Multiple scales in auroral plasmas

Journal of Atmospheric and Solar-Terrestrial Physics 64 (2002) 211 – 229

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Multiple scales in auroral plasmas Yu.I. Galperin∗;1 Solar-Terrestrial Environment Laboratory, Nagoya University, Toyokawa, Aichi 442-8507, Japan Received 27 January 2001; received in revised form 7 May 2001; accepted 7 May 2001

Abstract A review of the observed space scales of the auroral features ranging from the whole auroral oval of bright discrete forms down to the nonlinear moving solitary structures with the scales of the order of Debye length is given. The characteristic physical scale which determines the generation process is indicated whenever possible. Some problems of the auroral theory and modeling are brie0y discussed, and a cross-scale coupling between the auroral and magnetospheric altitudes is stressed. It becomes apparent that the 2rst in situ studied real astrophysical plasma object—the Earth’s magnetosphere=ionosphere=aurora— is a uni2ed multi-scale system which seems to be ordered at large scales, but sometimes looks as nearly nondeterministic, or chaotic, at small scales. The most powerful processes in this system operate in a very wide range of scales, with multifarious cross-scale couplings. The statistical behavior of magnetospheric=auroral plasmas in the regions of active auroras often can c 2002 Elsevier Science Ltd. All rights reserved. be reasonably described as the near-critical state.  Keywords: Aurora; Auroral oval; Magnetosphere; Magnetotail; Plasmasheet

1. Introduction “Though this be madness, yet there is method in’t”. W. Shakespeare, “Hamlet”,

Scene Two.

With the increase of understanding of the fundamental role of the highly variable auroral processes for the magnetosphere, and at the same time with the progress in the auroral global imagery, photometry and spectrometry, in the rocket experiments in aurora, and in the theory, a new interest is seen for auroral features, their space scales, time variations, characteristic forms, and their nonlinear behavior (see for example, Samson et al., 1992; Trondsen and Cogger, 1997, 1998; Trondsen et al., 1997; Safargaleev et al., 1997; Haerendel, 1999; Vogt et al., 1999; Lyons et al., 1999; Lui et al., 2000). ∗

Fax: 7-(095)-310-7023. E-mail address: [email protected] (Yu.I. Galperin). 1 Permanently at Space Research Institute, 117997, Moscow, Russia.

Many of these features occur at altitudes of luminous aurora, that is, around ∼ 100–200 km, below the satellite altitudes. They were, and are, extensively studied from ground observations. These altitudes are accessible for in situ measurements mostly from rockets. Due to dynamical and small-scale nature of active auroral phenomena, the multi-point rocket measurements are crucial to distinguish between spatial and temporal variations, and realization of such experiments has already started (see Lynch et al., 1999; Ivchenko et al., 1999; Pietrowski et al., 1999). Above the auroral altitudes the plasma is also very much disturbed by strong concentrated currents, particle beams, nonlinear waves and solitary structures. These features are now seen on many satellites and rockets with appropriate instrumentation, and were described in most detail by recent low-altitude high-resolution measurements from the satellites FREJA and FAST. They reach the smallest spatial scales in auroral plasma phenomena, down to the electron Larmor radius and the Debye length, so the scales involved in aurora range from tens of meters to hundreds of kilometers. The choice of the auroral features included in the review is rather arbitrary, so many interesting types are omit-

c 2002 Elsevier Science Ltd. All rights reserved. 1364-6826/02/$ – see front matter
PII: S 1 3 6 4 - 6 8 2 6 ( 0 1 ) 0 0 0 8 5 - 2

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ted, in particular, the periodic ones such as omega bands, torches, periodic bright spots, traveling convection vortices, small-scale KH-like vortices, etc. Here, a brief review is given of the typical auroral features observed, of the respective physical space scales in the auroral plasmas, and of some approaches used for their physical interpretation. The review is by no means complete, it deals only with a limited amount of topics chosen by the author and related to spatial scales of the auroral discrete forms. In the accompanying review by Lui (2002) the contemporary methods of analysis of the nonlinear multi-scale coupling processes in the magnetospheric plasmas are described and exciting examples of their application are shown, which reveal the existence of some general properties of the magnetosphere as a nonlinear system (see Section 5.1). Until now, these methods of statistical description of a conglomeration of auroral phenomena were not common in their analysis, while various nonlinear features observed suggest fruitful applications of such methods in future. A very interesting but extremely complicated auroral plasma environment indeed looks as a laboratory for studying nonlinear dynamic plasma processes in a collisional plasma, and as a test bed for numerical plasma modeling. 2. The largest spatial scale—the oval of discrete bright auroral forms The discovery of the auroral oval of bright discrete auroras as the continuously present large-scale feature in the magnetosphere (Feldstein, 1960, 1963), and of the substorm within the oval—the main and more or less reproducible sequence of disturbance features (Akasofu, 1964), were among the main results of the International Geophysical Year (1957– 1958). It appeared later that the oval of discrete auroras is the projection, or mapping, to the polar ionosphere of the plasmasheet—the main reservoir of the hot plasma in the outer magnetosphere. The respective space scale at a particular altitude at nightside is de2ned by the conservation of the magnetic 0ux between the ionosphere above the auroral oval of discrete auroral forms and the plasmasheet which is the main origin of the respective auroral currents and energy 0uxes. The problems of mapping to the polar ionosphere the gross magnetospheric plasma structures, and their imaging in diJerent auroral regions, are discussed at length, in particular, in Feldstein and Galperin (1985), and Galperin and Feldstein (1991). The oval at its scale may be divided into the so-called Regions 1 and 2 of the 2eld-aligned currents (Iijima and Potemra, 1976)—the large-scale regions at, respectively, higher and lower auroral latitudes distinguished by the predominantly upward or downward 2eld-aligned current (FAC) direction. Region 1 upward currents extend within the oval of discrete forms roughly from midday through evening to midnight, or more precisely, till the Harang discontinuity (HD). On the opposite side of the oval (with

some overlapping in longitude) Region 1 currents are downward. Region 2 currents are adjacent from the low-latitude side and have the opposite direction. This division appears in the averaged data, but not always is seen in particular geophysical conditions when small-scale FAC and auroral features can dominate. 3. Primary energy sources and current carriers for aurora While discrete aurora is well seen by a naked eye, the underlying physics of its particle acceleration=heating, of the electric current sources at high altitudes, and their relation to the space scales of the respective auroral features are still not fully understood. It is known, as follows from the evident relations div ˜J = 0, j =B = −div ˜J⊥ , that powerful auroral currents feeding discrete auroras originate in the magnetospheric regions, where large-scale strong perpendicular currents ˜J⊥ are 0owing. Evidently, some speci2c physical conditions must exist in the source region for the divergence of ˜J⊥ to generate small-scale FAC at a particular location (here, FACs of the scale of ∼ 10 km and more are meant which can be mapped to the magnetospheric sources). These conditions and their space–time evolution are still not fully understood, and hence are hardly predictable for a particular time and location. This means that auroral pattern and its structuring at the large and medium scales somehow re0ects the plasma active processes and structuring in the respective vast regions of the outer magnetosphere. According to the observations of discrete auroral forms and their mapping these structuring processes occur mostly within the plasmasheet, in the LLBL, and in the dayside cusp and cleft regions. New approaches for their physical description and analysis are being developed (see Lui et al., 2000; Lui, 2002; Milovanov et al., 2001). With a proper mapping between these low- and high-altitude plasma regions, the auroral imagery could provide a way to analyze remotely spatial and temporal structuring processes in the outer magnetosphere. (We do not discuss here the physical limitations of the MHD mapping concept which relies on the “frozen-in” condition, the applicability of the “magnetic 2eld line” concept, the absence of FACs, short-enough Alfven transit time, etc.) However, such a “remote sensing” of the magnetospheric active regions may be reliable only if no nonlinear scale changes occur at mid-way. Auroral energy 0uxes of up to 103 erg=cm2 s sometimes seen in the brightest auroras evidently cannot be mapped to the tail. In other words, we need to understand, if there is any process(es) in the auroral acceleration region at altitudes from ∼ 0:5RE to 2–3RE which are analogous to pinching, and=or lead to a transformation of extremely large Poynting 0uxes observed at higher altitudes at larger scales to very intensive particle beams and 2eld-aligned currents at very small scales? Or, better to say, how to predict in what physical conditions such a restructuring

