Relationship Between Substorm Auroras and Processes in the Near-Earth Magnetotail

Although the auroral substorm has been long regarded as a manifestation of the magnetospheric substorm, a direct relation of active auroras to certain magnetospheric processes is still debatable. To investigate the relationship, we combine the data of the UV imager onboard the Polar satellite with plasma and magnetic field measurements by the Geotail spacecraft. The poleward edge of the auroral bulge, as determined from the images obtained at the LHBL passband, is found to be conjugated with the region where the oppositely directed fast plasma flows observed in the near-Earth plasma sheet during substorms are generated. We conclude that the auroras forming the bulge are due to the near-Earth reconnection process. This implies that the magnetic flux through the auroral bulge is equal to the flux dissipated in the magnetotail during the substorm. Comparison of the magnetic flux through the auroral bulge with the magnetic flux accumulated in the tail lobe during the growth phase shows that these parameters have the comparable values. This is a clear evidence of the loading–unloading scheme of substorm development. It is shown that the area of the auroral bulge developing during substorm is proportional to the total (magnetic plus plasma) pressure decrease in the magnetotail. These findings stress the importance of auroral bulge observations for monitoring of substorm intensity in terms of the magnetic flux and energy dissipation.     

The Substorm Onset Location Controversy

Recent development of popular substorm onset models was driven by the apparent controversy between ground onset mapping in the near-Earth tail and statistics of tailward flow observations (reconnection signatures), pointing to ∼ -25 R _E downtail. However, several comprehensive multi-point event studies, taking into account backward tracing of flows, place plasmoid origin closer to the near-Earth location, in better consistency with auroral onset observations. Accuracy of such remote onset positioning is about a couple of Earth radii. We further discuss possibilities of reconciliation of different onset scenarios and future critical experiments.     

Global Particle Simulation Study of Substorm Onset and Particle Acceleration

This paper reports the spatial and temporal development of Bursty Bulk Flows (BBFs) created by the reconnection as well as current disruptions (CDs) in the near-Earth tail using our 3D global EM particle simulation with a southward turning IMF in the context of the substorm onset. Recently, observations show that BBFs are often accompanied by current disruptions for triggering substorms. We haver examined the dynamics of BBFs and CDs in order to understand the timing and triggering mechanism of substorms. As the solar wind with the southward IMF advances over the Earth, the near-Earth tail thins and the sheet current intensifies. Before the peak of the current density becomes maximum, the reconnection takes place, which ejects particles from the reconnection region. Because of the earthward flows the peak of the current density moves toward the Earth. The characteristics of the earthward flows depend on the ions and electrons. Electrons flow back into the inflow region (the center of reconnection region), which provides current closure. Therefore the structure of electron flows near the reconnection region is rather complicated. In contrast, the ion earthward flows are generated far from the reconnection region. These earthward flows pile up near the Earth. The ions mainly drift toward the duskside. The electrons are diverted toward the duskside. Due to the pile-up, dawnward current is generated near the Earth. This dawnward current dissipates rapidly with the sheet current because of the opposite current direction, which coincides with the dipolarization in the near-Earth tail. At this time the wedge current may be created in our simulation model. This simulation study shows the sequence of the substorm dynamics in the near-Earth tail, which is similar to the features obtained by the multisatellite observations. The identification of the timing and mechanism of triggering substorm onset requires further studies in conjunction with observations.     

