Stationary magnetospheric convection on November 24, 1981. 1. A case study of ''pressure gradient/minimum-<i>B</i>'' auroral arc generation

We present two case studies in the night and evening sides of the auroral oval, based on plasma and ®eld measurements made at low altitudes by the AUREOL-3 satellite, during a long period of stationary magnetospheric convection (SMC) on November 24, 1981. The basic feature of both oval crossings was an evident double oval pattern, including (1) a weak arctype structure at the equatorial edge of the oval/polar edge of the diuse auroral band, collocated with an upward ®eld-aligned current (FAC) sheet of 1.0 lA m, (2) an intermediate region of weaker precipitation within the oval, (3) a more intense auroral band at the polar oval boundary, and (4) polar diuse auroral zone near the polar cap boundary. These measurements are compared with the published magnetospheric data during this SMC period, accumulated by Yahnin et al. and Sergeev et al., including a semi-empirical radial magnetic ®eld pro®le BZ in the near-Earth neutral sheet, with a minimum at about 10±14 RE. Such a radial BZ pro®le appears to be very similar to that assumed in the ``minimumB/cross-tail line current'' model by Galperin et al. (GVZ92) as the ``root of the arc'', or the arc generic region. This model considers a FAC generator mechanism by Grad-Vasyliunas-BostroÈ m-Tverskoy operating in the region of a narrow magnetic ®eld minimum in the near-Earth neutral sheet, together with the concept of ion non-adiabatic scattering in the ``wall region''. The generated upward FAC branch of the double sheet current structure feeds the steady auroral arc/inverted-V at the equatorial border of the oval. When the semiempirical BZ pro®le is introduced in the GVZ92 model, a good agreement is found between the modelled current and the measured characteristics of the FACs associated with the equatorial arc. Thus the main predictions of the GVZ92 model concerning the ``minimum-B'' region are consistent with these data, while some small-scale features are not reproduced. Implications of the GVZ92 model are discussed, particularly concerning the necessary conditions for a substorm onset that were not ful®lled during the SMC period.


Introduction
Auroral homogeneous arcs are the typical stationary features of the auroral oval during steady conditions (see Oguti, 1981;Galperin, 1992Galperin, , 1994. Several dierent approaches were used to devise a theory of their formation since the very beginning of magnetospheric research (see, Borovsky, 1993 for a critical review). Without considering all these attempts, we mention here only three (not mutually exclusive) which somewhat escaped attention in that review, but are relevant for our observations.
One is that by Tverskoy (1982a, b) which derived, independently from Grad (1964), Vasyliunas (1970) and BostroÈ m (1975), but for a more general case of space scales comparable to the ion Larmor radius, the formula for a ®eld-aligned current (FAC) generator (see formula 2 in the Sect. 4.1) which we call the GVBT mechanism. In that theory, a steady auroral arc (or, multiple arcs) is considered as resulting from a speci®c instability of the magnetosphere-ionosphere system for an upward FAC. It arises due to an increased ion scattering in the plasma sheet, and leads to a decrease of the electric potential at the plasma sheet part of the plasma¯ux tube, and thus to generation of an upward FAC feeding the arc. A SchroÈ dinger-type equation was derived for the electric potential radial pro®le along the plasma sheet axis, which can accommodate for a single FAC feeding an arc/inverted-V, and also for multiple FAC sheets feeding several parallel arcs. The region of dipole-to-stretched magnetic ®eld transition in the near-Earth tail, i.e. the outer boundary of the radiation belt, was predicted to be the site of the steady arc generation, and to have a width of $100 km (Tverskoy, 1982a). It is dicult to directly compare this theory in its present form with measurements, but it obviously deserves a further study and development to be compared with experimental data. These ideas, and in particular the GVBT mechanism of FAC generation, were used in the``minimum-B'' model by Galperin et al. (1992) (hereafter, GVZ92) and by Galperin (1992), and are considered here quantitatively though with suitable approximations.
Another theory is that being developed by Samson et al. (1992) (see also, Liu et al., 1995), stimulated by high resolution ground-based optical observations of arcs from the Canadian CANOPUS network. Oscillations and splitting of homogeneous arcs with periods of order of 10±20 min are often observed, basely distinguishable by the naked eye. The theory considers various forms of AlfveÂ n resonance conditions on the respective plasma¯ux tubes when the energy from the continuum of oscillations feeds a narrow resonance in a shell with a dissipation at the ionospheric foot of a¯ux tube. But, the respective radial pro®le at the plasma sheet origin/generator of an arc's plasma¯ux tube, or shell, apparently was not fully speci®ed yet in this theory, so again direct comparisons with the highaltitude satellite measurements within the plasma sheet are still dicult. Some implications of these observations and concepts in respect to the model described here will be brie¯y discussed further.
The third approach, which will be followed here and compared with the data, was proposed in GVZ92. It considers the radial magnetic ®eld pro®le in the inner plasma sheet, or more precisely, in a region of dipole-tostretched magnetic ®eld transition close to the inner edge of the cross-tail current (CTC). The CTC¯owing in the dawn-dusk direction presumably maximizes near its inner edge. The CTC leads to a magnetic ®eld B CTC in opposite direction to the dipole ®eld B D , so that the resulting total ®eld is B TOT = B D + B CTC . If the inner edge of the CTC, at a radial distance R A , is suciently sharp, and the CTC density decreases suciently with distance down the tail, the radial pro®le of B TOT will form a narrow minimum close to R A . This magnetic ®eld minimum (MFM) presumably occurs at, or close to, the region of strong stochasticity for the plasma sheet ions, where their bounce motion resonates with the Larmor rotation (BuÈ chner and Zelenyi, , 1989. The resulting non-adiabatic westward motion of the ions (while electrons remain magnetized) leads to an additional westward``line current'' (WLC) in this direction. A ®eld-aligned current is created along the MFM shell due to an azimuthal divergence of the CTC and WLC. As we shall see the angle between the vectors of the radial pressure gradientr and gradient of unit magnetic uxr is quite small (of the order of a degree), so it is natural to suppose the proportionality betweenr andr . Thus a similar minimum in ther is supposed in this model, which leads to formation of a double sheet FAC pro®le. Forming of WLC, will modify in turn the total magnetic ®eld radial pro®le, so that some equilibrium pro®le is presumed to develop in steady conditions (see a qualitative discussion of this point in Galperin, 1992). However, a self-consistent description of this region is still lacking, though some eorts to develop it are continuing (see, Peroomian et al., 1997).
The importance of a local enhancement of the CTC due to the non-adiabatic motion of ions at its inner edge, which was earlier suggested in GVZ92, was then demonstrated by a large-scale kinetic model (LSK) of particle trajectories (Ashour-Abdalla et al., 1992a, b, 1993, 1994Bosqued et al., 1994). The non-adiabatic ion motions form a narrow``wall region'' de®ned by Ashour-Abdalla et al. (1994). LSK simulations in 3D (Bosqued et al., 1994) demonstrated the formation of strong radial and azimuthal plasma pressure gradients in the dusk-midnight region where the magnetic ®eld gradients are the strongest. Using the current closure relationship they were able to compute the net FAC density mapped down to the ionosphere. Two prominent regions of upward FACs appeared, (1) around 65°I LAT at midnight which must give rise to the equatorward-most auroral arc of the oval, and (2) a poleward oval arc around 72±76°ILAT, in good qualitative agreement with observations. The LSK approach, and model calculations, is a way potentially synthesizing the theories described already in a direct quantitative manner, but much work is still to be done to achieve the needed representation of the natural processes.
An important aspect of the simpli®ed analytical approach in GVZ92 is its direct relation to the problem of the substorm onset. Under certain conditions (increase of the CTC, and/or sharpening of its earthward edge or, its radial gradient), the magnetic ®eld B TOT within the MFM could reach low values sucient for the plasma sheet electron demagnetization, or even reach zero, or reverse its B Z direction. This kind of evolution of the MFM was suggested in GVZ92 as the probable cause for the substorm onset. According to GVZ92 a largescale CTC instability leading to a substorm onset must occur: (1) in the region of the MFM, (2) after a B Z decrease related to an increase of the CTC and, (3) at, or close to, the magnetic shell of the equatorward-most auroral arc. The last two predictions from GVZ92 are consistent with observations (see, Akasofu 1964 for the substorm onset location in respect to the auroral arc, and Baker et al. (1993) for a decrease of the magnetic ®eld in the neutral sheet leading to electron demagnetization just before the onset), while the ®rst one seems new. The extension of the GVZ92 model for a substorm onset, or a smaller scale auroral activation, is considered in Galperin and Bosqued (1998) and Galperin (1998).
A speci®c virtue of the GVZ92 analytic model is to propose an explicit relation, testable by measurements in the plasma sheet, between the magnetic ®eld radial pro®le B Z along the near-Earth neutral sheet, and the implied pro®le of the ®eld-aligned sheet currents presumably feeding the auroral arc/inverted-V auroral structure. However to ®nd a suitable experimental data set is not easy, because the radial pro®les of the magnetic ®eld B Z , and of the integral sheet current density t c , cannot be measured directly along a single satellite orbit, and thus awaits the CLUSTER mission.
An important exception from these experimental diculties is provided by a unique set of various magnetospheric data collected by Yahnin et al. (1994) (Y94) and Sergeev et al. (1994, 1996 for a long and stable stationary magnetospheric convection (SMC) interval on November 24, 1981. It includes a southern premidnight (840S) and a northern dusk (840N1) auroral oval crossing by the low-altitude polar orbiting AUREOL-3 satellite (hereafter A3) during that day; the preceding dayside crossing of the cusp region (840 N) is discussed in the companion paper (Galperin et al., 1999). The present study will describe observations made by A3 on two passes, 840N1 and 840S, together with other data collected during this SMC interval and, then, will compare them with the predictions of the GVZ92 model of auroral arc/inverted-V generation.
The work is organized as follows. In Sect. 2 the onboard instrumentation (particles, ®eld-aligned currents, electron density and temperature) will be summarized. The data collected on the consecutive eveningside and nightside auroral passes are presented in Sect. 3; we shall show that the electron intensity distribution across the auroral oval as measured by A3 resembles that of the double oval observed by satellite UV imagers (Elphinstone et al., 1995a, b) and, for the SMC period under study, by the DE-1 satellite. This set of A3 data will be used in the following parts for comparisons with the results of the arc/inverted-V model GVZ92 summarized in Sect. 4; at that point we shall introduce dierent radial B Z pro®les in the near-Earth tail and compute the observed shape and intensity of the FACs at ionospheric level. In Sect. 5 we shall discuss the characteristics of the double oval observed during the SMC period and its mapping to the plasma sheet. We shall show that this double oval maps to the whole extended plasma sheet from its inner edge to the far distant tail (100 50 R E ). Finally we shall try to answer to the question: why substorms onsets did not occur during the IMF-B Z < 0 conditions prevailing during that prolonged period?

