Energies of Electrons Accelerated in Turbulent Reconnecting Current Sheets in Solar Flares

Yohkoh observations strongly suggest that electron acceleration in solar flares occurs in magnetic reconnection regions in the corona above the soft X-ray flare loops. Unfortunately, models for particle acceleration in reconnecting current sheets predict electron energy gains in terms of the reconnection electric field and the thickness of the sheet, both of which are extremely difficult to measure. It can be shown, however, that application of Ohm's law in a turbulent current sheet, combined with energy and Maxwell's equations, leads to a formula for the electron energy gain in terms of the flare power output, the magnetic field strength, the plasma density and temperature in the sheet, and its area. Typical flare parameters correspond to electron energies between a few tens of keV and a few MeV. The calculation supports the viewpoint that electrons that generate the continuum gamma-ray and hard X-ray emissions in impulsive solar flares are accelerated in a large-scale turbulent current sheet above the soft X-ray flare loops.     

Effect of Collisions and Magnetic Convergence on Electron Acceleration and Transport in Reconnecting Twisted Solar Flare Loops

We study a model of particle acceleration coupled with an MHD model of magnetic reconnection in unstable twisted coronal loops. The kink instability leads to the formation of helical currents with strong parallel electric fields resulting in electron acceleration. The motion of electrons in the electric and magnetic fields of the reconnecting loop is investigated using a test-particle approach taking into account collisional scattering. We discuss the effects of Coulomb collisions and magnetic convergence near loop footpoints on the spatial distribution and energy spectra of high-energy electron populations and possible implications on the hard X-ray emission in solar flares.     

Multiperiodic irradiance changes caused by r-modes and g-modes

The acceleration of the influential 100 keV electrons in flares observed in hard X-rays and several radio emissions is unknown. Shock-waves and MHD turbulence, successfully applied to interprete interplanetary energetic particles, have recently been called in question concerning energetic flare electrons and ions. Other possible mechanisms are considered which are closely related to the primary flare energy release. In particular, runaway acceleration by the electric field of the reconnection current sheet, bulk heating by microturbulence, and cross-field ion currents due to bulk motion as a primary result of reconnection are reviewed. All three are likely to occur in some way. Their relative importance cannot be definitively assessed due to the lack of information on non-thermal, low energy protons.Proceedings of the Second CESRA Workshop on Particle Acceleration and Trapping in Solar Flares, held at Aubigny-sur-Nère (France), 23–26 June, 1986.     

Hard X-ray emission from the solar corona

This review surveys hard X-ray emissions of non-thermal electrons in the solar corona. These electrons originate in flares and flare-related processes. Hard X-ray emission is the most direct diagnostic of electron presence in the corona, and such observations provide quantitative determinations of the total energy in the non-thermal electrons. The most intense flare emissions are generally observed from the chromosphere at footpoints of magnetic loops. Over the years, however, many observations of hard X-ray and even γ-ray emission directly from the corona have also been reported. These coronal sources are of particular interest as they occur closest to where the electron acceleration is thought to occur. Prior to the actual direct imaging observations, disk occultation was usually required to study coronal sources, resulting in limited physical information. Now RHESSI has given us a systematic view of coronal sources that combines high spatial and spectral resolution with broad energy coverage and high sensitivity. Despite the low density and hence low bremsstrahlung efficiency of the corona, we now detect coronal hard X-ray emissions from sources in all phases of solar flares. Because the physical conditions in such sources may differ substantially from those of the usual “footpoint” emission regions, we take the opportunity to revisit the physics of hard X-radiation and relevant theories of particle acceleration.     

Evidence for prolonged acceleration based on a detailed analysis of the long-duration solar gamma-ray flare of June 15, 1991

Gamma-ray emission extending to energies greater than 2 GeV and lasting at least for two hours as well as 0.8–8.1 MeV nuclear line emission lasting 40 min were observed with very sensitive telescopes aboard the GAMMA and CGRO satellites for the well-developed post-flare loop formation phase of the 3B/X12 flare on June 15, 1991. We undertook an analysis of optical, radio, cosmic-ray, and other data in order to identify the origin of the energetic particles producing these unusual gamma-ray emissions. The analysis yields evidence that the gamma-rays and other emissions, observed well after the impulsive phase of the flare, appear to be initiated by prolonged nonstationary particle acceleration directly during the late phase of the flare rather than by a long-term trapping of energetic electrons and protons accelerated at the onset of the flare. We argue that such an acceleration, including the acceleration of protons up to GeV energies, can be caused by a prolonged post-eruptive energy release following a coronal mass ejection (CME), when the magnetic field above the active region, strongly disturbed by the CME eruption, relaxes to its initial state through magnetic reconnection in the coronal vertical current sheet.     

