Equatorward moving arcs and substorm onset

Transcription

1 Click Here for Full Article JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2009ja015117, 2010 Equatorward moving arcs and substorm onset Gerhard Haerendel 1 Received 19 November 2009; revised 11 February 2010; accepted 3 March 2010; published 15 July [1] Key observations of phenomena during the growth phase of a substorm are being reviewed with particular attention to the equatorward motion of the hydrogen and electron arcs. The dynamic role of the electron, the so called growth phase arc, is analyzed. It is part of a current system of type II that is instrumental in changing the dominantly equatorward convection from the polar cap into a sunward convection along the auroral oval. A quantitative model of the arc and associated current system allows determining the energy required for the flow change. It is suggested that high b plasma outflow from the central current sheet of the tail creates the current generator. Assessment of the energy supplied in this process proves its sufficiency for driving the arc system. The equatorward motion of the arcs is interpreted as a manifestation of the shrinkage of the near Earth transition region (NETR) between the dipolar magnetosphere and the highly stretched tail. This shrinkage is caused by returning magnetic flux to the dayside magnetosphere as partial replacement of the flux eroded by frontside reconnection. As the erosion of the NETR is proceeding, more and more magnetic flux is demanded from the central current sheet of the near Earth tail until highly accelerated plasma outflow causes the current sheet to collapse. Propagation of the collapse along the tail triggers reconnection and initiates the substorm. Citation: Haerendel, G. (2010), Equatorward moving arcs and substorm onset, J. Geophys. Res., 115,, doi: /2009ja Introduction [2] Ever since the seminal paper of Akasofu [1964], which introduced the notion of an auroral substorm, one has wondered about the role of the equatorward moving arc whose brightening signaled the beginning of the expansion phase of the substorm. Many researchers derived from this sequence of events the conviction that the substorm, i.e., the release of energy stored in the tail, was initiated at the near Earth edge of the tail. Following a theoretical model of Coroniti and Kennel [1972], McPherron et al. [1973] related the substorm onset to a current disruption at the near Earth edge of the tail and its rerouting through the polar ionosphere, thus forming the so called substorm current wedge. On the basis of these interpretations, various mechanisms were proposed for the cause of the current disruption. The best known ones are microinstabilities of the cross tail current [Lui, 1991; Lui et al., 1992] and drift ballooning instabilities [Roux et al., 1991; Pu et al., 1997; Cheng and Lui, 1998; Chen et al., 2003]. One opposing concept is the M I coupling model of Kan [1993]; another one is the appearance of an internal generator by flow braking and pressure forces [Haerendel, 1992; Birn et al., 1999]. Although the debate about the true nature of the current disruption is ongoing, the related controversy, namely, whether the substorm is initiated at the 1 Max Planck Institute for Extraterrestrial Physics, Garching, Germany. Copyright 2010 by the American Geophysical Union /10/2009JA near Earth edge of the tail or at 20 R E by neutral line formation, has not yet been settled. In any case, the community is essentially unified in attributing the energy release during the main phase of the substorm to the reconnection process. [3] The situation is quite interesting. On the one hand, there is ample proof for reconnection to occur somewhere in the not too distant tail, and, on the other hand, the most reliable signature of substorm onset is the sudden brightening of the most equatorward arc, both locations being separated by 10 R E. It is evident that a connection between the two events must exist. But what is it, and how does it function? Many studies have been performed with the aim of solving the initiation problem on the basis of the temporal sequence of the two events, with practically balanced results between the inward out or outward in sequence. The crux of the problem is the strong local variability of the processes and their always incomplete coverage by any set of observations. Another approach would be to look more closely into the evolution of the growth phase, i.e., the hour before onset, during which magnetic flux is eroded from the front side of the magnetosphere and transported to the tail and the auroral oval is moving equatorward [Aubry et al.,1970;coroniti and Kennel,1972]. With better understanding of the modifications of the nighttime magnetosphere and near Earth tail during this phase, one may gain new insights into the tricky problem of the substorm onset. [4] In the following sections, I review the known events during the growth phase and try to shed light on origin and function of the equatorward moving arcs. On that basis, I 1of9

