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.     

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.     

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.     

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.     

Magnetic reconnection,merging, and viscous interaction in the magnetosphere

Two ideas were advanced for the process of solar wind-magnetospheric interaction in the same year 1961. Dungey suggested that the interplanetary magnetic field (IMF), although weak, might determine the nature of this process by magnetic reconnection as the solar wind plasma flows across the separatrix surface which divides the IMF from the geomagnetic field. Axford and Hines pointed out that the flow inside the magnetopause is in the same sense as the magnetosheath flow and appears to be viscously coupled. Within a few years the dependence of geomagnetic activity on the IMF predicted by Dungey's mechanism was observed, and reconnection began to dominate current theories. One difficulty, that of the implied dissipation at the magnetopause, was troublesome; however, the ISEE-1/2 observations of the predicted high speed flows on several occasions was enough to convince many persons that reconnection ideas were basically correct. Several investigators found some evidence in the ISEE-3 data in the distant magnetotail for the steady-state reconnection line, as demanded by the Dungey model, in the form of a southward sense of the magnetic field through the current sheet. Here, again, there is some hard contrary evidence when the data are analyzed exactly at the cross-tail current sheet: the instantaneous values show a northward sense, even at high values of auroral activity. Coupled with the anti-Sunward plasma flow, this repudiates the steady-state Dungey model. On the other hand, it lends strong support to some kind of viscous effect through the medium of the magnetospheric boundary layer. This is not a semantic problem, as the sense of the electric field (as well as the magnetic field) is opposite for the two cases. The downfall of the reconnection model is its implicit use of frozen-field convection; this problem is obvious when the problem is viewed in three dimensions. Instead, the view is taken that the relevant process must be essentially time-dependent, three-dimensional, and localized. It is proposed that the term merging be used for this generalized timedependent form of reconnection. The merging process (whatever it is) must permit solar wind plasma to cross the magnetopause onto closed field lines of the boundary layer. Once it is there, it provides the viscous-like effect that Axford and Hines had envisaged.     

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.     

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.     

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.     

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.     

Coronal streamers' theories

Some theoretical aspects of solar coronal streamers are discussed with emphasis on the current sheet and reconnection processes going on along the axis of the streamer. The dynamics of the streamer is a combination of MHD and transport, with acceleration of particles due to reconnection and leakage of plasma outwards as a slow solar wind as the observable results. The presence of the almost-closed magnetic bottles of streamers that can store high-energy particles for significant times provides the birdcage for solar cosmic rays, the reconnection in the sheet feeds medium-energy protons into the corona for the large-scale storage needed for certain flare models, and the build-up of excess density sets the stage for coronal mass ejections.     

Cross-Scale Coupling Within Rolled-Up MHD-Scale Vortices and Its Effect on Large Scale Plasma Mixing Across the Magnetospheric Boundary

Kelvin-Helmholtz Instability (KHI) is an MHD-scale instability that grows in a velocity shear layer such as the low-latitude boundary layer of the magnetosphere. KHI is driven unstable when a velocity shear is strong enough to overcome the stabilization effect of magnetic field. When the shear is significantly strong, vortices in the nonlinear stage of KHI is so rolled-up as to situate magnetospheric plasma outward of the magnetosheath plasma and vice versa. The big question is if such highly rolled-up vortices contribute significantly to the plasma transport across the boundary and to the filling of the plasma sheet by cool magnetosheath component, which is observed under northward Interplanetary Magnetic Field (IMF) condition. Here we review our recent results from two-fluid simulations of MHD-scale KHI with finite electron inertia taken into account. The results indicate that there is coupling between the MHD-scale dynamics and electron-scale dynamics in the rolled-up stage of the vortices. While the details differ depending on the initial magnetic geometry, the general conclusion is that there is significant modification of the MHD-scale vortex flow pattern via coupling to the micro-physics. The kick-back from the parasitic micro-physics enhances highly the potential for large-scale plasma mixing of the parent MHD-scale vortices, which is prohibited by definition in ideal-MHD. We also review our recent 3-D MHD simulation results indicating that KHI vortex can indeed roll-up in the magnetotail-flank situation despite the strong stabilization by the lobe magnetic field. These results encouraged us to search for evidence of rolled-up vortices in the Cluster formation flying observations. As reviewed in this paper, a nice event was found during northward IMF interval. This interval is when the plasma transport via large scale reconnection becomes less efficient. The finding supports the argument that KHI is playing some role in transporting solar wind into the magnetosphere when the normal mode of transport cannot dominate.     