Instrumentation
The A3 satellite set up for magnetosphere-ionosphere interaction studies was a 3-axis gravity-gradient stabilized low-altitude (400 to 2000 km, inclination 82°) spacecraft launched from Plesetsk, Russia on September, 21, 1981 under the aegis of the Soviet-French space cooperation. The full description of the satellite and scienti®c payload, together with the ®rst results obtained, are presented in a special issue of Annales de GeÂ ophysique (38, N 5, 1982). The data used in this study came from the following onboard instruments: the 4channel electrostatic particle detector RIEP-2802, in the ®xed-energy mode at 100 eV and 1.8 keV both for electrons and ions; the multidirectional electrostatic analyzer SPECTRO/ROT for electrons and ions from 0.2 to 22 keV ; a standard onboard magnetometer aimed to the attitude restitution whose output was digitized and extended by the onboard TRAC device (Berthelier et al., 1982); and the mutual impedance interferometric double probe ISOPROBE for electron density and temperature measurements (BeÂ ghin et al., 1982).
The measurements for pass 840S, discussed later were made by direct transmission to ground-based telemetry station in Terre-AdeÂ lie, Antarctica. The pass 840N1 across the dusk oval, discussed later, and the pass 840N across the cusp (discussed in accompanying study Galperin et al., 1998) were recorded in memory mode with readout by Soviet telemetry stations. The data processing was made both at the Space Research Institute (IKI), Moscow, and in CNES and CESR, Toulouse.

Observations
Figure 1, adapted from Yahnin et al. (1994), displays the time dependence of the IMF components, and AE, AU, AL auroral indices, relevant for the SMC period of November 24, 1981. The times of the A3 crossings along orbit 840, ®rst of the northern dayside cusp and mantle regions (0738±0743 UT), second of the eveningside northern oval (0750±0800 UT, later in the text, pass 840N1), and, ®nally, of the nightside auroral oval ($0835±0837 UT, later in the text, pass 840S) are marked by vertical lines. Here we present and analyze the data collected on the consecutive eveningside and nightside auroral passes in order to insert them in the more global context of magnetospheric data collected during that long SMC time period, already presented by Y94 and SPP96. Figure 2 gives the electron and proton (ion) energy-time spectrograms at $10°pitch angle, obtained during the nightside southern pass 840S at altitudes from $1500 to $1300 km. In Fig. 3a we present: all the DB y and DB x components of the magnetic ®eld variations (approximately along and perpendicularly to the auroral oval direction; smoothed magnetic ®eld components interpolated between the sides of the oval with account of the s/ c attitude were subtracted), the 1.8 keV and 100 eV ®xed-energy electron intensity pro®les, (Fig. 3b) the proton¯ux pro®les at 1.8 keV and 100 eV, (Fig. 3c) the thermal electron density and temperature. (Fig. 3d) The electron spectrogram (Fig. 2) displays a typical sequence of particle spectra and intensities during a steady oval crossing (see, for example, Feldstein and Galperin, 1985;Newell et al., 1996). Towards the pole, a boundary of diuse auroral precipitation is ®rst crossed at $0833:25±30 UT (1.8 keV electron channel, RIEP high sensitivity spectrometer, see Fig. 3b); the diuse region extents up to $0835:18 UT; the average energȳ ux measured by the SPECTRO/ROT instrument was 4.2 ergs (cm 2 sr s) A1 . Then, as evidenced by the 100 eV electron pro®le (Fig. 3b), a weak (multiple) auroral arctype structure is crossed between 0835:18.4 and 0835:24.5 UT (ILAT $ 63.7±63.9, MLT $ 22.0). It coincides with a well-de®ned upward ®eld-aligned current band (d(DB y )/dt > 0) carrying a current density of 1.0 lA m A2 averaged for the band (Fig. 3a, vertical grey band). An expanded view of the 100 eV electron¯ux pro®le across the arc-like structure is shown in Fig. 4 on the top panel. It consists of several narrow maxima (some of them of Dt £ 200 ms, i.e. of a 1.5 km scale thickness or less) with two much more intense than the others at 0835:23±0835:25 UT. It must be noted that the maximum counting rates of the RIEP-2802 detector in the narrow intense arcs/®laments are near the level of saturation, so that these electron spikes are indeed even stronger in time/space. There the energy¯ux reached 4.8 ergs (cm 2 sr s) A1 from SPECTRO/ROT data. While the 1.8 keV electron precipitation (Fig. 3b) stays rather intense but structureless in this region, the ROT electron spectrogram shows locally enhanced electron intensities centred at 0835:24 UT, with rather¯at (or a Kappatype) energy spectra not typical for an inverted-V, and extended to more than 10 keV (Fig. 4, bottom panels).

