Reconnection In Current Sheets Research Articles

Particle acceleration and radiation in flaring complex solar active regions modeled by cellular automata

Context. We study the acceleration and radiation of electrons and ions interacting with multiple small-scale dissipation regions resulting from the magnetic energy release process. Aims. We aim to calculate the distribution functions of the kinetic energy of the particles and the X-ray spectra and γ-ray fluxes produced by the accelerated particles. Methods. The evolution of the magnetic energy released in an active region is mimicked by a cellular automaton model based on the concept of self-organized criticality. Each burst of magnetic energy release is associated with a reconnecting current sheet (RCS) in which the particles are accelerated by a direct electric field. Results. We calculate the energy gain of the particles (ions and electrons) for three different magnetic configurations of the RCS after their interactions with a given number of RCS. We finally compare our results with existing observations. Conclusions. The results of our simulation can reproduce several properties of the observations such as variable electron and ion energy contents and γ-ray line ratio. Even if very flat X-ray spectra have been reported in a few events, the X-ray spectra produced in this model are too flat when compared to most X-ray observations.

Coronal Observations of CMEs

CMEs have been observed for over 30 years with a wide variety of instruments. It is now possible to derive detailed and quantitative information on CME morphology, velocity, acceleration and mass. Flares associated with CMEs are observed in X-rays, and several different radio signatures are also seen. Optical and UV spectra of CMEs both on the disk and at the limb provide velocities along the line of sight and diagnostics for temperature, density and composition. From the vast quantity of data we attempt to synthesize the current state of knowledge of the properties of CMEs, along with some specific observed characteristics that illuminate the physical processes occurring during CME eruption. These include the common three-part structures of CMEs, which is generally attributed to compressed material at the leading edge, a low-density magnetic bubble and dense prominence gas. Signatures of shock waves are seen, but the location of these shocks relative to the other structures and the occurrence rate at the heights where Solar Energetic Particles are produced remains controversial. The relationships among CMEs, Moreton waves, EIT waves, and EUV dimming are also cloudy. The close connection between CMEs and flares suggests that magnetic reconnection plays an important role in CME eruption and evolution. We discuss the evidence for reconnection in current sheets from white-light, X-ray, radio and UV observations. Finally, we summarize the requirements for future instrumentation that might answer the outstanding questions and the opportunities that new space-based and ground-based observatories will provide in the future.

Magnetic Energy Release during the 2002 September 9 Solar Flare

We study the magnetic energy release during the 2002 September 9 flare using the high-cadence (40 ms) Hα filtergram at Big Bear Solar Observatory (BBSO), along with hard X-ray and microwave data from the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) and the Owens Valley Solar Array (OVSA), respectively. We take the Poynting vector approach with the standard two-dimensional geometry of the reconnecting current sheet (RCS) but suggest a new technique to infer the area of the RCS, in order to complete the magnetic energy calculation entirely with observed quantities. We found five peaks of impulsive magnetic energy release, concentrated within 10-30 s periods, that are episodic with the peaks of the hard X-ray light curve. The maximum amount of energy released per peak reaches ~2.6 × 1030 ergs s-1, and the electron energy deposition rate derived from the RHESSI spectra falls into the range of 10%-80% of the magnetic energy release rate. We briefly discuss this result in comparison with other studies thus far made toward understanding of the magnetic reconnection in solar flares and suggest the pulsating current sheet model as the most plausible interpretation of our result.

Cancelling magnetic feature and filament activation

AbstractWe report in this paper the analysis of the evolution of a magnetic fragment observed in NOAA 9445 on 5 May, 2001. This magnetic fragment emerged laterally to a filament which later split into two parts. The bifurcation site coincided with the magnetic fragment location and the part of the filament which split was later destabilized and a flare occurred. The magnetic flux variations in the magnetic fragment and in the surrounding area were analyzed and, considering their trends and other observational signatures (Hα brightenings and associated plasma motions), we could infer that it was a cancelling magnetic feature (CMF).We determined some geometrical and physical parameters of the CMF (area, magnetic flux variation, cancellation speed and flux cancellation rate) using high resolution magnetograms taken by BBSO. We compared the observed parameters of the CMF with the parameters of low‐lying reconnection current sheets given in the model proposed by Litvinenko (1999) and found good agreement between observed and theoretical values. Therefore, we conclude that a low‐lying magnetic reconnection process might be the cause of the filament activation. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Regular and chaotic dynamics in 3D reconnecting current sheets

