JournalofAtmospheric and TerrestrialPhysics, Vol. 57, No. 12, pp. 1397 1414, 1995
Elsevier Science Ltd Printed in Great Britain 0021 9169/95 $9.50+0.00
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Magnetospheric tail structure : concepts, problems and storm-time development of the auroral oval Yu. I. Galperin Space Research Institute of Russian Academy of Sciences, 117810, Moscow, Russia (Received in final form 18 July 1994; accepted 4 August 1994)
Abstract--Thispaper reviews current knowledge on links between the Earth's magnetic tail and the auroral oval, and identifies some problems remaining. It considers electrons as tracers of the geomagnetic field, boundaries between different regions, plasma flows, and pressure balance conditions. The auroral arc is considered as a standing discontinuity in the flow of central plasma sheet (CPS) plasma field-aligned current systems are also proposed. The plasma instability responsible for the breakup phase of an auroral substorm is also discussed.
1. INTRODUCTION Despite more than 30 years of magnetospheric tail exploration since its discovery by Ness (1965), the general understanding of its structure and governing physics is still inadequate. There are several ideas, some of them confimaed but some of them conflicting, despite the availability of very sophisticated and comprehensive data sets from high altitude satellites and many high level efforts in the modelling of the tail phenomena. When the data sets from a single spacecraft, on the magnetic field, particles, flows and currents began to be analyzed simultaneously and together with the data from other spacecraft and ground observations, it appeared that several simple tests for widely accepted paradigms of the tail structure show negative results, at least sometimes. However, in the last few years, significant progress in tackling these problems begin to emerge due to new experimental data from the AMPTE, Galileo and GEOTAIL spacecraft, thorough data analysis of some preceding missions, and new theoretical ideas supported by modeling on powerful supercoml:,uters. The recently launched GEOTAIL Probe together with the INTERBALL, RELIC-2, POLAR, W I N D and CLUSTER expected to be launched in 1994-1996 will be the most important experimental effort ever performed to resolve the basic problems of magnetotail physics. Therefore, it is of interest to review some contemporary concepts, results and puzzles concerning the structur,~ and dynamics of the tail for a critical analysis in the light of the new experimental possibilities. We shall consider here the tail during
approximately steady conditions with small, or moderate, southward Interplanetary Magnetic Field (IMF), as well as some problems related to the substorm growth phase and onset. This review is a part of the ongoing debates on most of the problems of magnetotail physics. It is obviously polarised by the opinions of the author which are by no means always shared by the magnetospheric community. 2. TAILMODELSAND MAPPING 2.1. Natural tracers o f the magnetospheric field Very significant progress in the understanding of general structure of the tail magnetic field was achieved in a series of average models constructed by Tsyganenko (1987, 1989) which are now being developed further and made more sophisticated (see Tsyganenko (1990)). These models were widely compared with various data sets and used to relate the auroral features observed at low altitudes to the particular plasma domains in the outer magnetosphere and in particular in the tail (see, for example, Galperin and Feldstein, 1991 ; Elphinstone et al., 1991a; Bosqued et al., 1986; Ashour-Abdalla et al., 1992). They were successfully modified to include an enhanced and thinned neutral sheet current during the substorm growth phase by Mcllwain (1992), Pulkkinen et al. (1991a,b; 1992), and Baker et al. (1993). But obviously some physical means, or tools, need to be found to check these models experimentally for particular case studies in a real, varying, magnetospheric structure, rather than the average one.
Y. I. Galperin PLASM.O31~ERIC ELECTROll I~Ngfrv
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Fig. 1. A schematic electron and ion energy-time spectrogram for a near-midnight polar pass of a lowaltitude satellite. Specific spectral features allow one to identify the Diffuse Zone with two (older and more recent) soft electron precipitation boundary positions (SEBI and SEB2), discrete precipitation structures inside the oval : inverted Vs for electrons and an "oblique inverted-V" (VDIS-I) for different ions, and a narrow polar diffuse zone with a discrete ion dispersion structure (VDIS-II) at the polar edge of the oval (bottom). Features of the precipitation pattern which are used as natural tracers to the magnetospheric plasma domains are indicated in the middle of the figure, and the gross magnetospheric structure mapping is shown at the top.
One of the main difficulties in comparing low altitude data with such averaged models is that extended plasma domains in the tail can map to rather narrow bands that are extended along the auroral oval with varying auroral precipitation structures. These narrow bands can sometimes be missed in analysis due to temporal or local variations. Thus, natural tracers, comprising a part of plasma characteristics observable both at low altitudes and in the tail, must be found and used to delineate the respective mappings. This was the line of reasoning taken by Feldstein and Galperin (1985, 1993a) and Galperin and Feldstein (1991). Several natural tracers (see Fig. l) for the near midnight region were ident-
ified and used in the analysis of the mapping problem by the above authors. The tracers are : the L-shell of the soft electron precipitation boundary Lseb, which is the equatorial boundary of precipitation for electrons of < ~ 1-2 keV during relatively stable conditions ; the "sharp" poleward boundary Ls for stable trapping of high energy electrons, and the two specific types of velocity-dispersed ion precipitation structures identified from the A U R E O L - 3 measurements--the VDIS-I and VDIS-II. We shall here briefly consider them. (1) The Soft Electron Precipitation Boundary (SEB) of soft electrons, which are precipitated pole-
Magnetospheric tail structure ward of the SEB L-shell, producing the so called diffuse aurora (Lui et al., 1973). It delineates the equatorial boundary of' the large-scale magnetospheric convection in the near-midnight local time sector. Hot magnetotail plasma from the tail during steady conditions can drift earthward until reaching this boundary, which arises due to the so called shielding process of the large-scale convection from the inner magnetosphere (connected mainly with the polarization of the hot plasma injected from the tail (see Erickson et al., 1991, and reference~ therein) and also of high energy trapped particles, especially at lower latitudes). This boundary can be easily measured as the equatorial boundary of the diffuse soft auroral precipitation at low altitudes and the boundary of dense hot plasma at high altitudes, from about 1800 to 0600 MLT. From about 2100 to 0600 hours MLT, it is closely related to the plasmapause if it is defined as a convection boundary associated with a sharp drop in the thermal (less than several e V ) plasma density. SEB statistics have been shown in Galperin et