Possible Role of ion Demagnetization in the Plasma Sheet in Auroral arc and Substorm Generation

Ion demagnetization in the plasma sheet causes the formation of field-aligned current that can trigger a magnetosphere-ionosphere coupling feedback instability, which may play an important role in substorm and auroral arc generation. Since field-aligned currents close ionospheric currents, their magnitude is controlled by ionospheric conductivity. The cause of instability is the impact of increasing upward field-aligned currents on ionospheric conductivity, which in turn stimulates an increase in the field-aligned currents. When the magnitude of these currents becomes sufficiently large for the acceleration of precipitating electrons, a feedback mechanism becomes possible. Upward field-aligned currents increase the ionospheric conductivity that stimulates an explosion-like increase in field-aligned currents. It is believed that this instability may be related to substorm generation. Demagnetization of hot ions in the plasma sheet leads to the motion of magnetospheric electrons through a spatial gradient of ion population. Field-aligned currents, because of their effect on particle acceleration and the magnitude of ionospheric conductivity, can also lead to another type of instability associated with the breaking of the earthward convection flow into convection streams. The growth rate of this instability is maximum for structures with sizes less than the ion Larmor radius in the equatorial plane. This may lead to the formation of auroral arcs with widths of the order of 10 km. This instability is able to explain many features of auroral arcs, including their conjugacy in opposite hemispheres. However, it cannot explain very narrow (less than 1 km) arcs.     

Substorm timings and timescales: A new aspect

The magnetospheric substorm is a fundamental element of magnetospheric disturbances. After more than 40 years of intensive studies, various aspects of substorm morphology have been qualitatively established. Observations from the International Solar-Terrestrial Physics (ISTP) mission during the last decade have provided more detailed and complete pictures of substorms than before and, consequently, have provided new insights into substorm mechanisms. From the global auroral imaging it is shown that substorm onsets are locally confined; however, the effects of substorms involve a very large space at different times. Observations relying on in situ techniques can be misleading and can introduce confusion if not properly interpreted. On the other hand, remote sensing techniques such as global auroral imaging not only provide a robust means for studying substorm phenomenology but also yield relatively consistent results. This article reviews and summarizes a number of substorm studies conducted based primarily on global auroral images from NASA's Polar satellite, with a main focus on “quantitative” substorm morphology (i.e., onset timing, locations, energy input, and substorm timescales). These studies conclude that (1) auroral breakups are the most reliable substorm indicator, whereas other commonly used onset proxies may not always be associated with substorms and are subject to a propagation delay; (2) after breakup, the expanded auroral bulge can move either westward (60%) or eastward (40%); and (3) a typical substorm expansion phase lasts ～10 minutes and increases with increasing distances from the onset. A key conclusion from some recent studies seems to suggest that magnetotail reconnection, if it ever exists, is a consequence of substorm expansion onset. These findings provide constraints for substorm models and theories.     

Potential Plasma Instabilities For Substorm Expansion Onsets

Space plasmas present intriguing and challenging puzzles to the space community. Energy accessible to excite instabilities exists in a variety of forms, particularly for the magnetospheric environment prior to substorm expansion onsets. A general consensus of the pre-expansion magnetosphere is the development of a thin current sheet in the near-Earth magnetosphere. This review starts with a short account of the two major substorm paradigms. Highlights of some observations pertaining to the consideration of potential plasma instabilities for substorm expansion are given. Since a common thread of these paradigms is the development of a thin current sheet, several efforts to model analytically a thin current sheet configuration are described. This leads to a review on the instability analyses of several prominent candidates for the physical process responsible for substorm expansion onset. The potential instabilities expounded in this review include the cross-field current, lower-hybrid-drift, drift kink/sausage, current driven Alfvénic, Kelvin-Helmholtz, tearing, and entropy anti-diffusion instabilities. Some recent results from plasma simulations relevant to the investigation of these plasma instabilities are shown. Although some of these instabilities are generally conceived to be excited in spatially localized regions in the magnetosphere, their potentials in yielding global consequences are also explored.     