2 propose a new concept of the sequence of events leading to substorm onset. 2. Origin and Function of the Equatorward Moving Arcs 2.1. Summary of Observations of the Growth Phase [5] The addition of magnetic flux, eroded from the frontside during southward interplanetary magnetic field, leads to growth of the tail s cross section and to an earthward shift of the inner edge of the current sheet, which is needed for balancing the increasing shear stresses exerted on the tail by the solar wind [Siscoe and Cummings, 1969; Coroniti and Kennel, 1972]. At the same time, the plasma and central current sheet become thinner [Hones, 1970]. It is astounding that almost 40 years after a basic understanding of the growth phase was achieved, we are still struggling with its transition to the substorm. However, the expanded net of ground based and space observations that have occurred in the meantime have helped researchers to obtain a clearer view of the evolution of magnetosphere and related auroral phenomena during the growth phase. But the question pertaining to the origin and function of the equatorward moving arcs has not yet found a clear answer. [6] The best visible ionospheric manifestation of the changes in the magnetosphere during the growth phase is the appearance and equatorward motion of a hydrogen arc, due to the diffuse precipitation of energetic protons, and of one or two electron arcs [Deehr and Lummerzheim, 2001; Lyons et al., 2002; Lessard et al., 2007]. The matter of the electron arcs is quite confusing. The situations may not be uniform, and the interpretations depend on sensitivity and resolution of the optical observations. Sometimes two different arcs are clearly distinguished: one dominated by more energetic (>1 kev) electrons and one by soft electrons, mostly <1 kev [Deehr and Lummerzheim, 2001; Lyons et al., 2002]; in other cases, only one electron arc is being identified [Lessard et al., 2007]. The more energetic electron arc often has low intensity and escapes observation. Furthermore, some of the 5577 Å luminosity may be attributable to energetic proton precipitation [Fukunishi, 1975]. Although the electron arcs are found inside the proton precipitation band, all observers agree that they are located clearly poleward, by 100 km, of the maximum brightness of the hydrogen arc. The latter is commonly identified as the ionospheric trace of the outer boundary of the trapping region of the protons or the inner edge of the strong pitch angle scattering region, owing to nonadiabatic motions in the stretched tail field. Thus it is a marker of the transition from dipole like field to taillike topology [Samson et al., 1992]. [7] Divergent reports exist about the exact location of the arc whose brightening signals the onset of the substorm. Deehr and Lummerzheim [2001] found it to take place in the more poleward, softer electron arc, whereas Lyons et al. [2002] and Rae et al. [2009] observed this to occur in a narrow structured arc that had appeared a few minutes before and equatorward of the soft growth phase arc. In other reports, only one arc has been identified, probably because the spatial resolution did not allow for finer separation. Also, the temporal evolution is quite variable. Sometimes the hydrogen and one electron arc appear early in the growth phase, but more often the electron arcs appear later, only min before onset [Deehr and Lummerzheim, 2002; Kadokura et al., 2002; Lessard et al., 2007]. In any case, substorm onset happens when the growth phase arcs have come close, typically within 1 or less, to the hydrogen arc [Oguti, 1973; Fukunishi, 1975; Samson et al., 1992]. [8] The brightening of the soft electron arc at the onset of the substorm is normally accompanied by the formation of a longitudinal wavy structure, folds, and localized arc splittings, which may evolve into bright spirals [Dubyagin et al., 2003; Liang et al., 2008; Rae et al., 2009]. The separation (wavelength) of these structures is typically km. The brightening spreads westward and eastward at speeds of km/s [Sakaguchi et al., 2009]. The electron distribution creating the growth phase or onset arcs, measured during satellite crossings, has not produced a unique nature either. Lessard et al. [2007] and Kadokura et al. [2002] identified inverted V distributions, and Dubyagin et al. [2003] and Mende et al. [2003] found strongly field aligned downward electron fluxes. The Mende et al. [2003] report was due to a fortuitous passage of the FAST spacecraft over the soft electron arc at substorm onset. The precipitating electron flux was strongly aligned along the magnetic field and had a broad energy distribution <1 kev. Ions up to a few tens of electron volts had a mainly perpendicular velocity distribution with dominance in the E B direction. The arc with total width of 30 km was part of a balanced field