We consider the possibility of particles being injected at the interior of a reconnecting current sheet (RCS), and study their orbits by dynamical systems methods. As an example we consider orbits in a 3D Harris type RCS. We find that, despite the presence of a strong electric field, a ‘mirror’ trapping effect persists, to a certain extent, for orbits with appropriate initial conditions within the sheet. The mirror effect is stronger for electrons than for protons. In summary, three types of orbits are distinguished: (i) chaotic orbits leading to escape by stochastic acceleration, (ii) regular orbits leading to escape along the field lines of the reconnecting magnetic component, and (iii) mirror-type regular orbits that are trapped in the sheet, making mirror oscillations. Dynamically, the latter orbits lie on a set of invariant KAM tori that occupy a considerable amount of the phase space of the motion of the particles. We also observe the phenomenon of ‘stickiness’, namely chaotic orbits that remain trapped in the sheet for a considerable time. A trapping domain, related to the boundary of mirror motions in velocity space, is calculated analytically. Analytical formulae are derived for the kinetic energy gain in regular or chaotic escaping orbits. The analytical results are compared with numerical simulations.

The Effects of Transverse Magnetic Field and Density Variations on the Particle Energy Spectra in a Reconnecting 3D Current Sheet

Electron and proton acceleration by a super-Dreicer electric field is further investigated in a non-neutral reconnecting current sheet (RCS) with a variable plasma density. The tangential Bz and transverse magnetic field components Bx are assumed to vary with the distances x and z from the X nullpoint linearly and exponentially, respectively; the longitudinal component (a ‘guiding field’) is accepted constant. Particles are found to gain a bulk of their energy in a thin region close to the X nullpoint where the RCS density increases with z exponentially with the index λ and the tangential magnetic field Bx also increases with z exponentially with the index α. For the RCS with a constant density (λ = 0), the variations of the tangential magnetic field lead to particle power-law energy spectra with the spectral indices γ1 being dependent on the exponent α as: \(\gamma_1 = 1 + \frac{1}{2\alpha}\) for protons and \(\gamma_1 = 1+ \frac{1}{\alpha}\) for electrons in a strong guiding field (β > 10−2) and \(\gamma_1 =\frac {1} 2 (1 +\frac{1}{\alpha})\) for electrons in a moderate or weak guiding field (β > 10−4). For the RCS with an exponential density increase in the vicinity of the X nullpoint (λ≥ 0) there is a further increase of the resulting spectral indices γ that depends on the density exponent index λ as \(\gamma = \gamma_1 +\frac{\lambda}{2\alpha}\) for protons and for electrons in weaker guiding fields and as \(\gamma = \gamma_1 + \frac{\lambda}{\alpha}\) for electrons in stronger guiding fields. These dependencies can explain a wide variety (1.5–10) of particle spectral indices observed in solar flares by the variations of a magnetic field topology and physical conditions in a reconnecting region. This can be used as a diagnostic tool for the investigation of the RCS dynamics from the accelerated particle spectra found from hard X-ray and microwave emission.

Particle dynamics in 3-D reconnecting current sheets in the solar atmosphere

The orbits of charged particles (electrons and protons), in a Harris-type 3D field topology of a reconnecting current sheet (RCS), are analyzed by dynamical systems methods. The focus is on values of the magnetic and electric fields relevant to RCSs in the solar atmosphere. First, a perturbative form of the equations of motion is used to determine the stability perpendicularly to the plane of reconnection, which is crucial in the efficiency of the RCS as an accelerator. The problem is shown to correspond to a case of “parametric resonance”. The orbits are then studied with the complete form of the equations of motion. These can be reduced to a two degrees of freedom Hamiltonian nonlinear system by exploiting the existence of an additional integral of motion besides the energy. The orbits are studied analytically by normal form theory. Regular and chaotic orbits are identified by the use of appropriate Poincare surfaces of section. The kinetic energy gain for escaping particles is calculated as a function of the initial conditions of injection of an orbit in the sheet. Formulae relating the kinetic energy gain to the physical parameters of the sheet and the initial conditions of the orbits are given both for electrons and protons.

Coronal Heating at Separators and Separatrices

Several ways have been proposed for heating the solar corona by magnetic reconnection in current sheets, depending on the nature of both the coronal magnetic field and the photospheric driving. Two ways that have recently been considered involve the formation of such current sheets either along separatrices (surfaces that separate topologically distinct regions) or along separators (intersections of separatrices linking one null point to another). The effect of slow photospheric motions on complex coronal magnetic configurations will in general be to generate three forms of electric current, namely, nonsingular distributed currents, singular currents on separatrices and singular currents on separators. These currents are not mutually exclusive but will in general coexist in the same configuration. The aim of this paper is to compare energy storage and heating that occurs at separatrices and separators. We use reduced MHD to model coronal loops that are much longer than they are wide, and we construct a series of examples for the formation of current sheets along separatrices and separators. We deduce that coronal heating is of comparable importance at separatrices and separators. Separatrices are twice as effective for observed small footpoint motions, while separators are twice as effective in the initial build-up of a new flux domain.

