulence. Moreover, the initial Fe xxi signal was found to be cospatial and cotemporal with microwave emission measured by the Expanded Owens Valley Solar Array, placing a population of nonthermal electrons in the same region as the LT turbulence. Evidence of electron acceleration at this time is further supported by hard X-ray measurements from the Spectrometer/Telescope for Imaging X-rays on board Solar Orbiter. Using the decay of nonthermal broadenings as a proxy for turbulent dissipation, we found the rate of energy dissipation to be consistent with the power of nonthermal electrons deposited into the chromosphere, suggesting a possible connection between turbulence and electron acceleration.

Non-thermal electrons in an eruptive solar event: Magnetic structure, confinement, and escape into the heliosphere

Filament eruptions and coronal mass ejections (CMEs) reveal large-scale instabilities of magnetic structures in the solar corona. Some of them are accompanied by radio emission, which at decimetric and longer wavelengths is a signature of electron acceleration that may be different from the acceleration in impulsive flares. The radio emission is part of the broadband continua at decimetre and metre wavelengths called type IV bursts. In this article we investigate a particularly well-observed combination of a filament eruption seen in Halpha and at extreme ultraviolet (EUV) wavelengths and a moving type IV burst on 2021 August 24. The aim is to shed light on the relationship between the large-scale erupting magnetic structure and the acceleration and transport of non-thermal electrons. We used imaging observations of a moving radio source and associated burst groups with the refurbished Nan c ay Radioheliograph and whole-Sun radio spectrography from different ground-based and space-borne instruments, in combination with X-ray, radio, and in situ electron observations at tens of keV from Solar Orbiter and EUV imaging by SDO/AIA. The radio sources are located with respect to the erupting magnetic structure traced by the filament (EUV 30.4 nm), and the timing of the electrons detected in situ is compared with the timing of the different radio emissions. We find that the moving radio source is located at the top of the erupting magnetic structure outlined by the filament, which we interpret as a magnetic flux rope. The flux rope erupts in a strongly non-radial direction, guided by the overlying magnetic field of a coronal hole. The electrons detected at Solar Orbiter are found to be released mainly in two episodes, 10 to 40 minutes after the impulsive phase. The releases coincide with two groups of radio bursts, which originate respectively on the flank and near the top of the erupting flux rope. The observation allows an unusually clear association between a moving type IV radio burst, an erupting magnetic flux rope as core structure of a CME, and particle releases into the heliosphere. Non-thermal electrons are confined in the flux rope. Electrons escape to the heliosphere mainly in two distinct episodes, which we relate to magnetic reconnection between the flux rope and ambient open field lines.

Acceleration of Nonthermal Electrons in Coordinated Interaction with Whistler Turbulence in a Flare Loop

Acceleration of Nonthermal Electrons in Coordinated Interaction with Whistler Turbulence in a Flare Loop

Electron Injection via Modified Diffusive Shock Acceleration in High-Mach-number Collisionless Shocks

The ability of collisionless shocks to efficiently accelerate nonthermal electrons via diffusive shock acceleration (DSA) is thought to require an injection mechanism capable of preaccelerating electrons to high enough energy where they can start crossing the shock front potential. We propose, and show via fully kinetic plasma simulations, that in high-Mach-number shocks electrons can be effectively injected by scattering in kinetic-scale magnetic turbulence produced near the shock transition by the ion Weibel, or current filamentation, instability. We describe this process as a modified DSA mechanism where initially thermal electrons experience the flow velocity gradient in the shock transition and are accelerated via a first-order Fermi process as they scatter back and forth. The electron energization rate, diffusion coefficient, and acceleration time obtained in the model are consistent with particle-in-cell simulations and with the results of recent laboratory experiments where nonthermal electron acceleration was observed. This injection model represents a natural extension of DSA and could account for electron injection in high-Mach-number astrophysical shocks, such as those associated with young supernova remnants and accretion shocks in galaxy clusters.