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Table 1 The two main types of auroral structures Type

Stability ¿ 103

Homogeneous arcs and bands=inverted-Vs (IBC I – IBC II)

Time stable for

s

Rayed forms (IBC I – IBC IV)

Nonstable, dynamic 6 1 s

which is usually accompanied by strong particle acceleration up to very high energies can start? The main current carriers are evidently hot magnetospheric electrons for an upward 2eld-aligned current (with usually only small contribution from the upward ion beams), and an upward beam of heated ionospheric electrons for a downward one. The energy is carried downward by the stationary FAC for the creation of a steady auroral form such as a homogeneous arc (which may be a prebreakup arc during a substorm growth phase). In dynamic and bright-rayed auroral forms, such as seen during auroral break-up, large Poynting 0ux values from small-scale Alfven waves were observed when the time resolution was adequate (Chmyrev et al., 1989; Knudsen, 1996; Stasiewicz et al., 2000; Wygant et al., 2000). The visual brightness of auroral forms is evaluated (Chamberlain, 1961; Vallance Jones, 1974) by the International Brightness CoePcient (IBC) ranging in logarithmic scale from IBC I (particle energy 0ux ∼ 1 erg=cm2 s) to IBC IV (∼ 1000 erg=cm2 s). Here, we shall 2rst consider more or less steady features within the auroral oval (which, however, is never really steady), and then more dynamic and bright active auroras which evidently are due to some additional powerful and highly localized physical processes. The most popular and extended auroral forms, but not the most often seen, are arcs. From visual and instrumental observations it is evident that there are two fundamentally diJerent types of discrete auroras: more or less quasi-steady homogeneous arcs, bands, patches, etc., and bright-rayed auroras forming various dynamic forms—rayed arcs, draperies, coronas, isolated ray bundles, etc. (see Stormer, 1955). Their main features are summarized in Table 1. Some of the items in the third and fourth columns of this table will be clari2ed below. Much shorter space=time scales to which the discrete-rayed auroras belong (down to milliseconds for high-energy electrons), and a wide range of electron energies involved (up to hundreds of kiloelectronvolts in the so-called red auroras of type B—with the red=orange lower border) are outside the MHD limitations. Hence, they generally

Structuring

3D current loops

Oval-elongated, 2lamented=structured in perpendicular direction

Two-sheet encircled current loops (“Matreshka” scheme)

rayed arcs,“draperies”, “coronas”, “bundles of rays”

Various types (Oguti, 1981; Velichko et al., 1985; Trondsen and Cogger, 1997, 1998; Trondsen et al., 1997; Vogt et al., 1999)

need a more elaborate theory for description. To an observer it looks as if the active bright auroras develop as a multi-scale turbulent plasma which is more or less ordered at large scales but often looks as nearly nondeterministic at the scales of tens to hundreds of meters with strong and variable particle beams. Some evidence for self-organization was found in particular scenarios in the studies of statistical properties of the auroral images (see below). It remains an unsolved problem how the characteristics of such a plasma can be adequately modeled, and how the results of the modeling can be compared with experiments. Hopefully, the new approaches to the analysis of such partly ordered systems, of which an excellent review is given in the accompanying paper by Lui (2002), will allow to delineate the general structural ordering in this apparent disorder. That serves as the motivation for the epigraph at the beginning of the paper. 4. Spatial scales within the quasi-steady (QUIET) auroral oval 4.1. Inverted-V precipitation bands Inverted-V events in the low-altitude satellite measurements are the most prominent and typical features in the auroral oval of discrete forms. These features coincide with upward FACs with the density higher than ∼ 0:5–1
A=m2 . They are consistent with the formation of a quasi-steady FA potential drop due to the loss-cone limitation which accelerates electrons downward and ions upward thus forming particle beams (Lyons et al., 1979). The electrostatic nature of particle acceleration within an inverted-V event was con2rmed by Bosqued et al. (1986) using adiabatic scaling relations which follow from magnetic moment conservation by the beam particles: j ∼ ’ ; P∼j2 , where j ; ’ , and P are, respectively, FA current density, accelerating FA potential diJerence (evaluated from the electron spectral peak within an inverted-V), and total precipitated power. Inverted-V events allow to discern the oval of discrete forms

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Fig. 1. The Fast Auroral Snapshot Small Explorer (FAST) satellite passing through multiple auroral arcs at ∼ 0920 UT, February 6, 1997. The 110-km conjugate to the satellite is shown in the all-sky image (left) and at 10 s intervals in a narrow-2eld camera view (right). The center panels are the electron energy-time spectrograms (integrated over all pitch angles). The left one shows a number of inverted-V structures. The bottom panels are the precipitated energy 0ux on a linear scale. The individual auroral arcs are clearly displayed here. The auroras, in particular the two arcs to the right (north), did change over the 4 min of the pass, so a detailed comparison between all sky image and particle data should not be attempted. (Courtesy of the FAST Science Team).

from the diJuse auroral zone in low-altitude satellite particle measurements. But the energy 0ux in them rarely exceeds several erg=cm2 s, so the resulting auroral brightness belongs at most to IBC I – IBC II, which is wide and so barely distinguishable by a naked eye within auroral oval above other forms of auroral luminosity. However, according to Stormer (1955) an experienced observer often can see weak but extended luminosity bands which can be well due to the inverted-V precipitation events. Latitudinal widths of the inverted-V events range up to 300 –500 km and can 2ll a signi2cant part of (or even the whole) the auroral oval of discrete auroral forms. Often a polar pass of a low-altitude satellite across the premidnight oval shows several

inverted-Vs in sequence. Such an example is shown in Fig. 1 (courtesy of the FAST science team). Presumably, such an event re0ects a respective structuring of the FA current generators in the plasmasheet. As was recently demonstrated by Newell (2000), from a large statistics of the particle measurements, the precipitation bands with speci2c spectral peaks called “inverted-Vs” most often do not form a symmetric Q-shaped structure. Note that the integral ionospheric Pedersen conductivity P is approximately proportional to the upward FAC density j , so the double-sheet current system associated with the inverted-V can adapt to some preferred width compatible with the steady current source in the

