During two flow burst events, earthward propagating dipolarization/injection fronts (DF) fortuitously stopped at ~9Re within a unique, compact multispacecraft constellation for the duration of a 30 min long substorm current wedge-related dipolarization. Observations inside and outside the halted flow burst indicate that it retained properties (including a narrow DF, a localized compression region ahead of it, and its structured, low density, low entropy (pV5/3) content) when arrived at its stopping point, where the entropy of the ambient plasma was nearly equal to that of the flow burst. We show that even short-duration flow bursts can significantly modify pressure and entropy distributions in the inner magnetosphere. The new distribution takes a long time to relax (a few tens of minutes, consistent with substorm recovery time scales). We argue that these pressure and entropy changes resulting from the incoming flow bursts can be responsible for the support/generation of a substorm current wedge.
Flow bursts (also known as bursty bulk flows, BBFs [Angelopoulos et al., 1992]) are narrow fast plasma streams in the plasma sheet, consisting of underpopulated plasma tubes that bring compressed magnetic field and accelerated plasma from the plasma sheet to the inner magnetosphere (see a summary in Sergeev et al. ). In observational studies [see, e.g., Keiling et al., 2009; Panov et al., 2010] the final stage of this process is thought to include azimuthal diversion of plasma flow-generating vortices, flow stoppage and tailward rebound, or overshoot and radial oscillations of the flux tube. Such observations, however, were made with spacecraft that passed into the flow burst, without identifying where and how the flow burst stopped. If a flow burst were to stop inside a dense spacecraft cluster, simultaneous measurements inside and outside of the flow burst could help distinguish spatial from temporal effects and determine the flow burst evolution near the stopping point. A scenario such as this is unlikely, however, because a compact grouping of existing spacecraft is extremely rare at distances between 6Re and 9Re in the magnetotail where most of flow bursts are expected to stop. Understanding what determines the stopping distance is another important question to address.
A related concern is the mechanism that generates the substorm current wedge (SCW), the main three-dimensional current system of the substorm expansion phase, which is thought to be responsible for the magnetic field dipolarization in the inner magnetosphere and for the specific pattern of bay-like magnetic perturbations observed at the nightside midlatitudes and geosynchronous spacecraft [McPherron et al., 1973]. Observational studies by Keiling et al. , Yao et al. , and Liu et al.  suggest that during its propagation, the flow burst-related flow shear may be able to generate SCW-like field-aligned currents strong enough to produce an SCW. However, it is unclear how a several-minutes-long flow burst can generate the several tens of minutes-long magnetic bays associated with the SCW, since those continue well after the flow burst has subsided. In situ observations near the stopping point may shed light on this problem by discovering the slow varying changes of plasma configuration.
In April 2009 closely spaced, radial conjunctions of the five NASA Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft (probes P1, P2, P3, P4, and P5) recurred once every 4 days, several times near midnight, in the near-Earth (r<11Re), equatorial magnetotail (Figures 1a and 2a). In this paper we analyze two events using THEMIS observations made inside and outside the flow burst's dipolarization front, near its stopping point. We emphasize the pressure and entropy parameter (pV5/3; entropy for short), distribution and variations of which provide clues for understanding flow burst's transformation, the location of its stopping point location, and what supports the generation of SCW-related field-aligned currents.
2 Observations of Flow Burst Stoppage
Between 08 h and 09 h UT on 4 April, and again on 8 April 2009, a dipolarization /injection front (DF) passed earthward of THEMIS probes P4 and P3 and, then, P2. However, no dipolarization/injection signatures were observed by the more earthward P1 (and GOES11) spacecraft (Figure 1 and spectrograms on Figure S1 in the supporting information), implying that the dipolarization front stopped between P2 and P1, with probe separations only 1.9Re and 1.1Re, respectively, in the two events. The relatively large radial distance of the stopping point (approximately 9 and 8.5Re, see below) is likely explained by the very dipole-like magnetic configuration on these magnetically quiet days. Although magnetic activity was low (the Kyoto AL magnetic bays had only 50 and 100 nT peaks, respectively), the dipolarization/injection was complemented by standard substorm onset signatures including (not shown) auroral brightening and expansion, 30 min long substorm current wedge (SCW)-associated midlatitude magnetic bays, and long-period Pi2s. Let us now examine the observations by probes P3 and P2, which crossed the earthward propagating dipolarization front and passed into the flow burst. In Figure 1 we compare data from P2 and P3 with those from P1. (All probes stayed continuously in the high-beta, central plasma sheet region, so we only show Bz component variations).
