Reconnection Regime Research Articles

Hall assisted forced magnetic reconnection

The role of the Hall effect in forced magnetic reconnection is investigated analytically for the so-called Taylor problem. In the latter, a tearing stable slab plasma equilibrium, which is chosen here to be a simple magnetic field reversal, is subjected to a small-amplitude boundary deformation that drives magnetic reconnection (hence the adjective “forced” ) at the neutral surface within the plasma. It is shown that such reconnection becomes substantially accelerated by the Hall effect when the nondimensional parameter di=(c∕ωpi)∕a exceeds S−1∕5. Here, c∕ωpi is the ion inertial skin depth, a is the width of the plasma slab, and S≫1 is the Lundquist number of a highly conducting plasma. Two different types of external perturbation are considered. In the case of continuous quasistatic driving, with a frequency ω such that ωτA≪1, τA being the Alfvén transit time, various reconnection regimes are identified. The corresponding heating rates, which are determined by the parameters di, S, and ωτA, are derived. In the case of a “one-off” reconnection event, we demonstrate when and how the transition from the Hall regime to the magnetohydrodynamic regime occurs in the course of the reconnection process. It is found that the peak instantaneous reconnection rate scales as dψ1(0)∕dt∼di1∕2S−1∕2(B0δ0∕τA), where ψ1(0) is the reconnected magnetic flux, B0 is the magnetic field strength, and δ0 is the amplitude of the boundary deformation.

Jets of energetic particles generated by magnetic reconnection at a three-dimensional magnetic null

AbstractMagnetic reconnection is a candidate mechanism for particle acceleration in a variety of astrophysical contexts. It is now widely accepted that reconnection plays a key role in solar flares, and reconstructions of coronal magnetic fields indicate that three-dimensional (3D) magnetic null points can be present during flares. We investigate particle acceleration during spine reconnection at a 3D magnetic null point, using a test particle numerical code. We observe efficient particle acceleration and find that two energetic populations are produced: a trapped population of particles that remain in the vicinity of the null, and an escaping population, which leave the configuration in two symmetric jets along field lines near the spine. While the parameters used in our simulation aim to represent solar coronal plasma conditions of relevance for acceleration in flares, the fact that the 3D spine reconnection configuration naturally results in energetic particle jets may be of importance in other astrophysical situations. We also compare the results obtained for the spine reconnection regime with those for the other possible mode of 3D reconnection, fan reconnection. We find that in the latter case energetic particle jets are not produced, though acceleration is observed.

Physical origin of the quadrupole out-of-plane magnetic field in Hall-magnetohydrodynamic reconnection

A quadrupole pattern of the out-of-plane component of the magnetic field inside a reconnection region is seen as an important signature of the Hall-magnetohydrodynamic regime of reconnection. It has been first observed in numerical simulations and just recently confirmed in the Magnetic Reconnection Experiment [Y. Ren, M. Yamada, S. Gerhardt, H. Ji, R. Kulsrud, and A. Kuritsin, Phys. Rev. Lett. 95, 055003 (2005)] and also seen in spacecraft observations of Earth’s magnetosphere. In this study, the physical origin of the quadrupole field is analyzed and traced to a current of electrons that flows along the lines in and out of the inner reconnection region to maintain charge neutrality. The role of the quadrupole magnetic field in the overall dynamics of the reconnection process is discussed. In addition, the bipolar poloidal electric field is estimated and its effect on ion motions is emphasized.

Jets of Energetic Particles Generated by Magnetic Reconnection at a Three-dimensional Magnetic Null

We investigate particle acceleration during magnetic reconnection at a three-dimensional magnetic null point, in the spine reconnection regime, using a test particle numerical code. We observe efficient particle acceleration and find that two energetic populations are produced: a trapped population of particles that remain in the vicinity of the null and an escaping population, which leave the configuration in two symmetric jets along field lines near the spine. While the parameters used in our simulation aim to represent solar coronal plasma conditions of relevance for acceleration in flares, the fact that the reconnection configuration we studied naturally results in energetic particle jets may be of importance in other astrophysical contexts.

