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.     

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.     

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.     

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     

The flares of April 1980

We discuss the spatial and temporal characteristics of X-ray flares occurring in the active region NOAA2372 from April 6 to 13, 1980. The flares are seen to extend in most cases across the whole active complex, involving several magnetic features. They originate in an intermediate bipole, between the two main sunspots of the active region, where high magnetic shear was detected. A rapid expansion is seen in some cases, in conjunction with the start of the impulsive hard X-ray bursts. We also detect, in the late phases of some of the events, a large soft X-ray structure overlying the whole active region, which also shows up as a noise storm region at metric wavelengths. These large loops cool by heat conduction but, in some cases, Hα condensations seem to appear, probably as a result of magnetic compression and a condensation mode of the thermal instability. The topological aspects of the field configuration are discussed, in the context of flare models invoking magnetic reconnection at the site of the primary energy release. In such a model, the intermediate bipole is the natural site of initial magnetic reconnection, particle acceleration and heating. In one particular case of a flare observed at the limb, we find possible evidence of particle acceleration in a neutral sheet at the boundary between two clearly defined magnetic structures.     

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.     

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.     

Relationship between CME dynamics and solar flare plasma

The relationship between the velocity of CMEs and the plasma temperature of the associated X-ray solar flares is investigated.The velocity of CMEs increases with plasma temperature(R=0.82)and photon index below the break energy(R=0.60)of X-ray flares.The heating of the coronal plasma appears to be significant with respect to the kinetics of a CME from the reconnection region where the flare also occurs.We propose that the initiation and velocity of CMEs perhaps depend upon the dominant process of conversion of the magnetic field energy of the active region to heating/accelerating the coronal plasma in the reconnected loops.Results show that a flare and the associated CME are two components of one energy release system,perhaps,magnetic field free energy.     

Motions of Flare Ribbons and Loops in Various Magnetic Configurations

Kopp–Pneuman-type magnetic configurations, which include a vertical current sheet, with various background fields are investigated. Dissipation of the current sheet as a result of magnetic reconnection produces bright flare ribbons on the solar disk and a growing flare loop system in the corona. In principle, the growth of flare loop system is governed by a reconnection process only, and the behavior of flare ribbons is also controlled by the background field. The flare ribbons may appear either separate or attached to one another at the onset of the flare depending on the background field distribution on the boundary surface. We calculate the decrease in height that magnetic field lines undergo after they have reconnected to form closed loops. Following previous practice, we refer to this decrease as field line shrinkage. Unlike the motions of flare ribbons, the shrinkage of flare loops depends weakly on the background field. Individual loops always shrink fastest at the moment it is produced by reconnection and just starts to leave the current sheet. The earlier the loop forms, the more and faster it shrinks. The relevant observations are explained on the basis of our calculations, and the aspects of the explanation that need improvement are also discussed.     

Magnetic reconnection,electric field,and particle acceleration in the July 14, 2000 solar flare

A topological model with magnetic reconnection at two separators in the corona is used to account for the recently discovered changes of the photospheric magnetic field in the active region NOAA 9077 during the July 14, 2000 flare. The model self-consistently explains the following observed effects: (1) the magnetic field strength decreases on the periphery of the active region but increases in its inner part near the neutral line of the photospheric magnetic field; (2) the center-of-mass positions of the fields of opposite (northern and southern) polarities converge; and (3) the magnetic flux of the active region decreases after the flare. The topological model gives not only a qualitative interpretation of the flare phenomena (the structure of the interacting magnetic fluxes in the corona, the location of the energy sources, the shape of the flare ribbons and kernels in the chromosphere and photosphere), but also correct quantitative estimates of the large-scale processes that form the basis for solar flares. The electric field emerging in the flare during large-scale reconnection is calculated. The electric field strength correlates with the observed intensity of the hard X-ray bremsstrahlung, suggesting an electron acceleration as a result of reconnection.     

