Emerging Parameter Space Map of Magnetic Reconnection in Collisional and Kinetic Regimes

In large-scale systems of interest to solar physics, there is growing evidence that magnetic reconnection involves the formation of extended current sheets which are unstable to plasmoids (secondary magnetic islands). Recent results suggest that plasmoids may play a critical role in the evolution of reconnection, and have raised fundamental questions regarding the applicability of resistive MHD to various regimes. In collisional plasmas, where the thickness of all resistive layers remain larger than the ion gyroradius, simulations results indicate that plasmoids permit reconnection to proceed much faster than the slow Sweet-Parker scaling. However, it appears these rates are still a factor of ～10× slower than observed in kinetic regimes, where the diffusion region current sheet falls below the ion gyroradius and additional physics beyond MHD becomes crucially important. Over a broad range of interesting parameters, the formation of plasmoids may naturally induce a transition into these kinetic regimes. New insights into this scenario have emerged in recent years based on a combination of linear theory, fluid simulations and fully kinetic simulations which retain a Fokker-Planck collision operator to allow a rigorous treatment of Coulomb collisions as the reconnection electric field exceeds the runaway limit. Here, we present some new results from this approach for guide field reconnection. Based upon these results, a parameter space map is constructed that summarizes the present understanding of how reconnection proceeds in various regimes.     

Magnetic field reconnection theory and the solar wind — Magnetosphere interaction: A review

This review considers the theory of the magnetic field line reconnection and its application to the problem of the interaction between the solar wind and the Earth's magnetosphere. In particular, we discuss the reconnection models by Sonnerup and by Petschek (for both incompressible and compressible plasmas, for the asymmetric and nonsteady-state cases), the magnetic field annihilation model by Parker; Syrovatsky's model of the current sheet; and Birn's and Schindler's solution for the plasma sheet structure. A review of laboratory and numerical modelling experiments is given.Results concerning the field line reconnection, combined with the peculiarities of the MHD flow, were used in investigating the solar wind flow around the magnetosphere. We found that in the presence of a frozen-in magnetic field, the flow differs significantly from that in a pure gas dynamic case; in particular, at the subsolar. part of the magnetopause a stagnation line appears (i.e., a line along which the stream lines are branching) instead of a stagnation point. The length and location of the stagnation line determine the character of the interaction of the solar wind with the Earth's magnetosphere. We have developed the theory of that interaction for a steady-state case, and compare the results of the calculations with the experimental data.In the last section of the review, we propose a qualitative model of the solar wind — the Earth's magnetosphere interaction in the nonsteady-state case on the basis of the solution of the problem of the spontaneous magnetic field line reconnection.     

Reconnection Diffusion in Turbulent Fluids and Its Implications for Star Formation

Astrophysical fluids are turbulent a fact which changes the dynamics of many key processes, including magnetic reconnection. Fast reconnection of magnetic field in turbulent fluids allows the field to change its topology and connections. As a result, the traditional concept of magnetic fields being frozen into the plasma is no longer applicable. Plasma associated with a given magnetic field line at one instant is distributed along a different set of magnetic field lines at the next instant. This diffusion of plasmas and magnetic field is enabled by reconnection and therefore is termed “reconnection diffusion”. The astrophysical implications of this concept include heat transfer in plasmas, advection of heavy elements in interstellar medium, magnetic field generation etc. However, the most dramatic implications of the concept are related to the star formation process. The reason is that magnetic fields are dynamically important for most of the stages of star formation. The existing theory of star formation has been developed ignoring the possibility of reconnection diffusion. Instead, it appeals to the decoupling of mass and magnetic field arising from neutrals drifting in respect to ions entrained on magnetic field lines, i.e. through the process that is termed “ambipolar diffusion”. The predictions of ambipolar diffusion and reconnection diffusion are very different. For instance, if the ionization of media is high, ambipolar diffusion predicts that the coupling of mass and magnetic field is nearly perfect. At the same time, reconnection diffusion is independent of the ionization but depends on the scale of the turbulent eddies and on the turbulent velocities. In the paper we explain the physics of reconnection diffusion both from macroscopic and microscopic points of view, i.e. appealing to the reconnection of flux tubes and to the diffusion of magnetic field lines. We make use of the Lazarian and Vishniac (Astrophys. J. 517:700, 1999) theory of magnetic reconnection and show that this theory is applicable to the partially ionized gas. We quantify the reconnection diffusion rate both for weak and strong MHD turbulence and address the problem of reconnection diffusion acting together with ambipolar diffusion. In addition, we provide a criterion for correctly representing the magnetic diffusivity in simulations of star formation. We discuss the intimate relation between the processes of reconnection diffusion, field wandering and turbulent mixing of a magnetized media and show that the role of the plasma effects is limited to “breaking up lines” on small scales and does not affect the rate of reconnection diffusion. We address the existing observational results and demonstrate how reconnection diffusion can explain the puzzles presented by observations, in particular, the observed higher magnetization of cloud cores in comparison with the magnetization of envelopes. We also outline a possible set of observational tests of the reconnection diffusion concept and discuss how the application of the new concept changes our understanding of star formation and its numerical modeling. Finally, we outline the differences of the process of reconnection diffusion and the process of accumulation of matter along magnetic field lines that is frequently invoked to explain the results of numerical simulations.     