al. (1977), Sauvaud et al. (1983), Gussenhoven et al. (1981, 1983). Valchuk et al. (1986). (2) The Sharp Boundary Ls of stable trapping of high energy outer belt electrons (say, 50-100 keV), extensively studied with Alouette and ISIS data (see McDiarmid and Burrows McDiarmid et al., 1975) and from the Azur data (Rossberg, 1978). This boundary is characterized by the change from anisotropic trapped pitch-angle distributions to the isotropic, or sometimes field-aligned, distributions in the near-midnight MLT-sector. This change delineates the L-shell at which a rather sharp transition occurs from a neardipolar magnetic field (at relatively quiet times) to a stretched "tail-like" magnetic field. The sharp increase of the magnetic field curvature (decrease of the radius of curvature Rc) leads to a violation of magnetic moment conservation for particles with comparable, or larger, L~trmor radius RL (Sergeev and Tsyganenko, 1982), and thus to rapid particle losses from the trapped orbits. Strong scattering in this region occurs for trapped particles whose Larmor radius RL ~ Rc, the so called strong stochasticity condition (Buchner and Zelenyi, 1989). A resonant interaction develops between the particle's two degrees of freedom--the Larmor rotation, and the boancing between the magnetic mirror points. It leads to strong scattering and/or acceleration of a part of Lhe particle distribution function, so that the magnetic moment for these particles is not conserved. As was shown by Sergeev and Tsyganenko (1982), Sergeev el al. (1993), this process in steady conditions is the main cause of the outer boundary of stable trapping and they call it "the isotropic bound-
ary". The rigidity-latitude profile of the stably trapped particles can be used to improve the description of the magnetic field curvature in magnetospheric models. Other processes of trapped particle removal are also involved as was demonstrated by Imhof et al. (1993). This boundary at local times near midnight is located close to the equatorial boundary of the auroral oval defined as the site of bright discrete auroral forms (Feldstein and Starkov, 1970 ; Feldstein, 1974; Deehr et al., 1976 ; Lui and Burrows, 1978). The boundary of the stably trapped high energy electrons of the outer belt Ls can be reliably measured both at low altitudes (see McDiarmid and Burrows, 1968) and at high equatorial altitudes (see West et al., 1973, 1978), and constitutes the most important and reliable tracer. From the location of this boundary in the near-midnight region and from its near co-location with the equatorial boundary of the bright discrete auroral forms in the oval, and also with the boundary between the Region I/Region II large scale field-aligned currents (see Feldstein and Galperin, 1985), it is clear that this boundary divides two qualitatively different large-scale magnetospheric plasma domains. It is also obvious that the diffuse auroral zone, in the near-midnight region, constitutes the precipitation which arises mostly from the hot thermal plasma drifted inward from the tail. This hot plasma is supplied more or less continuously by convection into the nightside part of the outer belt. It is altered, and mixed with, the decaying quasi-trapped populations of energetic particles, presumably the "plasma clouds", injected by preceding non-stationary magnetospheric activity processes (DeForest and Mcllwain, 1971). In other words, this hot plasma has come from the central plasma sheet (CPS), but is no longer on the CPS magnetic flux tubes, if a distinction is made between the outer radiation belt of trapped particles and the extended CPS plasma domain in the tail. In Feldstein and Galperin (1985), the plasma domain of the hot thermal plasma within the outer belt L-shells was called "the remnant layer" as it consists of remnants of the tail plasma convected, or injected, and decaying, in the near-dipolar inner magnetosphere. (3) Discovered from the data of the AUREOL-3 satellite for quiet times, the so called Velocity Dispersed Ion Structure of the first type (VDIS-I). About 80 cases of the VDIS-I were found from the AUREOL-3 data (see Bosqued et al., 1986). They were rather narrow (not more than 1-2 degrees of latitude), consisted mostly of H ÷ and sometimes O ÷ with ion energies of 0.1 5 keV, and appeared during quiet or weakly disturbed times, often during substorm growth
Y. I. Galperin
phases or recovery phases. A case of similarly dispersed but much wider ( > 5 degrees in latitude) ion precipitation was observed during a very disturbed time from the DE-1 satellite by Winningham et al. (1984), who suggested its origin to be upward ion acceleration in the conjugate auroral ionosphere. Thus the VDIS-I events, more narrow, and observed at quiet times, differ significantly from the unique case found from the DE-1. But the interpretation suggested by Winningham et al. (1984) was applied for the VD1S-I and found to be quite adequate quantitatively. Taking the energy-latitude dependence of the neighbouring electron inverted-V event located just poleward of the VDIS-I and fitting by only one free parameter--the bounce averaged equatorward electric drift velocity V~--the whole VDIS-I ion energy dispersion structure can be reproduced, sometimes for both H + and O + in the model magnetosphere (Bosqued et al., 1986). These cases, though relatively rare (about 10-15% of passes), show that, first, the field lines of the inverted-V events, typical for the auroral oval of discrete forms, are closed and do not extend far into the tail. They extend tailward to radial distances of not more than several tens of Earth radii (Re) and thus belong in the low-latitude part of the tail, to the CPS. In steady conditions, the auroral arcs and inverted-V events are conjugate. So the ions accelerated upwards in one hemisphere must be equally decelerated in the conjugate one, if they are not displaced by a drift from the 'parent' inverted-V flux tube. Indeed, in more than 85% of the AUREOL-3 passes at low altitudes no VDIS-I events are noted. Thus, it is still not completely clear what physical process leads to the appearance, or enhancement, of the earthward radial drift of the low-energy ions in a VDIS-I event, which allows them to escape the decelerating field-aligned potential difference at the descending branch of their trajectory. Probably, this could be the appearance of an induction electric field due to some current variations at these distances, at least during the growth phase cases when such a field was predicted (see Schindler, 1974; Murphy et al., 1975; Pellinen and Heikkila 1984). Secondly, the energies of the VDIS-I ions, which were accelerated upward in the conjugate ionosphere, are nearly the same as the energies of the downward accelerated electrons in the 'parent electron invertedV'. This implies that the dominant acceleration process for both electrons and the VDIS-I ions within the parent inverted-V flux tubes can be only the electrostatic field-aligned acceleration (or a quasi-electrostatic acceleration by multiple double layers) while other processes modifying the distribution functions must be secondary. Also, these structures imply that