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near-Earth tail. The characteristic latitudinal spatial scale across an inverted-V structure follows from the accelerating voltage drop, linear density of the closure current and ionospheric Pedersen conductivity (see Lyons and Williams, 1984, Chapter 4.4.5). If Xw is the half-width of an inverted-V, for medium amplitudes of FAC density, Xw = (P =k) = (P =e2 N )1=2 (2me Kth )1=4 ,where P is the Pedersen conductivity below the inverted-V, e and me are the electron charge and mass, N and Kth are the hot electron density and thermal energy, respectively. For N = 1 cm−3 and Kth ∼0:2–1 keV the full-width 2Xw ∼100 km, in qualitative accord with the data. The visible auroral arcs (see Section 4.2) are similarly extended along the oval as the inverted-Vs, but are brighter and=or narrower with widths ∼10–20 km, so they are easily distinguishable by visual and photographic ground observations. While the spectrum of widths seems to be continuous from these classical visible auroral arcs to the inverted-Vs (which are mostly observed from particle measurements from satellites), there can be physical diJerences between them because the arcs tend to be located at a side of an inverted-V event (Fennell et al., 1981). This property of the arcs with respect to inverted-Vs can be also seen in Fig. 1. A theory of inverted-Vs multiplicity was proposed by Tverskoy (1982a) as a result of convection strati2cation in the steady plasmasheet. It was further developed in Antonova et al. (1991). The quantity of the adjacent steady current sheets separated by more than about 10 km is predicted in this theory by the value of a dimensionless parameter G (which depends on the plasma sheet temperature and density in the plasmasheet as well as on the ionospheric conductivity and the structure’s width). It is argued that this “hot strati2cation” mechanism is applicable to the conditions of the enhanced ion scattering due to the ion nonadiabatic motions. For ranges of G∼1; G∼ 6; and G∼ 30– 40, the predicted quantity of inverted-Vs within the oval is one, two, three or more, respectively. This prediction was tested from the data of the Intercosmos - Bulgaria - 1300 satellite and recently from the AUREOL-3 data by Antonova et al. (1991, 1999). For the FAST data case shown in Fig. 1, where three or more inverted-Vs are seen, the evaluation made (courtesy by M. Stepanova and E. Antonova, 2000) gives G∼ 30, in accordance with other comparisons. Thus, the tests of the “hot strati2cation” theory of the plasmasheet by Tverskoy, though rather scarce in statistics, look quite positive for steady conditions. At the same time, the length of an inverted-V event is much longer than its width, and it maps to a rather long band in the near or middle tail. Presumably, it extends more or less across (or along) a signi2cant part of the tail plasma sheet. In this quasi-steady FAC generating region, due to some still unidenti2ed reason, a part of the cross-tail current is diverted to the ionosphere forming a double-sheet Birkeland current loop. Some indirect experimental data indicate that usually an inverted-V structure is time stable for at least tens of

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minutes which is an important constraint for a theory. There is still no accepted theory for this middle-scale quasi-steady FAC generator region. We shall return to this point when discussing similar problem for the “root of the arc” in the next section. 4.2. Homogeneous auroral arcs Steady homogeneous visual auroral arcs of 10 –20 km width are characteristic for a steady oval. They can be very long, up to several thousand kilometers along the oval, mostly in its evening and nightside sectors, but sometimes also in the postmidnight sector. Arc is brighter than a weak wider auroral band (presumably an inverted-V) and is well seen by a naked eye. Steady arcs are usually in the brightness range from IBC I to IBC II. (Sometimes an arc can reach IBC III but then it is short-lived.) Homogeneous arcs are often (or always?) striated to narrow 2laments (see Section 4.3.) but this can be seen from the ground only when looking at an arc along the direction of the magnetic 2eld (to the so-called magnetic zenith). It was found from satellite data (Fennell et al., 1981) that a narrow quasi-steady visual auroral arc is usually located at a side of the neighbor wider inverted-V, and this can be seen also in Fig. 1. So most probably there exists some physical relation between an inverted-V and arc, which leads to the intensi2cation of the energy 0ux and light emission at the edge of the former. Several theoretical approaches were proposed for the explanation of these “edge eJects” (see Galperin and Volosevich, 1995; Haerendel, 1999, and references therein). A typical arc-associated 3D current system is a double-sheet Birkeland current loop (Park and Cloutier, 1971). The typical homogeneous arc’s width scale is ∼ 10 km. A recent study of the optical steady arc widths (Knudsen et al., 2001) gives average arc width 18 ± 9 km with a sharp decrease in probability below 8 km. No tendency of correlation, or anti-correlation, was found between the arc brightness and width. The arcs can be very long, up to many thousand kilometers, and sometimes are stable during ∼ 10 h if the solar wind and magnetospheric conditions allow (see reviews by Davis, 1978, Borovsky, 1993; Galperin, 1994). Stable arcs, together with the adjacent inverted-Vs described above, often appear as double, triple, etc., “multiplet” structures with a wide range of the inter-arc distances up to 50 –100 km as described in the previous section. The adjacent steady arcs can have speci2c in-phase or anti-phase variations (Safargaleev et al., 1997), so their current systems are coupled. The complicated behavior of a “quasi-steady arc” involves various small-scale deformations, drifts, oscillations, splittings and mergings of the 2laments, etc. They were studied by Stormer and other early observers (see Stormer, 1955; Oguti, 1981), and an interesting attempt to interpret these variations as due to the current sources in the form of multiple X-lines is described in Atkinson et al. (1989). These

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arc variations=distortions are important as possible clues to the mechanism(s) of substorm onset which starts at those plasma 0ux tubes. Samson et al. (1992) have shown that a steady arc can experience periodic oscillations with periods ∼ 10 min. These oscillations have a resonance character: their phase reverses at the intensity maximum. Supposing that the Alfven transit time to the source is TA = =2 we come to the mid-tail distances which are incompatible with the mapping to the near-plasmasheet “root” of the observed equatorial arc of the auroral oval. However, if a signi2cant part of the wave propagation time is spent near the neutral sheet where the Alfven speed is rather low, the inferred distance to the “arc’ root” could be much shorter. Interesting experimental and theoretical developments of the steady homogeneous auroral arc generation and nonlinear evolution due to the resonance oscillations till the breakup were further considered in Trondsen et al. (1997), Samson et al. (1998), Rankin et al. (1999), and Wanliss et al. (2000). Theoretical analyses of such oscillations were performed also by Streltsov and Lotko (1996) and Pokhotelov et al. (2000). What determines the typical width of a steady homogeneous arc of ∼ 10–20 km? Recently, two diJerent approaches have led to similar results—one based on the properties of the plasmasheet source, another on the stability of the Alfven wave absorption and re0ection at and above the auroral ionosphere. One is the so-called “Minimum-B” (or, Min-B) model, or concept, of a steady arc’s source as proposed by Galperin et al. (1992), and Galperin (1998). It is supposed that the magnetic 2eld in the “arc’s root” in the near-Earth neutral sheet forms a minimum (∼ 1–3 nT) in the radial pro2le which is extended in longitude (MLT). This property arises in the model from a supposed tailward gradient of the integral cross-tail linear current density ∇J⊥ and allows to generate a double-sheet Birkeland current loop associated with the arc. According to Galperin and Bosqued (1999) in a single case study the model is in quantitative accord with experimental data from the AUREOL-3 satellite. In the model only one 2tting parameter was selected arbitrarily: the value of
the small angle  between the vectors ˜ ∇W (where W = dl=B is the unit 0ux volume) and the ˜ Such regions in stationary conditions pressure gradient ∇P. (see Tverskoy, 1982a, b; Heinemann et al., 1994), and 0ow vortices in the dynamic magnetosphere, act as generators of the medium-scale FACs (scales of hundreds of kilometers) within the limits of the MHD approach. In the model, the angle  was assumed to be 0:012 rad to 2t the observed amplitude of the upward FAC in the arc. With this model the arc’s width (more precisely, the width of the upward FAC feeding the arc) can be found from the magnetic 0ux conservation from the “arc’s root” width till the auroral arc. It follows that the width along the tail of the magnetic 2eld minimum of a couple of RE projects to a ∼ 10–20 km arc’s width. It is stressed that these scales, both at the ionosphere and in the near-Earth tail, were derived from the simultane-