Tracking X-Ray Source Movement in a Retracting Flux Tube

Solar flares produce sources of localized, enhanced X-ray emission, thought to be due to the acceleration of nonthermal electrons and the transport of energy away from the reconnection site. The 2002 November 28 C1.6 limb flare showed clear X-ray source motion in the Reuven Ramaty High Energy Solar Spectroscopic Imager observations at 3–10 keV propagating from the apex of the flaring arcade, down toward the footpoints, and then rising back into the corona. Previous work attempted to model this motion using simulations driven by heating with an electron beam or thermal conduction front, finding reasonable agreement only if there were large initial densities. This work extends the previous model by considering a flux tube that retracts through a current sheet away from a magnetic reconnection site. The retraction model includes drag to slow motion in the current sheet, which allows us to vary the energy released by the retraction. This retraction causes a dense and superhot plug of material to form at the loop apex, naturally causing a thermal X-ray source to form in the corona. We find that the observed X-ray source motion, however, is most likely thermal and a signature of the evaporation fronts after initially filling the flux tube.

Non-thermal electron acceleration from magnetically driven reconnection in a laboratory plasma

Magnetic reconnection is a ubiquitous astrophysical process that rapidly converts magnetic energy into some combination of plasma flow energy, thermal energy, and non-thermal energetic particles, including energetic electrons. Various reconnection acceleration mechanisms in different low-$\beta$ (plasma-to-magnetic pressure ratio) and collisionless environments have been proposed theoretically and studied numerically, including first- and second-order Fermi acceleration, betatron acceleration, parallel electric field acceleration along magnetic fields, and direct acceleration by the reconnection electric field. However, none of them have been heretofore confirmed experimentally, as the direct observation of non-thermal particle acceleration in laboratory experiments has been difficult due to short Debye lengths for \textit{in-situ} measurements and short mean free paths for \textit{ex-situ} measurements. Here we report the direct measurement of accelerated non-thermal electrons from low-$\beta$ magnetically driven reconnection in experiments using a laser-powered capacitor coil platform. We use kiloJoule lasers to drive parallel currents to reconnect MegaGauss-level magnetic fields in a quasi-axisymmetric geometry. The angular dependence of the measured electron energy spectrum and the resulting accelerated energies, supported by particle-in-cell simulations, indicate that the mechanism of direct electric field acceleration by the out-of-plane reconnection electric field is at work. Scaled energies using this mechanism show direct relevance to astrophysical observations. Our results therefore validate one of the proposed acceleration mechanisms by reconnection, and establish a new approach to study reconnection particle acceleration with laboratory experiments in relevant regimes.

Additional Stochastic Acceleration of Nonthermal Electrons during Their Interaction with Whistler Turbulence in Flare Loops

Additional Stochastic Acceleration of Nonthermal Electrons during Their Interaction with Whistler Turbulence in Flare Loops

Nonthermal electron acceleration at collisionless quasi-perpendicular shocks

Shock waves propagating in collisionless heliospheric and astrophysical plasmas have been studied extensively over the decades. One prime motivation is to understand the nonthermal particle acceleration at shocks. Although the theory of diffusive shock acceleration (DSA) has long been the standard for cosmic-ray acceleration at shocks, plasma physical understanding of particle acceleration remains elusive. In this review, we discuss nonthermal electron acceleration mechanisms at quasi-perpendicular shocks, for which substantial progress has been made in recent years. The discussion presented in this review is restricted to the following three specific topics: The first is stochastic shock drift acceleration (SSDA), which is a relatively new mechanism for electron injection into DSA. The basic mechanism, related in-situ observations and kinetic simulations results, and how it is connected with DSA will be discussed. Second, we discuss shock surfing acceleration (SSA) at very high Mach number shocks relevant to young supernova remnants (SNRs). While the original proposal under the one-dimensional assumption is unrealistic, SSA has now been proven efficient by a fully three-dimensional kinetic simulation. We discuss the multidimensional nature of SSA and its role in electron injection. Finally, we discuss the current understanding of the magnetized Weibel-dominated shock. It is essentially a magnetized shock in which the reflected-gyrating ions dominate the formation of the shock structure but with a substantial magnetic field amplification by the ion-Weibel instability. Spontaneous magnetic reconnection of self-generated current sheets within the shock structure is an interesting consequence of Weibel-generated strong magnetic turbulence. Although the exact condition for active magnetic reconnection has not been clarified, we argue that high Mach number shocks with both Alfvén and sound Mach numbers exceeding 20–40 will likely behave as a Weibel-dominated shock. Despite a number of interesting recent findings, the relative roles of SSDA, SSA, and magnetic reconnection for electron acceleration at collisionless shocks and how the dominant particle acceleration mechanisms change depending on shock parameters remain to be answered.