On 4 April, two pressure pulses seen by all THEMIS probes (dashed lines ♯1 and ♯2 at 0826:20 and 0831:15 in Figure 1) preceded DF passage of P3 at 0832:42 and of P2 at 0833:30 UT. These pressure pulses were initiated by earthward ion flow pulses (Figure 1c) the magnitude of which decreased inward (i.e., V3>V2>V1~0), and were closely associated with two poleward auroral activations demarcated by triangles. Such 1 min pressure increases in front of the DF are typical also of midtail flow bursts [see, e.g., Ohtani et al., 2004, Figure 3; Liu et al., 2013, Figure 3]. They manifest the plasma compression in front of the propagating flow burst, seen both in proton and electron moments, which is a good signature of an approaching flow burst [Sergeev et al., 2012]. In this event, flow rotates from earthward to dawnward direction as dipolarization front approaches.
The DF duration (time between the dBz minimum and maximum) is similarly short at P3 and P2 (12 s and 5 s) indicating very narrow fronts of ~1000 km (ion) scale. The DF normals are [0.84,−0.53,−0.10] and [0.13,−0.95,−0.20], respectively, typical for dawnside front crossings, and the DFs resemble the tangential discontinuities (from good consistence of MVA normal and normal based on tangential discontinuity formula, see, e.g., Liu et al. [2013, Appendix A]). The large tilt difference at such nearby locations suggests that either the planar DF rotates when propagating from P3 to P2 or that the DF shape strongly deviates from a planar geometry, possibly corrugated by some instability.
When crossing the earthward propagating DF, the probes P3 and P2 observed a strong drop in density, pressure, and entropy simultaneously with a sharp increase in electron temperature. After that the probes stayed inside the flow burst, without crossing the DF again (this can be better seen in the high-resolution data of P2, the probe closest to the final DF location, in Figure S2). The parameters are strongly variable during the first 10 min after DF arrival, with low-entropy, high-Bz plasma fragments alternating with high-density low-Bz ones. Evidence of tailward plasma rebound are found later in this event after 0835 UT. However, significant tailward flows (Vx<−100 km/s) are observed twice at P3, but not at P2, the one nearest the stopping point. Thus, a tailward rebound, if present, was not clearly observed in the frontal portion of the stopped flow burst.
The magnetic field variations observed by the innermost probe, P1 (Figure 1b), are periodic, well correlated with ground Pi2, and very different from dipolarizations. Diamagnetic in nature (plasma and magnetic pressures are anticorrelated, not shown here), they represent radial plasma tube oscillations (Figure 1c). Sharp changes in particle spectra, which characterize injections, are absent (Figure S1).
At ~0850 UT observations of a flow burst's stopping phase with a good coverage were made on 8 April 2009 (Figures 2a and S3). The separation between P2 ([-8.8, 1.0, 0.3] Re) and P1 (at [-7.7, 1.0, 0.6] Re) was only 1.1 Re, and the flow burst stopped between these two probes. The variations at P3 and P2 were similar to those on 4 April, including the compression seen at all probes after 0849:15 UT and the ensuing passage of a short-duration earthward propagating dipolarization front. As in 4 April observations, the density, pressure, and entropy dropped after the front passage, and particle energization was observed inside the very structured flow burst proper.
