Reconnection In Current Sheets Research Articles

Kinetic ballooning/interchange instability in a bent plasma sheet

We use Time History of Events and Macroscale Interactions during Substorms (THEMIS) and GOES observations to investigate the plasma sheet evolution on 28 February 2008 between 6:50 and 7:50 UT, when there developed strong magnetic field oscillations with periods of 100 s. Using multispacecraft analysis of the plasma sheet observations and an empirical plasma sheet model, we determine both the large‐scale evolution of the plasma sheet and the properties of the oscillations. We found that the oscillations exhibited signatures of kinetic ballooning/interchange instability fingers that developed in a bent current sheet. The interchange oscillations had a sausage structure, propagated duskward at a velocity of about 100 km/s, and were associated with fast radial electron flows. We suggest that the observed negative gradient of the ZGSM magnetic field component (∂BZ/∂X) was a free energy source for the kinetic ballooning/interchange instability. Tens of minutes later a fast elongation of ballooning/interchange fingers was detected between 6 and 16 RE downtail with the length‐to‐width ratio exceeding 20. The finger elongation ended with signatures of reconnection in an embedded current sheet near the bending point. These observations suggest a complex interplay between the midtail and near‐Earth plasma sheet dynamics, involving localized fluctuations in both cross‐tail and radial directions before current sheet reconnection.

The Flare-Energy Distributions Generated by Kink-Unstable Ensembles of Zero-Net-Current Coronal Loops

It has been proposed that the million degree temperature of the corona is due to the combined effect of barely-detectable energy releases, so called nanoflares, that occur throughout the solar atmosphere. Alas, the nanoflare density and brightness implied by this hypothesis means that conclusive verification is beyond present observational abilities. Nevertheless, we investigate the plausibility of the nanoflare hypothesis by constructing a magnetohydrodynamic (MHD) model that can derive the energy of a nanoflare from the nature of an ideal kink instability. The set of energy-releasing instabilities is captured by an instability threshold for linear kink modes. Each point on the threshold is associated with a unique energy release and so we can predict a distribution of nanoflare energies. When the linear instability threshold is crossed, the instability enters a nonlinear phase as it is driven by current sheet reconnection. As the ensuing flare erupts and declines, the field transitions to a lower energy state, which is modelled by relaxation theory, i.e., helicity is conserved and the ratio of current to field becomes invariant within the loop. We apply the model so that all the loops within an ensemble achieve instability followed by energy-releasing relaxation. The result is a nanoflare energy distribution. Furthermore, we produce different distributions by varying the loop aspect ratio, the nature of the path to instability taken by each loop and also the level of radial expansion that may accompany loop relaxation. The heating rate obtained is just sufficient for coronal heating. In addition, we also show that kink instability cannot be associated with a critical magnetic twist value for every point along the instability threshold.

CONDITIONS FOR PHOTOSPHERICALLY DRIVEN ALFVÉNIC OSCILLATIONS TO HEAT THE SOLAR CHROMOSPHERE BY PEDERSEN CURRENT DISSIPATION

A magnetohydrodynamic model that includes a complete electrical conductivity tensor is used to estimate conditions for photospherically driven, linear, non-plane Alfvenic oscillations extending from the photosphere to the lower corona to drive a chromospheric heating rate due to Pedersen current dissipation that is comparable to the net chromospheric net radiative loss of $\sim 10^7$ ergs-cm$^{-2}$-sec$^{-1}$. The heating rates due to electron current dissipation in the photosphere and corona are also computed. The wave amplitudes are computed self-consistently as functions of an inhomogeneous background (BG) atmosphere. The effects of the conductivity tensor are resolved numerically using a resolution of 3.33 m. The oscillations drive a chromospheric heating flux $F_{Ch} \sim 10^7 - 10^8$ ergs-cm$^{-2}$-sec$^{-1}$ at frequencies $\nu \sim 10^2 - 10^3$ mHz for BG magnetic field strengths $B \gtrsim 700$ G and magnetic field perturbation amplitudes $\sim 0.01 - 0.1$ $B$. The total resistive heating flux increases with $\nu$. Most heating occurs in the photosphere. Thermalization of Poynting flux in the photosphere due to electron current dissipation regulates the Poynting flux into the chromosphere, limiting $F_{Ch}$. $F_{Ch}$ initially increases with $\nu$, reaches a maximum, and then decreases with increasing $\nu$ due to increasing electron current dissipation in the photosphere. The resolution needed to resolve the oscillations increases from $\sim 10$ m in the photosphere to $\sim 10$ km in the upper chromosphere, and is proportional to $\nu^{-1/2}$. Estimates suggest that these oscillations are normal modes of photospheric flux tubes with diameters $\sim 10-20$ km, excited by magnetic reconnection in current sheets with thicknesses $\sim 0.1$ km.