Location of Decimetric Pulsations in Solar Flares

This work investigates the spatial relation between coronal X-ray sources and coherent radio emissions, both generally thought to be signatures of particle acceleration. Two limb events were selected during which the radio emission was well correlated in time with hard X-rays. The radio emissions were of the type of decimetric pulsations as determined from the spectrogram observed by Phoenix-2 of ETH Zurich. The radio positions were measured from observations with the Nançay Radioheliograph between 236 and 432 MHz and compared to the position of the coronal X-ray source imaged with RHESSI. The radio pulsations originated at least 30?–?240 Mm above the coronal hard X-ray source. The altitude of the radio emission increases generally with lower frequency. The average positions at different frequencies are on a line pointing approximately to the coronal hard X-ray source. Thus, the pulsations cannot be caused by electrons trapped in the flare loops, but are consistent with emission from a current sheet above the coronal source.     

Particle Acceleration by a Time-Varying Electric Field in Merging Magnetic Fields

Traditional models for particle acceleration by magnetic reconnection in solar flares assumed a constant electric field in a steady reconnecting magnetic field. Although this assumption may be justified during the gradual phase of flares, the situation is different during the impulsive phase. Observed rapid variations in flare emissions imply that reconnection is non-steady and a time-varying electric field is present in a reconnecting current sheet. This paper describes exploratory calculations of charged particle orbits in an oscillating electric field present either at a neutral plane or a neutral line of two-dimensional magnetic field. A simple analytical model makes it possible to explain the effects of particle trapping and resonant acceleration previously noted by Petkaki and MacKinnon in a numerical simulation. As an application, electron acceleration to X-ray generating energies in impulsive solar flares is discussed within the context of the model.     

Solar flares： radio and X-ray signatures of magnetic reconnection processes

This review summarizes new trends in studies of magnetic reconnection in solar flares. It is shown that plasmoids play a very important role in this primary flare process. Using the results of magnetohydrodynamic and particle-in-cell simulations, we describe how the plasmoids are formed, how they move and interact, and how a flare current sheet is fragmented into a cascade of plasmoids. Furthermore, it is shown that during the interactions of these plasmoids electrons are not only very efficiently accelerated and heated, but electromagnetic（radio） emission is also produced.We also describe possible mechanisms for the triggering of magnetic reconnection.The relevant X-ray and radio signatures of these processes（such as radio drifting pulsation structures, narrowband dm-spikes, and the loop-top and above-the-loop-top X-ray sources） are then described. It is shown that plasmoids can also be formed in kinked magnetic ropes. A mapping of X-points of the magnetic reconnection on the chromosphere（as e.g. a splitting of flare ribbons） is mentioned. Supporting EUV and white-light observations of plasmoids are added. The significance of all these processes for the fast magnetic reconnection and electron acceleration is outlined. Their role in fusion experiments is briefly mentioned.     

Coronal Mass Ejection of 15 May 2001: II. Coupling of the Cme Acceleration and the Flare Energy Release

We analyze the relationship between the dynamics of the coronal mass ejection (CME) of 15 May 2001 and the energy release in the associated flare. The flare took place behind the east limb and was disclosed by a growing system of hot soft X-ray (SXR) loops that appeared from behind the limb around the onset of the rapid acceleration of the CME. The highly correlated behavior of the SXR light-curve derivative and the time profile of the CME acceleration reveals an intrinsic relationship between the CME dynamics and the flare energy release. Furthermore, we found that the CME acceleration peak occurs simultaneously with the fastest growth (100 km s^-1) of X-ray loops, indicating that the reconnection plays an essential role in the eruption. Inspecting the CME/flare morphology we recognized in the Yohkoh-SXT images an oval feature that formed within the rising structure at the onset of the rapid acceleration phase, simultaneously with the appearance of the X-ray loops. The eruptive prominence was imbedded within the lower half of the oval, suggestive of a flux-rope/prominence magnetic configuration. We interpret the observed morphological evolution in terms of a reconnection process in the current sheet that presumably formed below the erupting flux-rope at the onset of the CME acceleration. Measurements of the tip-height of the cusped X-ray loop system and the height of the lower edge of the oval, enable us to trace the stretching of the current sheet. The initial distance between the oval and the loops amounted to 35 – 40 Mm. In about 1 h the inferred length of the current sheet increased to 150 – 200 Mm, which corresponds to a mean elongation speed of 35 – 45 km s^-1. The results are discussed in the framework of CME models that include the magnetic reconnection below the erupting flux-rope.     