aligned current system in the sense that the downward current was located on its poleward flank. This implies an equatorward closure current and electric field in the ionosphere and an eastward convection along the arc. All these features are consistent with a downward Alfvén wave picking up and accelerating cold plasma in the topside ionosphere. One must, however, be cautioned to generalize this event as exhibiting the nature of the growth phase or onset arcs, because the observation was made 2 3 min after substorm onset. The arc was located at the poleward edge of an already well developed auroral breakup. [9] Consistent with the equatorward arc motions, one also finds equatorward directed plasma convection of the order of a few hundred meters per second in the midnight sector. On the low latitude side of the growth phase arc, the convection assumes dominantly westward direction before midnight and eastward direction after midnight [Robinson and Vondrak, 1990; Kadokura et al., 2002; Gjerloev et al., 2003]. This is quite consistent with the convection pattern implied by the D p 2 current system found by Nishida [1968]. Gjerloev et al. [2003] showed that the widths of the convection channels or related eastward and westward electrojets increased with increasing separation from midnight. Sergeev et al. [2005] found enhanced convection directly at the geostationary orbit of the order of 10 km/s, mostly earthward during evening hours and sunward during morning hours. This is consistent with the radar measurements in the ionosphere [Robinson and Vondrak, 1990;Kadokura et al., 2002]. Particularly informative are the observations by Robinson and Vondrak [1990], because plasma drifts, ionospheric electron density enhancements, and auroral arcs were measured simultaneously, albeit at low temporal resolution. During evening hours (>1930 magnetic local time), a broad region of westward convection, 4 wide in latitude, with flow speeds up to 1 km/s and flanked by a quiet arc on the northern side, was seen to move equatorward and shrink in latitudinal 2of9

3 width. Judging from the poleward electric field gradient, the Pedersen current had a strong negative divergence at the position of the arc. A weak westward electric field was present as well, but it was stronger poleward of the arc. During a second event starting 1.5 hours before magnetic midnight, a similar pattern was observed. However, the westward electric field was much stronger than during the evening hours, corresponding to southward plasma drifts of 400 m/s. Dubyagin et al. [2003] found a narrow spike of the southward directed electric field just poleward of the above mentioned growth phase arc, shortly before magnetic midnight. All of this agrees with a convection pattern that continues the equatorward flow from the polar cap by transporting plasma and magnetic flux from the midnight sector toward daytime, more or less along the auroral oval, to partially replace the flux eroded on the frontside magnetopause [Coroniti and Kennel, 1973]. Figure 1. Schematic showing the evolution of the ionospheric phenomena during the growth phase at four selected times. NPSBL designates the near plasma sheet boundary layer aurora. Reprinted from Kadokura et al, [2002] The Role of the Growth Phase Arc [10] The equatorward motion of the hydrogen and electron arcs during the growth phase signal in the first place the increasing stretching of the outer magnetospheric field. This is well known. The second important feature is that the growth phase (electron) arc approaches the peak intensity of the hydrogen arc. A particularly impressive data set is contained in Figure 13 of Kadokura et al. [2002]. It shows the fading of both the hydrogen and electron arcs a few minutes before substorm onset. If one combines this development with the systematics of the convection pattern, one is naturally guided to the conclusions expressed by Kadokura et al. [2002] in their Figure 15, which is reproduced here as Figure 1. At or at least near the growth phase arc, the convective flow changes from equatorward on the poleward side to sunward on the equatorward side. This can be well judged by comparing the equatorward progression of the sign change of the magnetic z component (Figure 6 in Kadokura et al., 2002) with the progression of the growth phase arc (finite element method) in their Figures 12 and 13 in Kadokura et al. [2002]. A cartoon of the envisioned relation between arc and convection is contained in Figure 2. It resembles very much the flow and arc situation during the substorm around the socalled Harang discontinuity or reversal. The main difference is that the energy fluxes and the precipitation generated conductivities are considerably lower and the latitudinal extent is much narrower, just a few tens of kilometers rather Figure 2. Flow deflection (solid lines) from mainly equatorward to more sunward inside the convection channel associated with the growth phase arcs (shaded regions). Also shown are the ionospheric current sources and sinks (circles), the Pedersen currents, j P, and electric fields (solid arrows), and the directions of the longitudinal pressure gradients (dashed arrows) inside the generator plasma. The area between the horizontal straight lines is the projected area of the generator. 3of9