the upward ion beams have some stability, being capable of travelling from auroral altitudes through the CPS to the conjugate auroral oval. This is consistent with observations of the "source cone" ion structures observed from geostationary orbit (see McIlwain and Whipple, 1986). (4) Another type of the Velocity-Dispersed Ion Structures found from the AUREOL-3 data (Kovrazhkin et al., 1987 ; Zelenyi et al., 1990), the VDISII. They are located close to poleward of the polar edge of the bright discrete forms of the auroral oval, so that all the inverted-V events on a low-altitude pass are located equatorward from the VDIS-II structure. The ion energies observed in VDIS-II events can be higher than for the VDIS-I and range from about 3 keV to 25 keV or even more. The velocity-dispersion forms could vary, but in the majority of the events (from about a hundred observed) they are very similar to those within the Plasma Sheet Boundary Layer (PSBL) described by Takahashi and Hones (1988), if suitable account is given to the magnetic field convergence from the PSBL to the low altitudes of the AUREOL-3 (400-2000km). Recently very comprehensive measurements from the AKEBONO (EXOS-D) satellite by Saito et al. (1992), made above the main acceleration region, have fully confirmed the AUREOL-3 results on VDIS-II. They have also shown, as was expected, that the occurrence rate of these events at high altitudes is rather high (about 40%, i.e. several times higher than at low altitudes from the AUREOL-3 data), and that their latitudinal extent is not limited by the field-aligned potential drops above the oval. These data make a strong case for the identification of the VDIS-II events with the PSBL ion beams, thus establishing their mapping, one to another. It can be noted that these events are observed within the so called Polar Diffuse Zone adjacent, and poleward of, the bright discrete forms of the auroral oval (see Feldstein and Galperin, 1985, 1993a; Galperin and Feldstein, 1991). This band of mostly diffuse, low energy electron precipitation, sometimes structured by weak discrete features, can be very narrow, e.g. 50 km at ionospheric altitudes; however, they can extend to much larger widths during quiet times and substorm recovery phases. A new feature at the outer boundary of the PSBL was recently discovered by Parks et al. (1992) from the ISEE data : counter-streaming beams of very low energy ( ~ 100eV) electrons (earthward) and ions (tailward). They called this structure the Low Energy Layer, or LEL. It is concluded by Feldstein and Galperin (1993b) that at low altitudes the LEL maps to the outer part, or the boundary, of the Polar Diffuse
Magnetospheric tail structure Zone. The LEL structure is very interesting because the electron beam must have originated very far in the tail and could be a result of reconnection at a distant neutral line in the tail, or it might be due to some other acceleration processes there. We shall return below to the paradigrn of the Distant Neutral Line (DNL). Further poleward at low altitudes, within the Polar Cap, particle intensities generally drop to low, but measurable, values often called "the Polar Rain", But moderately intense particle bursts and discrete auroral features appear in the Polar Cap occasionally (see Obara et al., 1993), both during disturbed and quiet times (and also during Northward IMF B conditions in the form of the so called Theta Auroras which we shall not consider in this review). These polar cap auroras show that active dynamic processes with the generation of localized field-aligned currents and particle acceleration do occur in the far tail and along the Polar Cap flux tubes. From the above considerations Feldstein and Galperin (1985, 1993a I and Galperin and Feldstein (1991) arrived at a mapping scheme for the near-midnight part of the precipitation zones for steady conditions (i.e. mostly for small or moderate southward Interplanetary Magnetic Field, IMF), which is summarized in Table 1, and graphically in Figs 1 and 2. Table 1. Mapping scheme of the near-midnight auroral regions to the generic magnetospheric plasma domains * Natural field line tracers : Soft Electron Precipitation Boundary (SEB) Stable Trapping (or, Isotropic) Boundary A~ VDIS-I (Velocity Dispersed Ion Structure, type I) equatorward from an electron Inverted-V event, i.e. within the Auroral Oval VDIS-2 (VelocityDispersed Ion Structure, type II) poleward from the polewardmost Inverted-V event, i.e. within the Polar Diffuse Zone * Resulting mappings : Diffuse auroral zone equatorward of the bright discrete auroral forms of the oval Auroral oval with bright discrete auroral forms, strong field-aligned curents Polar diffuse zone just poleward from bright discrete auroras Outer part, or boundary, of the polar diffuse zone
Outer radiation belt up to the stable trapping boundary As Central plasma sheet (cps) including the neutral sheet Boundary plasma sheet
(BPS) velocity dispersed fieldaligned ion beams Low-energy layer (LEL)
Quite another type of particle tracer is the ionospheric photoelectron boundary moving with the solar terminator position at altitudes about 200 kin. A large upward flux of superthermal photoelectrons with a characteristic energy spectrum can be identified along magnetospheric flux tubes, if the satellite potential is kept low enough. The peaks are mainly in the range 20-30 eV due to the combination of strong solar UV lines and ionization potentials of the upper atmosphere constituents but are smoothed by energy diffusion in collisions and wave-particle interactions. Experiments show that in the Earth's magnetosphere the photoelectrons from the sunlit Polar Cap can sometimes reach the conjugate non-sunlit Polar Cap at invariant latitudes up to 80 degrees, and thus can really be used as a tracer of the solar terminator position in the conjugate polar ionosphere (Galperin and Muiliarchik, 1967). Recently a new tracer was found for the LLBL footprints at medium altitudes in the dawn-prenoon sector from the VIKING satellite by Woch and Lundin (1993). This consists of a Maxwellian ion population with a density 0.1-3 particles per cc, with temperatures of 0.2-0.8 keV, quite distinct from the plasma sheet ion population. These densities correlate quite well with the solar wind densities, as in the LLBL. Apparently field-aligned potential drops in this region of the auroral oval make it difficult to distinguish this low energy ion population at low altitudes. These flux tubes indeed map to the LLBL at large distances in the tail according to the T87 and T89 models. 2.2. Puzzles o f tail structure While the contribution of the planetary (dipole) field is quite important, at least to distances 20-30 Re down the tail in the Earth's magnetosphere, at much longer distances any role of the parent inner magnetosphere must vanish. The limiting distance is defined by the last closed magnetic flux tube which emerges from the southern Polar Cap. According to the Tsyganenko models (1987, 1989) the limiting distance is about 70-100 Re. This means that in the remaining part of the tail lobes the magnetic flux must be open, if the hydrodynamic approach is valid for the far tail (we consider here only cases when the IMF Bz < 0). The "openness" means field line connection to the arbitrarily oriented IMF somewhere far down the tail. However, observations from ISEE-3 (Heikkila, 1988 ; Fairfield, 1992; Owen and Slavin, 1992) have shown that the average magnetic field, though highly varable, still has northward direction as far down the tail as 220 Re, i.e. the tail looks as "closed" on average.