Premidnight sector
Concerning the ion precipitation in the discrete auroral region (mostly protons, as seen from the data of the ION mass-analyzer, not shown), successive and narrow intensity spikes at 100 eV are detected between $0835:10 and 0835:30 UT (Fig. 3c), i.e. equatorward, and superimposed onto, the equatorial electron arc/ inverted-V described already. At 1.8 keV an intensity maximum is clearly evident at $0835:40 UT, a little poleward from the electron arc. It is interesting to note that if the ion 1.8 keV intensity pro®le in this region is shifted equatorward by $20 s (i.e. $1.24°in ILAT), it looks rather similar to the 100 eV ion latitudinal pro®le. In the discussion we shall compare the locations of the two ion intensity maxima in Fig. 3c with the concept of stochastic ion scattering in the neutral sheet for the respective energies (thick arrows).
Coming back to the electron spectrogram ( Fig. 2) and, more precisely, to the central part of the wide $1300 km), measured by the SPECTRO/ROT_5 sensor (pitch angle: $30°). Dierential uxes are expressed in (cm 2 s sr keV) A1 units auroral oval, it is seen that, poleward of the already described equatorial arc/inverted-V structure, lies a region of depressed electron precipitation of £1 keV. It is extended from $0836:10 (ILAT = 65.5) to 0836:45 UT (ILAT = 67.3), as is well shown by a minimum in the 100 eV electron intensity pro®le (Fig. 3b), but less signi®cant at 1.8 keV. Appreciable, though depressed, ion intensities in the keV energy range are seen in Fig. 2 throughout this region of the electron intensity depression forming the``double oval'' structure.
Moving poleward, another very intense band of highly structured electron precipitation is clearly visible on the spectrogram (Fig. 2) at $0836:50±0837:30 UT (ILAT $ 67.2±68.6, MLT $ 22.4±22.6); it is evident as well in the 100 eV as in 1.8 keV electron¯ux pro®les (Fig. 3b). This intensive band constitutes the polar edge of the auroral oval of discrete forms, and is coincident with the band of strong ($3.3 lA m A2 ) upward current.
Further poleward from this intensive band, till the polar cap boundary, there is a narrow region of weak diuse electron precipitation, the polar diuse auroral zone. Although the 1.8 keV ion¯ux remains very low during this time, its comparison with the ROBE spectral data suggest that it could be the signature of a polar velocitydispersed ion structure (VDIS-2) (Bosqued, 1987;Kovrazhkin et al., 1987;Zelenyi et al., 1990;Saito et al., 1992;Bosqued et al., 1993). However, it is not identi-®able by the onboard ROBE spectrometer data  due to its low intensity, £10 5 ions/(cm 2 s sr keV).
The A3 data on DC electric ®elds across the equatorial arc/inverted-V (not shown) do not display a signi®cant¯ow shear. This is consistent with the implied absence of a signi®cant integral conductivity gradient at the arc.
To summarize this data presentation, the whole electron intensity distribution across the nightside auroral oval, as observed by the A3 satellite during pass 840S, resembles that of the double oval observed by satellite UV imagers (Elphinstone et al., 1995a, b). . A3 measurements during pass 840S: a DB x and DB y variations (nT) of the horizontal magnetic ®eld measured by the TRAC magnetometer, after subtraction of the background magnetic ®eld (DB x along the orbital direction, DB y perpendicular to it, sampling rate: 80 ms, running averages on 1.2 s); b electron dierential¯uxes (cm 2 s sr keV) A1 at 2 ®xed energies, 100 eV and 1.8 keV (bold curve,¯ux divided by 10), given by the RIEP spectrometer (pitch angle: $50°; sampling rate: 80 ms; running averages on 1.2 s); c proton dierential¯uxes at 100 and 1.8 keV (bold curve,¯ux divided by 10); d electron density N e (cm A3 ) and temperature T e (°K) measured by the ISOPROBE instrument (same scale). The region of the weak auroral arc is indicated in a and b by a vertical grey band. See text for vertical arrows in panel c However, the 1.8 keV electron pro®le obtained by the high time resolution RIEP spectrometers as well as the ROBE data reveal that the``gap'' in precipitation intensity between the equatorward and poleward bands is not very signi®cant at that energy. However, the total energy¯ux (which includes prominent 5±10 keV electrons and thus is directly proportional to the auroral brightness) is indeed signi®cantly depressed in between the equatorial auroral region and the bright polar band. This double oval structure is well con-®rmed by the global auroral images from the DE-1 satellite already presented in Y94 (their Fig. 7). But the steady auroral arc at the polar edge of the diuse auroral band was not noted in Y94 (see discussion of possible reasons for this lack of the arc detection in Sect. 5.1). We may notice that in the data presented in Y94 and SPP96, the thresholds for the plotted auroral brightness and for the imagery data were apparently setup at $1 kR, so that the depression could appear deeper than it really was.

Evening sector
Before the premidnight (southern) oval crossing 840S described in the previous section, on the same orbit 840 A3 made measurements in the Northern Hemisphere. Initially it crossed the cusp region and these data, (pass 840N) are described in the companion study by Galperin et al. (1999). Then it passed over the polar cap, and then successively through the northern eveningside auroral oval, the diuse auroral zone, and the ionospheric main trough (pass 840N1), and these data will be considered here. The data recording on the pass 840N1 was in a slow memory mode, so particle data only from RIEP-2802 are available.
As shown in Fig. 5, the polar and equatorial boundaries of the eveningside oval (i.e. the region of structured electron precipitation) are respectively crossed on 0747:25 (ILAT $ 71.2) and 0750:10 UT (ILAT $ 65.3, MLT $ 17.8) as may be deduced using only the RIEP-2802 data. From these data it seems that an intense arc/ inverted-V was present near the sharp polar boundary of the oval, at $0747:40 UT (ILAT = 71.3, MLT = 16.9). Moving equatorward, the total electron energȳ ux decreased and then, a series of arc/inverted-V structures, between $0748:55 UT and $0749:50 UT, was crossed on the trajectory oblique to the oval. Then at the equatorial boundary of the oval, a weak arc/ inverted-V of 100 eV electrons only was crossed at $0749:57±0750:08 UT (ILAT = 65.4, MLT = 17.8), near the polar edge of the diuse auroral zone. This lowintensity equatorial arc of the oval is collocated with an upward current of about 1 lA m A2 (Fig. 5a, vertical grey stripe), and is not detectable in the 1.8 keV electron ux channel (Fig. 5b). Finally, the equatorial edge of diuse auroral precipitation, called the soft electron precipitation boundary (SEB), is crossed around 0750:35 UT (ILAT = 64.3, MLT = 17.9). It can be noted that in this dusk sector the 100 eV low-energy ion precipitation extends to much lower latitudes than the SEB boundary, down to about 0753:05 UT (ILAT $ 58.5).
On a large-scale, the FAC structure displayed in Fig. 5a was of the classical region I/region II type for the eveningside auroral oval. Sequentially, (a) on its polar side, a wide upward FAC band of about 1.2 lA m A2 extended from the polar edge of the polar arc/inverted-V till the middle of the oval ($0749:00 UT); then (b) till $0749:50 UT the large-scale FAC was lower than our sensitivity threshold; then (c) a narrow band of FAC of $1 lA m A2 was crossed which is collocated with a weak low-energy arc/inverted-V; and (d) after that a largescale downward FAC band (region II) was crossed which extended from the equatorial oval arc at $0750:10 UT to $0752 UT (ILAT = 61.0, MLT = 18.2).
Electron density measurements from the ISOPROBE instrument, for this pass in the passive mode (not shown), give densities of about 2±3´10 4 cm A3 above the evening auroral oval and diuse auroral zone at altitudes of 1300±1600 km. It is known that at these altitudes the main trough is not easily distinguishable in the electron density data. As mentioned, the SEB was crossed at 0750:35 UT (ILAT = 64.3, MLT = 17.9).
It must be noted that the overall latitudinal pro®le in the dusk sector is qualitatively very similar to that in the The sampling rate for the TRAC and RIEP instruments is 320 ms, and running averages on 1.6 s are plotted in the three panels. The auroral arc is indicated by a vertical grey band, and the SEB boundary is referenced by a vertical dashed line (see text for details) premidnight sector described in the previous section. In particular, a weak arc collocated with an upward FAC of $1.0 lA m A2 at the oval equatorial boundary resembles that at the nightside and suggests that it was the same feature extended all along the oval boundary at least in the evening-premidnight sectors. However, the adjacent narrow downward FAC here was poleward from the arc, while in the premidnight sector it was equatorward. At the same time, the diuse auroral band at dusk was narrower than in the premidnight sector, while the low-energy ion precipitation extended well equatorward beyond the SEB which was not the case on the nightside pass 840S.