Observed Aspects of Reconnection in Solar Eruptions

The observed magnetic field configuration and signatures of reconnection in the large solar magnetic eruptions that make major flares and coronal mass ejections and in the much smaller magnetic eruptions that make X-ray jets are illustrated with cartoons and representative observed eruptions. The main reconnection signatures considered are the imaged bright emission from the heated plasma on reconnected field lines. In any of these eruptions, large or small, the magnetic field that drives the eruption and/or that drives the buildup to the eruption is initially a closed bipolar arcade. From the form and configuration of the magnetic field in and around the driving arcade and from the development of the reconnection signatures in coordination with the eruption, we infer that (1) at the onset of reconnection the reconnection current sheet is small compared to the driving arcade, and (2) the current sheet can grow to the size of the driving arcade only after reconnection starts and the unleashed erupting field dynamically forces the current sheet to grow much larger, building it up faster than the reconnection can tear it down. We conjecture that the fundamental reason the quasi-static pre-eruption field is prohibited from having a large current sheet is that the magnetic pressure is much greater than the plasma pressure in the chromosphere and low corona in eruptive solar magnetic fields.

Debye-scale solitary structures measured in a beam-plasma laboratory experiment

Abstract. Solitary electrostatic pulses have been observed in numerous places of the magnetosphere such as the vicinity of reconnection current sheets, shocks or auroral current systems, and are often thought to be generated by energetic electron beams. We present results of a series of experiments conducted at the UCLA large plasma device (LAPD) where a suprathermal electron beam was injected parallel to a static magnetic field. Micro-probes with tips smaller than a Debye length enabled the detection of solitary pulses with positive electric potential and half-widths 4–25 Debye lengths (λDe), over a set of experiments with various beam energies, plasma densities and magnetic field strengths. The shape, scales and amplitudes of the structures are similar to those observed in space, and consistent with electron holes. The dependance of these properties on the experimental parameters is shown. The velocities of the solitary structures (1–3 background electron thermal velocities) are found to be much lower than the beam velocities, suggesting an excitation mechanism driven by parallel currents associated to the electron beam.

Dependence of anomalous resistivity on bulk drift velocity of electrons in the reconnecting current sheets in solar flares

Anomalous resistivity is critical for triggering fast magnetic reconnection in the nearly collisionless coronal plasma. Its nonlinear dependence on bulk drift velocity is usually assumed in MHD simulations. However, the mechanism for the production of anomalous resistivity and its evolution is still an open question. We numerically solved the one dimension Vlasov equation with the typical solar coronal parameters and realistic mass ratios to infer the relationship between anomalous resistivity and bulk drift velocity of electrons in the reconnecting current sheets as well as its nonlinear characteristics. Our principal findings are summarized as follows: 1) the relationship between the anomalous resistivity and bulk drift velocity of electrons relative to ions may be described as Ωm for vd/ve in the range of 1.4–2.0 and Ωm for vd/ve in the range of 2.5–4.5; 2) if drift velocity is just slightly larger than the threshold of ion-acoustic instability, the anomalous resistivity due to the wave-particle interactions is enhanced by about five orders as compared with classic resistivity due to Coulomb collisions. With the increase of drift velocity from 1.4ve to 4.5ve, the anomalous resistivity continues to increase 100 times; 3) in the rise phase of unstable waves, the anomalous resistivity has the same order as the one estimated from quasi-linear theory; after saturation of unstable waves, the anomalous resistivity decreases at least about one order as compared with its peak value; 4) considering that the final velocity of electrons ejected out of the reconnecting current sheet (RCS) decreases with the distance from the neutral point in the neutral plane, the anomalous resistivity decreases with the distance from the neutral point, which is favorable for the Petschek-like reconnection to take place.