Y. I. Galperin
Can it be considered as "closed", or as "open", i.e. someway "connected" to IMF, when the average amplitude of the Z-component fluctuations is much higher than the average value, and sign reversals are often observed? The respective processes of magnetic field diffusion/mixing responsible for this "connection", and for the complete fading out of the tail-like magnetic fields and plasmas somewhere far down the tail, are apparently rather slow. A distorted tail, or wake, with peculiar particle fluxes distinct from an undisturbed solar wind flow, were noticed at great distances of order 500, 1000, and even 3000 Earth radii (Intrilligator et al., 1969; Vaisberg et al., 1972). Thus the enormous length of the Earth's tail and wake is a consequence of a slow rate for tail magnetic field diffusion, and/or mixing with the IMF in these remote regions down the tail. Even the largest scale magnetospheric substorms cannot significantly destroy the general tail structure. Large hot plasma bubbles, the plasmoids, that appear within the tail during substorms, are confined to the tail midplane and expelled tailward without altering the tail lobe structure, except for some compression (Slavin et al., 1990, 1992). The plasmoid phenomenon poses a problem with regard to the stability of the CPS cross-tail which depends, in particular, on the magnetic field gradients and curvature which must be distorted, or even diverted at, and around, the plasmoid location. It seems that moderate variations of the cross-tail current, and the field-aligned currents which constitute its small divergences, do not have much influence on the general tail structure. This is a puzzle of the general tail structure which deserves a thorough analysis. The recent model calculations by Hesse and Birn (1993a,b) suggest a hint to the tail's stability. They show that the Tsyganenko (1987) model (T87) is rather close to the magnetostatic force equilibrium, while a cross-tail current disruption/magnetic field dipolarization process in the tail is endoenergetic, i.e. it needs energy supplied from an external source. It follows that the time-averaged magnetospheric structure as is described by the T87 model, in a way, lies in a kind of a "potential well" that typical disturbances cannot overcome. But how large are these "typical" disturbances? We consider this problem in the next Section. The tail (see Fig. 2) constitutes the largest reservoir of stored plasma and magnetic field energy for the terrestrial magnetosphere. Even a large substorm releases only a small part of the total (magnetic + plasma) energy stored in the tail. At the same time, the tail of the Earth's magneto-
sphere is the site of continuous activity in the form of local bursts of plasma heating and acceleration (most probably, due to some form of "magnetic reconnection process") on various scales. Among the substorm features, ordered by decreasing scale and intensity, are "true" substorms (Akasofu, 1964; Rostoker et al., 1980, 1987), pseudosubstorms (Koskinen et al., 1993), microsubstorms, and isolated bursts (Sergeev et al., 1986) which probably are related to the Bursty Bulk Flows (BBFs) recently described by Angelopulos et al. (1992). 2.3. The near tail p l a s m a f l o w s The large scale flow or convection in the tail is one of the main factors of its structural stability (Axford and Hines, 1961 ; Dungey, 1961). The existence of the finite area of direct magnetosheath plasma penetration into the magnetosphere at the "cusp" on the dayside magnetopause indicate that there is nearly continuous magnetic flux erosion, or reconnection, which for a steady state necessitates a sunward flow in the tail and a potential of order of 30 kV (Cambou and Galperin, 1974). Indeed, a gradual increase of the average precipitating proton energies towards lower latitudes across the auroral oval is quite consistent with the adiabatic acceleration of the plasma sheet particles in their earthward electric drift by betatron and Fermi mechanisms (Galperin et al., 1978). At the same time, the flow along the tail flanks (within the Low Latitude Boundary Layer, LLBL) is tailward with velocities decreasing inward from the surrounding solar wind flow. As the magnetic field in the LLBL is closed, this flow, like in a magnetohydrodynamic generator, gives rise to a potential difference which allows for the tailward drift of the LLBL plasma. Its magnitude has not been well measured in situ and can be from several kV to 10-15 kV, or even more, on each side this can be significant for the sunward directed plasma flow in the inner tail (see Mitchell et al., 1987 and references therein). As argued by Lundin et al. (1991), the role of the LLBL current generator can be very important not only for the dayside, or cusp current, but also for the cross-tail current on the nightside. The inner cross-tail potential difference driving the more or less steady, laminar (except during substorms) convection flow in the tail, estimated from the ionospheric antisunward plasma flow across the Polar Cap, is typically about 50 kV, variations in both directions by a factor of two. A very serious drawback to these concepts was noted by Erickson and Wolf (1980), which they called the "pressure balance inconsistency". If the plasma
Magnetospheric tail structure
Periods of quiet aurora Remnantlayer
Central plasmasheet Boundaryplasmasheet
\ Boundarylayer Poleward auroralarc Innerboundaryof plasma sheet Equatorward auroral arc Isotropic precipitatingions Fig. 2. Schematics of the gross magnetospheric structure for periods of quiet aurora (a) and for substorm expansion phase (b), taken from Feldstein and Galperin (1993a). It takes into account the BPS ion beam generation all along the distant neutral sheet of the CPS by stochastic acceleration of field-alignedions due to magnetic moment non-conservation during neutral sheet crossings. See text for comments and doubts on the Distant Neutral Line Paradigm.