On magnetic reconnection regimes and associated three‐dimensional asymmetries: Hybrid, Hall‐less hybrid, and Hall‐MHD simulations

Magnetic reconnection in a plane current sheet is investigated in both two and three dimensions, using three different types of simulation codes, Hall MHD, hybrid (electron fluid, kinetic ions), and a new code called Hall‐less hybrid. The latter code, which is similar to the hybrid code but has the Hall term removed, enables us to clarify the differences between kinetic ion and Hall MHD approaches. The major findings of this research are (1) Sweet‐Parker regime of reconnection cannot be maintained and does not reach a steady state in a kinetic plasma for physically interesting parameter regimes. (2) Fast asymptotic reconnection rate of 0.15VA0B0 is obtained both in the hybrid and Hall‐less hybrid simulations with outflow boundaries. VA0 and B0 are the Alfvén velocity and magnetic field strength in the upstream region. This finding has two immediate implications. First, ion kinetics are sufficient to lead to fast reconnection even in the absence of the Hall term, and second, explanation of fast reconnection in terms of quadratic disperion of whistlers needs to be reconsidered, as whistlers are dispersionless in Hall‐less hybrid limit. (3) Unlike in MHD, diffusion region is different in size that the region of localized resistivity. (4) While both Hall and hybrid codes show that reconnection is inherently asymmetric in three dimensions, there are differences in the nature of the asymmetry. In Hall MHD we show that the X‐line grows in the direction of the electron drift, propagating as a (reconnection) wave because the current is carried by electrons, although the wave direction can change in the presence of a substantial ion flow. However, in the hybrid simulations here, as is the case for typical conditions at the magnetopause and magnetotail, ions carry the bulk of the current, and the observed asymmetry is found to be due to ion flow and not a wave motion unless the extent of finite resistivity in the third dimension is very thin, comparable to the current sheet thickness. Thus aside from scenarios where electrons are the dominant current carriers, such as very thin current sheets that are on electron scales, we do not expect the reconnection wave to form. This result is relevant to the magnetotail where dawn‐dusk asymmetries are observed in the motions of auroral brightenings and surges, as well as in the statistical location of pressure decreases, flows, and magnetic signatures associated with the near‐Earth neutral line and early plasmoids. We attribute the observed dawn‐dusk asymmetries to ion flows. One interesting question left for future work is the possibility that reconnection waves may form in thin electron‐scale current layers that are sometimes observed embedded within a thicker sheet in the magnetotail.

Kinetic regimes of high frequency magnetic reconnection in a neutral sheet configuration

A collisionless plasma configuration with a neutral magnetic sheet allows a fast electron tearing mode to grow due to a resonant wave–particle interaction near the null line. Using a fully kinetic treatment, a set of dispersion equations that bridges the resonant tearing mode and the well-known cold fluid tearing mode driven by electron inertia is derived. The whistler frequency range where magnetic reconnection does not involve the ion dynamics is considered. This frequency range is of interest to the study of the laser–plasma interaction, where magnetic reconnection is expected to play an important role in the magnetic field dynamics in the wake of an ultra intense laser pulse.

Magnetic reconnection in 2D stratified atmospheres

We explore the dynamical consequences of magnetic reconnection in a 2D stratified physical configuration representing a “quiet” solar environment. By including gravity, an initial magneto-hydrostatic solution is found that allows the magnetic field to expand with height. The change in kinetic gas pressure with height leads to the formation of a cold current “sheet” in the case of strong stratification, in contrast to a hot current “sheet” in the case of negligible stratification. Here the “sheet” temperature is measured relative to the temperature in the ambient background plasma. The dynamics of magnetic reconnection in a stratified atmosphere evolves through a new initial stage, with a more complex velocity structure than the quadrupolar velocity pattern present in traditional 2D X-point reconnection. As time progresses, the new initial phase is suppressed and the driven reconnection evolves into the traditional 2D reconnection pattern. The transition time between the two regimes is found to depend on the imposed stratification, and through this, on the degree of expansion of the initial magnetic field with height. The new reconnection regime undergoes a more complicated physical evolution and seems to have a lower reconnection rate than the classical 2D X-point reconnection. The faster the magnetic field expands with height, the slower and more complex are the dynamics of the magnetic reconnection at the early stages of its evolution.

The Generation of Nonthermal Particles in the Relativistic Magnetic Reconnection of Pair Plasmas

Particle acceleration in the magnetic reconnection of electron-positron plasmas is studied by using a particle-in-cell simulation. It is found that a significantly large number of nonthermal particles are generated by the inductive electric fields around an X-type neutral line when the reconnection outflow velocity, which is known to be an Alfv\'{e}n velocity, is on the order of the speed of light. In such a relativistic reconnection regime, we also find that electrons and positrons form a power-law-like energy distribution through their drift along the reconnection electric field under the relativistic Speiser motion. A brief discussion of the relevance of these results to the current sheet structure, which has an antiparallel magnetic field in astrophysical sources of synchrotron radiation, is presented.