4 Figure 3. The ionospheric end of a Boström type II current system with upward current, j k, and auroral arc on the equatorward side (postmidnight arc), and the connecting Pedersen current, j P. The cartoon also summarizes several quantities characterizing the arc observed by Dubyagin et al. [2003]. E s is the southward component of the transverse electric field, _W ion the ohmic dissipation rate of j P, and _W arc the auroral energy flux into the ionosphere. than a few hundred, because of rapid poleward expansion in the breakup phase. The associated ionospheric currents and magnetic perturbation fields are therefore comparatively weak, although clearly discernible (e.g., Figures 5 and 6 of Kadokura et al., 2002). In any case, it is obvious that the arc has a role in redirecting the flow from mainly equatorward to more sunward. [11] What happens when a magnetic flux tube is convected through an arc, as for instance on the western side of the reversal in Figure 2, or more generally, through an extended sheet of field aligned current? It enters a region of different, in this case enhanced, magnetic shear stresses, which transport the forces that redirect the flow into the sunward direction. The magnetic energy content of the flux tube is thus augmented, and it acquires a flow component in the direction of the driving forces. This requires an input of energy into the source region of the associated currents, not only to provide for the increased magnetic energy but also to generate the accompanying particle fluxes and balance the frictional (ohmic) losses in the ionosphere. At the exit through the opposing current sheet, the magnetic energy stored in the flux tubes is expended again. In the upward current sheet, the energy is invested in auroral particle beams; in the downward current region, it is expended in heating and injecting plasma into the magnetosphere (the pressure cooker model of Gorney et al. [1985]). The current configuration at some distance from the reversal is probably dominantly of type II of Boström [1964], i.e., composed of balanced upward and downward field aligned sheet currents closed through Pedersen currents in the ionosphere. On the eastward side of the reversal, the flux tubes first cross a downward current region; on the westward side, it is the arc that is encountered first. The energy requirements are similar to those on the evening side. The existence of a westward electric field, i.e., of the equatorward motion, implies the superposition of a Boström type I current system with maximum westward current near midnight. This renders the situation quite complex [Haerendel, 2009]. [12] Where is the source located that supplies the magnetic, kinetic, and dissipated energies in the arcs and convection channel? The obvious choice is the near Earth edge of the tail s central current sheet, because this is the only distinct feature between distorted dipole fields and the strongly stretched field of the steadily thinning current sheet of the tail. Furthermore, the earthward edge is known to approach the Earth during the growth phase. Indeed, careful evaluation of ground based and satellite data has led Kadokura et al. to conclude, Hence, the equatorial projection of the FEM arc (Fast Equatorward Moving arc) should be located around the earthward edge of the very thinned region [2002, p. SMP 36 19]. This identification is clearly marked in their Figure 16. However, these authors did not go beyond identifying the location of the current source in the tail. In the next subsection, the nature of the current generator is addressed A Quantitative Model of the Growth Phase Arc and Generator [13] Before turning to the generator, I adopt a quantitative model for the growth phase arc. On 28 January 2000, the FAST spacecraft crossed such an arc at very low altitude (390 km) and provided relatively complete characterizations of its physical properties [Dubyagin et al., 2003]. The crossing preceded a substorm onset by only 2.3 min. Formation of the wavy structure was already discernible. This means that the arc qualifies as an onset arc in the nomenclature of Lyons et al. [2002], but it should not be so different from the one earlier in the growth phase. The arc was associated with a triple system of field aligned currents, of which the first pair (down up) had higher current density and extended over 40 km. The arc coincided with upward currents of a mean density of 2.5 ma/m 2. Its width was 25 km. This leaves 15 km for the adjacent flow channel on the poleward flank of the arc, in which a spike in the southward (ionospheric) electric