flow is adiabatic, then, due to the large increase of the magnetic field towards the Earth, plasma pressure during the drift from the far tail must increase to unrealistically large values. It was shown that an account of lateral losses of the energetic particles from the tail of finite width can be sufficient to decrease this "inconsistency" even for a hydrodynamic flow, but probably not to remove it entirely (Spence and Kivelson 1993). Another highly important aspect of the problem is the question of the applicability of the magnetohydrodynamie, or better to say non-kinetic, approach for these flows. As was shown by AshourAbdalla et al. (1993), only the kinetic description of the particles' motion in the tail at distances more than about 10 Re should be valid due to violation of the particles' magnetic moment at the sharp magnetic field
reversal in the neutral sheet. As a result, the ion distribution function can be non-gyrotropic and the pressure tensor non-diagonal, so that the magnetohydrodynamic adiabatic law is not applicable. It can be added that the trajectories of the more energetic particles in the tail due to stochastic effects in their motion are turned to the dusk side, and their lateral loss is thus greatly enhanced. That is why a plasma pressure bulge, or a "wall", appears at the distance where the strong stochasticity condition RL ~ Rc occurs for the thermal ions of the plasma sheet. These kinetic effects significantly modify the thermodynamics of the tail plasma and must be accounted for in future models. Another important new aspect was recently introduced in the concepts of plasma motion in the tail as a result of the high time resolution (4.5 s) corn-
Y. I. Galperin
prehensive plasma measurements from the AMPTE/IRM spacecraft (see Baumjohann and Pasdimann, 1989). It appeared that all the macroscopic plasma parameters in the CPS can vary by at least an order of magnitude during rather short intervals/distances. Such variations evidently cannot be considered as simple fluctuations. Thus, they signify an inherent non-stable state of the tail plasma (Angelopulos et al., 1992, 1993). One very important type of these rapid non-adiabatic variations is the Bursty Bulk Flows (BBFs) Angelopulos et al. (1992). It was shown that the main part of the sunward magnetic flux transfer in the tail at distances of 10-19 Re occurs through multiple BBFs, i.e. by local short-term dipolarization, accompanied by plasma heating, acceleration, etc., but not as a laminar convection flow. This local non-stationarity, as was stressed by Angelopulos et al. (1993), does not allow the use of the simple magnetohydrodynamic adiabatic law for the tail plasma. It is seen that the real magnetospheric plasma appears to be much more complicated than was supposed before: in the tail it is non-stationary, nonhomogeneous, non-isotropic, and non-MaxweUian (see Christon et al., 1989, 1991). At the same time, its average properties can be rather close to magnetostatic equilibrium. So the gross magnetospheric structure remains relatively stable, though it could be highly variable locally on the scale of an Earth radius. The locations and origin of these smallscale space/time variations can be studied during future multipoint satellite missions, while for the present only the ever changing discrete auroras let us visualize the real complexity of plasma processes in the tail. It remains to be seen with the new generation of high resolution plasma instrumentation whether the time/space/phase space averaging introduced by the instruments used so far has led to a significant smoothing of the tail plasma characteristics, or was just enough for the local plasma time constants involved. If this is the case, as it seems to be, the main part of the small-scale auroral variability must take place at low and medium altitudes, and is decoupled from the tail plasma. This is another non-MHD aspect of the auroral/tail plasma description.
3. THE DISTANTTAILAND THE DISTANTNEUTRAL LINE PARADIGM After the classic paper by Coroniti and Kennel (1972), on the force balance of the tail and the role of tail flaring, it became clear that the force balance in
the near Earth tail, where the role of the Earth's dipole field is still significant, differs from the force balance in the distant tail. Measurements from ISEE-3 in the far tail plasma sheet (150-220 Re) show the generally antisunward plasma flow (Heikkila, 1988 ; Owen and Slavin, 1992). At first this seemed to be consistent with the existence of the so called Distant Neutral Line (DNL) somewhere between about 50 and 150 Re downtail. But for this hypothesis the Bz magnetic field component has to be southward (negative in the GSM frame), while the measurements during low activity consistently show a small, but northward, Bz. It was argued by Heikkila (1988) that this is a direct contradiction to the DNL concept. For the distant tail, flaring is no longer effective and some other way is needed to impart the antisunward momentum, especially for the central part (XZ plane), far from the LLBL flows. One possibility is the action of the Plasma Mantle antisunward ion flows. Moving nearly along the field lines these magnetosheath particles conserve their momentum, but gradually sink to the CPS and neutral sheet under the drift due to a dawn-dusk large-scale electric field (see Pritchett and Coroniti, 1992; Ashour-Abdalla et al., 1993). Their encounter with the magnetic field reversal in the distant neutral sheet can occur, depending on the crosstail electric field value there, at distances more than 50-100 Re. There existing models are inapplicable but, on average, the field is closed and the neutral sheet is present (Heikkila, 1988 ; Fairfield, 1992 ; Owen and Slavin, 1992). As was shown by the single particle trajectory calculations made by Ashour-Abdalla e t al. (1992, 1993), a part of the distribution function of these ions, in an encounter with the sharp field reversal, will be redirected backwards and accelerated. They will form the earthward field-aligned ion beams of the PSBL, which then will be reflected near the Earth by the magnetic mirror, and so on. But the momentum imparted by these ions to the neutral sheet plasma in each encounter can be very important (Pritchett and Coroniti, 1992). As was shown by Owen and Slavin (1992), the power of the particles supposedly penetrated from the LLBL flow inside the distant tail seems insufficientto drive the anti-sunward flow there. Thus a problem arises as to what momentum drives the antisunward convection across the distant tail. We suppose that, as a result of the mantle ions momentum, at some distance down the tail, the antisunward flow in the CPS integrated through all the ion distribution functions (whatever distortions are present) will start to dominate even on the average across the tail. But due to the tail inhomogeneity discussed above, irregular sunward and antisunward
Magnetospheric tail structure flows will appear (if measured only as moments of the non-gyrotropic, non-Maxwellian particle distribution function). Obviously, very detailed measurements of the real form of the distribution function in the distant tail are needed to check this possibility. It may be noted that the D N L concept in fact is a mathematical abstraction, where the "neutral line" can in fact be a three dimensional tube of finite width, with a spiral magne,tic field ifa Bz component is added. But again more stringent requirements for the system stability in the real tail environment seem more significant for the viability of the D N L concept. It is hard to believe that the reconnecting magnetic fields from the two tail lobes can form a time-stable configuration. The magnetic flux tubes are connected both to the winter and the summer Polar Caps with their quite different conductivities, neutral winds and electric currents, and with asymmetric ionospheric and Aifven wave disturbances. So it is difficult to imagine the symmetry of the reconnecting plasma flows homogeneously converging from the two tail lobes to the D N L at the tail midplane (Z = 0) keeping the pressure balance between them in the Z direction. It seems that a D N L reconnecti~ag configuration is unstable to any asymmetric disturbance, such as a solar wind discontinuity, Alfven wave burst from a BBF, or an auroral splash, etc. Each such disturbance can push the whole reconnecting configuration in the Z-direction, or even destroy its fragile force balance. The local variability of the tail parameters discussed above probably allows only local patches of bursty reconnection, or tearing, or any other dissipative process. Mapping of the antisunward flows observed in the distant tail to the Polar Caps presents a difficulty. In an M H D approac,h, mapping the respective central part of the Polar Caps must show a sunward flow during southward, I M F conditions, but no such regions in the Polar Caps were identified so far. If we look at the highly turbulent plasma flows above the dark (winter) Pol~LrCap during steady conditions, it could be imagined that they reflect the turbulent flows in the distant tail. But at the same time the flow in the sunlit Polar Cap is much more regular and the average flow direction in both Polar Caps is antisunward for small southward Bz IMF. This is one more puzzle of the tail plasma flows when considered in the M H D approach. But, within the kinetic concept described above, the field-aligned part of the ion distribution function, in principle, may drift sunward, communicating this flow to the Polar Caps, while the perpendicular part of the distribution function may at the same time drift antisunward, giving the general antisunward flow :in the distant tail. Detailed ion distribution function measurements in the far tail will
allow us to check this extravagant "purely kinetic" hypothesis. It must be also mentioned, as indicated by one of the referees, that neither induction electric fields, nor the field-aligned plasma flows in the tail are mapped to the ionosphere, while they could be important in the far tail. However, in the author's opinion described above, the relatively steady and smooth antisunward flows observed in the sunlit Polar Cap ionosphere must be driven by some sustained non-MHD momentum source in the far tail which has not been firmly identified so far.