First phase acceleration mechanisms and implications for hard X-ray burst models in solar flares

Requirements for the number of nonthermal electrons which must be accelerated in the impulsive phase of a flare are reviewed. These are uncertain by two orders of magnitude depending on whether hard X-rays above 25 keV are produced primarily by hot thermal electrons which contain a small fraction of the flare energy or by nonthermal streaming electrons which contain > 50% of the flare energy. Possible acceleration mechanisms are considered to see to what extent either X-ray production scenario can be considered viable. Direct electric field acceleration is shown to involve significant heating. In addition, candidate primary energy release mechanisms to convert stored magnetic energy into flare energy, steady reconnection and the tearing mode instability, transfer at least half of the stored energy into heat and most of the remaining energy to ions. Acceleration by electron plasma waves requires that the waves be driven to large amplitude by electrons with large streaming velocities or by anisotropic ion-acoustic waves which also require streaming electrons for their production. These in turn can only come from direct electric field acceleration since it is shown that ion-acoustic waves excited by the primary current cannot amplify electron plasma waves. Thus, wave acceleration is subject to the same limitations as direct electric field acceleration. It is concluded that at most 0.1% of the flare energy can be deposited into nonthermal streaming electrons with the energy conversion mechanisms as they have been proposed and known acceleration mechanisms. Thus, hard X-ray production above 10 keV primarily by hot thermal electrons is the only choice compatible with models for the primary energy release as they presently exist.     

X-ray and microwave emissions from the July 19, 2012 solar flare: Highly accurate observations and kinetic models

The M7.7 solar flare of July 19, 2012, at 05:58 UT was observed with high spatial, temporal, and spectral resolutions in the hard X-ray and optical ranges. The flare occurred at the solar limb, which allowed us to see the relative positions of the coronal and chromospheric X-ray sources and to determine their spectra. To explain the observations of the coronal source and the chromospheric one unocculted by the solar limb, we apply an accurate analytical model for the kinetic behavior of accelerated electrons in a flare. We interpret the chromospheric hard X-ray source in the thick-target approximation with a reverse current and the coronal one in the thin-target approximation. Our estimates of the slopes of the hard X-ray spectra for both sources are consistent with the observations. However, the calculated intensity of the coronal source is lower than the observed one by several times. Allowance for the acceleration of fast electrons in a collapsing magnetic trap has enabled us to remove this contradiction. As a result of our modeling, we have estimated the flux density of the energy transferred by electrons with energies above 15 keV to be ～5 × 10¹⁰ erg cm^?2 s^?1, which exceeds the values typical of the thick-target model without a reverse current by a factor of ～5. To independently test the model, we have calculated the microwave spectrum in the range 1–50 GHz that corresponds to the available radio observations.     

2 1/2-Dimensional Reconnection Model and Energy Release in Solar Flares

We employ a 2 1/2-dimensional reconnection model to analyse different aspects of the energy release in two-ribbon flares. In particular, we investigate in which way the systematic change of inflow region variables, associated with the vertical elongation of current sheet, affects the flare evolution. It is assumed that as the transversal magnetic field decreases, the ambient plasma-to-magnetic pressure ratio increases, and the reconnection rate diminishes. As the transversal field decreases due to the arcade stretching, the energy release enhances and the temperature rises. Furthermore, the magnetosonic Mach number of the reconnection outflow increases, providing the formation of fast mode standing shocks above the flare loops and below the erupting flux rope. Eventually, in the limit of a very small transversal field the reconnection becomes turbulent due to a highly non-linear response of the system to small fluctuations of the transversal field. The turbulence results in the energy release fragmentation which increases the release efficiency, and is likely to be responsible for the impulsive phase of the flare. On the other hand, as the current sheet stretches to larger heights, the ambient plasma-to-magnetic pressure ratio increases which causes a gradual decrease of the reconnection rate, energy release rate, and temperature in the late phase of flare. The described magnetohydrodynamical changes affect also the electron distribution function in space and time. At large reconnection rates (impulsive phase of the flare) the ratio of the inflow-to-outflow magnetic field strength is much smaller than at lower reconnection rates (late phase of the flare), i.e., the corresponding loss-cone angle becomes narrower. Consequently, in the impulsive phase a larger fraction of energized electrons can escape from the current sheet downwards to the chromosphere and upwards into the corona – the dominant flare features are the foot-point hard X-ray sources and type III radio bursts. On the other hand, at low reconnection rates, more particles stay trapped in the outflow region, and the thermal conduction flux becomes strongly reduced. As a result, a superhot loop-top, and above-the-loop plasma appears, as sometimes observed, to be a dominant feature of the gradual phase.     