3 Pressure and Entropy Variations
The bubble model of a fast flow [Wolf et al., 2009] provides an observationally and numerically tested model to describe the earthward injection of a flow burst [Sergeev et al., 2012]. The model predicts that reduced plasma pressure and entropy (S=pV5/3) in the flow burst proper are the key parameters controlling its ability to convect earthward, that the bubble entropy is conserved during its propagation, and that the bubble injection is stopped at the location where the entropy value in the background plasma is the same as in the bubble [see, e.g., Birn and Hesse, 2013, Figure 3]. Simulations also predict the localized plasma compression in front of the bubble and suggest that these same parameters p,V,S (more specifically, their gradients (∇p×∇V)) control field-aligned current generation [Yang et al., 2011; Birn and Hesse, 2013]. But the entropy parameter is difficult to measure because one must evaluate a nonlocal variable, the volume V of a flux tube with unit magnetic flux. In the analysis below we estimate this parameter in two ways. First, we use the [Wolf et al., 2006] formula which approximates the results from a number of pressure-equilibrated magnetospheric models. It allows us to compute V using spacecraft observations of the magnetic field and plasma pressure as well as spacecraft coordinates. Second, we used a time-dependent data-adaptive magnetospheric model (AM02 model) [see Kubyshkina et al., 2009] in which model parameters are varied to fit the magnetic field observed by a suite of spacecraft. Between 0815 and 0915 UT on both events we had good coverage of the inner magnetosphere by radially separated THEMIS spacecraft, allowing us to use this tool. By comparing the two methods, we found their Vvalues in reasonable agreement (within a factor of 1.4) everywhere in the near-tail region (r~6−11Re) (Figure S4), suggesting that the Wolf et al. approximation in this region works if spacecraft observations near the magnetic equator are used.
Having computed V and observed the plasma pressure P we are able, for the first time, to analyze the temporal and spatial variations of the entropy parameter. Figure 2 provides this information at radially separated P3, P2, and P1 spacecraft on 8 April 2009 and Figure 3 provides observations in the same format for 4 April event.
In these events, pressure variation is formed by spacecraft motion in a spatially varying pressure distribution (earthward pressure gradient, etc) as well as by global variations and flow bursts. The amplitude of the flow burst-related compression was small at around r=11Re but it increases just behind and, even more so, just in front of the flow burst stopping point, that is at r~ 7–9 Re. In the latter region the compression was as large as by a factor 2 in Figure 2c and by a factor 1.5 in Figure 3c.
Three key features should be noted when considering the entropy variations in Figures 2 and 3. First, the flow burst-initiated entropy depletions are largest at the periphery of the dipole-like magnetosphere (i.e., for all events recorded at P3), where Bz increases (dipolarizations) provide the major contribution to the entropy reduction. The depletions are less intense near the stopping point at P2, where the dipolarization is relatively less intense and the volume decrease is partly compensated by a pressure increase. No entropy depletion, but rather an entropy enhancement, was observed on the earthward side of the front at P1. Second, the main S variation in the dipole-like region is caused by the probe's inward motion in the strong dipole-dominated tailward S gradient. Third, the maximum entropy reduction (the minimum entropy value) in the incoming flow burst, as measured by P3 at the entry point to the dipole-like magnetosphere (the horizontal dashed lines in Figures 2f and 3f), is approximately equal (within a factor 2) to the entropy value near the stopping point (just earthward of the green triangles, showing the location of the P2 probe). The flow burst is thus stopped close to the location predicted by the bubble model. Note that a factor 1.4 uncertainty of the estimated tube volumes (Figure S3) and the entropy profile variations during the flow burst intrusion result in roughly 1Re uncertainty in the entropy-based prediction of the stopping point distance.
4 Summary of Observations and Discussion
We analyzed two THEMIS radial conjunctions in which the flow burst stopped within the spacecraft constellation, so that the probes were able to measure the relevant parameters on both sides of the halted flow burst front. We found the following:
The dipolarization front within the stopping flow burst retains all its main features previously shown for fronts propagating in the midtail plasma sheet, including the compression layer ahead of the DF; the ion-scale dipolarization front resembling a tangential discontinuity; and the depletion in density, pressure, and entropy following the DF passage. Therefore, the flow braking process does not drastically transform this structure. This agrees with the bubble scenario, which predicts that the bubble slowly stops (while keeping its depleted and energized plasma content and sharp boundary) as it approaches its destination. In other words, the bubble reaches its near-equilibrium state near its stopping point.
For the first time we present radial entropy profiles and find direct observational evidence (Figures 2f and 3f) that the flow burst stops where the entropy S=pV5/3 in the ambient plasma is nearly equal (within a factor of 2) to the depleted entropy inside the bubble, consistent with previous finding of Dubyagin et al.  and Birn and Hesse . Could other factors (like initial flow burst Vx, Bz, etc) also influence the stopping point location cannot be concluded here based on a limited number of good-coverage cases and because of a factor 2 uncertainty in the entropy estimation.