field with a peak field of 30 mv/m was found and the downward current was located. The energy spectrum of the auroral electrons showed a narrow peak at 1 2 kev,andthepeakenergyfluxwas3erg/(cm 2 ssr)or 5 erg/(cm 2 s) on average. All of these numbers, partially read from the graphs, contain inaccuracies that do not affect the following conclusions. [14] We are now deriving a few physical properties of the arc system from the above numbers. Multiplying the mean upward current density of 2.5 ma/m 2 with the arc width yields a sheet current above the arc: J k 0.063A/m. As sketched in Figure 3, we assume that we have a Boström type II system, in which a Pedersen current connects downward and upward field aligned current of equal magnitude. To evaluate the total Joule dissipation rate, we first derive 4of9

5 Figure 4. High b plasma out of the thin central current sheet of the near Earth tail fills the interface layer between the inner edge of the current sheet and the near dipolar outer magnetosphere (Figure 5b of [Haerendel, 2009]). The forces acting on the interface layer are also indicated. integrated Hall and Pedersen conductivities from knowledge of the accelerating voltage and energy flux using the empirical relations of Robinson et al. [1987]. Estimating the voltage from the peak energy as 1 kv, one finds S P,arc = 5.3mho and S H,arc = 2.4mho. If the upward sheet current is fully continued by a Pedersen current, the southward electric field inside the arc ise?,arc J k S P,arc = 11.9mV/m. As expected, this is distinctly below the measured field in the adjacent lowconductivity channel, which is dominated by the downward current. It may be even lower, because the Pedersen current diverges in the arc region. With these numbers, the ohmic losses, _W ion = J k E?, are 0.75 mw/m 2 inside the arc and 1.3 mw/m 2 in the adjacent flow channel if we use two thirds of the measured peak field as average electric field. Multiplying the mean electric field in the arc and adjacent channel with their respective widths yields a total voltage across the current system of 600 V, corresponding to a magnetic flux transport of Mx/s. Both the derived dissipated energy and transverse voltage are smaller than the measured auroral energy flux and field aligned potential drop, respectively. Figure 3 summarizes some of the derived quantities. [15] I now turn to the generator driving the arc system. I propose that it is created by ejection of high b plasma and magnetic flux from the central current sheet. This is a quasistatic version of the current sheet collapse proposed in Haerendel [2009] for the origin of the generator plasma during the main phase of the substorm. The next section deals with the cause of this ejection process. As sketched in Figure 4, the weak and highly stretched magnetic field of the central current sheet is transformed into a more dipolar shape as the plasma is squeezed out and, under compression, forms an extended plasma layer earthward of the inner edge of the narrow current sheet. This high b plasma layer is here proposed to be the generator of the current system associated with the growth phase arc. The underlying assumption is that this process is creating a pressure maximum in this layer near midnight. It is the expansion of this pressure maximum, west as well as eastward along magnetic shells, that drives the sunward convection in Haerendel [2007], equations We have a Boström type II current system, in which magnetic shear stresses and associated field aligned currents transfer the driving force and maintain convection against ionospheric friction. [16] I now address the balance of magnetic flux transport out of the central current sheet into the generator layer and along the arc system. During the time, t arc, that magnetic flux is transported through the arc, plasma and field are convecting along the arc covering a distance D arc. To maintain a quasi static situation, the same amount of magnetic flux must be ejected from the central current sheet of the tail duringt arc.ifd CS is the longitudinal scale of the flow ejection from the central current sheet corresponding to D arc and v n,cs, the earthward outflow speed, the flux balance can be written as follows: df dt ¼ B z;t D CS v n;cs ; ð1þ ion with df/dt = Mx/s being the flux transport along the arc as derived above. B z,t is the vertical field inside the central current sheet. Following [Sergeev et al., 1996], I adopt B z,t = 1 nt. [17] The main problem in evaluating this relation lies in determining a longitudinal length scale, D CS, of the energy source. The wavy structure of the arc, appearing at the brightening before the substorm, suggests the existence of such a scale also structuring the current sheet. Figure 5 is a cartoon inspired by the observations of Dubyagin et al. [2003] and Rae et al. [2009], showing the typical change in structure as the growth phase arc begins brightening as the first sign of substorm onset. What