Coalescence of two magnetic flux ropes via collisional magnetic reconnection

Quasi-two-dimensional coalescence of two parallel cylindrical flux ropes and the development of three-dimensional merged structures are observed and studied in the reconnection scaling experiment [Furno et al., Rev. Sci. Instrum. 74, 2324 (2003)]. These experiments were conducted in a collisional regime with very strong guide magnetic field (Bguide⪢Breconnection), which can be adjusted independently of plasma density, current density, and temperature. During initial coalescence, a reconnection current sheet forms between the two flux ropes, and the direction of the current is opposite to the flux rope currents. The measured current sheet thickness is larger than the electron skin depth but smaller than the ion skin depth. Furthermore, the thickness does not vary for three different values of the strong external guide field. It is shown that the geometry of the observed current sheet is consistent with the Sweet–Parker model using a parallel Spitzer resistivity. The flux ropes eventually become kink unstable due to increasing current and fast-gated camera images show the development of three-dimensional merged structures.

Magnetic Reconnection Rate and Flux‐Rope Acceleration of Two‐Ribbon Flares

Forbes & Lin derived simple equations to link the properties of magnetic reconnection in the corona to observed signatures of solar flares. We measured the photospheric magnetic fields and the flare ribbon separation speeds then applied these equations to derive two physical terms for the magnetic reconnection rates: the rate of magnetic flux change rec involved in magnetic reconnection in the low corona and the electric field Erec inside the reconnecting current sheet (RCS) that is generated during magnetic reconnection. The central interest in this work is to investigate and quantify the statistical correlation between the magnetic reconnection rate and the corresponding flux-rope acceleration. From a sample of 13 well-observed two-ribbon flares, which are associated with filament eruptions or coronal mass ejections (CMEs), the acceleration of erupting filaments is found mainly in the range of 0.05-0.4 km s-2, up to 3 km s-2. Correspondingly, the maximum Erec and rec mostly occur in the range of 0.2-5 V cm-1 and 0.5-6 × 1018 Mx s-1, respectively. A positive and strong correlation is found with a cross-correlation coefficient of 0.94-0.97 between the magnetic reconnection rate and the acceleration of erupting filaments that represents the early stages of flux-rope eruptions in the low corona. However, the inferred reconnection rate is not correlated to the acceleration of CME fronts measured by the Large Angle and Spectrometric Coronagraph (LASCO) observations in the range of 2-30 solar radii (the correlation coefficient is less than 0.2). A reasonable correlation is found between the reconnection rate and the velocity of CMEs, which indicates the cumulative acceleration of CMEs from the low corona to the LASCO C2 field of view. The temporal correlation between the magnetic reconnection rate and the flare nonthermal emissions has also been verified in this paper.

Energy spectra of particles accelerated in a reconnecting current sheet with the guiding magnetic field

Electron and proton acceleration by a super-Dreicer electric field is investigated in the nonneutral reconnecting current sheet (RCS) with a non-zero longitudinal component of the magnetic field (‘guiding field’). The guiding field is assumed parallel to the direction of electric field and constant within an RCS. The other two magnetic field components, transverse and tangential, are considered to vary with distances from the X null point of an RCS. The proton and electron energy spectra are calculated numerically from a motion equation using the test particle approach for model RCSs with constant and variable densities. In the presence of a strong or moderate guiding field, protons were found fully or partially separated from electrons at ejection from an RCS into the opposite, ‘electron’ and ‘proton’, semiplanes. In the case of a weak guiding field, both protons and electrons are ejected symmetrically in equal proportions as neutral beams. The particles ejected from an RCS with a very weak or very strong guiding field have power-law energy spectra with spectral indices of about 1.5 for protons and 2.0 for electrons. For a moderate guiding field, the energy spectra of electrons ejected into the opposite semiplanes are mixed, i.e. in the ‘electron-dominated’ semiplane power-law energy spectra for electrons and thermal-like for protons, while in the ‘proton’ semiplane they are symmetrically