Magnetic reconnection model for X-ray flare loop interaction

The subtle interactions between the magnetohydrodynamics (MHD) and transverse plasmons are investigated. It is shown that there is a resistive instability by the plasmon's soliton in a current sheet, which eventually turns into an eruptive instability at the magnetic field reconnection. In the case of ion-acoustic turbulence, the high temperature current sheet model must adopt the aromalous conductivity instead of the Coulomb conductivity. The numerical results are consistent with the observations obtained by Hanaoka (1994). Thus the flare caused by X-ray loop coalescence can be basically interpreted by this model of magnetic field reconnection driven by ponderomotive force.     

Electron acceleration in solar-flare magnetic traps: Model properties and their observational confirmations

Using an analytical solution of the kinetic equation, we have investigated the model properties of the coronal and chromospheric hard X-ray sources in the limb flare of July 19, 2012. We calculated the emission spectrum at the flare loop footpoints in the thick-target approximation with a reverse current and showed it to be consistent with the observed one. The spectrum of the coronal source located above the flare loop was calculated in the thin-target approximation. In this case, the slope of the hard X-ray spectrum is reproduced very accurately, but the intensity of the coronal emission is lower than the observed one by several times. Previously, we showed that this contradiction is completely removed if the additional (relative to the primary acceleration in the reconnecting current layer) electron acceleration in the coronal magnetic trap that contracts in the transverse direction and decreases in length during the impulsive flare phase is taken into account. In this paper we study in detail this effect in the context of a more realistic flare scenario, where a whole ensemble of traps existed in the hard X-ray burst time, each of which was at different stages of its evolution: formation, collapse, destruction. Our results point not only to the existence of first-order Fermi acceleration and betatron electron heating in solar flares but also to their high efficiency. Highly accurate observations of a specific flare are used as an example to show that the previously predicted theoretical features of the model find convincing confirmations.     

On the magnetic reconnection of electric currents in solar flares

The role of the electric currents distributed over the volume of an active region on the Sun is considered from the standpoint of solar flare physics. We suggest including the electric currents in a topological model of the magnetic field in an active region. Typical values of the mutual inductance and the interaction energy of the coronal electric currents flowing along magnetic loops have been estimated for the M7/1N flare on April 27, 2006. We show that if these currents actually make a significant contribution to the flare energetics, then they must manifest themselves in the photosphericmagnetic fields. Depending on their orientation, the distributed currents can both help and hinder reconnection in the current layer at the separator during the flare. Asymmetric reconnection of the currents is accompanied by their interruption and an inductive change in energy. The reconnection of currents in flares differs significantly from the ordinary coalescence instability of magnetic islands in current layers. Highly accurate measurements of the magnetic fields in active regions are needed for a quantitative analysis of the role of distributed currents in solar flares.     

Catastrophic Behavior of Multiple Coronal Flux Rope System

A major solar active event called Bastille Day Event occurred in AR 9077 on July 14, 2000. Simultaneous occurrence of a filament eruption, a flare and a coronal mass ejection was observed in this event. Previous analyses of this event show that before the event, there existed an activation and eruption of a huge trans-equatorial filament, which might play a crucial role in triggering the Bastille Day event. This implies that independent flux systems are closely related to and affect each other, which has encouraged us to investigate the catastrophic behavior of a multiple coronal flux rope system with the use of a 2.5-D time-dependent MHD model. A force-free field that contains three separate coronal flux ropes is taken to be the initial state. Starting from this state, we increase either the annular or the axial flux of a certain flux rope to examine the catastrophic behavior of the system in two regimes, the ideal MHD regime and the resistive MHD regime. It is found that a catastrophe occurs if the flux exceeds a certain critical value, or the magnetic energy of the system exceeds a certain threshold: the rope of interest breaks away from the base and escapes to infinity, leaving a current sheet below. Moreover, the destiny of the remainder flux ropes relies on whether reconnection takes place across the current sheet. In the ideal MHD regime, i.e., in the absence of reconnection, these ropes remain to be attached to the base in equilibrium, whereas in the resistive MHD regime they abruptly erupt upward during reconnection and escape to infinity. Reconnection causes the field lines to close back to the base and thus changes the background field outside the attached flux ropes in such a way that the constraint on these ropes is substantially relaxed and the corresponding catastrophic energy threshold is reduced accordingly, leading to a catastrophic eruption of these ropes. Since magnetic reconnection is generally inevitable when a current sheet forms and develops through an eruption of one flux rope, the eruption of this flux rope must lead to an eruption of the others. This provides an example to demonstrate the interaction between several independent magnetic flux systems in different regions, as implied by the Bastille Day event, and may serve as a possible mechanism for sympathetic events occurring on the Sun.     