has been added is the intuitive interpretation of the knots and distortions as locations of dominant entry of magnetic flux from the central plasma sheet into the arc system. The separation length between two such locations would then reflect the time of contact of that flux with the arc system, as sketched in Figure 2. Without having a clear concept for the mechanism underlying the current sheet collapse, it is difficult to present an a priori argument for the origin of this structuring. As these distortions are seen to evolve quickly into spirals, one may Figure 5. Cartoon showing the transformation of the knotty structure of a growth phase arc into poleward protrusions, which subsequently evolve into spirals. The knots and protrusions are interpreted as points of preferred entry of magnetic flux from the central current sheet of the tail into the generator layer of the arc system. 5of9

6 Figure 6. Idealized meridional cross section of the central current sheet near Earth showing the adopted field magnitudes and the spatial dimensions, mean width, h CS,and depth, d CS, as derived in the text. refer to studies of spiral streets [Davis and Hallinan, 1976; Partamies et al., 2001]. Typical ratios of wavelength to spiral diameter were found to range between 2 and 6. With widths of order 25 km, as for our model arc, and wavelengths between 50 and 150 km (see above), the arc structure falls into the same range of ratios. This is, of course, not an explanation, but suggests that there is a fundamental process at work involving the longitudinal structuring of current sheets. [18] To simplify our quantitative estimates, we do not try to model the longitudinal structure of the collapsing current sheet and work with an average width and a characteristic longitudinal length, D CS. It corresponds to the observed arc structure, for which we adopt D arc = 100km. With the average convection speed along the arc, v E, this defines the characteristic time scale for the magnetic flux transport into, along, and out of the arc, t arc = D arc /v E. The weighted average of the ionospheric electric field of arc and adjacent flow channel is 15 mv/m. This yields v E = 300 m/s and t arc = 330 s. Because t arc has been derived from observations of a growth phase arc a few minutes before its transformation into the bright and highly distorted breakup arc, it may be interpreted as characterizing the nonlinear time scale of current sheet collapse. [19] Turning to the generator region, we set the ratio D CS /D arc equal to the square root of the ratio of the magnetic fields in the polar ionosphere (0.5 G) and at the outer edge of the distorted dipole field (B z,m ), where the generator plasma piles up (see Figure 4). We adopt B z,m = 20 nt. This yields D CS 5000 km and v n,cs 120 km/s from equation 1. Needless to say that all these numbers are no more than reasonable guesses. [20] In the next step, we estimate the extension of the flux ejection region and the internal energy of the plasma injected into the generator during t arc. We visualize an elongated triangular cross section of the flux ejection region, as shown in Figure 6. Its mean width would be h CS =(B z,t /B z,m )xd CS, where d CS v n,cs t arc is the depth of the region. We adopt n CS = 0.5 cm 3 and W ions = 7 kev for density and average energy of the ions in the central current sheet, respectively [Baumjohann et al., 1989]. With an ejection speed of 120 km/s, the central current sheet loses plasma over a depth, d CS, which would be 40,000 km or 6.2 R E. With B z,t = 1nT inside the central current sheet, we estimate its mean width to be h CS =(B z,t /B z,m ) d CS = 2000 km, where B z,m = 20 nt. This is consistent with the upward projected width of the arc system of 40 km. The energy release rate from the current sheet into each hemisphere during t arc would be as follows: _W CS ffi 0:5 W ions n CS v CS h CS CS ð2þ Figure 7. Relation between the high altitude generator layer and the field aligned and closure currents in the ionosphere. The inset shows the current orientation and growth phase arc for the morning side of the flow reversal. The hydrogen arc is located near the poleward edge of the trapping region. 6of9

7 Figure 8. Three regions structuring the midnight magnetosphere with (1) trapping region, (2) a transition region (NETR) of distorted dipole like field, and (3) the strongly stretched field of the tail s plasma sheet. The latter contains closed field lines in its central part and open ones at higher latitudes. whichisthen W. The much lower kinetic energy of the outflow is derived from the relaxation of the stretched magnetic field. This energy and perhaps somewhat more is spent by doing work against the (assumed) 20 nt field while squeezing the plasma into a layer, the generator layer, just outside the mildly stretched dipole field (see Figure 4). [21] The numbers derived for the intrinsic time scale of magnetic flux ejection from the central