Hydrodynamic shock wave formation in the solar chromosphere and corona during flares

Basic mechanisms of the hydrodynamic shock wave formation in the solar atmosphere during flares are considered. Hydrodynamic plasma flows during flares arise due to fast energy release which is accumulated in the magnetic field of currents in the solar atmosphere. Shock waves arise as a result of rapid heating of the chromospheric upper layers from accelerated particles or heat fluxes. Powerful hydrodynamic phenomena can also arise due to explosive current sheet disruption in the region of strong magnetic field reconnection. Fundamental questions of shock wave formation and propagation in a non-homogeneous emitting solar atmosphere are discussed.An invited paper presented at STIP Workshop on Shock Waves in the Solar Corona and Interplanetary Space, 15–19 June, 1980, Smolenice, Czechoslovakia.     

Dayside Proton Aurora: Comparisons between Global MHD Simulations and IMAGE Observations

The IMAGE mission provides a unique opportunity to evaluate the accuracy of current global models of the solar wind interaction with the Earth's magnetosphere. In particular, images of proton auroras from the Far Ultraviolet Instrument (FUV) onboard the IMAGE spacecraft are well suited to support investigations of the response of the Earth's magnetosphere to interplanetary disturbances. Accordingly, we have modeled two events that occurred on June 8 and July 28, 2000, using plasma and magnetic field parameters measured upstream of the bow shock as input to three-dimensional magnetohydrodynamic (MHD) simulations. This paper begins with a discussion of images of proton auroras from the FUV SI-12 instrument in comparison with the simulation results. The comparison showed a very good agreement between intensifications in the auroral emissions measured by FUV SI-12 and the enhancement of plasma flows into the dayside ionosphere predicted by the global simulations. Subsequently, the IMAGE observations are analyzed in the context of the dayside magnetosphere's topological changes in magnetic field and plasma flows inferred from the simulation results. Finding include that the global dynamics of the auroral proton precipitation patterns observed by IMAGE are consistent with magnetic field reconnection occurring as a continuous process while the IMF changes in direction and the solar wind dynamic pressure varies. The global simulations also indicate that some of the transient patterns observed by IMAGE are consistent with sporadic reconnection processes. Global merging patterns found in the simulations agree with the antiparallel merging model, though locally component merging might broaden the merging region, especially in the region where shocked solar wind discontinuities first reach the magnetopause. Finally, the simulations predict the accretion of plasma near the bow shock in the regions threaded by newly open field lines on which plasma flows into the dayside ionosphere are enhanced. Overall the results of these initial comparisons between global MHD simulation results and IMAGE observations emphasize the interplay between reconnection and dynamic pressure processes at the dayside magnetopause, as well as the intricate connection between the bow shock and the auroral region.     

Theory and Simulation of Reconnection

Reconnection is a major commonality of solar and magnetospheric physics. It was conjectured by Giovanelli in 1946 to explain particle acceleration in solar flares near magnetic neutral points. Since than it has been broadly applied in space physics including magnetospheric physics. In a special way this is due to Harry Petschek, who in 1994 published his ground breaking solution for a 2D magnetized plasma flow in regions containing singularities of vanishing magnetic field. Petschek’s reconnection theory was questioned in endless disputes and arguments, but his work stimulated the further investigation of this phenomenon like no other. However, there are questions left open. We consider two of them – “anomalous” resistivity in collisionless space plasma and the nature of reconnection in three dimensions. The CLUSTER and SOHO missions address these two aspects of reconnection in a complementary way -- the resistivity problem in situ in the magnetosphere and the 3D aspect by remote sensing of the Sun. We demonstrate that the search for answers to both questions leads beyond the applicability of analytical theories and that appropriate numerical approaches are necessary to investigate the essentially nonlinear and nonlocal processes involved. Necessary are both micro-physical, kinetic Vlasov-equation based methods of investigation as well as large scale (MHD) simulations to obtain the geometry and topology of the acting fields and flows.     

