Recent Evolution in the Theory of Magnetic Reconnection and Its Connection with Turbulence

The concept of reconnection is found in many fields of physics with the closest analogue to magnetic reconnection being the reconnection of vortex tubes in hydrodynamics. In plasmas, magnetic reconnection plays an important role in release of energy associated with the magnetic shear into particle energy. Although most studies to date have focused on 2D reconnection, the availability of 3D petascale kinetic simulations have brought the complexity of 3D reconnection to the forefront in collisionless reconnection studies. Here we briefly review the latest advances in 2D and compare and contrast the results with recent 3D studies that address role of anomalous transport in reconnection, effects of turbulence on the rate and structure, among others. Another outcome of recent research is the realization of a deeper link between turbulence and reconnection where the common denominator is the generic formation of electron scale sheets which dissipate the energy through reconnection. Finally, we close the review by listing some of the major outstanding problems in reconnection physics.     

The Dawn Mission to Vesta and Ceres

A review of present understanding of the dissipation region in magnetic reconnection is presented. The review focuses on results of the thermal inertia-based dissipation mechanism but alternative mechanisms are mentioned as well. For the former process, a combination of analytical theory and numerical modeling is presented. Furthermore, a new relation between the electric field expressions for anti-parallel and guide field reconnection is developed.     

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.     

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.     

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.     

Turbulence, Magnetic Reconnection in Turbulent Fluids and Energetic Particle Acceleration

Turbulence is ubiquitous in astrophysics. It radically changes many astrophysical phenomena, in particular, the propagation and acceleration of cosmic rays. We present the modern understanding of compressible magnetohydrodynamic (MHD) turbulence, in particular its decomposition into Alfvén, slow and fast modes, discuss the density structure of turbulent subsonic and supersonic media, as well as other relevant regimes of astrophysical turbulence. All this information is essential for understanding the energetic particle acceleration that we discuss further in the review. For instance, we show how fast and slow modes accelerate energetic particles through the second order Fermi acceleration, while density fluctuations generate magnetic fields in pre-shock regions enabling the first order Fermi acceleration of high energy cosmic rays. Very importantly, however, the first order Fermi cosmic ray acceleration is also possible in sites of magnetic reconnection. In the presence of turbulence this reconnection gets fast and we present numerical evidence supporting the predictions of the Lazarian and Vishniac (Astrophys. J. 517:700–718, 1999) model of fast reconnection. The efficiency of this process suggests that magnetic reconnection can release substantial amounts of energy in short periods of time. As the particle tracing numerical simulations show that the particles can be efficiently accelerated during the reconnection, we argue that the process of magnetic reconnection may be much more important for particle acceleration than it is currently accepted. In particular, we discuss the acceleration arising from reconnection as a possible origin of the anomalous cosmic rays measured by Voyagers as well as the origin cosmic ray excess in the direction of Heliotail.     

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.     

Electron Physics of Asymmetric Magnetic Field Reconnection

There have been many significant advances in understanding magnetic field reconnection as a result of improved space measurements and two-dimensional computer simulations. While reviews of recent work have tended to focus on symmetric reconnection on ion and larger spatial scales, the present review will focus on asymmetric reconnection and on electron scale physics involving the reconnection site, parallel electric fields, and electron acceleration.     

A new paradigm for 3D Collisionless Magnetic Reconnection

A new paradigm is suggested for 3D magnetic reconnection where the interaction of reconnection processes with current aligned instabilities plays an important role. According to the new paradigm, the initial equilibrium is rendered unstable by current aligned instabilities (lower-hybrid drift instability first, drift-kink instability later) and the non-uniform development of kinking modes leads to a compression of magnetic field lines in certain locations and a rarefaction in others. The areas where the flow is compressional are subjected to a driven reconnection process. In the present paper we illustrate this series of events with a selection of simulation results. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Recent Advances in Understanding Particle Acceleration Processes in Solar Flares