Comparison with other data
Here we compare these A3 results with the available data from other low-altitude satellites and ground-based measurements during this SMC period.
The location of the polar cap boundary crossing by the A3 satellite in the dusk sector, as well as the location of the polar edge of the diuse auroral zone at its equatorial side, are in good agreement with the simultaneous DE-1 data images published in Y94. These images indicate that the global oval structure was rather stable in time, continuous and extended from the evening to premidnight sector, and even further in the post-midnight and morning sectors. However, as mentioned previously, the equatorial arc of the oval was not identi®ed in these images in Y94.
The A3 data in the evening sector considered already can be also compared with the DE-2 electric and magnetic ®eld measurements. The DE-2 satellite crossed the evening oval on the same day, on 0815±0818 UT, i.e. only 25±28 minutes later than A3 and in the same MLT sector. Magnetic ®eld data (Fig. 6, top panel, DB x and DB z components, and the zoom of the DB z component in the middle panel) show an upward FAC band of $1.0 lA m A2 with a latitudinal width of $50 km at ILAT = 66.7±66.1, MLT = 17.9, presumably the stable arc. (It is to be compared with $1 lA m A2 , ILAT = 65.4 and MLT = 17.8 for the neighbouring A3 arc crossing). A characteristic electric ®eld spike in the E x and E y components (Fig. 6, bottom panel) is collocated with a narrow downward current of comparable magnitude adjacent from its polar side to the narrow upward current band. At the polar side of the oval a wider ($80 km) band of upward current of $3 lA m A2 is seen around ILAT = 68.2 and MLT = 17.8. It is a really good agreement for the narrow upward current bands/stable auroral bands positions and FAC densities on both sides of the oval from the two satellites. The same arc-like feature at the equatorial edge of the region I current may be also seen on the preceding DE-2 passes (not shown). This con®rms that this weak FAC structure was indeed a time-stable one, and the whole structure was similar at least throughout the evening-premidnight MLT sector. The latitude of the region II current equatorial edge from the DE-2 data was also similar to that indicated from the A3 measurements.
Narrow bumps $1±2 ergs (cm 2 sr s) A1 in the lowenergy electron total energy¯ux at the polar border of the diuse auroral zone are also seen from the NOAA 7 data presented in Y94 (their Fig. 10) for the postmidnight and morning sectors during this same SMC period. They may be extensions of the same weak auroral arc to these sectors.
The SEB location at nightside and evening sectors is usually collocated with the large-scale convection boundary (Galperin et al., 1977. It can be compared with the simultaneous data from the DE-2 electric ®eld measurements cited already. As seen from Fig. 6 (bottom panel), the module of electric ®eld E X component signi®cantly decreases in magnitude at $63.6 £ ILAT £ 64.6, then becomes rather small and irregular down to $62.5, and then nearly stabilizes at a rather low level. As is seen, the large-scale convection electric ®eld magnitude from the DE-2 data indeed decreases rather close to the location of the SEB boundary determined from the A3 data (ILAT = 64.3, MLT = 17.9), taking into account the 27 min dierence between measurements by the two satellites.  Another check of the location of the large-scale convection boundary can be made using the longitudinal chain of ionosondes in northern Russia, at nearly the same ILAT values of about 65±66°N. According to Sivtseva et al. (1989), during the SMC on 24 November, 1981, due to the Earth's rotation, these stations sequentially entered a relatively stable sharp equatorial boundary of the ionospheric main trough at MLT $16.0. Poleward from this boundary, the F-region electron density was signi®cantly lower and strongly inhomogeneous, which is characteristic for a fast convection zone in the postnoon-dusk sector during enhanced activity. So the location of the equatorial edge of the fast convection zone from these ground-based data can be taken at ILAT $ 65.5 at MLT $ 16 h (Sivtseva et al., 1989). This is close to the ILAT = 64.3 of the SEB at MLT $ 17.9 H indicated already from the A3 data. These ionospheric observations again con®rm the overall time/space stability of the large-scale convection pattern during the SMC period.

Summary of observational data
Thus we can conclude that the premidnight oval structure, as observed from A3 on pass 840S, was qualitatively similar to that observed in the eveningside oval on the pass 840N1 about 50 min earlier, and on the DE-2 pass about 20 min earlier. It is also consistent with the global auroral images from the DE-1 satellite taken at the same time. It was a stable double oval structure with: (1) a low-energy arc/inverted-V present at the polar edge of the intense diuse auroral band delineating the equatorial boundary of the oval of discrete forms, (2) the wide oval of multiple discrete forms including an intensity depression in the middle oval, and (3) an intense structured auroral band at the polar oval boundary. However, the weak auroral arc-like structure which is the subject of this work was not distinguished from the diuse aurora neither from the DE-1 images, nor from ground-based data.
This set of the A3 data signi®cantly complements the more general framework of the SMC period on November 24, 1981 already presented in Y94 and SPP96. It will be used in following sections for comparisons with the results of the arc/inverted-V model GVZ92, together with the concept of the nonadiabatic ion scattering at the inner edge of the plasma sheet.
4 Modelling of the FAC density pro®le

On the``minimum-B'' model and its justi®cation
The``minimum-B'' model as described in GVZ92 (see Introduction), in brief, is based on the following. The key point is the radial magnetic ®eld pro®le along the neutral sheet (expressed as the r 0 coordinate) with a narrow minimum at about r 0 $ 10 R E (Fig. 7). The minimum in the magnetic ®eld B pro®le (or a negative gradient in the tailward direction) occurs at the supposed near-Earth's edge of the linear density j c of the cross-tail integrated sheet current (CTC) which decreases further tailward. Based only on physical considerations, the radial pro®le of the integrated cross-tail linear current density, j c (r 0 ) was freely chosen in the GVZ92 model, and its corresponding magnetic ®eld B CTC (r 0 ) was calculated. The radial pro®le of the total magnetic ®eld in the neutral sheet B Z (r 0 ) was obtained by adding the dipole magnetic ®eld component B D (r 0 ): The isotropic plasma pressure radial pro®le was deduced from the supposed pressure equilibrium in the Zdirection (or, from the tail approximation when the magnetic tension f Árf is negligible). In this case a pressure maximum (only its gradient enters the model) supposedly appears at, or close to, the location of the MFM in the neutral sheet to maintain the force balance in the Z-direction. The FAC density j m k , at the exit from the plasmasheet source region to an auroral arc system in one hemisphere, can be described by the well known GVBT relation (see, for a detailed derivation and analysis, Heinemann, 1990, Heinemann andPontius, 1991): The speci®c magnetic¯ux tube volume W integrated from a unit area at ionospheric base (l = 0) to the MFM, was approximated in GVZ92 as W $ K r 0 /B Z , where K = 4.5´10 15 m 3 /Wb. To generate a FAC, aǹ`a zimuthal'' pressure gradient r ce really enters Eq. (2). In other words, in the GVZ92 model the azimuthal pressure gradient was supposed to be proportional to the radial one due to smallness of the angle a between the vectorsr andr . In GVZ92 the angle a is a constant free parameter that determines only amplitude of the FAC density, not the form of its latitudinal pro®le, and hence the intensity of resulting auroral eects. It was assumed to be 0.01 to get a typical value of the resulting FAC for an arc/inverted-V. For a semiquantitative comparison with the measurements, attempted below, its value will be chosen to ®t the average FAC density, $1 lA m A2 , measured within the equatorial arc/inverted/V structure crossed by the A3 in the premidnight sector on the pass 840S.
When the magnetic ®eld B Z (r 0 ) pro®le in the neutral sheet can be considered as given from a semi-empirical model, or measurements, the approximate radial pro®le of the plasma pressure P (supposed to be isotropic, as in GVZ92) can be deduced directly from the simplest form of the magnetostatic equilibrium in the Z direction: 1 where B T is the tail lobe magnetic ®eld. This relation is valid in the MHD tail approximation when magnetic tension f Árf is negligible. Indeed, solutions of the Grad-Shafranov equation for stationary magnetospheric con®gurations with a MFM lead to quite dierent radial pressure pro®les (see, for example, Hau et al., 1989). However, there are several aspects of the magnetospheric neutral sheet structure in the``wall region'' that are not taken into account in the static Grad-Shafranov equation. First of all, the ion inertia is absent but is important in the``wall region''. This is because the convection plasma¯ow is sharply decelerated (and de¯ected westward) in the narrow B Z minimum region, and the inertia of ions tends to partly compensate the magnetic tension, especially for the high-b plasma in the neutral sheet. As a result, a pressure maximum most probably develops here due to decrease of the convection velocity and respective increase of density. Probably a local increase of pressure can occur here also due to some associated ion heating, as some calculations and observations in the``wall region'' suggest. However, the magnetic pile up may not occur here fully because of violation of the frozen-in condition for ions. This means, secondly, that the MHD approach of the static Grad-Shafranov equation, strictly speaking, is not applicable for the``wall region'' where the frozen-in condition for ions is violated and a crosstail``quasi-Pedersen'' current is generated in westward direction. Thirdly, the dominance of the parallel pressure in the distant tail disappears in the stochastically isotropized``wall region'', and the role of the magnetic tension is further decreased due to smallness of the magnetic ®eld in the MFM region. So the assumption made in GVZ92 about a pressure maximum in the MFM region does not seem unrealistic, while is not necessary: the main conclusions of the model described will follow even in the case wherer ce is a constant vector. If the near coincidence of the pressure maximum with the MFM assumed in GVZ92 does not occur, this will lead to corresponding variations in the j k pro®le according to Eq. (2). In our view, these considerations allow us to test the model GVZ92 for comparisons with experimental data, taking into account that the real pro®le of the j k may be more complicated than assumed in this simpli®ed scheme.
The sign ofr changes near R min , the location of the minimal value of the B Z . So the sign of the generated j k current must also change near Rz min forming a double sheet current. With Eq. (3) the sign ofr also changes at this location, but even if we suppose thatr ce is a constant vector, the double sheet current pattern will still result from Eq. (2). So an intensive upward FAC which feeds an arc/inverted-V must appear near the ionospheric footprint of the neutral sheet region where the B Z value sharply increases, while its sign is determined by the direction of ther in respect tor . Thus the steady auroral arc must originate from the``minimum-B'', and form a double sheet FAC structure. These are the main predictions of the GVZ92 model, and for comparison with this experiment we proceed with calculations on its base.