Flow burst arrival significantly modifies the pressure and entropy distribution in the inner magnetosphere. The pressure compressions at around the stopping distance are as large as a factor 2 and 1.5, correspondingly, in two “best coverage” events (Figures 2 and 3), and the entropy depletions at 11Re could be as strong as a factor of 3 or more. Large compressions in the inner region and their relative increase with the proximity to Earth are consistent with previous THEMIS statistics [Dubyagin et al., 2010] and simulation results. For example, the Rice Convection Model (RCM-E) simulations by Yang et al.  show a 1Re thick pressure increase region in front of the inward-propagating bubble, with the compression magnitude increasing up to a factor 2.5 [see Yang et al., 2011, Figures 7 and 9, and Birn and Hesse, 2013, Figure 9b] upon reaching their final destination. Note that a compressed plasma layer of that width also exists ahead of plasma sheet BBFs [Liu et al., 2013] but there the compression magnitude is small.
The strong modification of the inner magnetosphere continues well after the fading of the flows. As summarized in Figure 4, the duration of the substantial flows (and also the duration of both Pi2s and auroral expansion, not shown here) was fewer than 10–15 min, whereas the duration of the pressure and Bz increases (and of the entropy depletion) was about 30 and 50 min in the 4 April and 8 April events, respectively. Correspondingly, the relaxation time of the modified inner-magnetosphere structure seems to be rather long, more than 10 to 20 min.
This long relaxation time can be understood as a consequence of the nearly equilibrium state of the stopped flow burst as mentioned in point 1. The long time scale may be due to large-scale MHD relaxation, although the ionospheric dissipation and drifts can also contribute. Although recent simulation results did not address this question directly, they support the long relaxation time scale by showing that considerable amplitudes of dipolarization and enhanced pressure are still seen for 5–10 min after the fading of a particular flow burst [see, e.g., Birn and Hesse, 2013, Figure 6]. Interesting, a long memory of the passing flow burst is also seen in the tail plasma sheet, see, e.g., Ohtani et al. [2004, the statistical Figures 3–5] showing on a 10 min time scale, that the post-BBF values of pressure and density are significantly different from their pre-BBF values. Tsyganenko and Sitnov  estimated experimentally the relaxation time of the partial ring current (and of related global region-2 field-aligned currents) to be 1.7 h. The relaxation time of a more localized pressure inhomogeneity should be shorter, its exact value is a subject of future study. Anyway the short flow burst leaves a significant long-lasting trail in the magnetospheric plasma.
Data analyses by Yao et al.  and simulations mentioned above suggest that modification of the plasma pressure and entropy (and volume) during the flow braking provides a main contribution to the large-scale field-aligned currents of the substorm current wedge via the I∥=(Beq/Beq)(∇p×∇V) mechanism. According to their estimates, the flow vortex mechanism is less effective, and its action is limited to the brief periods of high plasma velocity. This is nicely confirmed by our observations. As shown in Figure 4, the duration and shape of the SCW-related midlatitude magnetic bays on the ground are very similar to those of pressure, entropy, and Bz variation in the inner tail. Of principal importance is that all of them continue well after the flow bursts and related Pi2 pulsations have subsided, that is, when the active processes and flow vortex mechanism are not operating anymore. It is not surprising that subsequent slow relaxation of this configuration generates slowly fading 3-D currents, which form the slowly fading 30–40 min long magnetic bays characteristic of the SCW. The long relaxation time is closely related to what was previously discussed in terms of the magnetic flux pile-up effects, e.g., by Nakamura et al. . In particular, a long relaxation time scale helps integrate the effects of multiple flow bursts (which are typically seen during intense events, e.g., Nishimura et al. ) to form a smooth, long-duration bay-like magnetic dipolarization signature commonly associated with the substorm current wedge.
We thank Judy Hohl for help in preparing the manuscript; C.W. Carlson and J.P. McFadden for the use of ESA data; K.H. Glassmeier, U. Auster, and W. Baumjohann for the use of FGM data provided under the lead of the Technical University of Braunschweig and with financial support through the German Ministry for Economy and Technology and the German Center for Aviation and Space (DLR) under contract 50 OC 0302. The work was partly supported by EU grant N269198 (Geoplasmas), SPbU grant 22.214.171.1241, and RFBR grant 13-05-00132, as well as by THEMIS contract NAS5-02099.
The Editor thanks Andris Vaivads and two anonymous reviewers for their assistance in evaluating this paper.