We review basic theoretical concepts in particle acceleration, with particular emphasis on processes likely to occur in regions of magnetic reconnection. Several new developments are discussed, including detailed studies of reconnection in three-dimensional magnetic field configurations (e.g., current sheets, collapsing traps, separatrix regions) and stochastic acceleration in a turbulent environment. Fluid, test-particle, and particle-in-cell approaches are used and results compared. While these studies show considerable promise in accounting for the various observational manifestations of solar flares, they are limited by a number of factors, mostly relating to available computational power. Not the least of these issues is the need to explicitly incorporate the electrodynamic feedback of the accelerated particles themselves on the environment in which they are accelerated. A brief prognosis for future advancement is offered.     

Radio Diagnostics of the Solar Flare Reconnection

First, high-frequency (HF) slowly drifting pulsating structures are interpreted as radio emissions of electron beams accelerated in the magnetic reconnection volume and injected into magnetic islands (plasmoids). Then, the time evolution of plasma parameters (density, magnetic field, etc.) in a 2-D MHD model of solar flare reconnection is computed numerically. Assuming plasma radio emission from locations where the “double-resonance’’ instability generates upper-hybrid (UH) waves due to unstable distribution function of suprathermal electrons, the radio spectra and spatial source structures in the reconnection region are modeled. By comparison of the modeled and observed spectra a remarkable similarity has been found between the computed narrow-band emission and the observed lace bursts. Finally, a new diagnostics of the reconnection process is proposed.     

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.     

The magnetotail and substorms

The tail plays a very active and important role in substorms. Magnetic flux eroded from the dayside magnetosphere is stored here. As more and more flux is transported to the magnetotail and stored, the boundary of the tail flares more, the field strength in the tail increases, and the currents strengthen and move closer to the Earth. Further, the plasma sheet thins and the magnetic flux crossing the neutral sheet lessens. At the onset of the expansion phase, the stored magnetic flux is returned from the tail and energy is deposited in the magnetosphere and ionosphere. During the expansion phase of isolated substorms, the flaring angle and the lobe field strength decrease, the plasma sheet thickens and more magnetic flux crosses the neutral sheet.In this review, we discuss the experimental evidence for these processes and present a phenomenological or qualitative model of the substorm sequence. In this model, the flux transport is driven by the merging of the magnetospheric and interplanetary magnetic fields. During the growth phase of substorms the merging rate on the dayside magnetosphere exceeds the reconnection rate in the neutral sheet. In order to remove the oversupply of magnetic flux in the tail, a neutral point forms in the near earth portion of the tail. If the new reconnection rate exceeds the dayside merging rate, then an isolated substorm results. However, a situation can occur in which dayside merging and tail reconnection are in equilibrium. The observed polar cap electric field and its correlation with the interplanetary magnetic field is found to be in accord with open magnetospheric models.     

On the Role of Interchange Reconnection in the Generation of the Slow Solar Wind

The heating of the solar corona and therefore the generation of the solar wind, remain an active area of solar and heliophysics research. Several decades of in situ solar wind plasma observations have revealed a rich bimodal solar wind structure, well correlated with coronal magnetic field activity. Therefore, the reconnection processes associated with the large-scale dynamics of the corona likely play a major role in the generation of the slow solar wind flow regime. In order to elucidate the relationship between reconnection-driven coronal magnetic field structure and dynamics and the generation of the slow solar wind, this paper reviews the observations and phenomenology of the solar wind and coronal magnetic field structure. The geometry and topology of nested flux systems, and the (interchange) reconnection process, in the context of coronal physics is then explained. Once these foundations are laid out, the paper summarizes several fully dynamic, 3D MHD calculations of the global coronal system. Finally, the results of these calculations justify a number of important implications and conclusions on the role of reconnection in the structural dynamics of the coronal magnetic field and the generation of the solar wind.     