Magnetic Flux Cancellation Observed in the Sunspot Moat

In this paper we study the evolution of magnetic fields of a 1F/2.4C solar flare and following magnetic flux cancellation. The data are Big Bear Solar Observatory and SOHO/MDI observations of active region NOAA 8375. The active region produced a multitude of subflares, many of them being clustered along the moat boundary in the area with mixed polarity magnetic fields. The study indicates a possible connection between the flare and the flux cancellation. The cancellation rate, defined from the data, was found to be 3×1019 Mx h−1. We observed strong upward directed plasma flows at the cancellation site. Suggesting that the cancellation is a result of reconnection process, we also found a reconnection rate of 0.5 km s−1, which is a significant fraction of Alfven speed. The reconnection rate indicates a regime of fast photospheric reconnection happening during the cancellation.

The theory of three-dimensional hetons and vortex-dominated spreading in localized turbulent convection in a fast rotating stratified fluid

The problem of lateral heat/buoyancy transport in localized turbulent convection dominated by rotation in continuously stratified fluids of finite depth is considered. We investigate the specific mechanism of the vortex-dominated lateral spreading of anomalous buoyancy created in localized convective regions owing to outward propagation of intense heton-like vortices (pairs of vortices of equal potential vorticity (PV) strength with opposite signs located at different depths), each carrying a portion of buoyancy anomaly. Assuming that the quasi-geostrophic form of the PV evolution equation can be used to analyse the spreading phenomenon at fast rotation, we develop an analytical theory for the dynamics of a population of three-dimensional hetons. We analyse in detail the structure and dynamics of a single three-dimensional heton, and the mutual interaction between two hetons and show that the vortices can be in confinement, splitting or reconnection regimes of motion depending on the initial distance between them and the ratio of the mixing-layer depth to the depth of fluid (local to bulk Rossby radii). Numerical experiments are made for ring-like populations of randomly distributed three-dimensional hetons. We found two basic types of evolution of the populations which are homogenizing confinement (all vortices are predominantly inside the localized region having highly correlated wavelike dynamics) and vortex-dominated spreading (vortices propagate out of the region of generation as individual hetons or heton clusters). For the vortex-dominated spreading, the mean radius of heton populations and its variance grow linearly with time. The law of spreading is quantified in terms of both internal (specific for vortex dynamics) and external (specific for convection) parameters. The spreading rate is proportional to the mean speed of propagation of individual hetons or heton clusters and therefore depends essentially on the strength of hetons and the ratio of local to bulk Rossby radii. A theoretical explanation for the spreading law is given in terms of the asymptotic dynamics of a single heton and within the frames of the kinetic equation derived for the distribution function of hetons in collisionless approximation. This spreading law gives an upper ‘advective’ bound for the superdiffusion of heat/buoyancy. A linear law of spreading implies that diffusion parameterizations of lateral buoyancy flux in non-eddy-resolving models are questionable, at least when the spreading is dominated by heton dynamics. We suggest a scaling for the ‘advective’ parameterization of the buoyancy flux, and quantify the exchange coefficient in terms of the mean propagation speed of hetons. Finally, we discuss the perspectives of the heton theories in other problems of geophysical fluid dynamics.

Three‐dimensional artificial neural network model of the dayside magnetopause

Artificial neural networks (ANN) from the package NeuroShell 2 are applied to the modeling of the dayside magnetopause. The model data set is based on magnetopause crossings and on the corresponding hour‐averaged measurements of the solar wind plasma and the interplanetary magnetic field. The ANN model represents the three‐dimensional shape and size of the dayside magnetopause as a function of the solar wind dynamic pressure and theBzandBycomponents of the interplanetary magnetic field. The model describes the dynamics of the magnetic cusp and global asymmetry of the dayside magnetopause under a wide range of external conditions. Small variations in the size of the magnetopause as a function of the absolute value ofByare presented quantitatively in the form of an analytic expression. The ANN model shows three regimes of magnetopause dynamics that are controlled by theBzcomponent: a pressure balance regime (Bz0 nT), a reconnection regime (0>Bz>−10 nT), and a regime of reconnection saturation (Bz<−10 nT). Also, three different regimes of magnetopause dynamics at the subsolar point are described by a modified pressure balance equation obtained from the ANN model.