Fig. 2. Modeled 2eld-aligned current (FAC) latitudinal pro2le (solid line) and respective DBy magnetic 2eld perturbation (dashed line) at ionospheric altitudes, compared with measured SBy variations (nT) of the horizontal magnetic 2eld (running averages on 1:2 s). The electron 0ux latitudinal pro2le at 100 eV (RIEP spectrometer) is given for comparison in the bottom panel and demonstrates that the upward FAC between ILAT = 63:9◦ and 64:45◦ (shaded area) coincides with the enhanced 0uxes of low-energy 6 1 keV electrons (the weak arc). X (RE ) is the projected X distance in the tail (from Galperin and Bosqued, 1999).

ous experimental data (see Fig. 2 taken from Galperin and Bosqued, 1999, their Fig. 8). Thus, assuming that the steady homogeneous arcs observed at, and near, the equatorial edge of the oval of discrete auroral forms, are due to the Min-B structure in the tail, a typical arc width of 10 –20 km is just the magnetic 0ux projection of the FAC generator region in the near tail. The narrow arc’s 2laments are neglected so far in the model; its extension to their much smaller scales is discussed in the next section. Another approach was developed by Kinney et al. (1999). It is based on the 2nding by Vogt and Haerendel (1998) that the Alfven wave re0ection coePcient RA from a region with a 2eld-aligned potential drop depends on the perpendicular scale. This is the situation which occurs above a steady homogeneous arc. Their analysis and the model led to the deduction that just at the width of ∼ 10 km a drastic change in the re0ection conditions occurs. At larger scales (characteristic for inverted-Vs) the re0ection is in phase that allows for a growing Alfven resonance oscillations between the source in the tail plasmasheet and auroral ionosphere. (This may be in accord with the data given by Samson et al. (1992) who observed oscillations in the arc intensity, or in the FAC den-

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sity, with periods ∼ 10 min.) At the scale ∼ 10 km the RA becomes zero, so this range of scales is selected for the best transport of the wave energy by the Poynting 0ux from the tail source to the acceleration region above the arc which acts as a sink. At still lower scales the RA changes sign, and the Alfven waves are re0ected in antiphase between the ionosphere and the potential drop, making it possible to form a steady standing wave pattern. As the Alfven speed above an arc is very high due to depleted plasma density, the Alfven travel time between the topside ionosphere and the acceleration region is very short, presumably less than a second, and this factor stabilizes the standing wave pattern against 0uctuations. According to Kinney et al. (1999), this time stability explains the appearance of the relatively steady narrow arc’s 2laments (see the next section). Galperin (2000) tried to combine these two approaches to suggest an updated scheme of the Min-B which now includes, besides the “arc’s root” in the near tail, also the Alfven wave absorption at the acceleration region, the 10 km wide arc, and its narrow 2laments. Thus, the characteristic scale of the arc width, ‘⊥A ∼ 10 km, is probably due to both factors. Firstly, at this scale the Alfven wave is absorbed in the acceleration region (RA ∼ 0). Secondly, the mapping of the “arc’s root” of a couple of Earth’s radius wide in the tail plasmasheet leads to the width of ∼ 10 km at ionospheric altitudes which happens to be a good absorber of the Poynting 0ux. 4.3. Multiple narrow =laments along a homogeneous auroral arc It was noticed from ground observations that a steady homogeneous arc, when seen along the magnetic 2eld, is a series of parallel curtains with the width of ∼ hundreds of meters to a kilometer or so (Nadubovich and Starkov, 1962; Maggs and Davis, 1968; Nadubovich, 1969; Oguti, 1981). These narrow arcs are separated by signi2cant gaps in brightness of comparable width and extend in altitude of tens of kilometers, so they may be seen only when they are observed near the magnetic 2eld direction within ◦ 1–2 . The distribution of the inter-arc distances is close to Poissonian. For the scales more than several kilometers the electrodynamic structures involved can be mapped to the outer magnetosphere, but the lower scales cannot. The striation mechanism of an arc to narrow 2laments was described and numerically modeled by Kinney et al. (1999). It is an adaptation to the inter-arc scales and further development of the ideas by Atkinson (1970), Trakhtengertz and Feldstein (1984, 1991), Lysak (1993), and Trakhtengertz and Rycroft (2000) about the Alfven wave resonator between the auroral ionosphere and the auroral acceleration region at altitudes 1–2RE . According to the model by Kinney et al. (1999) the 2laments are formed between the ionosphere and acceleration region due to the standing wave pattern with the period of order of 1 s, and their striation mechanism is decoupled from the plasmasheet. Evi-

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dently, further data analysis is needed to test this interesting hypothesis. The question arises what physical limit determines the minimal width of the 2lamentary quasi-stable auroral FACs that are feeding the energy to these narrow arc’s 2laments (see Borovsky, 1993). An attempt to approach this problem was described in Galperin et al. (1986). The following scenario of breaking the stability was supposed as typical for a substorm onset, or auroral activation. Consider a breakup of a quasi-stable homogeneous auroral arc, or of its 2lament, to bright-rayed forms with perpendicular scales of tens to hundreds of meters. It was supposed that double-sheet FAC, which in its upward branch steadily accelerates plasmasheet electrons downward forming a prebreakup arc, gradually gets narrower and intensi2es till some limit of linear stability is reached. A modi2ed tearing instability is excited due to oppositely directed perpendicular magnetic components (along the arc) at the sides of the FAC sheet, and its linear increment was evaluated. It appeared that perpendicular magnetic 2eld diJusion across the FAC sheet will start at arc’s width of order of electron inertia length ‘⊥F ∼c=!pe . In the model it is reached above an arc at altitudes ∼ 3000–5000 km and will lead to FAC 2lamentation to scales of order of ‘⊥F . The linear increment was evaluated as ∼ 103 s−1 at altitudes ∼ 3000 km. (Note that in this case, the millisecond time scale seen in high-energy electrons producing the auroral X-rays can be understood as the time characteristic of the resulting particle acceleration in oblique Alfven waves. In the above approach these waves occur as a result of the tearing instability at altitudes of several thousand kilometers.) Further studies and numerical modeling are needed to analyze nonlinear stage of this and other related instabilities of strong auroral FACs. Thus, a new characteristic scale—the electron inertial length ‘⊥F —determines the minimal width of the arc’s 2laments. On the other hand, it is easy to estimate the amplitude of a strong external Alfven wave which will certainly destroy the resonance system of parallel arc’s 2laments. If the drift displacement across the arc from the electric 2eld of the incoming wave comes near the inter-2lament distance, the coherence of the “auroral interferometer” will be destroyed, and some non-stationary active auroral burst is expected (Galperin, 2000). A simple evaluation leads to the wave amplitude of ¿ 50 mV=m, but somewhat lower values may be suPcient. 4.4. Summary of the scales of the steady auroral features In Table 2 the summary of diJerent space scales for steady conditions is shown. It is presented also in Fig. 3 as the “MATRESHKA” scheme of the nested Birkeland current loops taken from Timofeev and Galperin (1991). It must be understood that all the current loop features inside the oval can be multiple, not single, and that they map to the vast regions of the outer magnetosphere, mostly to the magnetotail.