Substorm Trigger Processes in the Magnetotail: Recent Observations and Outstanding Issues

The present article reviews recent studies about near-Earth substorm processes. A focus is placed on the relationship between two fundamental processes, that is, tail current disruption (TCD) and the formation of a near-Earth neutral line (NENL). The former is inferred to cause dipolarization, and the latter is often associated with the fast plasma flow in the plasma sheet. Whereas it is inferred from the directions of fast plasma flows that the NENL is formed at 20–30 R _E from the Earth, dipolarization is most manifest in the near-Earth (6.6–12 R _E) region. The observation of the fast plasma flow prior to substorm (Pi2) onsets favors the idea that the NENL is formed first and dipolarization is the effect of the pile-up of magnetic flux convected earthward from the NENL, which is called the pile-up model. The present paper addresses several outstanding issues regarding this model, including (1) the interpretation of plasma flow deceleration in terms of the flux pile up, (2) highly irregular magnetic fluctuations observed in the near- Earth region, (3) the spatial coherency of the fast plasma flow, (4) the spatial structure and expansion of dipolarization region, and (5) the explosive growth phase. The paper also proposes the possibility that TCD is an independent process, but the formation of the NENL sets a favorable condition for it.     

Wave-particle interactions and their relevance to substorms

Wave-particle effects are implicit in most models of radial diffusion and energization of Van Allen belt particles; they were explicitly used in the wave turbulence model for trapped particle precipitation and trapped flux limitations by Kennel and Petschek, Cornwall and by many others. Liemohn used wave-particle interactions to work out a theory of path-integrated whistler amplification process to explain the lack of large per-hop attenuation of multiple-hop LF whistlers.Others have now used wave-particle interactions to construct theories of ELF and VLF chorus. In the present paper we shall review the observations and some of the pertinent theoretical interpretations of wave-particle effects as they relate to substorm and storm-time phenomena. If substorms develop as a result of magnetic merging, then it seems clear that wave-particle interactions in the dissipative or so-called diffusion region of the reconnection zone may be of great importance. The plasma sheet thinning and flow towards the Earth lead inevitably to the development of particle distribution functions that contain free energy in a pitch-angle anisotropy. Such free energy can be released via plasma wave instabilities. The subsequent wave-particle interactions can result in both strong and weak diffusion of particles into loss cones with consequent precipitation fluxes into the auroral zone. Ring current proton spectra also should be unstable against various plasma instabilities with consequent ring current decay and precipitations. Wave-particle interactions must play some important roles in auroral arcs, electrojets and other phenomena related to substorms. These aspects of wave-Paticle interaction will be covered     

Role of ionospheric effects and plasma sheet dynamics in the formation of auroral arcs

At the ionospheric level, the substorm onset (expansion phase) is marked by the initial brightening and subsequent breakup of a pre-existing auroral arc. According to the field line resonance (FLR) wave model, the substorm-related auroral arc is caused by the field-aligned current carried by FLRs. The FLRs are standing shear Alfvén wave structures that are excited along the dipole/quasi-dipole lines of the geomagnetic field. The FLRs (that can cause auroral arc) thread from the Earthward edge of the plasma sheet and link the auroral arc to the plasma sheet region of 6–15 R _E. The region is associated with magnetic fluctuations that result from the nonlinear wave-wave interactions of the cross-field current-instability. The instability (excited at the substorm onset) disrupts the cross-tail current which is built up during the growth phase of the substorms and results in magnetic fluctuations. The diversion of the current to polar regions can lead to auroral arc intensification. The current FLR model is based on the amplitude equations that describe the nonlinear space-time evolution of FLRs in the presence of ponderomotive forces exerted by large amplitude FLRs (excited during substorms). The present work will modify the FLR wave model to include the effects arising from magnetic fluctuations that result from current disruption near the plasma sheet (6–15 R _E). The nonlinear evolution of FLRs is coupled with the dynamics of plasma sheet through a momentum exchange term (resulting from magnetic fluctuations due to current disruption) in the generalized Ohm's law. The resulting amplitude equations including the effects arising from magnetic fluctuations can be used to study the structure of the auroral arcs formed during substorms. We have also studied the role of feedback mechanism (in a dipole geometry of the geomagnetic field) in the formation of the discrete auroral arc observed on the nightside magnetosphere. The present nonlinear dispersive model (NDM) is extended to include effects arising from the low energy electrons originating from the plasma sheet boundary layer. These electrons increase the ionospheric conductivity in a localized patch and enhance the field-aligned current through a feedback mechanism. The feedback effects were studied numerically in a dipole geometry using the the NDM. The numerical studies yield the magnitude of the field-aligned current that is large enough to form a discrete auroral arc. Our studies provide theoretical support to the observational work of Newell et al. that the feedback instability plays a major role in the formation of the discrete auroral arcs observed on the nightside magnetosphere.     