Forced magnetic field line reconnection in electron magnetohydrodynamics

The forced reconnection of magnetic field lines within the framework of electron magnetohydrodynamics (EMHD) has been investigated. A broad class of solutions that describe stationary reconnection have been found. The time evolution of the plasma and of the magnetic field when perturbations are imposed from the boundary of a high conductivity plasma slab are also studied. The initial magnetic field has a null surface. Following this discussion, the so-called Taylor’s problem for EMHD in which the perturbations cause a change in the topology of the magnetic field has been solved. The plasma and the magnetic field are seen to evolve with the time scale of the linear tearing mode. Their time evolution is described by exponential dependences. Analytic and numerical simulation results of the nonlinear regime of forced magnetic reconnection in EMHD are also presented. Finally, the above results are compared with a case where the reconnection is mediated by dissipative electron viscosity effects.

Forced magnetic reconnection and the persistence of current sheets in static and rotating plasmas due to a sinusoidal boundary perturbation

The problem of forced reconnection in static and rotating plasmas due to a sinusoidal boundary perturbation is revisited. The primary focus of this paper is on inner region dynamics, including the effects of resistivity as well as viscosity. It is shown that for high-Lundquist-number plasmas, the use of the ‘‘constant-ψ’’ approximation in the linear and nonlinear regimes of forced reconnection is not justified. The linear and nonlinear dynamics in the inner region are characterized by the persistence of current sheets. Explicit analytical solutions for the time dependence of the reconnected flux and current sheet density are given, and tested by numerical simulations. These results differ qualitatively from earlier analytical results on forced reconnection in static plasmas [T. S. Hahm and R. M. Kulsrud, Phys. Fluids 28, 2412 (1985)] (except in a very restricted range of parameters) as well as rotating plasmas [R. Fitzpatrick and T. C. Hender, Phys. Fluids B 3, 644 (1991)]. Some qualitative implications for laboratory and space plasmas are discussed.

Nonlinear magnetic reconnection with collisionless dissipation

An analytical model of two-dimensional collisionless reconnection in an X-type magnetic geometry is presented. The conversion of magnetic energy to the kinetic energy of accelerated ions takes place in the vicinity of the neutral line. The structure of this dissipation region and the magnetic energy release rate have been investigated both for linear and nonlinear regimes of collisionless reconnection. A simple model of global reconnection flow has been constructed, assuming an incompressible ideal magnetohydrodynamics approximation outside the dissipation region. The corresponding scaling for the external Mach number (Me) is found, which predicts a maximum reconnection rate Me=1/2R̃m −1/2, where R̃m≊(Le/λi)2≫1 is the effective magnetic Reynolds number for collisionless reconnection (Le is the global size of the system and λi is the ion inertial skin depth).

Steady linear X‐point magnetic reconnection

In the main part of this paper a model for linear reconnection is developed with a current spike around the X‐point and vortex current sheets along the separatrices, which are resolved by the effects of viscosity and magnetic diffusivity. The model contains three regions. In the external ideal region, diffusion effects are negligible, and the flow is purely radial but becomes singular both along the separatrices and at the X‐point. Near the separatrix there is a self‐similar boundary layer with strong electric current and vorticity, where resistivity and viscosity resolve the singularity and allow the flow to cross the separatrix. A composite solution is set up that matches the external and separatrix solutions. Near the origin diffusion also resolves the singularity and is described approximately by a biharmonic solution. A classification of steady two‐dimensional reconnection regimes is proposed into viscous reconnection (Me > Re), extra slow (linear) reconnection (Me < Rme−1), slow reconnection (Rme−1 < Me Rme−½), and fast reconnection (Rme−½ < Me), where Me is the dimensionless reconnection rate, Rme the magnetic Reynolds number, and Re the Reynolds number, all based on the Alfven speed far from the reconnection point. Also, an antireconnection theorem is proved, which has profound effects on the nature of linear reconnection. It states that steady two‐dimensional MHD reconnection with plasma flow across the separatrices is impossible in a plasma which is inviscid, highly sub‐Alfvenic, and has uniform magnetic diffusivity.

A general family of nonuniform reconnection models with separatrix jets

Abstract The Nonuniform Magnetic Reconnection model presented by Priest and Lee (1990) was the first to incorporate several features observed in previous numerical models, in particular the highly curved field in the inflow region, which relaxes one of the key assumptions of the classical Almost-Uniform reconnection model of Petschek (1964). Also present is a strong jet of plasma emerging from the reconnection region along the separatrix and a negative current spike at the outflow from the central diffusion region. In this paper we present a generalisation of the Priest-Lee model to include pressure gradients in the inflow region, so relaxing the other main assumption of the Petschek and Priest-Lee models, namely that the inflow is current-free or potential. This produces several reconnection regimes similar to those described by Priest and Forbes (1986) in their Unified Almost-Uniform solutions, where significant pressure gradients are included, but their inflow, like Petschek's, is almost-uniform with s...

