Steady magnetic reconnection in three dimensions

The concepts of magnetic reconnection that have been developed in two dimensions need to be generalised to three-dimensional configurations. Reconnection may be defined to occur when there is an electric field (E) parallel to field lines (known as potential singular lines) which are potential reconnection locations and near which the field has an X-type topology in a plane normal to that field line. In general there is a continuum of neighbouring potential singular lines, and which one supports reconnection depends on the imposed flow or electric field. For steady reconnection the nearby flow and electric field are severely constrained in the ideal region by the condition that E = 0 there. Potential singular lines may occur in twisted prominence fields or in the complex magnetic configuration above sources of mixed polarity of an active region or a supergranulation cell. When reconnection occurs there is dynamic MHD behaviour with current concentration and strong plasma jetting along the singular line and the singular surfaces which map onto them.     

Line-tied magnetic reconnection

We present two-dimensional numerical simulations of magnetic reconnection in a configuration relevant to two-ribbon solar flares. The calculations extend those of Forbes and Priest (1982a, b, 1983) and some puzzling aspects of their results are clarified. In particular, the roles of magnetic diffusion, of the tearing mode and of turbulence are individually examined. We stress the important part played by boundary conditions in determining the evolution of the initial current sheet and suggest that in future the evolution of the entire overlying magnetic arcade be modelled as well as the current sheet that is created below the rising arcade. Tearing at very high magnetic Reynolds numbers is likely to develop into an impulsive bursty regime of reconnection after a time which depends on the initial level of turbulence.     

On continuous transitions between discontinuous MHD solutions in the magnetic reconnection problem

The possibility that the type of magnetohydrodynamic (MHD) discontinuity changes as the plasma flow conditions gradually change is investigated in a general form. The conservation laws in MHD admit such transitions if there exist the so-called transition solutions that simultaneously satisfy two types of discontinuities. These solutions have been sought for. The system of possible transitions between MHD discontinuities obtained on their basis is presented in a clear schematic form. The ultimate general scheme of transitions includes all of the previously described schemes of transitions known to us. The system of discontinuities and transitions between them is studied in a self-consistent solution of the analytical problem of reconnection in a strong magnetic field.     

Spontaneous magnetic reconnection

The present review concerns the relevance of collisionless reconnection in the astrophysical context. Emphasis is put on recent developments in theory obtained from collisionless numerical simulations in two and three dimensions. It is stressed that magnetic reconnection is a universal process of particular importance under collisionless conditions, when both collisional and anomalous dissipation are irrelevant. While collisional (resistive) reconnection is a slow, diffusive process, collisionless reconnection is spontaneous. On any astrophysical time scale, it is explosive. It sets on when electric current widths become comparable to the leptonic inertial length in the so-called lepton (electron/positron) “diffusion region”, where leptons de-magnetise. Here, the magnetic field contacts its oppositely directed partner and annihilates. Spontaneous reconnection breaks the original magnetic symmetry, violently releases the stored free energy of the electric current, and causes plasma heating and particle acceleration. Ultimately, the released energy is provided by mechanical motion of either the two colliding magnetised plasmas that generate the current sheet or the internal turbulence cascading down to lepton-scale current filaments. Spontaneous reconnection in such extended current sheets that separate two colliding plasmas results in the generation of many reconnection sites (tearing modes) distributed over the current surface, each consisting of lepton exhausts and jets which are separated by plasmoids. Volume-filling factors of reconnection sites are estimated to be as large as \({<}10^{-5}\) per current sheet. Lepton currents inside exhausts may be strong enough to excite Buneman and, for large thermal pressure anisotropy, also Weibel instabilities. They bifurcate and break off into many small-scale current filaments and magnetic flux ropes exhibiting turbulent magnetic power spectra of very flat power-law shape \(W_b\propto k^{-\alpha }\) in wavenumber k with power becoming as low as \(\alpha \approx 2\). Spontaneous reconnection generates small-scale turbulence. Imposed external turbulence tends to temporarily increase the reconnection rate. Reconnecting ultra-relativistic current sheets decay into large numbers of magnetic flux ropes composed of chains of plasmoids and lepton exhausts. They form highly structured current surfaces, “current carpets”. By including synchrotron radiation losses, one favours tearing-mode reconnection over the drift-kink deformation of the current sheet. Lepton acceleration occurs in the reconnection-electric field in multiple encounters with the exhausts and plasmoids. This is a Fermi-like process. It results in power-law tails on the lepton energy distribution. This effect becomes pronounced in ultra-relativistic reconnection where it yields extremely hard lepton power-law energy spectra approaching \(F(\gamma )\propto \gamma ^{-1}\), with \(\gamma \) the lepton energy. The synchrotron radiation limit becomes substantially exceeded. Relativistic reconnection is a probable generator of current and magnetic turbulence, and a mechanism that produces high-energy radiation. It is also identified as the ultimate dissipation mechanism of the mechanical energy in collisionless magnetohydrodynamic turbulent cascades via lepton-inertial-scale turbulent current filaments. In this case, the volume-filling factor is large. Magnetic turbulence causes strong plasma heating of the entire turbulent volume and violent acceleration via spontaneous lepton-scale reconnection. This may lead to high-energy particle populations filling the whole volume. In this case, it causes non-thermal radiation spectra that span the entire interval from radio waves to gamma rays.     