A Multiscale Model for Substorms

Most substorm researchers assume substorms to be caused by a unique large-scale process. However, a critical evaluation of substorm observations indicates that a new paradigm is needed to understand the substorm phenomenon and the magnetospheric dynamics in general. It is proposed here that substorms involve a number of physical processes covering over a wide range of spatial and temporal scales. Potential candidates include the kinetic or shear ballooning instability, the Kelvin-Helmholtz instability, the cross-field current instability, the tearing instability, and magnetic reconnection. An observational constraint on the qualified process for substorm onset is that it must be associated with magnetic field lines of auroral arcs since substorm onsets start with brightening of a pre-existing auroral arc. Which particular process dominates in a given substorm depends on the present and past states of the magnetosphere as well as the external solar wind. The magnetosphere is almost perpetually driven by the solar wind to be near a critical point and in a metastable state. Magnetospheric disturbances occur sporadically in multiple localized sites. A substorm is realized when the combined effect of these localized disturbances become global in extent, much like the system-wide activity in a sandpile or avalanche model.     

Physics of Substorm Growth Phase,Onset, and Dipolarization

A new scenario of substorm growth phase, onset and dipolarization during expansion phase and the corresponding physical processes are presented. During the growth phase, as a result of enhanced plasma convection, the plasma pressure and its gradient continue to be enhanced over the quiet-time values in the plasma sheet. Toward the late growth phase, a strong cross-tail current sheet is formed in the near-Earth plasma sheet region, where a local magnetic well is formed. The equatorial plasma beta (β _eq ) can reach a local maximum with value larger than 50 and the cross-tail current density can be enhanced to over 10nA/m² as obtained from 3D quasi-static magnetospheric equilibrium solutions for the growth phase. The most unstable kinetic ballooning instabilities (KBI) are expected to be located in the tailward side of the strong cross-tail current sheet region. The field lines in the most unstable KBI region map to the transition region between the region-l and region-2 currents in the ionosphere, which is consistent with the observed initial brightening location of the breakup arc in the intense proton precipitation region. The KBI explains the AMPTE/CCE observations that a low frequency instability with a wave period of 50–75 seconds is excited about 2–3 min prior to substorm onset and grows exponentially to a large amplitude at the onset of current disruption (or current reduction). At the onset of current disruption higher frequency instabilities are excited so that the plasma and electromagnetic field fluctuations form a strong turbulent state. Plasma transport takes place due to the strong turbulence to relax the ambient plasma pressure profile so that the plasma pressure and current density are reduced and the ambient magnetic field intensity increases by more than a factor of 2–3 in the high-β _eq region and the field line geometry recovers from tail-like to dipole-like – dipolarization.     