Magnetic Reconnection for Coronal Conditions: Reconnection Rates, Secondary Islands and Onset

Magnetic reconnection may play an important role in heating the corona through a release of magnetic energy. An understanding of how reconnection proceeds can contribute to explaining the observed behavior. Here, recent theoretical work on magnetic reconnection for coronal conditions is reviewed. Topics include the rate that collisionless (Hall) reconnection proceeds, the conditions under which Hall reconnection begins, and the effect of secondary islands (plasmoids) both on the scaling and properties of collisional (Sweet-Parker) reconnection and on the onset of Hall reconnection. Applications to magnetic energy storage and release in the corona are discussed.     

Reconnection on open field lines ahead of coronal mass ejections

Plasma and magnetic field signatures from 29 November 1990 indicate that the Ulysses spacecraft passed through a series of interplanetary structures that were most likely formed by magnetic reconnection on open field lines ahead of a coronal mass ejection (CME). This reconnection changed the magnetic topology of the upstream region by converting normal open interplanetary magnetic field into a pair of regions: one magnetically disconnected from the Sun and the other, a tongue, connected back to the Sun at both ends. This process provides a new method for producing both heat flux dropouts and counterstreaming suprathermal electron signatures in interplanetary space. In this paper we expand upon the 29 November case study and argue that reconnection ahead of CMEs should be less common at high heliolatitudes.     

Review of Ionospheric Effects of Solar Wind Magnetosphere Coupling in the Context of the Expanding Contracting Polar Cap Boundary Model

This paper reviews the coupling between the solar wind, magnetosphere and ionosphere. The coupling between the solar wind and Earth’s magnetosphere is controlled by the orientation of the Interplanetary Magnetic Field (IMF). When the IMF has a southward component, the coupling is strongest and the ionospheric convection pattern that is generated is a simple twin cell pattern with anti-sunward flow across the polar cap and return, sunward flow at lower latitudes. When the IMF is northward, the ionospheric convection pattern is more complex, involving flow driven by reconnection between the IMF and the tail lobe field, which is sunward in the polar cap near noon. Typically four cells are found when the IMF is northward, and the convection pattern is also more contracted under these conditions. The presence of a strong Y (dawn-dusk) component to the IMF leads to asymmetries in the flow pattern. Reconnection, however, is typically transient in nature both at the dayside magnetopause and in the geomagnetic tail. The transient events at the dayside are referred to as flux transfer events (FTEs), while the substorm process illustrates the transient nature of reconnection in the tail. The transient nature of reconnection lead to the proposal of an alternative model for flow stimulation which is termed the expanding/contracting polar cap boundary model. In this model, the addition to, or removal from, the polar cap of magnetic flux stimulates flow as the polar cap boundary seeks to return to an equilibrium position. The resulting average patterns of flow are therefore a summation of the addition of open flux to the polar cap at the dayside and the removal of flux from the polar cap in the nightside. This paper reviews progress over the last decade in our understanding of ionospheric convection that is driven by transient reconnection such as FTEs as well as by reconnection in the tail during substorms in the context of a simple model of the variation of open magnetic flux. In this model, the polar cap expands when the reconnection rate is higher at the dayside magnetopause than in the tail and contracts when the opposite is the case. By measuring the size of the polar cap, the dynamics of the open flux in the tail can be followed on a large scale.     

The Topology and Behavior of Magnetic Fields Emerging at the Solar Photosphere

The nature of flux emerging through the surface layers of the Sun is examined in the light of new high-resolution magnetic field observations from the Hinode space mission. The combination of vector magnetic field data and visible-light imaging from Hinode support the hypothesis that active region filaments are created as a result of an emerging, twisted flux system. The observations do not present strong evidence for an alternate hypothesis: that the filaments form as a result of localized shear flows at the photospheric level. Examination of the vector magnetic field at very small scales in emerging flux regions suggests that reconnection at the photospheric level and below, followed by submergence of flux, is a likely and essential part of the flux emergence process. The reconnection and flux submergence are driven by granular convection.     

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.