Driven magnetic field reconnection

We consider the magnetic field reconnection in a plasma induced by perturbing the boundaries of a slab of incompressible plasma with a magnetic neutral surface inside. We assume that the boundaries of the plasma slab are perturbed at a rate which is fast compared with the hydromagnetic evolution rate; and investigate the ensuing adjustments in the plasma and the magnetic field threading through it.     

Spontaneous magnetic reconnection mechanisms in plasma

Using the kinetic theory and model collision integral of Bhatnagar-Gross-Krook we obtain the general dispersion relation for different regimes of the tearing-mode instability development in configuration with sheared magnetic field. Thus, we can construct the general picture of the applicability of different mechanisms of the tearing-mode dependent on collision frequency and value of the shear.     

Coronal heating by magnetic reconnection

The theory of magnetic reconnection has advanced substantially over the past few years. There now exists a new generation of fast two-dimensional models known as almost-uniform reconnection and nonuniform reconnection, depending on the boundary conditions. Also, we are beginning to explore the uncharted region of three-dimensional reconnection, where regimes of “spine reconnection” and “fan reconnection” have been discovered. Furthermore, part of the coronal heating problem appears to have been solved with recent observational support for the Converging Flux Model in which heating is produced by coronal reconnection driven by footpoint motions.     

On the relativistic magnetic reconnection

Reconnection of the magnetic lines of force is considered in case the magnetic energy exceeds the rest energy of the matter. It is shown that the classical Sweet–Parker and Petschek models are generalized straightforwardly to this case and the reconnection rate may be estimated by substituting the Alfven velocity in the classical formulae with the speed of light. The outflow velocity in the Sweet–Parker configuration is mildly relativistic. In the Petschek configuration, the outflow velocity is ultrarelativistic whereas the angle between the slow shocks is very small. As a result of the strong compression, the plasma outflow in the Petschek configuration may become strongly magnetized if the reconnecting fields are not exactly antiparallel.     

Filament activation and magnetic reconnection

Solar Physics - A curved filament in a decaying active region (AR&;nbsp;8329) was observed on 9 September 1998 with a combination of several instruments. The main data base is a 4-hour long time...     

Quick triggering of magnetic reconnection in magnetotail

Recently, quick triggering of magnetic reconnection (QMRT) even in an ion-scale current sheet is found to be possible with the help of the nonlinear evolution of the lower hybrid drift instability (LHDI). The details of the QMRT mechanism are reviewed mostly based on three-dimensional full-particle simulation results of our group. QMRT is mediated by LHDI and its time scale is comparable to the saturation time scale of LHDI. Depending on the initial current sheet thickness, two types of QMRT, so-called Type-I and Type-II QMRT, are demonstrated.     