Comparisons with experiment during SMC period
To compare the GVZ92 model with observations for this particular case, instead of assuming a hypothetical J c radial pro®le for a narrow minimum of B Z , we shall use the semi-empirical radial B Z pro®le in the neutral sheet derived for this SMC period by Sergeev et al. (1991Sergeev et al. ( , 1996 (hereafter SPP96). Comparisons will be made with the shape and relative intensity of the FACs measured from the A3 at ionospheric level at, and near, the equatorward-most arc, and those predicted by the GVZ92 model. The pro®le SPP96 was deduced from the sequence of high-energy particle isotropy boundaries (IB) as measured by the detectors on the NOAA-6 and NOAA-7 satellites. In Fig. 7 the SPP96 semi-empirical pro®le and the hypothetical B Z pro®le from GVZ92 are plotted as solid and dotted lines, respectively. It can be noticed that the radial pro®les GVZ92 and SPP96, qualitatively, have the same shape, but the spatial scale of the GVZ92 pro®le is smaller, while the respective radial gradients are correspondingly higher. Just to illustrate the similarity in shapes of the two curves, the GVZ92 pro®le was shifted outwards for 1.55 R E and extended in radial direction by a factor of 4 around the minimum to make the distance between maximum and minimum, and the location of the minimum, the same as for SPP96. The modi®ed curve GVZ92m is shown in Fig. 7 as a dashed line GVZ92m and its similarity to SPP96 is evident. Though there is no speci®c physical signi®cance in these modi®cations of the model pro®le, except to ®t the observations better, this shows that radial gradients in the GVZ92 pro®le are qualitatively similar to the SPP96 pro®le, and that a much narrower magnetic ®eld minimum (or several minima) are feasible in the frame of the GVZ92 model.
To map the resulting FAC densities to the auroral ionosphere we use the empirical mapping relations from the radial distances to auroral invariant latitudes, deduced in SPP96 from the IB algorithm and shifted by 0.5 degrees equatorward for the southern oval according to Sergeev et al. (1994).
As in the GVZ92 paper, the following simplifying approximations are adopted: Here r is expressed in Earth's radii R E , magnetic ®elds B D , B T , and B Z are in nT, W in m 3 /Wb, FAC density at exit from the plasma sheet, j m k , and at the ionospheric level, j i k , are in A/m 2 , and the FA potential drop, DU k , is in volts. It can be noted that these approximations are consistent with a small FA acceleration DU k in the observed equatorial arc/inverted-V of $0.6 kV.
Two semi-empirical pro®les of the B Z in the neutral sheet were deduced in SPP96: one from the locations of particle isotropy boundaries measured from low-altitude satellites (IB-algorithm), and another from adaptive magnetic ®eld modelling based on magnetic ®eld data from several high-altitude satellites. These pro®les are very similar which indicates their validity. Both these pro®les and the ®tted value a, are used here in the GVZ92 model to deduce the FAC pro®les at the ionospheric level to be compared with the measured pro®le on the A3 pass 840S (Fig. 8). To make the comparison clearer, we plot not only the modelled FAC density, but also its integral along the orbit which gives the modelled DB y (plus a constant). The main variation of the DB y component which implies a double sheet current loop with the upward current branch collocated with the arc/inverted-V (bottom panel) is well reproduced by the model. The total widths of the upward FAC observed and modelled agree quite well: they are both about 0.5 degrees ILAT (see Fig. 8). The most intense part which we identify with the arc is indeed much narrower, and we consider it as one of the most important results of the model: this shows a simple explanation of the narrow arc width ($10±20 km) due to just magnetic moment conservation in the¯ux tubes of the magnetic ®eld minimum.
The total width of the upward FAC region is de®ned in the model mainly by the width of large radial gradient in the B Z magnetic ®eld minimum region. It needs to be noted that according to the IB-derived mapping, the upward FAC region in this case originated from the plasma sheet region from $12.2 to $16.2 R E which is a wide enough region for various small-scale variations to be present, but not described by the adopted smoothed magnetic minimum shape. Thus except for the intense upward current in the main arc, the detailed structure of the upward current region, and to some extent its intensity, is not a critical model parameter. It can be easily adapted within the frame of the model, by slightly changing either magnetic ®eld minimum shape, or the pressure gradient shape (not measured directly), or both, if the self-consistency is neglected. We do not consider such adaptations as warranted at this stage of the model development. Thus we state that striations and other small-scale details are not reproduced by the model.
Consider now the comparison of the model with the downward current branch of the double sheet current associated with the arc. Its existence (the double sheet FAC pattern) is inherent in the magnetic minimum origin and the Eq. (2). So we consider it as an aspect of the model supported by observations. The narrow modelled region of the downward current (tens of kilometres wide) encompasses the magnetic minimum in the plasma sheet from $10.5 to 12.2 R E . Again, this extended tail region can well have additional details not included in the model. The modelled width and shape depends on the mentioned uncertainties in the realistic is the projected X distance in the tail detailed pressure and magnetic ®eld pro®les (possibly deviating from the smoothed shape of SPP96), and also on some other factors which we do not consider here. But the region of the observed downward current, according to the mapping given in SPP96, extends inward to the geostationary orbit, i.e. far outside the magnetic ®eld minimum region modelled here. Thus no correspondence can be expected between the model and the full width of the downward current. So, a comparison of the full width of the observed and modelled downward current region cannot be considered as a test for the model.
An additional small-scale FAC feature (also in the form of a double sheet current loop) seen in the centre of the observed wide double sheet current loop, is not quite reliable due to low amplitude of the respective disturbance in the measured DB y component, but it can be real. In such a case it maps to some structure located at $9 R E in the plasma sheet, possibly a secondary smallscale minimum or from another feature located well earthward from the main``minimum-B'' region, or from another feature.
We can conclude that generally the agreement of the model FAC pro®les, resulting from a rather simple GVZ92 model, with the experimental data gathered during the SMC period, may be considered as reasonably good both in the shape (a double sheet current loop) and location in latitude, while the modelled FAC amplitude remains arbitrary.