Pulsar Wind Nebulae as Cosmic Pevatrons: A Current Sheet’s Tale

I outline, from a theoretical and somewhat personal perspective, significant features of Pulsar Wind Nebulae (PWNe) as Cosmic Accelerators. I pay special attention to the recently discovered gamma ray “flares” in the Crab Nebula’s emission, focusing on the possibility, raised by the observations, that the accelerating electric field exceeds the magnetic field, suggesting that reconnection in the persistent current layer (a “current sheet”) plays a significant role in the behavior of this well studied Pevatron. I address the present status of the termination shock model for the particle accelerator that converts the wind flow energy to the observed non-thermal particle spectra, concluding that it has a number of major difficulties related to the transverse magnetic geometry of the shock wave. I discuss recent work on the inferred pair outflow rates, which are in excess of those predicted by existing theories of pair creation, and use those results to point out that the consequent mass loading of the wind reduces the wind’s bulk flow 4-velocity to the point that dissipation of the magnetic field in a pulsar’s wind upstream of the termination shock is restored to life as a viable model for the solution of the “σ” problem. I discuss some suggestions that current starvation in the current flow supporting the structured (“striped”) upstream magnetic field perhaps induces a transition to superluminal wave propagation. I?show that current starvation probably does not occur, because those currents are carried in the current sheet separating the stripes rather than in the stripes themselves.     

Critical Issues on Magnetic Reconnection in Space Plasmas

The idea of expedient energy transformation by magnetic reconnection (MR) has generated much enthusiasm in the space plasma community. The early concept of MR, which was envisioned for the solar flare phenomenon in a simple two-dimensional (2D) steady-state situation, is in dire need for extension to encompass three-dimensional (3D) non-steady-state phenomena prevalent in space plasmas in nature like in the magnetosphere. A workshop was organized to address this and related critical issues on MR. The essential outcome of this workshop is summarized in this review. After a brief evaluation on the pros and cons of existing definitions of MR, we propose essentially a working definition that can be used to identify MR in transient and spatially localized phenomena. The word “essentially” reflects a slight diversity in the opinion on how transient and localized 3D MR process might be defined. MR is defined here as a process with the following characteristics: (1) there is a plasma bulk flow across a boundary separating regions with topologically different magnetic field lines if projected on the plane of MR, thereby converting magnetic energy into kinetic particle energy, (2) there can be an out-of-the-plane magnetic field component (the so-called guide field) present such that the reconnected magnetic flux tubes are twisted to form flux ropes, and (3) the region exhibiting non-ideal MHD conditions should be localized to a scale comparable to the ion inertial length in the direction of the plasma inflow velocity. This definition captures the most important 3D aspects and preserves many essential characteristics of the 2D case. It may be considered as the first step in the generalization of the traditional 2D concept. As a demonstration on the utility of this definition, we apply it to identify MR associated with plasma phenomena in the dayside magnetopause and nightside magnetotail of the Earth’s magnetosphere. How MR may be distinguished from other competing mechanisms for these magnetospheric phenomena are then discussed.This revised version was published online in July 2005 with a corrected cover date.     

Primary sources of large-scale Birkeland currents

We review generation mechanisms of Birkeland currents (field-aligned currents) in the magnetosphere and the ionosphere. Comparing Birkeland currents predicted theoretically with those studied observationally by spacecraft experiments, we present a model for driving mechanism, which is unified by the solar wind-magnetosphere interaction that allows the coexistence of steady viscous interaction and unsteady magnetic reconnection. The model predicts the following: (1) the Region 1 Birkeland currents (which are located at poleward part of the auroral Birkeland-current belt, and constitute quasi-permanently and stably a primary part of the overall system of Birkeland currents) would be fed by vorticity-induced space charges at the core of two-cell magnetospheric convection arisen as a result of viscous interaction between the solar wind and the magnetospheric plasma, (2) the Region 2 Birkeland currents (which are located at equatorward part of the auroral Birkeland-current belt, and exhibit more variable and localized behavior) would orginate from regions of plasma pressure inhomogeneities in the magnetosphere caused by the coupling between two-cell magnetospheric convection and the hot ring current, where the gradient-B current and/or the curvature current (presumably the hot plasma sheet-ring current) are forced to divert to the ionosphere, (3) the Cusp Birkeland currents (which are located poleward of and adjacent to the Region 1 currents and are strongly controlled by the interplanetary magnetic field (IMF)) might be a diversion of the inertia current which is newly and locally produced in the velocity-decelerated region of earthward solar wind where the magnetosphere is eroded by dayside magnetic reconnection, (4) the nightside Birkeland currents which are connected to a part of the westward auroral electrojet in the Harang discontinuity sector might be a diversion of the dusk-to-dawn tail current resulting from localized magnetic reconnection in the magnetotail plasma sheet where plasma density and pressure are reduced.     

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.