Global Imaging of Proton and Electron Aurorae in the far Ultraviolet

The IMAGE spacecraft carries three FUV photon imagers, the Wideband Imaging Camera (WIC) and two channels, SI-12 and SI-13, of the Spectrographic Imager. These provide simultaneous global images, which can be interpreted in terms of the precipitating particle types (protons and electrons) and their energies. IMAGE FUV is the first space-borne global imager that can provide instantaneous global images of the proton precipitation. At times a bright auroral spot, rich in proton precipitation, is observed on the dayside, several degrees poleward of the auroral zone. The spot was identified as the footprint of the merging region of the cusp that is located on lobe field lines when IMF B_z was northward. This identification was based on compelling statistical evidence showing that the appearance and location of the spot is consistent with the IMF B_z and B_y directions. The intensity of the spot is well correlated with the solar wind dynamic pressure and it was found that the direct entry of solar wind particles could account for the intensity of the observed spot without the need for any additional acceleration. Another discovery was the observation of dayside sub-auroral proton arcs. These arcs were observed in the midday to afternoon MLT sector. Conjugate satellite observations showed that these arcs were generated by pure proton precipitation. Nightside auroras and their relationship to substorm phases were studied through single case studies and in a superimposed epoch analysis. It was found that generally there is substantial proton precipitation prior to substorms and the proton intensity only doubles at substorm onset while the electron auroral brightness increases on average by a factor of 5 and sometimes by as much as a factor of 10. Substorm onset occurs in the central region of the pre-existing proton precipitation. Assuming that nightside protons are precipitating from a quasi-stable ring current at its outer regions where the field lines are distorted by neutral sheet currents we can associate the onset location with this region of closed but distorted field lines relatively close to the earth. Our results also show that protons are present in the initial poleward substorm expansion however later they are over taken by the electrons. We also find that the intensity of the substorms as quantified by the intensity of the post onset electron precipitation is correlated with the intensity of the proton precipitation prior to the substorms, highlighting the role of the pre-existing near earth plasma in the production of the next substorm.     

Ballooning Instability as a Mechanism of the Near-Earth Onset of Substorms

After introducing a mathematical definition of the tail-like equilibrium and the dipole-like equilibrium in the magnetosphere, it is shown by using physical intuition based on the Energy Principle that the incompressible assumption for the ballooning instability is more valid for the tail-like configuration when the unstable ballooning mode is strongly localized near the equator. Therefore, before the substorm onset, the near-Earth plasma sheet becomes more tail-like and more likely to be subject to the ballooning instability without the stabilizing influence of the compressibility, when the critical plasma due to the stabilizing tension force is exceeded. The onset of the ballooning instability in the near-Earth plasma sheet seems promisingly relevant to the substorm onset phenomena. Also, the effect of the stochastic plasma dynamics on the ballooning and interchange instabilities is clearly shown.     

Substorms and Their Solar Wind Causes

Consequences of the solar wind input observed as large scale magnetotail dynamics during substorms are reviewed, highlighting results from statistical studies as well as global magnetosphere/ionosphere observations. Among the different solar wind input parameters, the most essential one to initiate reconnection relatively close to the Earth is a southward IMF or a solar wind dawn-to-dusk electric field. Larger substorms are associated with such reconnection events closer to the Earth and the magnetotail can accumulate larger amounts of energy before its onset. Yet, how and to what extent the magnetotail configuration before substorm onset differs for different solar wind driver is still to be understood. A strong solar wind dawn-to-dusk electric field is, however, only a necessary condition for a strong substorm, but not a sufficient one. That is, there are intervals when the solar wind input is processed in the magnetotail without the usual substorm cycle, suggesting different modes of flux transport. Furthermore, recent global observations suggest that the magnetotail response during the substorm expansion phase can be also controlled by plasma sheet density, which is coupled to the solar wind on larger time-scales than the substorm cycle. To explain the substorm dynamics it is therefore important to understand the different modes of energy, momentum, and mass transport within the magnetosphere as a consequence of different types of solar wind-magnetosphere interaction with different time-scales that control the overall magnetotail configuration, in addition to the internal current sheet instabilities leading to large scale tail current sheet dissipation.     