Arc/inverted-V at the equatorial edge of auroral oval
Firstly, we compare the position of the equatorward arc/ inverted-V structure observed by A3 around ILAT = 63.5, MLT = 22.0, with the locations of the particle boundaries determined, or compiled by Y94 (their Fig. 11). According to Y94 the isotropic boundary (IB) for 30 keV ions at MLT $22 h was located at ILAT $64.0; so the arc/inverted-V location observed by A3 well coincides with this IB, as was supposed in the theory by GVZ92 based on the mapping concepts developed earlier (Feldstein and Galperin, 1985;Galperin and Feldstein, 1991). The time duration and stability of this arc/inverted-V system cannot be determined from a single spacecraft crossing. But the auroral imagery data from the DE-1 satellite presented in Y94, very similar latitude pro®les recorded from the A3 satellite both in the premidnight and evening sectors of the oval, about 45 minutes apart, and nearly simultaneous similar data from the DE-2 satellite, all give con®dence for a long time (³1 h) stability and large longitudinal extent of the arc/inverted-V system at the equatorial boundary of the oval.
However, the existence of the weak equatorial arc, its time stability and location at the equatorial edge of the oval of discrete forms, and its respective mapping to the near-Earth edge of the CTC, are all facts in contrast to the views previously described in Y94 and SPP96. In the latter papers all this region is considered as the diuse precipitation region with only transient auroral features. Possibly, it was dicult to show by the all-sky cameras used in Y94 the discrete arc/inverted-V structure at the equatorial edge of the oval/polar edge of the diuse auroral zone. We admit that its location at the polar edge of the bright diuse auroral glow and its low contrast in the total energy¯ux (only lowest energies were enhanced) makes its identi®cation really dicult in visible light outside the near-zenith observations. As a result, the oval of discrete forms is characterized in Y94 and SPP96 only by the bright polar band, while the region between it and the diuse zone was considered as a``depleted luminosity region'', with only transient auroral features poleward from the diuse auroral zone. Consequently it was concluded there (SPP96, p. 573) that these observations``...imply that the discrete auroral arcs map to the distant tail (R > 30 R E ) and to the plasma sheet boundary layer as observed at R = 20 R E ...''. Evidently this conclusion contradicts the data described already, as well as the oval mapping concepts developed by Feldstein and Galperin (1985), Feldstein (1991, 1996), and others. These concepts, at least for the near-Earth plasma sheet, now are directly con®rmed by various data (see, for example, Hones et al., 1996), and seem well established. Bosqued et al. (1993) described latitude distributions of electron and ion intensities in a steady nightside oval from the A3 satellite data which are similar to those described in the SMC period. They noted a``gap'' in the low energy ion intensity usually appearing between the polar band of electron precipitation, and an arc/inverted-V equatorward from the gap. From their statistical results it is seen that an arc is``routinely present'' equatorward from the gap. Obviously, the``gap'' depends on the instrument sensitivity threshold and must not be taken too formally. These results have many similarities with the pass 840S described here, and again indicate that the inferred tail structure during this pass was rather typical for steady conditions. The auroral gap in that paper, as a whole, is ascribed to the projection of the near-Earth tail region were nonadiabatic ion scattering is taking place due to a decrease in the B Z pro®le, and resulting Kappa parameter $1 (BuÈ chner and Zelenyi, 1989). In the equatorial plane the earthward boundary of this region is referred as thè`w all region'' by Ashour-Abdalla et al. (1993), and Bosqued et al. (1994). Arguments were presented already for a more precise mapping of this region to the equatorial arc/inverted-V and the region around it, which was supposed in GVZ92 to be the projection of the MFM at the earthward edge of the neutral sheet. Also, Pulkkinen et al. (1995) concluded that the``gap'' during a typical double oval case is mapped to 20±30 R E downtail (which is far beyond the MFM), while the polar auroral band mapped to beyond 30±40 R E . These independent results are consistent with the above mapping of the MFM.
To summarize, during the SMC period studied here, a large latitudinal width for the double oval of discrete auroral forms is thus implied. This double oval maps to the whole extended plasma sheet from its inner edge or, more precisely, from the negative gradient (in the GSM X direction) of the large-scale CTC (at about 12.5±15 R E in this case), as far as its distant part located probably around 100 50 R E (see Sect. 5.4) These characteristics of the oval and its mapping are all in full agreement with the mapping concepts advocated by Feldstein and Galperin (1985), and Galperin and Feldstein (1991).