Topics in Microphysics of Relativistic Plasmas

Astrophysical plasmas can have parameters vastly different from the more studied laboratory and space plasmas. In particular, the magnetic fields can be the dominant component of the plasma, with energy-density exceeding the particle rest-mass energy density. Magnetic fields then determine the plasma dynamical evolution, energy dissipation and acceleration of non-thermal particles. Recent data coming from astrophysical high energy missions, like magnetar bursts and Crab nebula flares, point to the importance of magnetic reconnection in these objects. In this review we outline a broad spectrum of problems related to the astrophysical relevant processes in magnetically dominated relativistic plasmas. We discuss the problems of large scale dynamics of relativistic plasmas, relativistic reconnection and particle acceleration at reconnecting layers, turbulent cascade in force-fee plasmas. A number of astrophysical applications are also discussed.     

Basic Physical Mechanism of Fast Reconnection Evolution in Space Plasmas

Large dissipative events, such as solar flares and geomagnetic substorms, may result from sudden onset of fast (explosive) magnetic reconnection. Hence, it is a long-standing problem to find the physical mechanism that makes magnetic reconnection explosive; in particular, how can the fast magnetic reconnection explosively evolve in space plasmas? In this respect, we have proposed the spontaneous fast reconnection model as a nonlinear instability that grows by the positive feedback between plasma microphysics (anomalous resistivity) and macrophysics (global reconnection flow). On the basis of MHD simulations, we demonstrate for a variety of physical situations that the fast reconnection mechanism involving slow shocks in fact evolves explosively as a nonlinear instability and is sustained quasi-steadily on the nonlinear saturation phase. Also, distinct plasma processes, such as large-scale plasmoid propagation, magnetic loop development and loop-top heating, and asymmetric fast reconnection evolution, directly result from the spontaneous fast reconnection model. Obviously, MHD simulations are very useful in understanding the basic physics of explosive fast reconnection evolution in space plasmas. However, they cannot treat the details of microphysics near an X neutral point, which should be precisely studied in the coming 21st century.     

Three-Dimensional Simulations of Magnetic Reconnection with or Without Velocity Shears

The properties of spontaneous reconnection of a current sheet analyzed via direct three-dimensional simulations are presented. In particular the non-linear dynamics of resistive instabilities has been studied in absence or in presence of velocity shears. It is shown that full three-dimensional simulations allow the inclusion of a rich variety of (ideal) secondary instabilities which, depending on the initial equilibrium magnetic field configuration, determine the final fate of the system in the fully non linear regime. In particular in presence of a guide-field the dynamic is similar to what observed in two-dimensional simulations with energy driven toward both smaller and larger scales and energy spectra anisotropy. For different magnetic field configurations, the final state is characterized by the disruption of the coalesced structure created during the resistive phase and the system is characterized by a more chaotic state. A?discussion on the importance of high-order numerical techniques in numerical simulations of magnetic reconnection is also present.     

Notes on Magnetohydrodynamics of Magnetic Reconnection in Turbulent Media

Astrophysical fluids have very large Reynolds numbers and therefore turbulence is their natural state. Magnetic reconnection is an important process in many astrophysical plasmas, which allows restructuring of magnetic fields and conversion of stored magnetic energy into heat and kinetic energy. Turbulence is known to dramatically change different transport processes and therefore it is not unexpected that turbulence can alter the dynamics of magnetic field lines within the reconnection process. We shall review the interaction between turbulence and reconnection at different scales, showing how a state of turbulent reconnection is natural in astrophysical plasmas, with implications for a range of phenomena across astrophysics. We consider the process of magnetic reconnection that is fast in magnetohydrodynamic (MHD) limit and discuss how turbulence—both externally driven and generated in the reconnecting system—can make reconnection independent on the microphysical properties of plasmas. We will also show how relaxation theory can be used to calculate the energy dissipated in turbulent reconnecting fields. As well as heating the plasma, the energy dissipated by turbulent reconnection may cause acceleration of non-thermal particles, which is briefly discussed here.     