4. THE HOMOGENEOUS
AURORAL ARC, SUBSTORM
ONSET AND THE INJECTION BOUNDARY
4.1 The homogeneous auroral arc: a standing discontinuity in the CPS plasma flow As we have seen, the auroral oval with bright discrete auroral forms is the projection to ionospheric altitudes of the Central Plasma Sheet. One way to study the large-scale inhomogenieties of the plasma flow in the CPS is to study their ionospheric projections--auroral features, in particular, auroral arcs. During quiet, or steady, conditions in the magnetosphere one of the typical auroral discrete structures is a homogeneous auroral arc, with a thickness of 1020 km, length often more than 1000 km, and moderate brightness of Class I or II. Sometimes multiple arcs appear with a spacing of 50-100 km. Measurements from rockets and incoherent scatter radars have shown that such an arc is usually located along a convection reversal, or change of the plasma flow direction. An arc is fed by an upward field-aligned current carried by downward accelerated electrons of about 0.J to 10 keV. Many experimental results on auroral arcs were summarized in the reviews by Kan (1982), Lundin and Eliasson (1990, Timofeev and Galperin (1991), Lyons (1992), and Galperin (1993). In the latter paper it is stressed that a qualitative physical distinction exists between stable homogeneous arcs with the time scales of 1000 s, which are characteristic for quiet or steady conditions, and bright dynamic rayed arcs and curtains, with time scales of a second or even less, which are characteristic for a substorm breakup or local auroral activation. We shall concentrate here on the steady arcs/inverted-Vs because they can also be used as specific natural tracers from the generic outer magnetospheric regions, in particular, the CPS and LLBL sheared plasma flows, not adequately measured so far. Timofeev and Galperin (1991) tried to select cases when both space and ground-based electrodynamical and visual information on the homogeneous arc/in-
Y. I. Galperin
1406 "Matreshka" model (meridional section) Evening type of the convection
Morning type of the convection
merid, scale 1}1 `3
101 10-~ 103 km
ion. Pedersen resistivity
Fig. 3. The "MATRESHKA" scheme of auroral encircled double sheet current loops hierarchy (see Timofeev and Galperin, 1991). Each double sheet loop encircles a smaller one, with similar current directions. The largest scale loop is the Region I/Region II one ; it encircles an inverted-V associated loop (or several such loops), and the auroral arc loop can be located within the inverted-V loop at its side where the Pedersen ionospheric current enters the inverted-V loop. The scheme somewhat resembles the Russian children's toy "Matreshka", a series of wooden dolls enclosed one within another.
verted-V structure is available to study time and space stability. From the small set collected and analyzed they proposed for steady conditions a simple unifying scheme of the "encircled double-sheet current loops" with different meridional scales called " M A T R E S H K A " shown in Fig. 3. The largest scale current loop is the Region II/Region I loop. Inside it, and close to the field-aligned current reversal, lies a similar loop with a smaller scale structure, the inverted-V loop (or several such loops); inside it, with a still smaller scale, lies an auroral arc loop. In the evening and premidnight sector at the equatorward edge of the auroral oval, where the Pedersen current is poleward, the arc/inverted-V pair is located at the border between the Region I and Region II currents. In the postmidnight sector of the oval, where the Pedersen current enters the oval from the poleward side and is equatorward, the arc/inverted-V pair is located at the poleward edge of the oval. In fact, the current struc-
tures at the poleward part of the premidnight and evening oval were not analyzed because of the lack of observational data, and this limits the region of the applicability of the proposed M A T R E S H K A scheme. The M A T R E S H K A scheme of the steady threedimensional current system generated at the earthward edge of the cross-tail current in the premidnight sector was quantitatively modelled in Galperin et al. (1992). Several other electrodynamical schemes for arcs/inverted-Vs were proposed on the basis of observational data obtained in various conditions (see Timofeev and Galperin (1991) for references and discussion). It is hard to say now when and where the necessary conditions are met for any of these schemes. The sheet field-aligned (FA) currents, which feed the power to a near-midnight stable homogeneous arc, are generated in the tail plasma sheet. This generator region must be stationary in the magnetospheric frame, not in the convecting plasma frame. For steady premidnight conditions these F A currents are the result of a divergence of the cross-tail current sheet extended azimuthally in a band of order of 1 Re wide at distances somewhere in the range 6 20 Re. It must be associated with a stationary plasma pressure gradient and some three-dimensional curvature of the field lines in the plasma sheet (see Hesse and Birn, 1993a). But bending from the magnetic meridian to an angle of order 0.01 rad is sufficient to drive the F A currents of order of several microamps per square meter at auroral altitudes in a steady arc of Class I or II. Neither the gradients of pressure nor the three-dimensional curvature of the field lines are easy to measure experimentally in the plasma sheet, but require careful multipoint measurements. So far no positive experimental identifications are known of the F A current generators for steady homogeneous arcs. Even for the large-scale Region I currents, the generation mechanisms and their locations in the tail are still under discussion (Birn, 1991). Thus the characteristic double-sheet current structures of these arcs can also serve as tracers to front the respective generic regions in the magnetosphere. In Galperin et al. (1992), it was supposed that the cross-tail current has, at some distance of the order of 10 Re, a strong tailward directed gradient of the Zintegrated current density. Such a gradient must be unstable if an M H D approach is applied. It was suggested that the effects of stochastic ion motions will dominate here, so that in the generator region the total cross-tail current will be westward and will form a narrow band ("Line current model"). Such a radial gradient of the cross-tail current and pressure near its earthward edge seems not inconsistent with the