Evidence of Magnetic Reconnection in Solar Flares and a Unified Model of Flares

The solar X-ray observing satellite Yohkoh has discovered various new dynamic features in solar flares and corona, e.g., cusp-shaped flare loops, above-the-loop-top hard X-ray sources, X-ray plasmoid ejections from impulsive flares, transient brightenings (spatially resolved microflares), X-ray jets, large scale arcade formation associated with filament eruption or coronal mass ejections, and so on. It has soon become clear that many of these features are closely related to magnetic reconnection. We can now say that Yohkoh established (at least phenomenologically) the magnetic reconnection model of flares. In this paper, we review various evidence of magnetic reconnection in solar flares and corona, and present unified model of flares on the basis of these new Yohkoh observations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Current state of the problem of solar flares: New observations and new models

A review of current questions related to the problem of large solar flares is given. The basic physical principles applied in numerical simulation of flares are presented and illustrated. The main attention is given to the phenomenon of magnetic reconnection in large-scale current layers at separators of magnetic field in the corona. This phenomenon is demonstrated within the framework of the Rainbow topological model. The model provides the possibility of explaining specific features of large-scale reconnection as a physical process that makes it possible to accumulate large energy in the form of the magnetic energy of current layers before a flare and to quickly transform this energy to the kinetic energy of particles during a flare. The secondary effects in the solar atmosphere caused by energy fluxes from reconnecting current layers are also discussed. These consequences of the primary energy release are responsible for the flare pattern observed in X-ray, optical, UV, and other spectral ranges.     

Current sheet models of solar flares

Current sheets have been suggested as the site for flare energy release because they can convert magnetic energy very rapidly into both heat and directed plasma energy. Also they contain electric fields with the potential of accelerating particles to high energies.The basic properties of current sheets are first reviewed. For instance, magnetic flux may be carried into a current sheet and annihilated. An exact solution for such a process in an infinitely long sheet has been found; it describes the annihilation of fields which are inclined at any angle, not just 180°. Moreover, field lines which are expelled from the ends of a current sheet can be described as having been reconnected. The only workable model for fast reconnection in the solar atmosphere, namely Petschek's mechanism, has recently been put on a firm foundation; it gives a reconnection rate which depends on the electrical conductivity but is typically a tenth or a hundredth of the Alfvén speed. A current sheet may be formed when the sources of an initially potential field start to move; a simple analytic technique for finding the position and shape of such a sheet in two dimensions now exists. Finally, a sheet with no transverse magnetic field component is subject to the tearing-mode instability, which rapidly produces a series of loops in the field.The main ways in which current sheets have been used for solar flare models is described. Syrovatskii's mechanism relies on the increase of the electric current density during the formation of a sheet, to a value in excess of the critical value j ^* for the onset of microinstabilities. But Anzer has recently demonstrated that the critical value is most unlikely to be reached during the initial formation process. Sturrock, on the other hand, has advocated the occurrence of the tearing-mode instability in an open streamer-like configuration (which may result from the eruption of a force-free field). But recent observations do not point to that as the relevant configuration. Rather, they suggest that flares are triggered by the emergence of new magnetic flux from below the solar photosphere. This has led Heyvaerts, Priest, and Rust (1976) to propose a new emerging flux model, according to which, as more and more flux emerges, so reconnection occurs, producing some preflare heating. When the current sheet reaches such a height (around the transition region) that its current density exceeds j ^*, then the impulsive phase of the flare is triggered. The main phase is caused by an enhanced level of magnetic energy conversion in a turbulent current sheet. The type of flare depends on the magnetic environment in which the emerging flux finds itself. A surge flare results if the flux appears near a strong unipolar region such as a simple sunspot, whereas a two ribbon flare may be produced by flux emergence near an active region filament, in which case the main phase energy is released from the field that surrounds the filament.     

太阳爆发过程中的大尺度磁重联电流片:理论和观测

从理论和观测两个方面来介绍和讨论出现在太阳爆发过程中的磁重联电流片及其物理本质和动力学特征。首先介绍在理论研究和理论模型中,磁重联电流片是如何在爆发磁结构当中形成并发展的,对观测研究有什么指导意义。然后介绍观测工作是从哪几个方面对理论模型预测的电流片进行证认和研究的。第三,将介绍观测研究给出了哪些过去所没有能够预期的结果,这些结果对深入研究耀斑一CME电流片以及其中的磁重联过程的理论工作有什么重要的、挑战性的意义。第四,讨论最新的与此有关的理论研究和数值实验。最后,对未来的研究方向和重要课题进行综述和展望。     

