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.     

On the magnetic reconnection of electric currents in solar flares

The role of the electric currents distributed over the volume of an active region on the Sun is considered from the standpoint of solar flare physics. We suggest including the electric currents in a topological model of the magnetic field in an active region. Typical values of the mutual inductance and the interaction energy of the coronal electric currents flowing along magnetic loops have been estimated for the M7/1N flare on April 27, 2006. We show that if these currents actually make a significant contribution to the flare energetics, then they must manifest themselves in the photosphericmagnetic fields. Depending on their orientation, the distributed currents can both help and hinder reconnection in the current layer at the separator during the flare. Asymmetric reconnection of the currents is accompanied by their interruption and an inductive change in energy. The reconnection of currents in flares differs significantly from the ordinary coalescence instability of magnetic islands in current layers. Highly accurate measurements of the magnetic fields in active regions are needed for a quantitative analysis of the role of distributed currents in solar flares.     

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 the three-dimensional structure of the solar magnetic field in interplanetary space

The three-dimensional structure of the solar magnetic field in the interplanetary space is inferred from a theoretical point of view. We use the magnetic field produced by a magnetic dipole rotating obliquely in vacuum. The correction for the presence of a plasma surrounding the Sun is taken into account in terms of a phenomenological approximation.Our method well reproduces the basic features of the polarity-reversal-surface (the neutral sheet in the two-hemisphere model by Saito (1975)) obtained on the basis of observational data, i.e. the snail-shell like structure and variation of its precise shape in accordance with the solar cycle, except for the folding of the surface.     

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.     

Energetic particle acceleration in a three-dimensional magnetic field reconnection model: the role of magnetohydrodynamic turbulence

The role of magnetohydrodynamic (MHD) turbulence in the cosmic ray acceleration process in a volume with a reconnecting magnetic field is studied by means of Monte Carlo simulations. We performed modelling of proton acceleration, with the three-dimensional analytic model of stationary reconnection of Craig et al. providing the unperturbed background conditions. Perturbations of particle trajectories resulting from a turbulent magnetic field component were simulated using small-amplitude pitch-angle momentum scattering, enabling modelling of both small- and large-amplitude turbulence in a wide wavevector range. Within the approach, no second-order Fermi acceleration process is allowed. Comparison of the acceleration process in models involving particle trajectory perturbations with the unperturbed model reveals that the turbulence can substantially increase the acceleration efficiency, enabling much higher final particle energies and flat particle spectra.     

Large-scale three-dimensional structure of the interplanetary magnetic field

Analysis of observations of the white-light corona performed aboard OSO-7 is evidence for the existence of coronal ribbon-structures, which may be observed on the limb as coronal streamers. It is shown that prolongation of these structures into interplanetary space forms a curved surface; intersection of this surface is accompanied by a change of polarity of the interplanetary magnetic field, which existed in May–July 1973; and its connection with several phenomena in the solar atmosphere, has been found.     

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 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.     

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...     

Electric field with bipolar structure during magnetic reconnection without a guide field

We present a study on the polarized electric field during the collisionless magnetic reconnection of antiparallel fields using two dimensional particle-in-cell simulations. The simulations demonstrate clearly that electron holes and electric field with bipolar structure are produced during magnetic reconnection without a guide field. The electric field with bipolar structure can be found near the X-line and on the separatrix and the plasma sheet boundary layer, which is consistent with the observations. These structures will elongate electron’s time staying in the diffusion region. In addition, the electric fields with tripolar structures are also found in our simulation.     

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.     

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.     

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.     

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.     

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 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.