Magnetospheric tail structure available single point measurement data (see Spence et al., 1989). It will cause a southward B~ component earthward from it to have a radial scale of order of the current gradient scale length, which was supposed to be about 1 Re. This field is of the opposite direction to the Earth's dipole field, so a minimum, or at least a change of the gradient, will appear in the total field at, and earthward From, the site of the cross-tail current gradient. For stability in the Z-direction, the plasma pressure faust increase in the region of a depressed magnetic field and the respective plasma pressure gradients, together with the magnetic field variation, can produce a double-sheet F A current structure. The appearance of the bulge at about 10 Re and a sharp drop in the cross-tail current profile earthward from it is attributed in this model to the formation of the "wall" region where the strong stochasticity condition RL ~ Rc occurs for the thermal plasma sheet protons of several keV, whose trajectories as a result are strongly bent westward and thus form a plasma pressure bulge here. Besides that, moving nonadiabatically westward, these ions are accelerated by the dawn~lusk ele~ztric field and thus produce a duskward pressure gradient. Earthward from this region the total plasma pressure drops. So a narrow band with enhanced duskward plasma pressure gradient which mainly drives a powerful upward field-aligned sheet current of the arc/inverted-V follows naturally from this concept (Galperin, 1993; Galperin et al., 1992). An accounl of the implied radial gradients in the magnetic field provides an explanation for the double-sheet form of the F A current structure. The two-dimensional problem of the plasma flow discontinuity in the arc generating region was not considered quantitatively in the above arc/inverted-V models. But an interesting qualitative analysis of this flow by Lyons and Samson (1992), which shows the azimuthal flow reversal for a steady arc in the premidnight sector, is apparently generally consistent with the above described concepts. 4.2 The prernidniyht auroral arc and substorm onset Another highly :important aspect of the "Line Current" concept described above is a natural way to explain the well known location of the substorm onset at the site of the equatorwardmost homogeneous auroral arc (Akasofu, 1964). The appearance of a local minimum in the total magnetic field (or even a stationary variation of the total field gradient in the neutral sheet) at the earthward edge of the neutral sheet current was implied by Galperin et al. (1992), for steady conditions. As a
result of the current increase, or a steepening, during a growth phase, it can lead to the local decrease of the magnetic field until the system becomes unstable to the tearing instability. Thus, according to this concept, the very beginning of the substorm onset will occur just at the arc location, in full accord with the observations. Thus this picture implies a direct relation between the nearly stable position of the prebreakup arc's "root" in the magnetospheric frame, and the respective large-scale and small-scale gradients in the tail magnetic field. These gradients, and/or the magnetic field minimum there, are supposed to be responsible for the F A current generation in the prebreakup arc/inverted-V. If externally driven unstable, these standing structures are distorted and become especially susceptible to current instabilities in a narrow magnetic field minimum, causing auroral activation or a substorm. Indeed, as was shown in a comprehensive case study during the C D A W 9 interval by Baker et al. (1993), the thinning of the near-earth plasma sheet during the growth phase just before the onset reaches the state when the strong stochasticity condition occurs for the plasma sheet electrons, which causes tearing in accord with the prediction by Buchner and Zelenyi (1987). The variability of auroral activations and substorm sequences probably does not allow the description of all the observed patterns to one and the same chain of processes. One of the likely options is an involvement of dayside auroral phenomena in some of the magnetospheric substorm sequences. 4.3 Dayside auroral phenomena and the tail One of the most spectacular discoveries made in the V I K I N G space project with the aid of the auroral imager is the global development of pre-onset auroral phenomena at the dayside auroral oval. It became possible due to the "cinematographic" sequences of global auroral display images with high time/space resolution even above the sunlit part of the oval. It was shown (see Elphinstone et al., 1991b; Lundin et al., 1992; Cogger and Elphinstone 1992, and references therein) that quite characteristic auroral features appear during a growth phase, intensify, and move generally to the nightside, or antisunward, along the morning and evening auroral oval. At some stage of this expansion, starting on the flux tubes which map to the nightside LLBL, auroral activation begins to develop across the nightside tail accompanied by an increase and an earthward motion of the cross-tail current, i.e. by a typical growth phase sequence. Thus, a typical substorm sequence can, at least sometimes, be extended to include the development starting from
Y. I. Galperin
the dayside magnetopause, evolving along the LLBL and comprising the whole cross-tail current system, not only its near-midnight portion. This full tail current system is supposed to be theta-shaped in the tail YZ plane ; it includes the cross-tail currents in the CPS and BPS, and also the mantle and tail magnetopause currents, as well as the field-aligned currents originating in the tail. It is remarkable that auroral activations along the oval accompany these current and field reconfigurations, apparently communicating the stress changes in the LLBL regions to the ionospheric flows. The onset of a major magnetospheric substorm occurs in the near-midnight region at the earthward edge of the cross-tail current. It is a problem of great scientific and practical importance to learn how the development of an exceptionally strong substorm can be predicted, so that warnings could be given of possible disruptions to electric power systems and oil pump lines. However, the auroral activity at the dayside cleft which maps to the LLBL in the tail is not only a substorm phenomenon. It is nearly always present, and its occurrence does not depend on the I M F in the way that the nightside activity does. The auroral forms are usually rayed dynamic arcs that appear, intensify and move (or extend) nightward and poleward, finally decaying in about 10 minutes (see Vorobiev et al., 1976, 1988; Sandholt, 1992). In the evening oval these dayside originating arcs can sometimes join, or transform to, steady homogeneous premidnight arcs drifting equatorward (Vorobiev and Starkov, Vorobiev et al., 1988). Apparently this is the first case to be reported of as tracers of the sheared plasma flows in the distant tail, because the change of the arc's drift direction from poleward to equatorward means a transition from the antisunward LLBL-type flow to the sunward CPS-type flow somewhere in the distant tail. 4.4 The injection boundary, near-earth neutral line and substorm breakup The injection boundary concept introduced by McIlwain (1974) and Mauk and McIlwain (1974) plays a very significant role in organizing various particle injection/acceleration data at high and low altitudes, taken after a substorm. According to this concept a single Injection Boundary (IB) exists in the near tail. Beyond the IB the CPS particles are energized during a substorm breakup (within not more than 10-15 min). However, inward from the IB there is no local acceleration, and the newly injected/ accelerated particles from the IB and beyond drift there in the rather undisturbed environment of the