A nanoflare distribution generated by repeated relaxations triggered by kink instability

Context: It is thought likely that vast numbers of nanoflares are responsible for the corona having a temperature of millions of degrees. Current observational technologies lack the resolving power to confirm the nanoflare hypothesis. An alternative approach is to construct a magnetohydrodynamic coronal loop model that has the ability to predict nanoflare energy distributions. Aims: This paper presents the initial results generated by such a model. It predicts heating events with a range of sizes, depending on where the instability threshold for linear kink modes is encountered. The aims are to calculate the distribution of event energies and to investigate whether kink instability can be predicted from a single parameter. Methods: The loop is represented as a straight line-tied cylinder. The twisting caused by random photospheric motions is captured by two parameters, representing the ratio of current density to field strength for specific regions of the loop. Dissipation of the loop's magnetic energy begins during the nonlinear stage of the instability, which develops as a consequence of current sheet reconnection. After flaring, the loop evolves to the state of lowest energy where, in accordance with relaxation theory, the ratio of current to field is constant throughout the loop and helicity is conserved. Results: The results suggest that instability cannot be predicted by any simple twist-derived property reaching a critical value. The model is applied such that the loop undergoes repeated episodes of instability followed by energy-releasing relaxation. Hence, an energy distribution of the nanoflares produced is collated. Conclusions: The final energy distribution features two nanoflare populations that follow different power laws. The power law index for the higher energy population is more than sufficient for coronal heating.

Formation of electron clouds during particle acceleration in a 3D current sheet

AbstractAcceleration of protons and electrons in a reconnecting current sheet (RCS) is investigated with the test particle and particle-in-cell (PIC) approaches in the 3D magnetic configuration including the guiding field. PIC simulations confirm a spatial separation of electrons and protons towards the midplane and reveal that this separation occur as long as protons are getting accelerated. During this time electrons are ejected into their semispace of the current sheet moving away from the midplane to distances up to a factor of 103 – 104 of the RCS thickness and returning back to the RCS. This process of electron circulation around the current sheet midplane creates a cloud of high energy electrons around the current sheet which exists as long as protons are accelerated. Only after protons gain sufficient energy to break from the magnetic field of the RCS, they are ejected to the opposite semispace dragging accelerated electrons with them. These clouds can be the reason of hard X-ray emission in coronal sources observed by RHESSI.

On the role of a nonscalar electron pressure in the collisionless magnetic reconnection

Collisionless tearing instability in a sheared force-free magnetic field is considered in the framework of electron magnetohydrodynamics. A rigorous analytical analysis demonstrates that the bulk inertia of electrons is the dominant reconnection mechanism in a sufficiently low-β plasma, when the reconnection current sheet width exceeds the electron gyroradius. Otherwise a fluidlike approach fails, and fully kinetic treatment of the problem is required. A recently raised issue of the role of the electron gyroviscous cancellation in collisionless reconnection is also addressed.

Particle acceleration in a reconnecting current sheet: PIC simulation

AbstractThe acceleration of protons and electrons in a reconnecting current sheet (RCS) is simulated with a particle-in-cell (PIC) 2D3V (two-dimensional in space and three-dimensional in velocity space) code for the proton-to-electron mass ratio of 100. The electromagnetic configuration forming the RCS incorporates all three components of the magnetic field (including the guiding field) and a drifted electric field. PIC simulations reveal that there is a polarization electric field that appears during acceleration owing to a separation of electrons from protons towards the midplane of the RCS. If the plasma density is low, the polarization field is weak and the particle trajectories in the PIC simulations are similar to those in the test particle (TP) approach. For the higher plasma density the polarization field is stronger and it affects the trajectories of protons by increasing their orbits during acceleration. This field also leads to a less asymmetrical abundance of ejected protons towards the midplane in comparison with the TP approach. For a given magnetic topology electrons in PIC simulations are ejected to the same semispace as protons, in contrast to the TP results. This happens because the polarization field extends far beyond the thickness of a current sheet. This field decelerates the electrons, which are initially ejected into the semispace opposite to the protons, returns them back to the RCS, and, eventually, leads to the electron ejection into the same semispace as protons. The energy distribution of the ejected electrons is rather wide and single-peaked, in contrast to the two-peak narrow-energy distribution obtained in the TP approach. In the case of a strong guiding field, the mean energy of the ejected electrons is found to be smaller than it is predicted analytically and by the TP simulations. The beam of accelerated electrons is also found to generate turbulent electric field in the form of Langmuir waves.

Electron acceleration in the turbulent reconnecting current sheets in solar flares

Context. We investigate the nonlinear evolution of the electron distribution in the presence of the strong inductive electric field in the reconnecting current sheets (RCS) of solar flares.