The magnetic nature of solar flares

The main challenge for the theory of solar eruptions has been to understand two basic aspects of large flares. These are the cause of the flare itself and the nature of the morphological features which form during its evolution. Such features include separating ribbons of H emission joined by a rising arcade of soft x-ray loops, with hard x-ray emission at their summits and at their feet. Two major advances in our understanding of the theory of solar flares have recently occurred. The first is the realisation that a magnetohydrodynamic (MHD) catastrophe is probably responsible for the basic eruption and the second is that the eruption is likely to drive a reconnection process in the field lines stretched out by the eruption. The reconnection is responsible for the ribbons and the set of rising soft x-ray loops, and such a process is well supported by numerical experiments and detailed observations from the Japanese satellite Yohkoh. Magnetic energy conversion by reconnection in two dimensions is relatively well understood, but in three dimensions we are only starting to understand the complexity of the magnetic topology and the MHD dynamics which are involved. How the dynamics lead to particle acceleration is even less well understood. Particle acceleration in flares may in principle occur in a variety of ways, such as stochastic acceleration by MHD turbulence, acceleration by direct electric fields at the reconnection site, or diffusive shock acceleration at the different kinds of MHD shock waves that are produced during the flare. However, which of these processes is most important for producing the energetic particles that strike the solar surface remains a mystery. Received 2 January 2001 / Published online 17 July 2001     

Ion-cyclotron instability and electron acceleration in coronal loops

Quasi-electrostatic electron and ion-cyclotron instabilities are studied. The result indicates that the higher harmonic ion cyclotron instabilities (ICI) can be excited while the fast ions produced from reconnection are injected into a coronal loop. Part of the energetic ions can be dragged out of the magnetic mirror turning points and a negative plasma potential is generated. The plasma potential may directly accelerate the electrons up to the relativistic velocity within a short time. This acceleration is similar to the processes occurring in the magnetic mirror devices of controlled thermonuclear fusion. The spectrum and flux of accelerated electrons have also been obtained. Some observational results during the solar flare might be explained by this acceleration mechanism.     

Magnetospheric substorms and solar flares

Assuming that basic plasma processes associated with magnetospheric substorms and solar flares are similar and thus assuming also that a flare ribbon is produced by the impact of field-aligned current-carrying electrons on the chromosphere, a chain of processes leading to solar flares is considered, including the dynamo process in the photospheric level in the vicinity of bipolar sunspots, the formation of a sheet current in the lower coronal level, the interruption of the sheet current, the subsequent diversion of it to the chromosphere, the development of a potential drop along magnetic field lines, the acceleration of current-carrying electrons and their impact on the chromosphere, producing a pair of flare ribbons.     

Interpretation of the observed motions of hard X-ray sources in solar flares

In connection with the RHESSI satellite observations of solar flares, which have revealed new properties of hard X-ray sources during flares, we offer an interpretation of these properties. The observed motions of coronal and chromospheric sources are shown to be the consequences of three-dimensional magnetic reconnection at the separator in the corona. During the first (initial) flare phase, the reconnection process releases an excess of magnetic energy related predominantly to themagnetic tensions produced before the flare by shear plasma flows in the photosphere. The relaxation of a magnetic shear in the corona also explains the downward motion of the coronal source and the decrease in the separation between chromospheric sources. During the second (main) flare phase, ordinary reconnection dominates; it describes the energy release in the terms of the “standard model” of large eruptive flares accompanied by the rise of the coronal source and an increase in the separation between chromospheric sources.