Efficient Nonthermal Ion and Electron Acceleration Enabled by the Flux-Rope Kink Instability in 3D Nonrelativistic Magnetic Reconnection.

The relaxation of field-line tension during magnetic reconnection gives rise to a universal Fermi acceleration process involving the curvature drift of particles. However, the efficiency of this mechanism is limited by the trapping of energetic particles within flux ropes. Using 3D fully kinetic simulations, we demonstrate that the flux-rope kink instability leads to strong field-line chaos in weak-guide-field regimes where the Fermi mechanism is most efficient, thus allowing particles to transport out of flux ropes and undergo further acceleration. As a consequence, both ions and electrons develop clear power-law energy spectra that contain a significant fraction of the released energy. The low-energy bounds are determined by the injection physics, while the high-energy cutoffs are limited only by the system size. These results have strong relevance to observations of nonthermal particle acceleration in space and astrophysics.

Quasi-Periodic Pulsations Detected in Ly $\alpha $ and Nonthermal Emissions During Solar Flares

We report quasi-periodic pulsations (QPPs) with double periods during three solar flares (viz. SOL2011-Feb-15T01:44, SOL2011-Sep-25T04:31, SOL2012-May-17T01:25). The flare QPPs were observed from light curves in Ly$\alpha$, hard X-ray (HXR) and microwave emissions, with the Ly$\alpha$ emission recorded by the Geostationary Operational Environmental Satellite, the HXR emission recorded by the Reuven Ramaty High-Energy Solar Spectroscopic Imager and the Fermi Gamma-ray Burst Monitor, and the microwave emission recorded by the Nobeyama Radio Polarimeters and Radioheliograph. By using the Markov chain Monte Carlo (MCMC) method, QPPs with double periods of about two minutes and one minute were first found in the Ly$\alpha$ emission. Then using the same method, a QPP with nearly the same period of about two minutes was also found in HXR and microwave emissions. Considering the possible common origin (nonthermal electrons) between Ly$\alpha$ and HXR/microwave emission, we suggest that the two-minute QPP results from the periodic acceleration of nonthermal electrons during magnetic reconnections. The ratio between the double periods in the Ly$\alpha$ emission was found to be close to two, which is consistent with the theoretical expectation between the fundamental and harmonic modes. However, we cannot rule out other possible driving mechanisms for the one-minute QPPs in HXR/microwave emissions due to their relatively large deviations.

Periodicities in an active region correlated with Type III radio bursts observed by Parker Solar Probe.

Context.Periodicities have frequently been reported across many wavelengths in the solar corona. Correlated periods of ~5 min, comparable to solar p-modes, are suggestive of coupling between the photosphere and the corona.Aims.Our study investigates whether there are correlations in the periodic behavior of Type III radio bursts which are indicative of nonthermal electron acceleration processes, and coronal extreme ultraviolet (EUV) emission used to assess heating and cooling in an active region when there are no large flares.Methods.We used coordinated observations of Type III radio bursts from the FIELDS instrument on Parker Solar Probe (PSP), of EUV emissions by the Solar Dynamics Observatory (SDO) Atmospheric Imaging Assembly (AIA) and white light observations by SDO Helioseismic and Magnetic Image (HMI), and of solar flare X-rays by Nuclear Spectroscopic Telescope Array (NuSTAR) on April 12, 2019. Several methods for assessing periodicities are utilized and compared to validate periods obtained.Results.Periodicities of ~5 min in the EUV in several areas of an active region are well correlated with the repetition rate of the Type III radio bursts observed on both PSP and Wind. Detrended 211 and 171 Å light curves show periodic profiles in multiple locations, with 171 Å peaks sometimes lagging those seen in 211 Å. This is suggestive of impulsive events that result in heating and then cooling in the lower corona. NuSTAR X-rays provide evidence for at least one microflare during the interval of Type III bursts, but there is not a one-to-one correspondence between the X-rays and the Type III bursts. Our study provides evidence for periodic acceleration of nonthermal electrons (required to generate Type III radio bursts) when there were no observable flares either in the X-ray data or the EUV. The acceleration process, therefore, must be associated with small impulsive events, perhaps nanoflares.