Magnetic Reconnection Phenomena In Interplanetary Space

Interplanetary magnetic reconnection(IMR) phenomena are explored based on the observational data with various time resolutions from Helios, IMP-8, ISEE3, Wind, etc. We discover that the observational evidence of the magnetic reconnection may be found in the various solar wind structures, such as at the boundary of magnetic cloud, near the current sheet, and small-scale turbulence structures, etc. We have developed a third order accuracy upwind compact difference scheme to numerically study the magnetic reconnection phenomena with high-magnetic Reynolds number (R _M=2000–10000) in interplanetary space. The simulated results show that the magnetic reconnection process could occur under the typical interplanetary conditions. These obtained magnetic reconnection processes own basic characteristics of the high R _M reconnection in interplanetary space, including multiple X-line reconnection, vortex velocity structures, filament current systems, splitting, collapse of plasma bulk, merging and evolving of magnetic islands, and lifetime in the range from minutes to hours, etc. These results could be helpful for further understanding the interplanetary basic physical processes. This revised version was published online in August 2006 with corrections to the Cover Date.     

Relativistic Reconnection and Particle Acceleration

This chapter mainly deals with magnetic reconnection and particle acceleration in relativistic astrophysical plasmas, where the temperature of the current sheet exceeds the rest mass energy and the Alfvén velocity is close to the speed of light. Magnetic reconnection now receives a great deal of interest for its role in many astrophysical systems such as pulsars, magnetars, galaxy clusters, and active galactic nucleus jets. We review recent advances that emphasize the roles of reconnection in high-energy astrophysical phenomena.     

Cause and Effect At the Magnetopause

Recent analyses of spacecraft data, especially AMPTE/IRM data, provide a test of reconnection theory; an analysis for the signature of a local tangential stress balance in a one-dimensional time-stationary rotational discontinuity has left crucial questions unanswered. A key result is that the electron temperature profile inward through the magnetopause current sheet shows heating followed by cooling. Electrons must be one of the carriers of the current; hence this result reflects the sign of E · J in the frame of reference of the magnetopause current carriers. Since the current is directed from dawn to dusk, the inescapable conclusion is that the electric field must reverse within the current sheet. This is direct evidence of a load–dynamo combination; in that dynamo, energy is transferred from the solar wind plasma to the electromagnetic field. A dynamo is not included in the reconnection model which includes only the electrical load; therefore, we argue that the reconnection problem is improperly posed. A second compelling observation is a remarkable difference of the normal component of the plasma velocity between inbound and outbound crossings. For an inbound crossing (outward current meander) this component does reverse, but not quite as assumed in the reconnection model; on the other hand, for outbound crossings of the spacecraft (corresponding to erosion) there is no reversal at all. The normal component is approximately constant at 20 km s^-1, anti-Sunward throughout. Since the typical motion of the magnetopause is 10 km s^-1 this revealing result shows that solar wind plasma can go across the magnetopause, even onto closed field lines to feed the low latitude boundary layer. This is in stark contrast to the reconnection model where the plasma goes to open field lines. The interaction can be understood by appealing to Poynting's theorem, where E · J describes the net effect on or by the plasma. Time-dependent terms (even in the initial conditions) must be used so that it is possible to draw upon energy which has been stored locally in both electrical and magnetic forms. An extended discussion of observational results from ground-based, rocket, and satellite instruments indicate the impulsive nature of the solar wind–magnetospheric interaction. There is a lot of plasma involved in this interaction, over 10²⁷ ions electrons^-1 per second; the anti-Sunward flow takes place in the low latitude boundary layer. There is no flux catastrophe produced by this flow since the frozen-field theorem does not hold for plasma transfer across the magnetopause. The LLBL completely envelops the plasma sheet; the LLBL is the source of its plasma, not the plasma mantle as hypothesized in the reconnection model of the magnetotail. A number of serious errors have occurred in some articles in the literature on reconnection, and we list and discuss the most important of these. In the conclusion it is emphasized that the failure to provide a viable energy source, within the necessary spatial and temporal constraints, is responsible for the failure of reconnection model. This does not mean that the state of interconnection between the geomagnetic field and the interplanetary magnetic field can not change, but it does mean that the advocated process is not relevant to such changes. True reconnection requires that the electric field has a curl so that an electromotive force = E · dl = -d_Mdt exists through which energy can be interchanged with stored magnetic energy.     