Steady magnetospheric convection: A review of recent results

Theoretical pressure balance arguments have implied that steady convection is hardly possible in the terrestrial magnetotail and that steady energy input necessarily generates a cyclic loading-unloading sequence, i.e., repetitive substorms. However, observations have revealed that enhanced solar wind energy input to the magnetospheric system may either lead to substorm activity or enhanced but steady convection. This topic is reviewed with emphasis on several recent case studies of the Steady Magnetospheric Convection (SMC) events. In these cases extensive data sets from both satellite and ground-based instruments from various magnetospheric and ionospheric regions were available.Accurate distinction of the spatial and temporal scales of the magnetospheric processes is vital for correct interpretation of the observations during SMC periods. We show that on the large scale, the magnetospheric configuration and plasma convection are stable during SMC events, but that both reveal considerable differences from their quiet-time assemblies. On a shorter time scale, there are numerous transient activations which are similar to those found during substorms, but which presumably originate from a more distant tail reconnection process, and map to the poleward boundary of the auroral oval. The available observations and the unresolved questions are summarized here.The tail magnetic field during SMC events resembles both substorm growth and recovery phases in the neartail and midtail, respectively, but this configuration may remain stable for up to ten hours. Based on observations and model results we discuss how the magnetospheric system avoids pressure balance problems when the plasma convects earthward.Finally, the importance of further coordinated studies of SMC events is emphasized. Such studies may shed more light on the substorm dynamics and help to verify quantitatively the theoretical models of the convecting magnetosphere.     

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.     

Observations of inverted-V electron precipitation

The characteristics of inverted-V electron precipitation fluxes deduced predominantly from observations by the Atmosphere Explorer satellites are reviewed. The energy and pitch angle distributions are presented and shown to be generally in agreement with acceleration by a parallel electrostatic potential. Characteristics of secondary electrons are examined, and effects of beam plasma instabilities on these electrons are discussed. The properties of the monoenergetic component are compared with theoretical models of creating parallel DC electric fields, and found to favor the anomalous resistivity model. The article also discusses relations of inverted-V events with other auroral phenomena including auroras, electrostatic shocks, convective electric field reversals, field-aligned currents and wave emissions. The principal conclusions are: (1) plasma sheet electrons are continuously accelerated to form inverted-V structures in the pre-midnight hemisphere independent of substorm phase, (2) the acceleration processes are probably related to large scale electrostatic wave turbulence observed at altitudes of a few thousand kilometers, (3) narrow bursts of intense electron precipitation fluxes are found to be imbedded within some inverted-V's. It is argued that the narrow bursts of intense electron precipitation have the proper characteristics to cause discrete auroral arcs in the atmosphere. We suggest that these narrow bursts are accelerated by an electrostatic shock at higher altitude and capable of producing discrete auroral arcs below the observing satellite.     

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.     

Transient phenomena in the magnetotail and their relation to substorms

Recent observations of magnetic field, plasma flow and energetic electron anisotropies in the magnetotail plasma sheet during substorms have provided strong support for the idea that a magnetospheric substorm involves the formation of a magnetic neutral line (the substorm neutral line) within the plasma sheet at X _SM — 10R _E to -25R _E. An initial effect, in the tail, of the neutral line's formation is the severance of plasma sheet field lines to form a plasmoid, i.e., a closed magnetic loop structure, that is quickly (within 5–10 min) ejected from the tail into the downstream solar wind. The plasmoid's escape leaves a thin downstream plasma sheet through which plasma and energetic particles stream continuously into the solar wind, often throughout the duration of the substorm's expansive phase. Southward oriented magnetic field threads this tailward-flowing plasma but its detection, as an identifier of the occurrence of magnetic reconnection, is made difficult by the thinness and turbulence of the downstream plasma sheet. The thinning of the plasma sheet downstream of the neutral line is observed, by satellites located anywhere but very close to the tail's midplane, as a plasma dropout. Multiple satellite observations of plasma droputs suggest that the substorm neutral line often extends across a large fraction (> ) of the tail's breadth. Near the time of substorm recovery the substorm neutral line moves quickly tailward to a more distant location, progressively inflating the closed field lines earthward of it, to reform the plasma sheet.Proceedings of the Symposium on Solar Terrestrial Physics held in Innsbruck, May–June 1978.     

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.