The shock-reprocessing model of electron acceleration in impulsive solar flares

We propose a new two-stage model for acceleration of electrons in solar flares. In the first stage, electrons are accelerated stochastically in a post-reconnection turbulent downflow. The second stage is the reprocessing of a subset of these electrons as they pass through a weakly compressive fast shock above the apex of the closed flare loop on their way to the chromosphere. We call this the 'shock-reprocessing' model. The model reproduces the sign and magnitude of the energy-dependent arrival time delays for both the pulsed and smooth component of impulsive solar flare X-rays, but requires either enhanced cooling or the presence of a loop-top trap to explain the concavity of the observed time delay energy relation for the smooth component. The model also predicts an emission site above the loop-top, as seen in the Masuda flare. The loop-top source distinguishes the shock-reprocessing model from previous models. The model makes testable predictions for the energy dependence of footpoint pulse strengths and the location and spectrum of the loop-top emission, and can account for the observed soft-hard-soft trend in the spectral evolution of footpoint emission. The model also highlights the concept that magnetic reconnection provides an environment which permits multiple acceleration processes. Which combination of processes operates within a particular flare may depend on the initial conditions that determine, for example, whether the reconnection downflow is turbulent or laminar. The shock-reprocessing model comprises one such combination.     

An electric-current description of solar flares

The presently prevailing theories of solar flares rely on the hypothetical presence of magnetic flux tubes beneath the photosphere and the two subsequent hypotheses, their emergence above the photosphere and explosive magnetic reconnection, converting magnetic energy carried by the flux tubes to solar flare energy. In this paper, we discuss solar flares from an entirely different point of view, namely in terms of power supply by a dynamo process in the photosphere. By this process, electric currents flowing along the magnetic field lines are generated and the familiar ‘force-free’ fields or the ‘sheared’ magnetic fields are produced. Upward field-aligned currents thus generated are carried by downward streaming electrons; these electrons can excite hydrogen atoms in the chromosphere, causing the optical Hα flares or ‘low temperature flares’. It is thus argued that as the ‘force-free’ fields are being built up for the magnetic energy storage, a flare must already be in progress.     

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.     

Energetics and Propagation of Coronal Mass Ejections in Different Plasma Environments

Based on previous work, we investigate the propagation of CMEs in a more realistic plasma environment than the isothermal atmosphere, and find that it is a slightly faster reconnection for flux ropes to break free. The average Alfven Mach number MA for the inflow into the reconnection site has to be at least 0.013 in order to give a plausible eruption (compared to MA = 0.005 for the isothermal atmosphere). Taking MA = 0.1, we find that the energy output and the electric field induced inside the current sheet match the temporal behavior inferred from the energetic, long duration, CME-associated X-ray events. The results indicate that catastrophic loss of equilibrium in the coronal magnetic field provides the most promising mechanism for major solar eruptions, and that the more energetic the eruption is, the earlier the associated flare peaks. The variation of the output power with the background field strength revealed by our calculations implies the poor correlation between slow CMEs and solar flares. Th     

Energetics of two-ribbon solar flares

A theory of two-ribbon solar flares is presented which identifies the primary energy release site with the tops of the flare loops. The flare loops are formed by magnetic reconnection of a locally opened field configuration produced by the eruption of a pre-flare filament. Such eruptions are commonly observed about 15 min prior to the flare itself. It is proposed that the flare loops represent the primary energy release site even during the earliest phase of the flare, i.e., the flare loops are in fact the flare itself.Based upon the supposition that the energy release at the loop tops is in the form of Joulean dissipation of magnetic energy at the rising reconnection site, a quantitative model of the energy release process is developed based upon an analytic reconnecting magnetic field geometry believed to represent the basic process. Predicted curves of energy density vs time are compared with X-ray observations taken aboard Skylab for the events of 29 July, 13 August, and 21 August in 1973. Considering the crudity of the model, the comparisons appear reasonable. The predicted field strengths necessary to produce the observed energy density curves are also reasonable, being in the range 100–1000 G.The National Center for Atmospheric Research is sponsored by the National Science Foundation.