Numerical study of line-tied magnetic reconnection

A two-dimensional configuration, analogous to that at the start of the main phase in two-ribbon flares, is modelled numerically by self-consistently solving the time-dependent MHD equations. The initial state consists of a vertical current sheet with an external plasma beta value of 0.1 and a magnetic Reynolds number of 10^–3. Although the model does not yet include gravity or a full energy equation, many of the principal dynamical features of the main phase in a flare are present. In particular, the numerical results confirm the earlier prediction of the kinematic Kopp-Pneuman (1976) model that a neutral line forms at the base of the corona and rises upwards as open, extended field lines close back down to form loops (i.e., post-flare loops). By the end of the computation a state of nonlinear reconnection containing slow shocks has developed, and the velocity of the plasma flowing into the neutral line region is approximately 0.06 times the corresponding inflow Alfvén velocity - a value consistent with the steady-state nonlinear reconnection theory of Soward and Priest (1977). The speed at which the neutral line rises in the numerical simulation varies from an initial value of 0.02 to a final value of - 0.12 times the inflow Alfvén speed.     

The study of magnetic reconnection in solar spicules

This work is devoted to study the magnetic reconnection instability under solar spicule conditions. Numerical study of the resistive tearing instability in a current sheet is presented by considering the magnetohydrodynamic (MHD) framework. To investigate the effect of this instability in a stratified atmosphere of solar spicules, we solve linear and non-ideal MHD equations in the x?z plane. In the linear analysis it is assumed that resistivity is only important within the current sheet, and the exponential growth of energies takes place faster as plasma resistivity increases. We are interested to see the occurrence of magnetic reconnection during the lifetime of a typical solar spicule.     

Test particle acceleration in torsional spine magnetic reconnection

Three-dimensional (3D) magnetic reconnection is taking place commonly in astrophysical and space plasmas, especially in solar flares which are rich sources of highly energetic particles. One of the proposed mechanisms for steady-state 3D magnetic reconnection is “torsional spine reconnection”. By using the magnetic and electric fields for “torsional spine reconnection”, we numerically investigate the features of test particle acceleration with input parameters for the solar corona. We show that efficient acceleration of a relativistic proton is possible near the null point where it can gain up to 100 MeV of kinetic energy within a few milliseconds. However, varying the injection position results in different scenarios for proton acceleration. A proton is most efficiently accelerated when it is injected at the point where the magnetic field lines change their curvature in the fan plane. Moreover, a proton injected far away from the null point cannot be accelerated and, even in some cases, it is trapped in the magnetic field. In addition, adopting either spatially uniform or non-uniform localized plasma resistivity does not much influence the features of trajectory.     

Fast magnetic reconnection and energetic particle acceleration

Our numerical simulations show that the reconnection of magnetic field becomes fast in the presence of weak turbulence in the way consistent with the Lazarian and Vishniac (1999) model of fast reconnection. We trace particles within our numerical simulations and show that the particles can be efficiently accelerated via the first order Fermi acceleration. We discuss the acceleration arising from reconnection as a possible origin of the anomalous cosmic rays measured by Voyagers.     

The dynamics of driven magnetic reconnection in coronal arcades

The dynamics of interacting coronal loops and arcades have recently been highlighted by observations from theYohkoh satellite and may represent a viable mechanism for heating the solar corona. Here such an interaction is studied using two-dimensional resistive magnetohydrodynamic (MHD) simulations. Initial potential field structures evolve in response to imposed photospheric flows. In addition to the anticipated current sheet about theX-point separating the colliding flux systems, significant current layers are found to lie all the way along the separatrices that intersect at theX-point and divide the coronal magnetic field into topologically distinct regions. Shear flows across the separatrices are also observed. Both of these features are shown to be compatible with recent analytical studies of two-dimensional linear steady-state magnetic reconnection, even though the driven system that has been simulated is not strictly ‘open’ in the sense implied by steady-state calculations. The implications for future steady-state models are also discussed. The presence of the neutral point also brings into question any constant-density approximations that have previously been used for such quasi-steady coronal evolution models. This results from the intimate coupling between the neutral point and its separatrices communicated via the gas pressure. In terms of the detailed energetics during the arcade evolution, preliminary results reveal that on the order of 3% of the energy injected by the footpoint motions is lost purely through ohmic dissipation. We would therefore anticipate a local hot spot between the interacting flux systems, and a brightening distributed along the length of any separatrix field lines. Furthermore, as the resistivityη is reduced, the flux annihilation rate and the ohmic dissipation rate are found to scale independently ofη.     