Proton versus electron heating in solar flares

Proton and electron heating of a flaring atmosphere is compared in a kinetic approach for the particles ejected from a non-neutral reconnecting current sheet (RCS) located above the top of reconnected flaring loops in a two-ribbon flare. Two kinds of high-energy particles are considered: particles accelerated by a super-Dreicer electric field and those ejected from the reconnection region as neutral outflows, or separatrix jets. The beam electrons are assumed to deposit their energy in Coulomb collisions and Ohmic heating of the ambient plasma particles by the electric field induced by the precipitating beams. The protons are assumed to deposit their energy in generation of kinetic Alfvén waves (KAWs), which, in turn, dissipate due to Cherenkov resonant scattering on the ambient plasma electrons. The beam electrons are found to provide a fast (within a few tenth of a second) heating of the atmosphere that is well spread in depth from the corona to the lower chromosphere. The protons are shown to precipitate to the lower atmosphere much slower (up to few seconds for beam and up to 10–20 s for slow jets). Slow jet protons provide heating of the two compact regions: the first located at the top of a flaring loop just below the RCS, and the second one appearing at the transition region (TR) and upper chromosphere; fast beam protons deposit their energy in the TR and chromosphere only.

Near-Infrared Observations at 1.56 Microns of the 2003 October 29 X10 White-Light Flare

We present high-resolution observations of an X10 white-light flare in solar NOAA Active Region 10486 obtained with the Dunn Solar Telescope (DST) at the National Solar Observatory/Sacramento Peak on 2003 October 29. Our investigation focuses on flare dynamics observed in the near-infrared (NIR) continuum at 1.56 μm. This is the first report of a white-light flare observed at the opacity minimum. The spatial resolution was close to the diffraction limit of the 76 cm aperture DST. The data benefited from a newly developed high-order adaptive optics system and a state-of-the-art NIR complex metal oxide semiconductor focal plane array. In addition, we compared hard X-ray (HXR) data of RHESSI and magnetograms of the Michelson Doppler Imager on board SOHO with the NIR continuum images. Although it is still possible that some high-energy electrons penetrate deep to this layer, a more likely explanation of the observed emission is back-warming. During the impulsive phase of the flare, two major flare ribbons moved apart, which were both temporally and spatially correlated with RHESSI HXR ribbons. The maximum intensity enhancement of the two flare ribbons is 18% and 25%, respectively, compared to the quiet-Sun NIR continuum. The separation speed of the ribbons is about 38 km s-1 in regions with weak magnetic fields and decreases to about 19 km s-1, where stronger magnetic fields are encountered. The derived electric field in reconnection current sheet Ec is of the order of 45 V cm-1 during the flare maximum.

Particle Acceleration Asymmetry in a Reconnecting Nonneutral Current Sheet

The acceleration of electrons and protons caused by a super-Dreicer electric field directed along the longitudinal component By of the magnetic field is investigated. The three-component magnetic field in a nonneutral current sheet occurring at the top of the reconnecting flaring loops on the charged particle trajectories and energies is considered. Particle trajectories in the reconnecting current sheet (RCS) and their energy spectra at the point of ejection from the RCS are simulated from the motion equation for different sheet thicknesses. A super-Dreicer electric field of the current sheet is found to accelerate particles to coherent energy spectra in a range of 10-100 keV for electrons and 100-400 keV for protons with energy slightly increasing with the sheet thickness. A longitudinal By component was found to define the gyration directions of particles with opposite charges toward the RCS midplane, i.e., the trajectory symmetry. For the ratio By/Bz < 10-6 the trajectories are fully symmetric, which results in particle ejection from an RCS as neutral beams. For the ratio By/Bz > 10-2 the trajectories completely lose their symmetry toward the RCS midplane, leading to the separation of particles with opposite charges into the opposite halves from an RCS midplane and the following ejection into different legs of the reconnecting loops. For the intermediate values of By/Bz the trajectories are partially symmetric toward the midplane, leading to electrons prevailing in one leg and protons in the other.

Magnetic Reconnection and Mass Acceleration in Flare–Coronal Mass Ejection Events

An observational relationship has been well established among magnetic reconnection, high-energy flare emissions and the rising motion of erupting flux ropes. In this paper, we verify that the rate of magnetic reconnection in the low corona is temporally correlated with the evolution of flare nonthermal emissions in hard X-rays and microwaves, all reaching their peak values during the rising phase of the soft X-ray emission. In addition, however, our new observations reveal a temporal correlation between the magnetic reconnection rate and the directly observed acceleration of the accompanying coronal mass ejection (CME) and filament in the low corona, thus establishing a correlation with the rising flux rope. These results are obtained by examining two well-observed two-ribbon flare events, for which we have good measurements of the rise motion of filament eruption and CMEs associated with the flares. By measuring the magnetic flux swept through by flare ribbons as they separate in the lower atmosphere, we infer the magnetic reconnection rate in terms of the reconnection electric field Erec inside the reconnecting current sheet (RCS) and the rate of magnetic flux convected into the diffusion region. For the X1.6 flare event, the inferred Erec is ~5.8 V cm-1 and the peak mass acceleration is ~3 km s-2, while for the M1.0 flare event Erec is ~0.5 V cm-1 and the peak mass acceleration is 0.2-0.4 km s-2.