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.     

Magnetic Reconnection in Extreme Astrophysical Environments

Magnetic reconnection is a fundamental plasma physics process in which ideal-MHD??s frozen-in constraints are broken and the magnetic field topology is dramatically re-arranged, which often leads to a violent release of the free magnetic energy. Most of the magnetic reconnection research done to date has been motivated by the applications to systems such as the solar corona, Earth??s magnetosphere, and magnetic confinement devices for thermonuclear fusion. These environments have relatively low energy densities and the plasma is adequately described as a mixture of equal numbers of electrons and ions and where the dissipated magnetic energy always stays with the plasma. In contrast, in this paper I would like to introduce a different, new direction of research??reconnection in high energy density radiative plasmas, in which photons play as important a role as electrons and ions; in particular, in which radiation pressure and radiative cooling become dominant factors in the pressure and energy balance. This research is motivated in part by rapid theoretical and experimental advances in High Energy Density Physics, and in part by several important problems in modern high-energy astrophysics. I first discuss some astrophysical examples of high-energy-density reconnection and then identify the key physical processes that distinguish them from traditional reconnection. Among the most important of these processes are: special-relativistic effects; radiative effects (radiative cooling, radiation pressure, and radiative resistivity); and, at the most extreme end??QED effects, including pair creation. The most notable among the astrophysical applications are situations involving magnetar-strength fields (10¹⁴?C10¹⁵ G, exceeding the quantum critical field B _??4×10¹³ G). The most important examples are giant flares in soft gamma repeaters (SGRs) and magnetic models of the central engines and relativistic jets of Gamma Ray Bursts (GRBs). The magnetic energy density in these environments is so high that, when it is suddenly released, the plasma is heated to ultra-relativistic temperatures. As a result, electron-positron pairs are created in copious quantities, dressing the reconnection layer in an optically thick pair coat, thereby trapping the photons. The plasma pressure inside the layer is then dominated by the combined radiation and pair pressure. At the same time, the timescale for radiation diffusion across the layer may, under some conditions, still be shorter than the global (along the layer) Alfvén transit time, and hence radiative cooling starts to dominate the thermodynamics of the problem. The reconnection problem then becomes essentially a radiative transfer problem. In addition, the high pair density makes the reconnection layer highly collisional, independent of the upstream plasma density, and hence radiative resistive MHD applies. The presence of all these processes calls for a substantial revision of our traditional physical picture of reconnection when applied to these environments and thus opens a new frontier in reconnection research.     

MHD ANALYSIS OF PETSCHEK-TYPE RECONNECTION IN NON-UNIFORM FIELD AND FLOW GEOMETRIES

Analytical studies of reconnection have, for the most part, been confined to steady and uniform current sheet geometries. In contrast to these implifications, natural phenomena associated with the presence of current sheets indicate highly non-uniform structure and time-varying behaviour. Examples include the violent outbursts of energy on the Sun known as solar flares, and magnetospheric phenomena such as flux transfer events, plasmoids, and auroral activity. Unlike the theoretical models, reconnection therefore occurs in a highly dynamic and structured plasma environment. In this article we review the mathematical tools and techniques which are available to formulate models capable of describing the effects of reconnection in such situations. We confine attention to variants of the reconnection model first discussed by Petschek in the 1960s, in view of its successful application in predicting and interpreting phenomena in the terrestrial magnetosphere. The analysis of Petschek-type reconnection is based on the equations of ideal magnetohydrodynamics (MHD), which describe the large-scale behaviour of the magnetic field and plasma flow outside the diffusion region, which we determine as a localised part of the current sheet in which reconnection is initiated. The approach we adopt here is to transform the MHD equations into a Lagrangian or so-called 'frozen-in' coordinate system. In this coordinate system, the equation of motion transforms into a set of coupled nonlinear equations, in which the presence of inhomogeneous magnetic fields and/or plasma flows gives rise to a term similar to that which appears in the study of the ordinary string equation in a non-homogeneous medium. As demonstrated here, this approach not only clarifies and highlights the effects of such non-uniformities, it also simplifies the solution of the original set of MHD equations. In particular, this is true for those types of problem in which the total pressure can be considered as a known quantity from the outset. To illustrate the method, we solve several 2D problems involving magnetic field and flow non-uniformities: reconnection in a stagnation-point flow geometry with antiparallel magnetic fields; reconnection in a Y-type magnetic field geometry with and without velocity shear across the current sheet; and reconnection in a force-free magnetic field geometry with field lines of the form xy = const. These case examples, chosen for their tractability, each incorporate some aspects of the field and flow geomtries encountered in solar-terrestrial applications, and they provide a starting point for further analytical as well as numerical studies of reconnection.     