Classification of magnetic reconnection during two current-loop coalescence

We present a classification of magnetic reconnection during two current loop coalescence, which may be quite important for the physical process of both solar flares and coronal loop heating in the solar active region. It is suggested that different kinds of the current loop coalescence processes could be identified from the soft X-ray telescope(SXT) of the Yohkoh satellite and the magnetic field data in the active region.     

X-ray bright point flares due to magnetic reconnection

Ground-based optical observations coordinated with Yohkoh/SXT X-ray observations of an old, disintegrating bipolar active region AR NOAA 7493 (May 1, 1993) provided a multiwavelength data base to study a flaring active region X-ray bright point (XBP) of about 16 hr lifetime, and the activity related to it in different layers of the solar atmosphere. The XBP appeared to be related to a new minor bipole of about 10²⁰ Mx. Superposed on a global evolution of soft X-ray brightness, the XBP displayed changes of brightness, lasting for 1–10 min. During the brightenings the XBP apparently had a spatial structure, which was (tiny) loop-like rather than point-like. The X-ray brightenings were correlated with chromospheric activity: (i) brightenings of underlying chromospheric faculae, and (ii) appearance of strong turbulent velocities in the arch filament system. We propose that the XBP brightenings were due to reconnection of the magnetic field lines (sketched in 3D) between the new bipole and a pre-existing plage field induced by the motion of one of the new pores (v = 0.2 km s^–1) towards the plage, and that the XBP itself was a reconnected hot loop between them.     

Fast magnetic reconnection with Cowling’s conductivity

The aim of the present paper is to explore the mechanism of fast Sweet–Parker’s magnetic reconnection with the Cowling’s conductivity. Cowling derived the resistivity of plasma with three components: electrons, ions and neutral particles in magnetic field theoretically after Spitzer. The resistivity is much larger than the Spitzer’s. According to the idea of partially ionized plasmas ejected into the corona as the trigger of flares, we adopt Cowling’s Conductivity to Sweet–Parker’s reconnection model in this paper. The result shows that the reconnection rate can be improved a lot in solar corona and approaches the timescale of solar flare in the absence of anomalous resistivity.     

Nonplanar magnetic reconnection associated with conical slow shocks

We study a nonplanar model of magnetic reconnection associated with conical slow shocks, assuming that the shock surfaces are two identical cones with circular cross sections symmetrical about the ±x-axis. In the inflow region upstream of the shocks, two oppositely directed magnetic fields are separated by a current sheet. The model treats the current sheet as a tangential discontinuity and treats shocks and tangential discontinuity as surfaces of zero thickness. The dynamical structure of the global magnetic field in the continuous regions is studied using compressible, non-resistive MHD equations. In the inflow region, nonplanar magnetic field lines first move toward the current sheet. Near the sheet, the middle sections of the field lines become highly flattened, almost parallel to the sheet. Eventually, then oppositely directed field lines merge across the tangential discontinuity between the two shocks, and the magnetic lines are reconnected at the intersection of the shock and the tangential discontinuity. Reconnected magnetic lines are carried away at high speeds by the MHD flow in the outflow region, downstream of the shocks.     

The rate of flux pile-up magnetic reconnection in reduced MHD

The rate of two-dimensional flux pile-up magnetic reconnection is known to be severely limited by gas pressure in a low-beta plasma of the solar corona. As earlier perturbational calculations indicated, however, the pressure limitation should be less restrictive for three-dimensional flux pile-up. In this paper the maximum rate of reconnection is calculated in the approximation of reduced magnetohydrodynamics (RMHD), which is valid in the solar coronal loops. The rate is calculated for finite-magnitude reconnecting fields in the case of a strong axial field in the loop. Gas pressure effects are ignored in RMHD but a similar limitation on the rate of magnetic merging exists. Nevertheless, the magnetic energy dissipation rate and the reconnection electric field can increase by several orders of magnitude as compared with strictly two-dimensional pile-up. Though this is still not enough to explain the most powerful solar flares, slow coronal transients with energy release rates of order 10²⁵– 10²⁶ erg s^–1and heating of quiet coronal loops are within the compass of the model.