Interpretation of a complex CME event: Coupling of scales in multiple flux systems

Using multi-wavelength observations, in particular in imagery, recorded by SOHO/LASCO-MDI, Yohkoh/SXT, the Meudon spectroheliograph and the Nancay radioheliograph, and performing a linear force-free field extrapolation, we analyzed the triggering and the development of a complex eruptive event in the chromosphere and in the corona. This event included an X1 class flare and an eruptive filament within an active region, but it also involved a whole active complex spanning over 40 degrees of heliolongitude. It resulted in a fast and decelerating partial halo CME, associated with a Moreton wave and a complex series of metric, decimetric and microwave radio bursts. The presence of a coronal null point combined with the occurrence of two distant and nearly simultaneous radio sources give strong arguments in favor of the generalized breakout model for the triggering of the eruption. The observations are consistent with the occurrence of magnetic reconnection at the null point three minutes before the start of the eruption, which is consistent with other observed CME precursors. The analysis of the subsequent development of the event suggests that large interconnecting loops were ejected together with the CME, and that secondary reconnections at low altitude probably occurred remotely in the active complex. Our results show that the triggering and evolution of this complex CME involved multiple magnetic flux systems over a large coronal volume surrounding the flare site, and that it resulted from the coupling of scales from narrow reconnection current sheets to very large inter active region magnetic connections.

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.

Magnetic Reconnection Solutions Based on a Generalized Ohm's law

It is known that exact magnetic reconnection solutions can be constructed for collisionally dominated resistive plasmas. In this paper we refine the collisional resistive description by invoking an Ohm's law that includes Hall current and plasma inertial contributions. We first demonstrate the surprising fact that the analytic treatment of both two and three dimensional current sheet reconnection remains valid for the generalized Ohm's law description. A discussion of planar reconnection shows that while the influence of inertial effects is generally small, the Hall current is likely to be important in most physically realistic plasma regimes, even for turbulent current sheet models. In particular, by influencing the magnetic and electric fields within the current sheet, the Hall current can be expected to have a strong influence on the particle acceleration capabilities of magnetic merging solutions. We also address the extent to which the new solutions alleviate the need for enhanced, anomalous resistivities to moderate the large current densities that arise in collisional resistive merging.

Elemental Abundances and Post–Coronal Mass Ejection Current Sheet in a Very Hot Active Region

A peculiar young active region was observed in 1998 March with the Ultraviolet Coronagraph Spectrometer (UVCS) over the southwest limb. The spectra showed strong emission in the λ974 line of fluorine-like iron, [Fe XVIII], which is brightest at an electron temperature of 106.8 K, and lines of Ne IX, [Ca XIV], [Ca XV], Fe XVII, [Ni XIV], and [Ni XV]. It is the only active region so far observed to show such high temperatures 0.5 R☉ above the solar limb. We derive the emission measure and estimate elemental abundances. The active region produced a number of coronal mass ejections (CMEs). After one CME on March 23, a bright post-CME arcade was seen in EIT and Yohkoh/SXT images. Between the arcade and the CME core, UVCS detected a very narrow, very hot feature, most prominently in the [Fe XVIII] line. This feature seems to be the reconnection current sheet predicted by flux rope models of CMEs. Its thickness, luminosity, and duration seem to be consistent with the expectations of the flux rope models for CME. The elemental abundances in the bright feature are enhanced by a factor of 2 compared to those in the surrounding active region, i.e., a first ionization potential enhancement of 7-8 compared to the usual factor of 3-4.

The characteristics of microwave burst source and energy budget in disappering filament

On 7 May, 1992 a complex event with the disappearence of a filament and a two ribbon flare was well observed in Hα filtergrams, Yorkoh soft X-ray data, and radio data. This event is studied by using the flare-filament current model. The momentum equation and the energy equation of the filament current have been solved. By using the measured time variation of the filament height, the corresponding evolution of the current intensity and the total energy of the current filament were computed. The magnetic field strength and the energy flux of energetic electrons in the source region of microwave bursts have also been estimated by using the microwave spectrum. During the main phase, the mean magnetic strength and the energy flux of energetic electrons are about 300–400G and 1 × 10 11 erg cm −2s −1, respectively. By using these physical parameters, the energy budget has been made. These results show that the flare of 7 May, 1992 may be the result of reconnection of current sheet beneath the disappearing filament and the flare energy is provided by current filament.