Why space physics needs to go beyond the MHD box

Magnetohydrodynamic (MHD) theory has been used in space physics for more than forty years, yet many important questions about space plasmas remain unanswered. We still do not understand how the solar wind is accelerated, how mass, momentum and energy are transported into the magnetosphere and what mechanisms initiate substorms. Questions have been raised from the beginning of the space era whether MHD theory can describe correctly space plasmas that are collisionless and rarely in thermal equilibrium. Ideal MHD fluids do not induce electromotive force, hence they lose the capability to interact electromagnetically. No currents and magnetic fields are generated, rendering ideal MHD theory not very useful for space plasmas. Observations from the plasma sheet are used as examples to show how collisionless plasmas behave. Interpreting these observations using MHD and ideal MHD concepts can lead to misleading conclusions. Notably, the bursty bulk flows (BBF) with large mean velocities left(〈 v 〉≥400 km s right) that have been interpreted previously as E×B flows are shown to involve much more complicated physics. The sources of these nonvanishing 〈 v 〉 events, while still not known, are intimately related to mechanisms that create large phase space gradients that include beams and acceleration of ions to MeV energies. The distributions of these nonvanishing 〈 v 〉 events are associated with large amplitude variations of the magnetic field at frequencies up to and exceeding the local Larmor frequency where MHD theory is not valid. Understanding collisionless plasma dynamics such as substorms in the plasma sheet requires the self-consistency that only kinetic theory can provide. Kinetic modeling is still undergoing continual development with many studies limited to one and two dimensions, but there is urgent need to improve these models as more and more data show kinetic physics is fundamentally important. Only then will we be able to make progress and obtain a correct picture of how collisionless plasmas work in space.     

Structure of reconnection layers in the magnetosphere

Magnetic reconnection can lead to the formation of observed boundary layers at the dayside magnetopause and in the nightside plasma sheet of the earth's magnetosphere. In this paper, the structure of these reconnection layers is studied by solving the one-dimensional Riemann problem for the evolution of a current sheet. Analytical method, resistive MHD simulations, and hybrid simulations are used. Based on the ideal MHD formulation, rotational discontinuities, slow shocks, slow expansion waves, and contact discontinuity are present in the dayside reconnection layer. Fast expansion waves are also present in the solution of the Riemann problem, but they quickly propagate out of the reconnection layer. Our study provides a coherent picture for the transition from the reconnection layer with two slow shocks in Petschek's model to the reconnection layer with a rotational discontinuity and a slow expansion wave in Levy et al's model. In the resistive MHD simulations, the rotational discontinuities are replaced by intermediate shocks or time-dependent intermediate shocks. In the hybrid simulations, the time-dependent intermediate shock quickly evolves to a steady rotational discontinuity, and the contact discontinuity does not exist. The magnetotail reconnection layer consists of two slow shocks. Hybrid simulations of slow shocks indicate that there exists a critical number,M _c, such that for slow shocks with an intermediate Mach numberM _IM _c, a large-amplitude rotational wavetrain is present in the downstream region. For slow shocks withM _I<M _c, the downstream wavetrain does not exist. Chaotic ion orbits in the downstream wave provide an efficient mechanism for ion heating and wave damping and explain the existence of the critical numberM _c in slow shocks.     