Spectroscopic observations of a flare-related coronal jet

Context. Coronal jets are ubiquitous in active regions and coronal holes. Aims. In this paper, we study a coronal jet related to a C3.4 circular-ribbon flare in the active region 12434 on 2015 October 16. Methods. The flare and jet were observed in ultraviolet and extreme ultraviolet wavelengths by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory (SDO). The line-of-sight magnetograms of the photosphere were observed by the Helioseismic and Magnetic Imager on board SDO. The whole event was covered by the Interface Region Imaging Spectrograph during its imaging and spectroscopic observations. Soft X-ray fluxes of the flare were recorded by the GOES spacecraft. Hard X-ray (HXR) fluxes at 4−50 keV were obtained from observations of RHESSI and Fermi. Radio dynamic spectra of the flare were recorded by the ground-based stations belonging to the e-Callisto network. Results. Two minifilaments were located under a 3D fan-spine structure before flare. The flare was generated by the eruption of one filament. The kinetic evolution of the jet was divided into two phases: a slow rise phase at a speed of ∼131 km s−1 and a fast rise phase at a speed of ∼363 km s−1 in the plane-of-sky. The slow rise phase may correspond to the impulsive reconnection at the breakout current sheet. The fast rise phase may correspond to magnetic reconnection at the flare current sheet. The transition between the two phases occurred at ∼09:00:40 UT. The blueshifted Doppler velocities of the jet in the Si IV 1402.80 Å line range from −34 to −120 km s−1. The accelerated high-energy electrons are composed of three groups. Those propagating upward along the open field generate type III radio bursts, while those propagating downward produce HXR emissions and drive chromospheric condensation observed in the Si IV line. The electrons trapped in the rising filament generate a microwave burst lasting for ≤40 s. Bidirectional outflows at the base of jet are manifested by significant line broadenings of the Si IV line. The blueshifted Doppler velocities of outflows range from −13 to −101 km s−1. The redshifted Doppler velocities of outflows range from ∼17 to ∼170 km s−1. Conclusions. Our multiwavelength observations of the flare-related jet are in favor of the breakout jet model and are important for understanding the acceleration and transport of nonthermal electrons.

Nonthermal electron and ion acceleration by magnetic reconnection in large laser-driven plasmas

Magnetic reconnection is a fundamental plasma process that is thought to play a key role in the production of nonthermal particles associated with explosive phenomena in space physics and astrophysics. Experiments at high-energy-density facilities are starting to probe the microphysics of reconnection at high Lundquist numbers and large system sizes. We have performed particle-in-cell (PIC) simulations to explore particle acceleration for parameters relevant to laser-driven reconnection experiments. We study particle acceleration in large system sizes that may be produced soon with the most energetic laser drivers available, such as at the National Ignition Facility. In these conditions, we show the possibility of reaching the multi-plasmoid regime, where plasmoid acceleration becomes dominant. Our results show the transition from X point to plasmoid-dominated acceleration associated with the merging and contraction of plasmoids that further extend the maximum energy of the power-law tail of the particle distribution for electrons. We also find for the first time a system-size-dependent emergence of nonthermal ion acceleration in driven reconnection, where the magnetization of ions at sufficiently large sizes allows them to be contained by the magnetic field and energized by direct X point acceleration. For feasible experimental conditions, electrons and ions can attain energies of ϵ max , e / k B T e > 100 and ϵ max , i / k B T i > 1000. Using PIC simulations with binary Monte Carlo Coulomb collisions, we study the impact of collisionality on plasmoid formation and particle acceleration. The implications of these results for understanding the role reconnection plays in accelerating particles in space physics and astrophysics are discussed.