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Table 2 Nested Birkeland double-sheet current loops (“Matreshka” scheme for steady conditions) Feature

Region-1=Region-2

Inverted-V

Stable arc

Filament

Typical scale

∼ 500 km

∼ 100 km

∼ 10 km

∼ 0:1–1 km

Scale origin

CPS mapping

l⊥ ( # ; P ; j )

l⊥ (RA ∼ = 0)

l⊥ ∼c=!pe ; rLi; ; rLe ,

Reference

Feldstein and Galperin (1985)

Lyons (1980)

Kinney et al. (1999)

Kinney et al. (1999)

accepted theory was proposed for the extremely high-energy 0uxes observed in rayed forms. 5.1. Medium-scale regions of active aurora seen in global auroral imagery from space

Fig. 3. Schematics of the auroral encircled Birkeland current loops hierarchy, the “Matreshka model”, proposed earlier (see Timofeev and Galperin, 1991). A smaller Bostrom-type two-sheet current loop (or several such loops) is encircled by a larger-scale one but similar in form and having the same direction of the closing Pedersen current in the ionosphere. It resembles the Russian folkloric children’s toy “Matreshka” which is a series of similar wooden dolls enclosed one within another. RA- radar arc, arc- steady homogeneous arc, index A for the arc’s FA currents, index a for arc’s 2laments.

5. Bright dynamic auroral features: active auroras Most of the popular photographs and movies of auroras are made from the bright and dynamic auroral features. Their intensity can be much higher than for the nearly steady auroral forms described above, while smaller spatial scales in the perpendicular direction and quick motions appear. Table 1 above have summarized the main characteristics of the rayed auroras. Now, we will consider their scales in more detail. We start again from the largest scales, and then descend to the lower ones. It is to be stressed that, to our knowledge, no

Most of the published results of global auroral imagery from high-altitude satellites DE-1, KYOKKO, AKEBONO, VIKING and POLAR were obtained in the UV range, where the contrast of auroral emissions to dayglow is the highest. There exist experimental limitations in auroral imagery from satellites such as available telemetry rate, satellite rotation, instrument sensitivity and resolution, and also some physical constraints (satellite and aurora relative motions during exposure, multiple scattering in thermosphere of the OI 130 nm resonance quanta—the brightest UV auroral emission, etc.). Due to these constraints, the resulting space resolution for auroral images from space is rarely better than 30 –50 km. So in fact, typical discrete auroral forms of characteristic scale of 10 km (for arcs only in perpendicular direction) are often not resolved in such imagery. By compensation, these global images have revealed medium-scale patches, or “blobs” of enhanced aurora with a scale of hundreds to thousands of kilometers. This scale evidently re0ects the medium-scale FA current generating regions in the varying plasmasheet and LLBL during disturbances. The respective medium-scale regions of auroral enhancement are comparable, or larger, than the visible 2eld of view from a ground station. This makes it diPcult to delineate them from ground optical observations. However, magnetic eJects of the respective ionospheric currents in such regions are space-averaged and apparently often dominate the ground magnetometer readings which show a much smoother pattern than in situ measurements of discrete aurora currents. Note that discrete auroral forms are well resolved on the DMSP snapshot images down to the scales of 6 10 km (Akasofu, 1974; Valchuk et al., 1979; Shiokawa and Fukunishi, 1991) taken in the visible range. Unfortunately, the cross-orbit scanning technique on DMSP satellites does not allow to see auroral dynamics, and these optical observations are limited to the nonsunlit part of the auroral oval. However, the global auroral imagery allows to well resolve the auroral features with the scales which are

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intermediate between these medium-scale “auroral blobs” and typical visible discrete auroras, and these global images have revolutionized the studies of the aurora and magnetosphere. Among many results of this new vision we can mention here the recent analysis of the distribution of the global auroral energy input which was monitored during entire January, 1997, including both quiet and substorm intervals (Lui et al., 2000; Lui, 2002). While the distributions of signi2cant auroral inputs according to their size and power during quiet intervals were of the power law with a slope near −1, during substorms an additional prominent peak of large sizes and power appears. These distributions are shown to be consistent with the appearance of the self-organized criticality component and the “avalanche” in the magnetosphere as a whole. It is interesting that these medium-scale enhanced auroral regions begin to be reproduced from the recent MHD dynamic modeling with the real-time IMF and solar wind dynamic pressure input when the grid resolution projected to ionosphere reached 300 km (Ashour-Abdalla et al., 1999; Papadopulos, 2000). In this kind of modeling the generic medium-scale pressure gradients arise as a result of nonstationary plasma 0ows in the magnetosphere. In some ˜ , so that the regions they are skewed with respect to ∇W angle  = 0 , and thus act as the FAC generators. The recent MHD model results (those cited above and several others) show reasonable agreement with the medium-scale auroral “blobs” revealed from the global auroral imagery for selected model periods. This agreement is very encouraging as it supports the validity of the adopted MHD description for the medium-scale (in space and time) magnetospheric plasma processes. Hopefully, future MHD modeling eJorts with the resolution ∼ 100 km (projected to auroral altitudes) will meet most of the practical needs of the “space weather hazards” predictions including location, strength and time variations of ionospheric currents in auroral regions. But the necessity of a signi2cant upgrading of the computer base is only one of the problems. Another quite important problem is the necessity of inclusion in the models of some semi-empirical relations to substitute the eJects of complicated multiscale and partially nearly chaotic auroral processes which are at present poorly known. (It may be noted in the outset that for reliable model predictions, even when a good magnetospheric=auroral model is available, at least a two-point monitoring of the solar wind discontinuities is needed as the input data. This is because it is necessary to know better their fronts’ orientation and motion near the Earth which in0uence the dynamics of magnetospheric and auroral currents.) 5.2. Bright-rayed auroral forms As early as in 1920 Vegard from the widths of rayed aurora (down to hundreds of meters or less) concluded that this perpendicular scale is of the order of electron Larmor

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radius, so the discrete aurora excitation is mainly due to energetic electrons, not due to protons “of solar corpuscular streams” (Vegard, 1920). Auroral-rayed forms can appear as “bundles of rays”, as draperies, or coronas (when seen near the magnetic zenith). They are very dynamic but bright enough to be seen at distances of hundreds of kilometers with diameters of tens of meters, especially when observed with a small telescope. Their photometric studies become available with the use of the most sensitive low-level TV. Their brightness can be from barely distinguishable by a naked eye (∼ IBC I or lower) to the maximal observed in aurora (IBC IV). Their physical modeling and theory are still at the initial stage, especially for their perpendicular scales and dynamics. It is generally believed that the electron acceleration mechanism that is manifested in these rayed forms is due to the oblique Alfven waves—a supposition that has some observational support. We do not elaborate here on this problem and con2ne ourselves to noting one of the constraints on a theory of the most intensive features observed. Evidently, cases of a satellite crossing of an extremely powerful (rayed) auroral splash (of IBC III or IBC IV brightness) are unique: these brightest auroras appear rarely, short-lived, and of a very limited spatial extent (several kilometers to tens of kilometers). So the probability of their crossing by a low-altitude satellite is very low, and the amount of comprehensive measurements is very limited. However, during strong auroras, such bright-colored dynamic features sometimes appear in the sky and attract the attention of an observer. Consider the strongest exciting auroral particle beams. They cannot be mapped to the outer magnetosphere even from considerations based on the energy 0ux in the most bright auroral bursts, where ¿ 103 erg=cm2· s are dissipated. A simple argument about the problems with the mapping may be presented. It is based on a case study of an exceptionally strong auroral burst measured from the AUREOL-3=ARCAD-3 experiment on 11:07:53–11:07:59 ◦ UT, March 02, 1982 at MLT = 22:77, ILAT = 74:99 at altitude of 1039 km (see Fig. 4 taken from Beghin et al., 1985, their Fig. 10). The electron distribution function measurement time was 1:6 s (see Bosqued et al., 1982). This burst had auroral electron energy 0ux (¿ 103 erg=cm2 s) and AC electric 2elds (¿ 100 mV=m rms). Then as the particle 0ux was nearly isotropic, its energy density has to be nearly constant along the plasma 0ux tube till the acceleration region. With such a power, taking average electron energy as 5 keV we get an electron density of ∼ 80 cm−3 , and an energy density of 2:5×10−7 erg=cm3 . This plasma energy density leads to the plasma * ¿ 1 at altitudes more than ∼ 4:5RE . Neither such a high number density of hot electrons, nor the respective plasma energy density is feasible in the near-Earth’s plasmasheet. A bulk ambient plasma heating=acceleration is thus implied at least for the IBC IV auroras. Another example of crossing such a powerful auroral burst by AUREOL-3 was described in Chmyrev et al. (1989).