current sheet and for the depth of that sheet are quite remarkable. They imply that the effect of this process progresses by 6 R E in the course of 5 min. The resulting thinning of the near Earth plasma and current sheets should be felt out to 14 R E a few minutes before substorm onset. Indeed, Machida et al. [2009] derived from geotail data the appearance of a strong duskward electric field between X = 9 R E and 15 R E during the last 3 min before onset. [22] The energy supply to the generator must not only cover the energy dissipated in the arc and the adjacent convection channel but also account for the magnetic energy flowing into the sheared field between the downward and upward sheet currents (Figure 7). The latter can be evaluated by using the formalism presented by Haerendel [2007]: with the integrated wave impedance: _W shear ¼ R w J 2 jj ; ð3þ R w ¼ 2m 0R E L arc G 2 : ð4þ R E is the Earth s radius, L is the magnetic shell parameter, and G 2 is a geometric constant of order unity ( 1.2). Comparing this with equation 4 in Haerendel [2009], one can see that t arc has been set equal to four Alfvénic transit times between ionosphere and generator. With L = 8, one finds that 1.27 mw/m 2 are expended in shearing the field. Adding to that the dissipated energy of 2.05 mw/m 2 plus the auroral energy flux of 5.0 mw/m 2 and multiplying with the cross section in the ionosphere of size, D arc (w arc + w ch )= m 2,(w arc and w ch are the widths of arc and channel) yields W, or 10% of the calculated energy supplied to the generator within a length D CS.Thisisquite satisfactory because much of the internal energy of the generator layer must be conserved, the free energy being of the order of the magnetic energy stored in the shear stresses. Furthermore, all our estimates are based on rather uncertain numbers. An inverse ratio of consumed over supplied energies, on the other hand, would have cast doubt on the proposed concept. Furthermore, not all of the generator s free energy content should be consumed over the length D arc, because the flow must continue outside the arc. [23] With these uncertainties in mind, one can say that attributing the origin of the growth phase arc to the release of high b plasma from the central current sheet does not raise any conflicts. The pressure force of that plasma drives the associated current system and thereby causes the deflection of an equatorward polar cap flow into a sunward direction. Our estimates work, of course, as well for the arc on the evening side. 3. Substorm Onset: A Cry For Reconnection [24] So far, we have concentrated on the growth phase arcs, specifically on the soft electron arc, which was shown to deflect the equatorward plasma flow toward the sunward direction. This has to be seen in a global context, namely, the attempt of the magnetosphere to replace the magnetic flux eroded at the frontside by flux moved in from the nightside [Coroniti and Kennel, 1972, 1973]. The flux transfer from the dayside magnetopause to the tail establishes a gradient of total pressure between the near Earth tail and the frontside magnetosphere, which is the ultimate driver of the convection during this phase. Friction with the ionospheric plasma prevents a fast replacement of the missing flux on the frontside. Only after reconnection has set in can this be accomplished. [25] During the growth phase, only magnetic flux of closed, dipole like, but possibly somewhat distorted field can be carried sunward along the oval, because the tail field is either anchored in the solar wind or trapped between the tail lobes in the current sheet. Looking at the midnight meridian 7of9

8 Figure 9. Plasma outflow from the central current sheet into a pressure minimum, releasing magnetic stresses, and causing current sheet collapse and an anti sunward traveling expansion wave. during the growth phase, we can thus distinguish three regimes: the dipolar magnetosphere with trapped particles, a near Earth transition region (NETR) of distorted, still dipolelike field, populated with isotropic protons and electrons, and the strongly stretched tail field (Figure 8). The latter contains dense, hot plasma in the central parts, the plasma sheet, and low density plasma in the tail lobes. Much of these field lines are open, i.e., extend into the solar wind. It is here where the energy to be released during the substorm is being stored, mainly as magnetic energy. [26] The key issue of this study is that the magnetic flux transport to the dayside depletes the NETR during the growth phase. The earthward edge of the plasma sheet approaches the dipolar field region and is thinning. As a consequence, the region between the growth phase arc and the hydrogen arc shrinks, as is beautifully manifested in Figure 13 of Kadokura et al. [2002]. In the late phase of this process, when the NETR is almost fully depleted, more and more magnetic flux has to be supplied from the central current sheet to