Electron Firehose Instabilities in High-β Intracluster Shocks

Abstract The preacceleration of electrons through reflection and shock drift acceleration (SDA) is essential for the diffusive shock acceleration of nonthermal electrons in collisionless shocks. Previous studies suggested that, in weak quasi-perpendicular (Q ⊥) shocks in the high-β ( ) intracluster medium (ICM), the temperature anisotropy due to SDA-reflected electrons can drive the electron firehose instability, which excites oblique nonpropagating waves in the shock foot. In this paper, we investigate, through a linear analysis and particle-in-cell simulations, the firehose instabilities driven by an electron temperature anisotropy (ETAFI) and also by a drifting electron beam (EBFI) in β ∼ 100 ICM plasmas. The EBFI should be more relevant to describing the self-excitation of upstream waves in Q ⊥-shocks, since backstreaming electrons in the shock foot behave more like an electron beam rather than an anisotropic bi-Maxwellian population. We find that the basic properties of the two instabilities, such as the growth rate, γ, and the wavenumber of fast-growing oblique modes, are similar in the ICM environment, with one exception; while the waves excited by the ETAFI are nonpropagating (ω r = 0), those excited by the EBFI have a nonzero frequency ( ). However, the frequency is small with ω r < γ. Thus, we conclude that the interpretation of previous studies for the nature of upstream waves based on the ETAFI remains valid in Q ⊥-shocks in the ICM.

Broken-up spectra of the loop-top hard X-ray source during a solar limb flare

Solar hard X-rays (HXRs) appear in the form of either footpoint sources or coronal sources. Each individual source provides its own critical information on acceleration of nonthermal electrons and plasma heating. Earlier studies found that the HXR emission in some events manifests a broken-up power-law spectrum, with the break energy around a few hundred keV based on spatially-integrated spectral analysis, and it does not distinguish the contributions from individual sources. In this paper, we report on the broken-up spectra of a coronal source studied using HXR data recorded by Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) during the SOL2017–09–10T16:06 (GOES class X8.2) flare. The flare occurred behind the western limb and its footpoint sources were mostly occulted by the disk. We could clearly identify such broken-up spectra pertaining solely to the coronal source during the flare peak time and after. Since a significant pileup effect on the RHESSI spectra is expected for this intense solar flare, we have selected the pileup correction factor, p = 2. In this case, we found the resulting RHESSI temperature (∼30 MK) to be similar to the GOES soft X-ray temperature and break energies of 45–60 keV. Above the break energy, the spectrum hardens with time from spectral index of 3.4 to 2.7, and the difference in spectral indices below and above the break energy increases from 1.5 to 5 with time. However, we note that when p = 2 is assumed, a single power-law fitting is also possible with the RHESSI temperature higher than the GOES temperature by ∼10 MK. Possible scenarios for the broken-up spectra of the loop-top HXR source are briefly discussed.

On High-energy Particles in Accretion Disk Coronae of Supermassive Black Holes: Implications for MeV Gamma-rays and High-energy Neutrinos from AGN Cores

Abstract Recent observations with ALMA have revealed evidence for nonthermal synchrotron emission from the core regions of two nearby Seyfert galaxies. This suggests that the coronae of accretion disks in active galactic nuclei (AGNs) can be conducive to the acceleration of nonthermal electrons, in addition to the hot, thermal electrons responsible for their X-ray emission through thermal Comptonization. Here, we investigate the mechanism of such particle acceleration, based on observationally inferred parameters for AGN disk coronae. One possibility to account for the observed nonthermal electrons is diffusive shock acceleration, as long as the gyrofactor η g does not exceed ∼106. These nonthermal electrons can generate gamma-rays via inverse Compton scattering of disk photons, which can appear in the MeV band, while those with energies above ∼100 MeV would be attenuated via internal γγ pair production. The integrated emission from all AGNs with thermal and nonthermal Comptonization can reproduce the observed cosmic background radiation in X-rays as well as gamma-rays up to ∼10 MeV. Furthermore, if protons are accelerated in the same conditions as electrons and η g ∼ 30, our observationally motivated model is also able to account for the diffuse neutrino flux at energies below 100–300 TeV. The next generation of MeV gamma-ray and neutrino facilities can test these expectations by searching for signals from bright, nearby Seyfert galaxies such as NGC 4151 and IC 4329A.

Nonthermal relativistic electron acceleration due to laser-induced incoherent wakefields with external static magnetic fields

Wakefield acceleration has been considered as a candidate of the origin of cosmic rays and the electron power-law spectra with an index of −2 and it has been demonstrated experimentally and numerically. In order to further support the universality of wakefield acceleration to address the power-law spectra of cosmic rays, we investigate the nonthermal acceleration of relativistic electrons due to the laser-induced wakefield acceleration with a static external magnetic field using two-dimensional particle-in-cell simulation.The results indicate that the power-law spectra with an index of −2 still remain even in the presence of external magnetic field.