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It follows that at least in these cases the electron acceleration has taken place at relatively low altitudes, not higher than one–two Earth’s radii. Similar arguments may be applied at least to IBC III auroras, which are an order of magnitude less intense but they occur much more often. The primary energy source, its perpendicular spatial scale, the energy transport to the acceleration region, and the FAC concentration to the observed small perpendicular scales remain to be understood. The ultimate source of the energy in this discrete auroral form must be in the tail current sheet where strong perpendicular currents exist, and their divergence or curl can lead to the FAC. The only feasible way to achieve such a high-energy density at low altitude, seems to be possible by the magnetic 2eld convergence. It may occur with a strictly 2eld-aligned energy propagation which indicates shear Alfven waves and their Poynting 0ux as the energy carrier. The perpendicular scale of the bright auroral bursts is of the order of 10 km or even less, and this is consistent with the AUREOL-3 particle and wave data shown in Fig. 4 for this one and for some other exceptional bursts. Thus, the Alfven wave was most probably a oblique one, the electron acceleration was produced by 2eld-aligned electric 2eld and occurred along a wide range of altitudes within the outer ionosphere. One more example of a very bright small-scale aurora was found by Lanchester et al. (1994) from observations with the EISCAT together with a suitable photometry. They used a very high space=time resolution of bright auroral features drifting across the 2eld of the radar during an active auroral display. It appeared that an “elemental auroral structure” they observed was consistent with an energy 0ux of 400 erg=cm2 s carried by a 0ux of a rather monoenergetic (Gaussian distribution) 8 keV electrons with a FAC density of 50
A=m2 . These unique but quite signi2cant cases show that for a bright auroral form, i.e. for a concentrated very strong driving FAC, it would be better to speak not on its “mapping” but of a direct physical connection between the two widely separated regions in the near-Earth space with understanding that the propagation path could be oblique to the magnetic 2eld. One of the regions is a bright small-scale auroral feature with a high dissipated power at ionospheric altitudes. The other is its generic region in the outer magnetosphere with a distorted and varying magnetic 2eld which supplies the energy 0ux, and channels it more or less along the magnetic 2eld to the auroral acceleration region at mid-altitudes. Presumably, the channeling and transport are accomplished by the Poynting 0ux carried by a strong Alfven wave, and some additional nonlinear processes at small scales are needed at mid-altitudes and below leading to bulk 2eld-aligned electron acceleration. These processes can involve acceleration= turbulence= self-organization or even pinching down to altitudes ∼ 1–3RE leading to the transition from medium-scale currents to concentrated small-scale currents in auroral discrete forms. It was shown

by Galperin et al. (1986) that some modi2ed form of tearing is possible at auroral current sheets at mid- and low altitudes between the perpendicular magnetic components arising from the magnetic 2eld diJusion across thin current sheets of the thickness comparable to the electron inertia length c=!pe (∼ 0:1–1 km). It is known that AKR bursts are associated with the rayed auroral bursts. Observationally, these two powerful generation processes are correlated in space and time, and could be both related to the small-scale structuring, or 2lamentation, of the “parent” Alfven wave coming from the generation region in the outer magnetosphere. Some clues to the mechanisms of the small-scale structuring of a strong upward 2eld-aligned current to the perpendicular scales of auroral rays could be gained from the analysis of the in situ measurements of the AKR generation processes. Recently, a signi2cant progress in understanding of the AKR driving mechanism(s) has been achieved from in situ measurements from FAST (Ergun et al., 1998a,b), where a “horse-shoe” electron distribution function driving the AKR generation was found. It can be noted that momentum conservation considerations by Calvert (1987, 1995) indicate the importance of the small-scale perpendicular forces to electron beams in the region of the intensive AKR waves generation at altitudes of several thousand kilometers, and these forces could be related to the beam’s structuring. As was described above, the re0ection of such small-scale Alfven waves from the ionosphere occurs quite diJerently from the one for the large-scale Alfven waves—it is scale-dependent (Forget et al., 1991; Vogt and Haerendel, 1998; Kinney et al., 1999). This evaluation shows that the auroral system is nonlinear: at high-enough FAC densities, or Alfven wave amplitudes, new phenomena occur in the auroral plasma which, in particular, change (split) the space scales and concentrate the Poynting 0ux, aside from the obvious eJects of the magnetic 2eld convergence to low altitudes. Another puzzle of very bright discrete auroras is the often-observed quick changes of their color. These color changes are evidently due to drastic variations of the distribution functions of the electrons mostly in the energy range of tens to a hundred electron volts which can be induced only by strong wave–particle interactions within the very intense FACs. An important example of such localized interactions is the so-called type B red aurora (Stormer, 1955; Chamberlain, 1961; Vallance Jones, 1974). It is of red=orange color that appears at the lower border of active rayed “draperies”. The color is due to collisional quenching of the auroral green line, OI 557:7 nm at altitudes lower than ∼ 90 km, so that 1PG N2 and 1NG O+ 2 band systems together with other auroral emissions dominate the visible optical spectrum. The lower border of type B red auroras was often observed at altitudes 80 km and even below that (Stormer, 1955). Note that these altitudes correspond to a range of ¿ 100 keV electrons in the atmosphere coming along the magnetic 2eld. These high-energy electrons are generated as the tail of the

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Fig. 4. Above: Strong total electron downward energy 0ux (30 eV–30 keV, 6 s average), and (below) HF electric 2eld 0uctuation spectra in an extraordinary strong auroral burst registered by the AUREOL-3 satellite at the polar edge of the premidnight auroral oval on March 2, 1982 at 11:08 UT at the altitude 1040 km. Strong electrostatic emission is seen at the electron plasma frequency fp (marked by an arrow) in the HF spectra each taken during 3 s. (The time sequence of the spectra shown is upper–lower–upper–lower.). Note that small-scale variations were present within the 6 s (not shown), so the peak particle energy 0ux reached values even signi2cantly higher than 1000 erg=cm2 s.

distribution, within the auroral rays, that is, in the dynamic concentrated FACs, or Alfven waves. These high-energy electrons, and the auroral X-rays produced by them, can have time variations down to millisecond scale as shown by balloon auroral X-ray measurements. Thus, the acceleration= modulation of these high-energy electrons occurs at ionospheric altitudes. Type A aurora is the enhanced red line oxygen emission, 630 nm, with a lifetime of ∼ 110 s which is not quenched in collisions only at altitudes higher than ∼ 150 km. It usually

shows “red caps” above strong rayed aurora due to increase of electron temperature up to several thousand degrees. The emission is excited by collisions of hot electrons with oxygen atoms. It spreads from the excitation region due to motions of metastable oxygen atoms. Thus it occupies a wider region, and lasts longer, than the generic-rayed auroras. Besides that other rapid changes in auroral color are often observable even by naked eye. They presumably indicate the appearance, within bright auroral forms, of rapid changes in the electron distribution function in the region