Comparisons with the GVZ92 model
Here we discuss how the radial plasma density pro®le and the resulting minimum-B pro®le in the plasma sheet aect the modelled FAC pro®le, and thus the arc's intensity. In GVZ92 this pro®le (reproduced in Fig. 7), was chosen to obtain a narrow double FAC sheet generator for a typical narrow auroral arc/inverted-V supposing the B ZMIN $5 nT. However, the SPP96 pro®le derived by Sergeev et al. (1991Sergeev et al. ( , 1994 for the SMC period considered here, leads to a wider radial/ latitudinal extent (approximately 4 times) of the MFM considered to be the FAC generating structure in the plasma sheet, but with about 3 times lower B ZMIN . Correspondingly, the respective magnetic ®eld and pressure gradients are comparable, as well as the resulting FACs and auroral eects.
During the development and further discussions of the GVZ92 model during recent years, a question was risen concerning the stability of the additional line current (ALC) sheet in the XY plane which was not considered in the simple 1D form of the model. Evidently, for the isotropic pressure case, a more rigorous treatment is possible, in comparison with that in GVZ92, of the magnetic ®eld structure in equilibrium with plasma pressure with the use of magnetic vectorpotential A(r 0 ,z) and Grad-Shafranov equation. Its solution, with the given B Z (r 0 ) as a boundary condition, can be sought in a way described in Hau et al. (1989), and Hau (1991). For an adiabatic lossless convection, Hau et al. (1989) show that to avoid the``pressure balance inconsistency'', a minimum must appear in the magnetic ®eld B Z (r 0 ) pro®le. We must note that the steady-state B Z (r 0 ) pro®les deduced in GVZ92 and in SPP96 are very similar to those deduced in Hau et al. (1989), and Hau (1991), as was noted in the two former papers. However, it was stated in Sect. 4.1. that the static Grad-Shafranov equation does not take into account some speci®c features of the MFM region, such as ion inertia of the decelerated and de¯ected ion¯ow there, and a violation of the frozen-in condition for ions. As shown by Ashour-Abdalla et al. (1994) and Bosqued et al. (1994), the pressure anisotropy, and even the nondiagonal components of the stress tensor, are important in the``wall region'' for a pressure balance. The total con®guration of magnetic ®elds, currents and particle distributions obtained in their modelling appeared to be rather close to equilibrium and in many aspects resembled observations. In particular, it was concluded that in the``wall region'' the ions are strongly heated and isotropized, and that in the equatorial plane the pressure increases signi®cantly towards the duskside. This means that ions obtain just an azimuthal pressure gradient that is needed for a FAC generation in this region. These results were recently con®rmed by measurements (Frank et al., 1995), and ampli®ed by more advanced calculations using magnetic and electric ®elds self-consistent within a dynamic MHD model (Peroomian et al., 1997). In view of these results it seems that the simplest plasma pressure and magnetic ®eld distributions adopted in GVZ92 are qualitatively reasonable, though evidently a rough approximation.
One speci®c, though indirect additional piece of evidence for the``wall region'' origin of the arc is the shape of the electron spectrum not typical for an inverted-V structure (see Fig. 4), i.e. a power-law, or Kappa-distribution shape, with a decrease both at low and high energies, and no evidence for a potential drop ³1.0 kV. We note that this spectral distribution is very similar to the plasma sheet electron spectra observed from ISEE-1 at $30 R E by Christon et al. (1991) during disturbed periods and, thus, is consistent with a``wall region'' origin, without signi®cant acceleration. The reason for this is that, in contrast to non-adiabatic ions, electrons remained adiabatic in the``wall region''. Thus entering the MFM region they had to restore their original distribution in the distant tail where the B Z value was comparable to that in the``wall region'', i.e. was $1.5±2 nT. These values are not inconsistent with the magnetic data in the tail collected in SPP96 (see their Fig. 7c, left side, and Fig. 8a).
An independent consistency test of the B Z tail pro®le and the mapping relation can be furnished by the location of the ion intensi®cations near the equatorial arc (see Sect. 3), around $0835:40 UT for 1.8 keV ions and around $0835:20 UT for 0.1 keV ions. Such a maxima could be tentatively interpreted as resulting from non-adiabatic loss cone scattering of the earthward drifting ions (Delcourt et al., 1996) at the tailward side of the MFM. Thus it can be supposed that some ion precipitation intensity maxima will appear at the ionospheric locations mapped from their respective resonance scattering regions in the equatorial plane if convection will not displace them in latitude. By using the semi-empirical SPP96 B Z pro®le for this SMC interval we determined the locations in the neutral sheet where the non-adiabatic resonance condition (K$1) is ful®lled for the 1.8 keV and 0.1 keV ions. These locations appear to be at 16.8 0.35 R E and 12.4 0.3 R E respectively. As convection in this region was mainly zonal (see Figs. 4 and 5 in Y94), the respective latitudinal time-of-¯ight shift of precipitating ions is probably small and can be neglected in mapping these plasma sheet regions to ionospheric altitudes by using the semi-empirical mapping relation already de®ned in Sect. 4.2. While its precision is rather low (due to a small slope of the mapping curve in the MFM), the expected precipitating regions are at ILAT = 64.8 0.2 for 1.8 keV, and at ILAT = 64.1 0.1 for 0.1 keV (Fig. 3c, wide black arrows below the respective¯ux pro®les), which is close to observed ion maxima, and have similar separation in latitude but slightly displaced poleward (about 50 km). At the same time, the equatorial auroral arc happened to be close to these two ion intensity maxima, i.e. in the region of the MFM where the main part of the ion distribution function is stochastic as was supposed in GVZ92 and in Galperin (1992).
Finally we may comment about the model developed by Samson et al. (1992) and Liu et al. (1995), which considers the slow time evolution of a homogeneous arc. We suppose that the MFM could be a stable location of a slowly oscillating arc. The implied decrease of the Alfven velocity in the MFM¯ux tube (due to decrease of equatorial magnetic ®eld and increase of plasma density) and thus an increase of the resonance period, could be qualitatively consistent with that oscillation theory. The MFM then could be a site of resonance oscillations with a lifetime much longer than the oscillation period and determined by the lifetime and stability of the MFM. So we consider this model to be complementary to ours, but only further development of both could show their consistency.
A last comment concerns the splitting of the equatorial arc/inverted-V to narrow ®laments (£1.5 km) in the 100 eV intensity (Figs. 4 and 8); it cannot be reproduced by the GVZ92 model. Such narrow arc ®laments are often observed within a homogeneous auroral arc (Nadubovich and Starkov, 1962;Nadubovich, 1969;Oguti, 1981;Trondsen and Cogger, 1997), but they usually involve higher auroral electron energies. An approach to describe them is undertaken in the models by Tverskoy (1982 a, b) and by Samson et al. (1992), though their comparisons with rare high resolution measurements such as shown in Fig. 4, or more comprehensive, such as from the FAST satellite, are still to be completed.

Why were there no substorms during the SMC period?
In summary, data obtained during the November 24, 1981 SMC period on convection both at the dayside (Despirak et al., 1994;SPP96;Galperin et al., 1998), and on the nightside (Y94; Sergeev et al., 1990, 1991, 1994, consistently with the results of this study, indicate (1) stationary conditions throughout the magnetosphere with a strong convection, (2) quasi-steady intensive electrojets, and (3) a generally stable auroral double oval pattern. They show a relatively stable polar cap area and a cross-polar cap potential dierence of 80±90 kV. In other words, the magnetic¯ux is steadily, or quasi-steadily eroded at the dayside magnetopause, and quasi-steadily returns from the nightside tail, without large-scale explosive reconnection bursts in the near tail.
Naturally, an obvious question arises in connection with a prolonged SMC period: what is the cause of the absence of substorm onsets during such a prolonged IMF-B Z <0 condition prevailing during that period? This question is, at the same time, about at least one of the necessary conditions for a substorm onset, which apparently was not met during the SMC period. Was it a lack of some pre-condition for a speci®c local plasma instability (Lui, 1991a, b;1992), or a lack of a local exhaust of hot plasma in the plasma sheet caused by reconnection at the near-Earth neutral line and manifested in the equatorward motion of the prebreakup arc (Atkinson, 1982(Atkinson, , 1986(Atkinson, , 1996Baker et al., 1993), or an inhibition of some kind of an interchange instability, or something else?
One of the main ®ndings of this study seems to be the steady existence, during the SMC period, of a weak arclike feature observed at the equatorial edge of the oval compared to rather intensive arc/inverted-Vs typically observed in this region. Could this dierence in brightness (i.e. precipitating energy¯ux), or in the FAC density, or in the implied conductivity gradient in ionosphere, be important for the long-term stability of the arc/inverted-V structure, and hence for all the near-Earth's tail? Evidently, the observed weak FACs and resulting low electron acceleration will not alter much the ionospheric conductivity pro®le across the arc in comparison with that in the diuse auroral band. Thus, among various mechanisms of the substorm onset (see reviews by Lui, 1991a, b, andErickson, 1993), those which are based on the conductivity variations in the underlying ionosphere, such as proposed by Kan et al. (1988), Rothwell et al. (1988Rothwell et al. ( , 1991, or by Erickson et al. (1991), can be inoperative in these conditions. The near absence, or at least a low value, of a¯ow shear at the arc as revealed from the electric ®eld data obtained by A3 (see earlier) does not provide conditions necessary for the Harang Discontinuity mechanism proposed by Lyons and Samson (1992), at least near the location of the A3 arc crossing. At the plasma sheet altitudes, fast large-scale convection during the SMC together with weak FACs in the arc apparently could slow down, or even impede, the exhaust of the hot plasma from the magnetospheric¯ux tubes of the arc/inverted-V considered by Atkinson (1986Atkinson ( , 1996 as a possible cause of substorm onset. As was shown by Hau et al. (1989) and others (see earlier), the existence of the minimum in the B Z radial pro®le allows for stationary solutions avoiding the``pressure balance inconsistency'' (Erickson and Wolf, 1980). These qualitative considerations are insucient to conclude that a substorm onset was indeed impeded by these factors, but they favor at least a longer recovery phase, or a longer delay to the next substorm. However the direct cause of a substorm onset, as well as its absence during the SMC periods, remains an unsolved problem.
A natural way for a substorm onset development was suggested by GVZ92, as was mentioned above: a decrease of the minimum-B ®eld in the equatorial plane to low enough B ZMIN values, say, £1 nT. The smooth minimum in the semi-empirical B Z radial pro®le, B ZMIN $1.5±2 nT, apparently was nearly steady during the SMC period on November 24, 1981 according to Fig. 7c in SPP96, and no substorms occurred. Such B ZMIN values would not allow for the non-adiabatic scattering for the core of the plasma sheet electron distribution function for which a lower magnetic ®eld is needed. So the stability of the CTC during the SMC was maintained at least in respect to the tearing processes, while conditions for the electron demagnetization were not reached. It can be also noted that in several other case studies Pulkkinen et al. (1992) have found a good correspondence between substorm onsets, or a local auroral activation cases, and the time/space region in the plasma sheet where the electron motion chaots was expected due to a decrease of the magnetic ®eld as deduced from the adaptive magnetospheric modelling. These comparisons seem to be qualitatively consistent with the plasma sheet stability conditions during the SMC period. Evidently further study of this interesting problem is needed.
We conclude that the data described concerning on the magnetospheric conditions during the long SMC period without substorms are consistent with some views about necessary conditions for a substorm onset. In particular, these data are consistent with the dominant role of a local deepening of the MFM as the immediate cause of the substorm onset, or of a local auroral activation, as was suggested by GVZ92. Indeed, in the latter scenario the deep minimum in the magnetic ®eld can arise quite naturally during a growth phase when cross-tail current is growing, and at the right place and time for an onset. Further development of the GVZ92 model for the substorm onset, or local auroral activation, is considered in Galperin and Bosqued (1998) and Galperin (1998).