Nonlinear collisionless magnetic reconnection.

Collisionless magnetic reconnection in regimes where the mode structure is characterized by global convection cells is found to exhibit a quasiexplosive time behavior in the early nonlinear stage where the fluid displacement is smaller than the equilibrium scale length. This process is accompanied by the formation of a current density sublayer narrower than the skin depth. This sublayer keeps shrinking with time.

Does fast magnetic reconnection exist?

The classical Petschek model of fast, steady state reconnection has been generalized in two families of reconnection regimes. The first family, which we refer to as “almost uniform,” models the reconnection of nearly uniform, antiparallel magnetic fields, and it includes Petschek's model as a special case. The second family, which we refer to as nonuniform, models the reconnection of strongly curved magnetic fields, and it includes separatrix jets and reversed current spikes at the ends of the diffusion region. In general, both families contain regimes having fast reconnection rates, but we show here that these fast reconnection regimes do not occur when the boundary conditions often used in numerical experiments are adopted. In 1986, D. Biskamp carried out a series of numerical experiments to check Petschek's prediction that the maximum reconnection rate should scale with the magnetic Reynolds number, Rme, as [ln (Rme)]−1. Biskamp found that the maximum reconnection rate in his experiments did not scale in this way but instead as Rme−1/2. Because this corresponds to the scaling predicted by the slow reconnection theory of Sweet (1958) and Parker (1957), Biskamp has argued that his numerical experiments show that fast reconnection does not exist at high magnetic Reynolds numbers. However, by applying boundary conditions similar to Biskamp's to the “nonuniform” family of reconnection regimes, we are able to explain Biskamp's scaling results and to explain why he did not achieve fast reconnection in his numerical experiments. Therefore, we conclude that numerical experiments with suitably designed boundary conditions are highly likely to exhibit fast reconnection and that such reconnection is a common process in astrophysical and space plasmas.

Fast magnetic reconnection with small shock angles

The steady state fast magnetic reconnection process with small separatrix angles proposed by Pestchek (1964) and generalized by Priest and Forbes (1986) is studied by a two‐dimensional incompressible magnetohydrodynamic (MHD) code. In the code a uniform tangential magnetic field and normal plasma speed are specified on the inflow boundary. On the outflow boundary the tangential flow speed and tangential magnetic field are specified to be those in the Priest‐Forbes' model in order to obtain different reconnection regimes. In our simulations both a uniform and a nonuniform resistivity are used. For a nonuniform resistivity model in which the resistivity in the outflow region is highly reduced, our simulations are in many aspects consistent with those in the analytical results. A steady state magnetic reconnection configuration with small separatrix angle is obtained. The plasma is heated and accelerated by the current sheets associated with slow shocks. We also obtain various regimes predicted by Priest and Forbes for different boundary conditions on the outflow boundary which are characterized by a parameter b0. They are a weak fast‐mode expansion (b0=0), slow‐mode compression (b0 < 0), slow‐mode expansion (b0 ≥ 0), and a hybrid regime of fast‐mode and slow‐mode expansion (0 < b0 < 1). The width and length of the current sheet for different parameters obtained in the simulations are found to be consistent with theoretical values. When the magnetic Reynolds number or the reconnection rate given on the inflow boundary increases, the diffusion region becomes smaller. However, for cases with a uniform resistivity imposed in the simulation domain it is found that the diffusion region tends to lengthen indefinitely and no steady state configuration is obtained. Magnetic islands are usually formed at the later stage of the simulation.

Numerical models of magnetic reconnection

Abstract This paper contains a review of numerical experiments concerning steady state magnetic reconnection. The Sweet/Parker current sheet model and Petschek's standing slow mode shock wave model for magnetic reconnection are reviewed briefly along with the recently developed unified theory of Priest and Forbes. All these analytical models do not provide a detailed description of the diffusion layer. Because of the inherent mathematical difficulties involved in solving analytically the full resistive problem, one is forced to perform numerical studies of the reconnection process. All numerical experiments performed so far have not been able to produce fast steady state reconnection at high Reynolds numbers in a system with uniform resistivity. Fast steady state reconnection seems only possible if the resistivity is spatially limited to a small region. In the case of free boundary conditions Petschek-type reconnection results, and in the case of driven reconnection all reconnection regimes derived by Pri...