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of tens of electronvolts where maxima are located of the excitation cross-sections for most of auroral emissions. Evidently, only strong wave–particle interactions are capable of rapidly changing the electron distribution function in these conditions, but they are still not well measured and analyzed. It follows that bright discrete auroral forms are the sites of very complicated nonlinear plasma processes, strong wave– particle interactions, leading to bulk electron heating and acceleration of the tail of the distribution up to relativistic energies. Even visual observations show bright 2laments, or auroral rays, of much smaller scales within active, dynamic auroras. (They are not always well resolved on auroral photographs, but are observable by low-level TV cameras with exposures less than 0:1 s, see below.) So within the above example shown in Fig. 4 the energy 0uxes and currents within individual auroral rays could be even higher than the indicated above. The characteristic scales of auroral rays are studied less than those of other forms mostly due to their rapid dynamics and inadequate sensitivity. Eye observations with small telescopes made by many auroral researchers including the author of this review, indicate widths of the rays down to 15 m—the order of a hot electron Larmor radius rLe .

From the AUREOL-3 measurements with high resolution an attempt was made to de2ne the characteristic perpendicular scale of the strong electric (50 –200 mV=m) and magnetic 2eld variations in active auroras (Titova et al., 1985). The average value derived was ∼ 100 m, and it was attributed either to superthermal ion Larmor radius rLi or to electron inertial length l⊥ ∼c=!pe . Recent measurements with high resolution from the FREJA and FAST satellites allow to greatly extend these studies. It could be also a projection to auroral altitudes of the ‘⊥F from the electron acceleration=small-scale current generation region at mid-altitudes. Evidently, this problem deserves further studies. 5.3. Small-scale auroral features: curls, spirals, vortices, black aurora Low-light television observations of aurora with resolution down to tens of meters or even meters at ∼ 100 km altitude (looking along the 2eld line) with time resolution down to 0:1 s or less (decay time for the secondary electrons which dominate the emission excitation) reveal a world of speci2c small-scale auroral features. Observations by Oguti (1981), Velichko et al. (1985, 1987), Safargaleev et al.

Fig. 5. Asymmetric small-scale auroral arcs. Histograms showing the distributions of the (a) arc separation; (b) arc width; and (c) equatorward drift speed of the 22 observed asymmetric multiple arc events (from Trondsen et al., 1997); (d) distribution of the thickness of 135 black arcs observed during the 2eld trip; (e) thickness of 92 emitting diJuse surfaces separating black arcs in the cases of multiple arcs; (f) black auroral arc spacing-to-thickness ratio (from Trondsen and Cogger, 1997). An altitude of 105 km has been assumed.

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(1997), Trondsen and Cogger (1997, 1998), and Trondsen et al. (1997) made with low-level TV cameras from the ground show a multitude of well-organized discrete forms and motions of visible small-scale auroras. Analyses of some of these phenomena such as curls (see Hallinan and Davis, 1970; Vogt et al., 1999), and thin arcs (Wei et al., 1994, Haerendel, 1999) has been started, others still await a thorough analysis and modeling. We do not discuss here the physical mechanisms of their formation, and con2ne ourselves to showing in Fig. 5 some statistics of the space and time scales taken from Trondsen and Cogger (1997, 1998). Characteristic scales of these phenomena are similar to those of the other rayed auroras mentioned above. However, for the periodic features apparently related to interchange motions, the scales of the KH instability are also observed (Trondsen et al., 1997). 6. Auroral plasmas at micro-scales: strongly nonlinear waves and solitary structures High-resolution plasma measurements from satellites S3-3 (see Mozer et al., 1980; Temerin et al., 1982), VIKING (see Bostrom et al., 1988; Malkki et al., 1994), FREJA (see Eriksson et al., 1994, 1997; Dovner et al., 1997), GEOTAIL (see Matsumoto et al., 1994; Kojima et al., 1994), INTERBALL-2 (Lefeuvre et al., 1998), EQUATOR-S (see Baumjohann et al., 1999), and in most details, FAST (see Ergun et al., 1998a,b; McFadden et al., 1999a,b) have shown a multitude of various micro-scale nonlinear moving plasma structures and waves in diJerent magnetospheric environments. Most often they are observed in regions of electron or ion beams and=or FACs. Waveforms observed can have a form of electron or ion phase-space holes, small double layers, electrostatic shocks or strongly nonlinear waves. The lifetime of these structures is not measured. They can 2ll quite an important part of the plasma 0ux tube at low-to-medium auroral altitudes (up to 10% or more) and sometimes are found in conditions where no signi2cant in situ turbulence is seen. So it is reasonable to suppose that their lifetime is not too short, and they propagate with the particle beam (at some relative velocity to the beam) a rather long distance from their remote turbulent source. A large body of theoretical work and numerical modeling was done to describe these structural formation, lifetime and decay (see, for example, Schamel, 1986; Koskinen et al., 1990; Koskinen and Malkki, 1993; Seyler, 1994; Seyler and Wahlund, 1996; Robinson et al., 1996; Robinson, 1997; Volosevich and Galperin, 1995, 2000a, b). Among these papers the review by Robinson (1997) actually deals with Langmuir solitons, while most of the others with ion-acoustic and=or lower hybrid-type ones. The approach by Volosevich and Galperin to the theory and models of the nonlinear electrostatic plasma struc-

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tures considers explicitly the waveforms of quasi-stationary moving structures and their parameter space regions, in particular, in the multi-component auroral and magnetospheric plasma with electron or ion beams. Their scales lay in the range from several Debye lengths to the ion sound speed times inverse lower hybrid frequency. It is still too early for any reasonable comparisons of this MHD electrostatic waveform theory with experimental data, but a qualitative agreement was noted with some published waveforms, scales, velocities, etc., of the moving solitary structures. An illustrative example of application of this theory to the high-resolution observations from FAST is shown in Fig. 6. Figs. 6a and b (courtesy of R. Ergun, 2000) shows an interesting solitary structure’s waveform in the electric 2eld and electron density, respectively, with a positively charged core, and an envelope of the opposite sign with a scale of several Debye lengths. A search was made, based on the theory described in Volosevich and Galperin (2000a, b), to 2nd a suitable combination of a cold electron beam in a thermal plasma background in which such a moving electrostatic structure may be quasi-stable. Two options were considered: a structure with positive core potential (as observed), and a similar waveform but with the negative potential in the core. The structure with the negative core potential has a three-component plasma solution (not shown). The derived plasma parameters look plausible: a cold electron beam in a background plasma. But with the positive core potential (as observed) no suitable solutions were found to describe the structure with the three plasma populations (cold electron beam, background electrons and the typical background ion population). To obtain the model waveform (shown in Fig. 6f), which looks similar to the one observed (Fig. 6b), a low-density superthermal ion population was added which density slightly increases at higher potentials as seen in Fig. 6e at the structure’s center (courtesy of F.Trukhachev). Such an additional ion population is not self-consistent in a one-dimensional model, but in real converging magnetic 0ux tube it could be due to the ion trapping between the magnetic mirror below and the positive potential region above. Sample model parameters shown in the 2gure caption of Fig. 6 could be matched with those of a downward current region. So far no direct comparisons with the observed plasma characteristics were performed, but the 0exibility of the multi-component model allows to check it in various plasma environments. One of the most important questions in the relevant experiments and theory is the net 2eld-aligned potential drop in the structure, i.e. of its asymmetry. This is because any particle with the energy higher than the amplitude of the potential variation either gains or loses its energy in passing through an asymmetric structure. The majority of the published observed cases show symmetric structures with the zero net potential drop, while some asymmetric cases were also noted. It was concluded that the