feed the sunward convection. A negative pressure gradient develops from current sheet toward the NETR, thus driving the plasma outflow into the generator region (Figure 9). The geometry of the generator plasma as a relatively thin layer draped along the outer edge of the trapping region determines the location of the growth phase arc more or less along magnetic parallels. The critical moment comes when all of the NETR field has been eroded and the inner edge of the by now very thin current sheet has come close to the outer edge of the dipolar trapping region. The sunward convection is still ongoing and has too much inertia, i.e., shear stresses and pressure gradients still exist along the morning and evening flanks, to come simply to a halt. Therefore, the underpressure in the midnight sector (Figure 9) is demanding more and more flux from the still closed but highly stretched field of the central current sheet. At this point, the outflow, discussed in section 2.3, gains speed rapidly until reaching the Alfvén velocity, which is of the order of km/s in the central current region. [27] The onset of a rapid outflow is the beginning of the current sheet collapse postulated by Haerendel [2009], without discussing its cause. As an outcome of the present analysis of the growth phase, we find a natural reason for this process without invoking instabilities or other exotic processes. The findings of Machida et al. [2009] (see section 2.3) add observational support to a current sheet collapse. However, their explanation of its cause differs from the scenario presented here. In their catapult (slingshot) current sheet relaxation model, the origin is attributed to an enhanced Poynting flux from the tail lobes toward the neutral sheet of the tail, causing thinning and earthward flows followed by current disruption at the inner edge and reconnection near 20 R E. By contrast, our model sees the origin in the magnetic flux erosion by the sunward convection on the earthward side of the tail current sheet. [28] This accelerated outflow has three consequences. (1) The braking of the plasma outflow at the outer edge of the trapping region excites flux tube oscillations in its outer layers, the Pi1 and Pi2 magnetic pulsations long known to signal substorm onset. (2) The arc driven by the accumulating plasma brightens, and the sunward convection accelerates. (3) The information of the accelerated plasma outflow and collapse of the near Earth current sheet is propagated anti sunward along the tail. Within a time of the order of 8 R E divided by the Alfvén speed, i.e., very few minutes, the tail reacts by reconnection to this cry for more flux and dramatic earthward flows set in. A substorm is initiated with all the known manifestations of bursty bulk flows, dipolarizations, and turbulence. Although the mechanism for the sudden creation of a pressure minimum earthward of the near Earth edge of the tail current sheet is different from the one suggested by Haerendel [1992], its consequences agree with those of thesis IV of that paper. [29] Much of the above scenario for the substorm onset is in the nature of a conjecture, which needs further investigation and confirmation by numerical modeling. However, it has distinct advantages. It clearly reflects the observed sequence of events, with the onset occurring when the growth phase arc has come into contact with the hydrogen arc. Oguti [1973] named this onset the contact breakup. The substorm appears as an unavoidable consequence of the growth phase and the depletion of magnetic flux on the nightside available for sunward convection. The brightening of the onset arc is just seen as an intensification of the process that is creating the growth phase arc all along. The excitation of the Pi1 and Pi2 pulsations at substorm onset appear as the logical outcome of the fast ejection flow bumping against the outer magnetospheric field. Even the fading of the hydrogen as well as oxygen emissions, often observed a few minutes before onset, can be attributed to the erosion of the NETR flux with its electron and ion population. On the other hand, there are perhaps some observational details that are not yet accounted for, such as, for instance, the differentiation between growth phase and onset arcs elaborated by Lyons et al. [2002]. [30] This new scenario does not need micro or macroinstabilities as triggers of the substorm. However, in the phase of the enhanced high b plasma outflow from the central current sheet, instabilities may well be generated, for instance as the origin of the wavy structure appearing in the onset arc shortly before it brightens. It should be noted that I do not claim that the scenario presented here is the only way to initiate a substorm from the near Earth edge of the tail, invalidating the concepts of current disruption, ballooning instability, and others, or the initiation by spontaneous 8of9

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