Off-axis emission of short GRB jets from double neutron star mergers and GRB 170817A

The short-duration ($\lesssim2\;$s) GRB 170817A in the nearby ($D=40\;$Mpc) elliptical galaxy NGC 4993 is the first electromagnetic counterpart of the first gravitational wave (GW) detection of a binary neutron-star (NS-NS) merger. It was followed by optical, IR, and UV emission from half a day up to weeks after the event, as well as late time X-ray and radio emission. The early UV, optical, and IR emission showed a quasi-thermal spectrum suggestive of radioactive-decay powered kilonova-like emission. Comparison to kilonova models favors the formation of a short-lived ($\sim1\;$s) hypermassive NS, which is also supported by the $\Delta t\approx1.74\;$s delay between the GW chirp signal and the prompt GRB onset. However, the late onset of the X-ray (8.9$\;$days) and radio (16.4$\;$days) emission, together with the low isotropic equivalent $\gamma$-ray energy output ($E_{\rm\gamma,iso}\approx5\times10^{46}\;$erg), strongly suggest emission from a narrow relativistic jet viewed off-axis. Here we set up a general framework for off-axis GRB jet afterglow emission, comparing analytic and numerical approaches, and showing their general predictions for short-hard GRBs that accompany binary NS mergers. The prompt GRB emission suggests a viewing angle well outside the jet's core, and we compare the afterglow lightcurves expected in such a case to the X-ray to radio emission from GRB 170817A. We fit an afterglow off-axis jet model to the X-ray and radio data and find that the observations are explained by a viewing angle $\theta_{\rm obs}\approx16^\circ-26^\circ$, GRB jet energy $E\sim10^{48.5}-10^{49.5}~{\rm erg}$, and external density $n\sim10^{-5}-10^{-1}~{\rm cm}^{-3}$ for a $\xi_e\sim 0.1$ non-thermal electron acceleration efficiency.

Electron Surfing and Drift Accelerations in a Weibel-Dominated High-Mach-Number Shock.

How electrons get accelerated to relativistic energies in a high-Mach-number quasiperpendicular shock is presented by means of abinitio particle-in-cell simulations in three dimensions. We found that coherent electrostatic Buneman waves and ion-Weibel magnetic turbulence coexist in a strong-shock structure whereby particles gain energy during shock surfing and subsequent stochastic drift accelerations. Energetic electrons that initially experienced the surfing acceleration undergo pitch-angle diffusion by interacting with magnetic turbulence and continuous acceleration during confinement in the shock transition region. The ion-Weibel turbulence is the key to the efficient nonthermal electron acceleration.

RELATIVISTIC ELECTRONS PRODUCED BY RECONNECTING ELECTRIC FIELDS IN A LASER-DRIVEN BENCH-TOP SOLAR FLARE

ABSTRACT Laboratory experiments have been carried out to model the magnetic reconnection process in a solar flare with powerful lasers. Relativistic electrons with energy up to megaelectronvolts are detected along the magnetic separatrices bounding the reconnection outflow, which exhibit a kappa-like distribution with an effective temperature of ∼109 K. The acceleration of non-thermal electrons is found to be more efficient in the case with a guide magnetic field (a component of a magnetic field along the reconnection-induced electric field) than in the case without a guide field. Hardening of the spectrum at energies ≥500 keV is observed in both cases, which remarkably resembles the hardening of hard X-ray and γ-ray spectra observed in many solar flares. This supports a recent proposal that the hardening in the hard X-ray and γ-ray emissions of solar flares is due to a hardening of the source-electron spectrum. We also performed numerical simulations that help examine behaviors of electrons in the reconnection process with the electromagnetic field configurations occurring in the experiments. The trajectories of non-thermal electrons observed in the experiments were well duplicated in the simulations. Our numerical simulations generally reproduce the electron energy spectrum as well, except for the hardening of the electron spectrum. This suggests that other mechanisms such as shock or turbulence may play an important role in the production of the observed energetic electrons.