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Fig. 6. An example of a small-scale solitary structure with positive core potential registered from FAST (courtesy of R. Ergun, 2000) and its modeling. Experimental results: (a) electric 2eld waveform in the scale of the Debye length ,D ; (b) electron number density waveform in % from background, deduced in two options—for a spherical structure and for a plane one. Model parameters: Cold electron beam. Beam velocity Vebeam = 500 km=s in the laboratory frame (upward); solitary structure velocity with respect to the beam V = 25 km=s; beam-to-background electron density ratio . = 0:6 and temperature ratio = 0:5. Model waveforms; (c) electric 2eld E waveform; (d) electric potential # waveform; (e) particle number density waveforms for diJerent populations normalized to their values outside the structure: solid curve—background electrons (Te = 5000 K); dotted curve—electron beam (Tebeam = 2500 K), and dot–dashed curve—the sum of the background ions and of the “quasi-trapped” ion population seen in the center (TieJ = 16750 K); (f) Resulting model waveform of the relative total electron density Ne in the solitary structure resembling the measured waveform shown in (b).

asymmetric structures do not contribute signi2cantly to the auroral acceleration. However, it seems quite possible that a part of the symmetric structures evolve from the original asymmetric ones due to interactions with the medium. We stress that the lifetime of the asymmetric structures must be much lower than for the symmetric ones. Then the symmetric cases are seen in the experiments mostly far from their origin, thus in a larger volume of space, and hence more often, while they have evolved from the asymmetric ones concentrated near their origin. So it remains to be seen whether an FA particle acceleration by the asymmetric structures (a kind of double layers) occurs at their localized origin and in its near

vicinity. This is a kind of question which is to be answered by the experimental analysis of structures’ waveforms, and by the theoretical analysis of their generation, evolution, and lifetimes. With the increase of the number of particle populations involved in the model calculations, as is evident, some (but not all!) aspects of a kinetic approach can be incorporated. Such an analysis can allow to indicate the parameter ranges for the particle populations involved for which the electrostatic structure can be quasi-stable, and thus for the space environments allowing the generation and motion of nonlinear micro-scale structures.

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7. Cross-scale coupling in the magnetosphere–ionosphere system Thus medium-scale auroral regions (∼hundreds of kilometers) split to discrete auroral forms with scales one–two orders of magnitude lower (∼ 10 km), but these also can split to smaller scales (∼ tens to hundreds of meters, i.e. again one–two order lower). But the mechanisms and locations of these splitting processes remain unidenti2ed. The coupling between the current-carrying auroral structures is easier to see from the so-called “Matreshka” scheme of nested Birkeland current loops (see Fig. 3). In the scheme, within the scale of the double FAC sheet forming an inverted-V structure, a smaller two-sheet current loop of a steady auroral arc is located at the FAC direction reversal, which in turn is split-up to similar current loops of narrower arc’s 2laments. The scheme is suggested by observations, but the physical reasons for such a structure and its space=time stability remain debatable. It may be noted that the appearance in the particular plasma 0ux tube of small-scale nonlinear moving plasma structures described in Section 5, leads to the collisionless scattering of thermal plasma particles and their heating=acceleration in encounter with the structure (Volosevich and Galperin, 2000a, b). Such eJects may be very important, for example in the early re2lling stages of the outer plasmasphere after a storm. Here, a collisionless scattering of the ions which are ascending from the ionosphere due to the polar wind and=or other mechanism, is needed to rise their mirror points above the parent ionosphere—a necessary condition for a re2lling of equatorial regions of the outer plasmasphere. This could be one more example of the cross-scale coupling where the scattering due to the smallest-scale structures in0uences the rate of the global electron density recovery in the outer plasmasphere after a storm. Other scenarios are also possible where this type of collisionless particle scattering can play a role in transforming beams or shears in the plasma particle motions into heat. Evidently, the whole plasma content of the 0ux tube then changes, and larger scales are involved. Two other important examples of the cross-scale coupling were brought up during the First S-RAMP Symposium. As was mentioned above, the rayed-auroral forms are accompanied by bursts of very high-energy electrons which make the conductivity pattern at the lower E- and upper D-regions of ionosphere very inhomogeneous. In the report by Alperovich and Fidel (2000) it was shown that in such case the average Pedersen conductivity and Pedersen-to-Hall conductivity ratio change drastically and lead to spreading of the closure currents in the auroral ionosphere, i.e. to a kind of “reverse cascade”. Another example is related to the large-scale current generation in the near tail, which in0uences the ionospheric closure of Regions 1 and 2 currents in the HD. In the report by Israelevich et al. (2000) it was shown from the analysis of the GEOTAIL magnetic 2eld measurements that in the near tail there exists a new, so far not identi-

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2ed, large-scale tailward current along the tail axis with the total strength of order of 106 A. Apparently, the nonadiabatic scattering of the plasmasheet ions in the neutral sheet leads not only to the “quasi-Pedersen current” along the dawn-to-dusk direction as was suggested by Galperin et al. (1992), but also to this “quasi-Hall current” in the perpendicular (i.e. radial) direction as was suggested by Israelevich et al. (2000). This new radial tail current maps to the region of the HD and needs to be considered in its theory and models. Its account can also in0uence the analysis and modeling of the currents at the substorm onset which tends to occur in this same region. The above examples show that multi-scale coupling processes in auroral plasmas in all the ranges from the micro-scales to medium and large scales can be important for the total magnetospheric plasma system behavior. For example, a localized instability or energetic particle burst in the tail lead to enhanced precipitation in ionosphere ⇒ conductivity change there ⇒ localized modi2cation of electric 2eld at and around the place ⇒ launching of upward-moving Alfven waves ⇒ modi2cation of the magnetic 2eld ⇒ spreading of the disturbance. Another example is the so-called cleft ion fountain, or the “heating wall” in the cusp, where intense FAC leads to strong local heating =perpendicular acceleration and out0ow of thermal ionospheric ions H+ , O+ , He+ . These ions when further accelerated in their way along the 0ux tube, can reach near-Earth plasmasheet and modify the hot plasma population there and reach even the distant tail (Seki et al., 1998). According to some views this modi2cation can lead to local instability in the tail and result in auroral activation or even in a substorm, i.e. to a medium- or to a large-scale phenomenon in the magnetosphere. Such nonlocal responses pose signi2cant problems for detailed modeling of the active processes in the system which, as follows from the results summarized in the accompanying paper by Lui, are consistent with speci2c near-critical type of nonlinear behavior. Much work is still needed in this domain, in particular, to de2ne what details of the observations, and at what scales, may be neglected in a deterministic model of the system’s evolution to make it tractable and still providing reasonable predictions. The studies of complex and variable highly nonlinear auroral and magnetosphere plasma serve as our 2rst real encounter with a real astrophysical plasma system including all its interrelationships and nonlocal responses to external forcing by changing solar wind and to internal nonstationary plasma processes. Its most powerful processes operate in a very wide range of scales, with various cross-scale couplings, and which statistical properties were reasonably described as if for a complex system being in the near-critical state. From this it may be concluded that the aurora is one of the ways for the magnetosphere=ionosphere system to relax the tensions which resulted from a nonlinear evolution and growing local stresses, by channeling a part of the excess energy, momentum and currents, to the absorbing upper

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