The effect of magnetic topology on particle acceleration in a three-dimensional reconnecting current sheet: a test-particle approach

AbstractElectron and proton acceleration by a drifted super-Dreicer electric field is investigated in a strongly compressed non-neutral reconnecting current sheet (NRCS). The guiding field is assumed to be constant within a reconnecting current sheet (RCS) and parallel to the direction of the drifted electric field. The other two magnetic field components, transverse and tangential, are considered to vary exponentially and linearly with distances from the X-nullpoint. The proton and electron energy spectra are calculated numerically in a model RCS with different magnetic field topologies by solving an equation of motion in the test-particle approach with some test with a particle-in-cell (PIC) approach. Three kinds electric field generated inside a RCS are considered: a drifted electric field caused by the plasma inflows formed during a magnetic reconnection process; a polarization electric field induced by the accelerated protons and electrons; and a turbulent electric field induced by instabilities generated by accelerated particles. Electron and proton densities, and energy spectra inside a RCS and at ejection are found to be strongly affected by the magnetic field topology: for stronger magnetic fields the spectra are softer having a small higher-energy cutoff while for weaker magnetic fields the spectra are harder with much larger upper cutoff energies. Depending on the magnetic component ratios and drifted electric field magnitude, particles are found to be ejected either as quasi-thermal flows with very high temperatures or as focused power-law beams. A polarization field is found to reduce the acceleration time inside a RCS and to increase the energy gained by particles at acceleration by a pure drifted electric field by a few orders of magnitude. The turbulent electric field induced by the two beam instabilities of the same kind of particles leads to a significant increase in the number of particles with higher energies resulting in a flattening of their energy spectra.

Particle Interactions with Single or Multiple 3D Solar Reconnecting Current Sheets

The acceleration of charged particles (electrons and protons) in flaring solar active regions is analyzed using numerical experiments. The acceleration is modeled as a stochastic process taking place by the interaction of the particles with local magnetic reconnection sites via multiple steps. Two types of local reconnecting topologies are studied: the Harris-type and the X-point. A formula for the maximum kinetic energy gain in a Harris-type current sheet, found in a previous work of ours, fits well the numerical data for a single step of the process. A generalization is then given approximating the kinetic energy gain through an X-point. In the case of the multiple step process, in both topologies the kinetic energy distribution of the particles is found to acquire a practically invariant form after a small number of steps. This tendency is interpreted theoretically. Other characteristics of the acceleration process are given, such as the mean acceleration time and the pitch angle distributions of the particles.

Fast magnetosonic waves launched by transient, current sheet reconnection

A model is investigated describing the resistive dissipation of a finite, two-dimensional current sheet subject to suddenly enhanced resistivity. The resistivity rapidly diffuses the current to a distance where it couples to fast magnetosonic modes. The current then propagates away as a sheath moving at the local Alfvén speed. A current density peak remains at the X-point producing a steady electric field independent of the resistivity. This transfers flux across the separatrix at a rate consistent with the external wave propagation. The majority of the magnetic energy stored by the initial current sheet is converted into kinetic energy, far from the reconnection site, during the fast mode propagation.

The effect of the longitudinal propagating waves on the electron acceleration in the reconnecting current sheet

Based upon the most efficient electron acceleration near the midplane of 3D non-neutral driven reconnecting current sheet (RCS) and the electrostatic wave excitation by the drift Maxwellian distribution of electrons in Vlasov simulation, we assume that the electrostatic waves mainly propagate opposite to the reconnecting electric field and investigated how these waves affect the electron acceleration. The main results are: (1) when the electron’s velocity equals to the phase speed of the waves, they will be trapped and have the different accelerating characteristics from the untrapped electrons through solving the momentum equations of electrons analytically; (2) the test particle simulations further prove that the number of the energetic electrons decreases with the increasing intensity of unstable waves, and the distribution of the energetic electrons takes on the double power-law.

Particle distributions and X-ray spectra in single or multiple solar current sheets

The acceleration of charged particles in a site of magnetic reconnection is analysed by detailed numerical simulations. Single or multiple encounters of the particles with Harris-type reconnecting current sheets (RCSs) are modelled as an overall stochastic process taking place within an active region. RCS physical parameters are selected in a parameter space relevant to solar flares. Initially, the charged particles form a thermal (Maxwellian) distribution corresponding to coronal temperature � 2 × 10 6 K. Our main goal is to investigate how the acceleration process changes the shape of the particles’ kinetic energy distribution. The evolution of the kinetic energy distribution, calculated numerically after one encounter of the particles with a single RCS, is found to be in good agreement with our previously published analytical formulae. In the case of consecutive encounters, we find that the kinetic distribution tends to converge to a practically invariant form after a relatively small number of encounters. We construct a discrete stochastic process that reproduces the numerical distributions and we provide a theoretical interpretation of the asymptotic convergence of the energy distribution. We finally compute the theoretical X-ray spectra that would be emitted by the simulated particles in a thick target model of radiation.

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)