inner magnetosphere, in rather steady (but Kp-dependent) magnetic and electric fields. The nature of the physical processes that occur during the substorm injection/acceleration at the IB was not ascertained for a long time, despite several comprehensive applications of this concept in data analysis and modelling. Recently it was shown by Lopez et al. (1990) with good statistics that the IB is colocated with, and varies similarly to, the energetic ion dispersionless injection events observed from AMPTE/CCE. This was interpreted as the result of local current disruption. The respective substorm onset phenomena (or local activations) were identified with the process of the injection/acceleration as a result of the current disruption starting at this boundary and then propagating mainly tailward. Indeed, the study of the magnetic variations from several highaltitude satellites by Jacquey et al. (1993) shows that the current disruption, once started during the substorm breakup in the near-Earth tail, then expands tailward with velocities 150-250 km/s over some 10s of Earth radii during the expansion phase. At the same time, with smaller velocities, the front of the accelerated particles propagates earthward and also longitudinally. These results are fully consistent with many other studies of particle injection/acceleration at high altitudes and with the known global auroral development during a substorm. For example, high time/space resolution radar aurora measurements during auroral breakups by Shaftan and Vassilliev (1989) and Shaftan (1990) show the appearance, on a time scale of 10 of seconds, of multiple localised bursty radar reflections in a rather limited region of the breakup. These results were interpreted as the effects of multiple, localised and strong F A currents which were generated in the plasma sheet during a breakup and reached ionospheric altitudes as kinetic Alfven waves. It was mentioned before that the tearing instability may be a likely candidate for the current disruption mechanism. Pulkkinen et al. (1991a,b, 1992) and Baker et al. (1993) have shown that at least during some cases the increase of the field curvature in the neutral sheet during a substorm growth phase reaches values which imply the strong stochasticity condition for the plasma sheet electrons. In this case the tearing instability can develop to produce the current disruption, i.e., a substorm onset, or local activation (Buchnet and Zelenyi, 1987). However, in situ data on the current disruption events collected and analyzed by Lui et al. (1992) are consistent with the Ion Weibel Instability 0 W I ) as the direct cause of the current disruption (Lui et al. (1993)). These two dissipative processes could be coupled in the real neutral sheet,
Magnetospheric tail structure or could form different options for substorm development (Lui (1992)). From the data on magnetospheric variability described above it is hard to believe that there is a unique mode of the large-scale plasma instability which causes all substorms. Indeed, various models were proposed. Probably the most appealing is the synthesis model L~ai (1991), which reasonably incorporates many observational results, concepts and models proposed so far. Anyway, a current instability must have a threshold in the current density and/or current sheet thickness (which, for the neutral sheet, are closely related). This leads to a partial cross-tail current disruption and diversion to the auroral ionosphere via FAC's :forming a so called substorm Current Wedge (McPherron et al. (1973)). In fact, a cross-tail current reduction by only 1030% is sufficient for a strong substorm. Once the current is abruptly changed (disrupted), the Alfven wave launched to the polar ionosphere can produce most, or all, of the observable substorm effects at ionospheric altitudes as was shown by Kan et al. (1988). At the same time, ionospheric conditions play a very important role in a particular substorm's development (see LopeT, 1992; Koskinen et al., 1993). Only multipoint measurements in the current disruption region during an interval of substorm development are capable of producing detailed data to verify the basic physical concepts concerning the mode of instability, the particle and wave behaviour, and the threedimensional current pattern of the substorm onset. One such case of accidental multipoint measurements which brought significant new insight to the substorm processes was recently described by Baker et al. (1993). Seve:~al high-altitude spacecraft, two of them with imagery, successfully monitored magnetic field, particles ancL global auroral displays of a substorm during the PROMIS C D A W 9 interval. The main result of thi,; study, as mentioned before, concerned the extreme thinning and stretching of the magnetic field during the growth phase. So the strong stochasticity condition for the plasma sheet electrons was reached just before onset, at distances of the geostationary orbit or even closer to the Earth. This strongly favours the tearing mode as the current disruption mechanism, but o~:her options of current instabilities such as IWI cannot be excluded. Another important observation during this interval was that a strong westward electrojet (an ionospheric closure part of the Current Wedge) was noted about 10 degrees poleward of the initial aurcral brightening at the onset. This
means that the main part of the Current Wedge developed in this case in a broad region of the tail, while the local current disruptions/auroral activations first occurred considerably earthward from it, but then that region rapidly expanded tailward (or poleward). A very plausible scenario to explain this uniquely documented sequence of events (which was certainly not unique) was proposed by Baker et al. (1993). It is based on an earlier suggestion by Baker and McPherron (1990) that the Near-Earth Neutral Line (X-line) indeed was formed, but not at the onset; it formed earlier, during the growth phase. It was nearly stationary for some time, and slowly reconnected the CPS magnetic flux tubes that were filled with dense plasma. (This is consistent with the southward Bz field observed further downtail during the growth phase.) But when the CPS magnetic flux reconnection was completed, the process jumped to the lobe flux tubes with low plasma density and correspondingly high Alfven velocity and reconnection rate. Baker et al. (1993) attribute the substorm onset to this rapid increase of the reconnection rate. 5. FINAL REMARKS
The very significant progress that has been made in magnetospheric tail research during recent years was in part due to the understanding that text-book plasma physics is too simple to describe the very complicated, non-linear, variable and localized phenomena in the Earth's magnetosphere. New concepts, such as chaotic particle motions, cross-tail current instabilities with an important role of sharp gradients in the plasma parameters and current space distributions, the inherent time variability and non-steadiness of the magnetospheric plasma, overwhelm the data interpretations and modeling efforts. Solutions to many new problems in modelling will depend on the availability of powerful supercomputers to look for three-dimensional non-stationary, non-linear filamentary plasmas with sharp spatial gradients. Repeated and systematic measurements by many spacecraft will undoubtedly lead to new results. Acknowledgements--During preparation of this review I benefited from stimulating discussions of magnetospheric problems with Maha Ashour-Abdalla, C. F. Kennel, R. Lopez, A. T. Y. Lui, C. E. McIlwain, D. Sibeck, E. Szuszczewicz and L. M. Zelenyi, and would like to express my gratitude to them. I thank the three referees for helpful comments, suggestions and corrections. I would also like to thank the Organizing Committee of the URSI General Assembly at Kyoto for supporting my participation there.
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