Polar auroral band and its mapping to the distant tail
Throughout the long SMC period there existed a bright and relatively steady auroral band at the polar edge of the auroral oval (see, Y94, SPP96). Thus it is tempting to identify this observed polar band of the double oval with the result of the ®eld-aligned currents originated at the distant turbulent reconnection region.
It was conjectured long ago (Russell, 1972;Coroniti and Kennel, 1972; and for a recent discussion, Lockwood and Cowley, 1992;Kennel, 1995) that as the average reconnection rate at the dayside is generally not matched by the reconnection rate in the far tail, substorms, or localized magnetic ®eld dipolarisations (and BBF-type bursts in the tail) are needed to restore the average magnetostatic equilibrium throughout the magnetospheric system. It is clear that, for an SMC interval, such an equilibrium is maintained quasisteadily, so that substorms are``not needed'' to impulsively return the magnetic¯ux from the tail to the near-Earth's magnetosphere. This requires a relatively steady location of the distant reconnection region, as well as the adequate steady reconnection rate and plasma supply in the far tail. Usually it is assumed that the quasi-steady reconnection occurs at a distant neutral line (DNL). Another possibility (Galperin, 1995;Galperin and Feldstein, 1996) is a vast turbulent plasma sheet region in the far tail where quasi-steady turbulent magnetic ®eld reconnection is maintained.
During a substorm, Elphinstone et al. (1995b) demonstrated that the space/time development of the polar auroral band, which usually appears during the recovery phase, is separated from the equatorial auroral band related to the near-Earth central plasma sheet and may be directly related to the DNL. The polar auroral band of the double oval can be collocated with the VDIS-2 ion precipitation structures at the polar edge of the oval. Elphinstone et al. (1995b) concluded that at least occasionally, the polar auroral band is to be mapped to the PSBL where the VDIS-2 structures are observed. We note that this association is by no means typical. In all the VDIS-2 cases found from the A3 satellite (99 events), a VDIS-2 structure was distinct from the polewardmost inverted-V, and located poleward from it by about 1 degree of latitude in average (Bosqued et al., 1993a). Consequently, the polar auroral band usually maps to the distant plasma sheet, and not to the PSBL. However we may note that the quasistationary, extended, and durable polar auroral band observed during the SMC (on the DE-1 images presented in Y94) is quite distinct from the dynamic, and relatively short-term ($0.5±1 h) polar auroral band of the double oval during a recovery phase in a typical substorm.
Large-scale kinetics (LSK) modelling can shed new light on the association between the distant tail and associated auroral features. It has been demonstrated (see for a review, Ashour-Abdalla et al., 1993) that ions injected from the plasma mantle and crossing the distant neutral sheet will undergo a strong non-adiabatic scattering. 2D (Bosqued et al., 1993), as well as 3D simulations (Bosqued et al., 1994), have shown that a part of accelerated ions will follow Speiser-type orbits and precipitate as a band of superimposed VDIS-type 2 structures at the poleward edge of the auroral oval (Bosqued et al., 1994). For steady conditions (not necessarily very quiet) the same simulations showed that a strong cross-tail current (CTC) develops near the DNL around 100 R E downtail which leads to an intense upward FAC (and a bright polar auroral band) around ILAT $ 72±76°at ionospheric altitudes extending from MLT $21 h to $03 h. The VDIS oval is immersed in this poleward region of intense FACs, i.e. presumably at, or poleward from, the polar auroral band, which is detached poleward from the equatorial band of discrete forms at lower latitudes (Bosqued et al., 1994). This polar auroral band together with the equatorward-most arc, or band, of the oval described above will form the double oval appearance. These results were con®rmed by model calculations by Onsager and Mukai (1995) that were able to reproduce the observed ion precipitation characteristics across the auroral oval, including a VDIS structure at its polar edge and a mid-oval``gap'' mapped to the rather distant plasma sheet region, at 45±55 R E , much tailward from the``wall region''. All these ®ndings are consistent with the GVZ92 model and mapping of the equatorial auroral arc of the oval to the``wall region''.
A last comment is related with the A3 observation of an auroral polar band striated to multiple narrow auroral arcs. This arc's splitting is in qualitative accord with the layering of the FAC sheets in the double oval polar band as observed by Echim et al. (1997) from the MAGION-2 and MAGION-3 satellites during double oval conditions. Such a FAC layering reminds us of the concepts by Atkinson et al. (1989) about multiple X-line origins of such arcs, but favors a radially extended reconnection region, not a single DNL.
Thus, to summarize, these observations allow us to reformulate the question on the absence of substorms during the SMC period in relation to the polar auroral band. So the question is: why, at least during this particular SMC period, this band which is presumably related to the distant reconnection region, or DNL, was stable and persisted for a very long time? In other words, what plasma parameters in this case determined the steady reconnection rate in the far tail (probably re¯ected to some extent by the polar auroral band)? Or, what speci®c features determined the regular supply of magnetic¯ux and plasma to the magnetosphere from the nightside, which matched the average dayside reconnection rate (magnetic¯ux erosion)? The answers to these questions apparently may be obtained only when the phenomena at the far magnetospheric tail, at the dayside magnetopause, and in the auroral oval, are considered as inherent, interdependent processes within a uni®ed, and nearly equilibrated, plasma system.

Conclusions
1. A steady weak auroral arc, located at the polar edge of the diuse auroral band, i.e. at the equatorial boundary of the stationary oval, was observed by the A3 and DE-2 satellites during the November 24, 1981 SMC period. 2. This arc is shown to be formed inside a relatively narrow, but extended in local time, magnetic ®eld minimum, MFM (down to 1±2 nT) located in the transition region from the dipole-like to stretched magnetic ®eld in the nightside near-Earth's plasma sheet. This unique observation con®rms the main hypothesis of the GVZ92``minimum-B'' model concerning the``arc root'' location. 3. Only a very small angle a $0.01 between the vectors r andr is needed to match the observed FAC density in the arc and supports the hypothesis adopted in the GVZ92 model that the azimuthal pressure gradientr is proportional to the radial pressure gradientr . 4. The observed narrow double sheet FAC structure associated with the arc with a total width £0.5°ILAT, is correctly predicted, due to the changing sign of thẽ r at the MFM. The narrowness of the observed arc's main intensity maximum, the location and width of the upward current region, are all reasonably well reproduced by the modelled FAC. However multiple striations of the arc precipitation are not reproduced by the adopted simple form of the MFM. Obviously, by introducing arbitrarily additional small details in ther andr pro®les it seems possible to formally reproduce these observations within the frame of the model.

5.
The observed wider downward current region which extends down to ILAT £63.0 degrees (the region II current) is mapped inward from the MFM. According to the SPP92 mapping, this current was generated in the wide region from about the geostationary orbit till $10 R E . 6. These observations and modelling support the assumptions made in GVZ92 that the prebreakup arc also originates from the narrow elongated MFM, and thus that substorm onset starts within the MFM. 7. The steady appearance over a long period of time of a band of intense precipitation and resulting bright auroral band at the polar oval border during this SMC period allows us to suppose its origin from, and mapping to, the radially extended quasi-steady distant turbulent reconnection region in the far tail, or the DNL. 8. These comparisons were made for only one particular SMC period. So it seems necessary to check the applicability of these conclusions for other SMC periods, and for other cases of steady, or quasi-steady auroral arcs in the oval, and especially for the prebreakup arcs in view of their importance for the substorm onset problem.