Grad-Shafranov Reconstruction of Magnetic Flux Ropes in the Near-Earth Space

Electric currents permeate space plasmas and often have a significant component along the magnetic field to form magnetic flux ropes. A larger spatial perspective of these structures than from the direct observation along the satellite path is crucial in visualizing their role in plasma dynamics. For magnetic flux ropes that are approximately two-dimensional equilibrium structures on a certain plane, Grad-Shafranov reconstruction technique, developed by Bengt Sonnerup and his colleagues (see Sonnerup et al. in J. Geophys. Res. 111:A09204, 2006), can be used to reveal two-dimensional maps of associated plasma and field parameters. This review gives a brief account of the technique and its application to magnetic flux ropes near the Earth’s magnetopause, in the solar wind, and in the magnetotail. From this brief survey, the ranges of the total field-aligned current and the total magnetic flux content for these magnetic flux ropes are assessed. The total field-aligned current is found to range from ∼0.14 to ∼9.7×10⁴ MA, a range of nearly six orders of magnitude. The total magnetic flux content is found to range from ∼0.25 to ∼2.3×10⁶ MWb, a range of nearly seven orders of magnitude. To the best of our knowledge, this review reports the largest range of both the total field-aligned current and the total magnetic flux content for magnetic flux ropes in space plasmas.     

Complexity,Forced and/or Self-Organized Criticality,and Topological Phase Transitions in Space Plasmas

The first definitive observation that provided convincing evidence indicating certain turbulent space plasma processes are in states of ‘complexity’ was the discovery of the apparent power-law probability distribution of solar flare intensities. Recent statistical studies of complexity in space plasmas came from the AE index, UVI auroral imagery, and in-situ measurements related to the dynamics of the plasma sheet in the Earth's magnetotail and the auroral zone. In this review, we describe a theory of dynamical ‘complexity’ for space plasma systems far from equilibrium. We demonstrate that the sporadic and localized interactions of magnetic coherent structures are the origin of ‘complexity’ in space plasmas. Such interactions generate the anomalous diffusion, transport, acceleration, and evolution of the macroscopic states of the overall dynamical systems. Several illustrative examples are considered. These include: the dynamical multi- and cross-scale interactions of the macro-and kinetic coherent structures in a sheared magnetic field geometry, the preferential acceleration of the bursty bulk flows in the plasma sheet, and the onset of ‘fluctuation induced nonlinear instabilities’ that can lead to magnetic reconfigurations. The technique of dynamical renormalization group is introduced and applied to the study of two-dimensional intermittent MHD fluctuations and an analogous modified forest-fire model exhibiting forced and/or self-organized criticality [FSOC] and other types of topological phase transitions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Tearing instability of reconnecting current sheets in space plasmas

Magnetic reconnection provides an efficient conversion of the so-called free magnetic energy to kinetic and thermal energies of cosmic plasmas, hard electromagnetic radiation, and accelerated particles. This phenomenon was found in laboratory and space, but it is especially well studied in the solar atmosphere where it manifests itself as flares and flare-like events. We review the works devoted to the tearing instability — the inalienable part of the reconnection process — in current sheets which have, inside of them, a transverse (perpendicular to the sheet plain) component of the magnetic field and a longitudinal (parallel to the electric current) component of the field. Such non-neutral current sheets are well known as the energy sources for flare-like processes in the solar corona. In particular, quasi-steady high-temperature turbulent current sheets are the energy sources during the main or hot phase of solar flares. These sheets are stabilized with respect to the collisionless tearing instability by a small transverse component of magnetic fiel, normally existing in the reconnecting and reconnected magnetic fluxes. The collision tearing mode plays, however, an important and perhaps dominant role for non-neutral current sheets in solar flares. In the MHD approximation, the theory shows that the tearing instability can be completely stabilized by the transverse fieldB _n if its value satisfies the conditionB _n /BS ^–3/4 B is the reconnecting component of the magnetic field just near the current sheet,S is the magnetic Reynolds number for the sheet. In this case, stable current sheets become sources of temporal spatial oscillations and usual MHD waves. The application of the theory to the solar atmosphere shows that the effect of the transverse field explains high stability of high-temperature turbulent current sheets in the solar corona. The stable current sheets can be sources of radiation in the radio band. If the sheet is destabilized (atB _n /BS ^–3/4) the compressibility of plasma leads to the arizing of the tearing instability in a long wave region, in which for an incompressible plasma the instability is absent. When a longitudinal magnetic field exists in the current sheet, the compressibility-induces instability can be dumped by the longitudinal field. These effects are significant in destabilization of reconnecting current sheets in solar flares: in particular, the instability with respect to disturbances comparable with the width of the sheet is determined by the effect of compressibility.