Jet front-driven mirror modes and shocklets in the near-Earth flow-braking region



[1] We investigate the small-scale structure of jet fronts through a case study of multi-spacecraft Cluster observations in the near-Earth flow-braking region at ∼−10 RE. We find that the interaction between the earthward moving fast plasma jet and the high-β ambient plasma in the plasma sheet results in magnetic pileup and compression ahead of the jet and rarefaction trailing the jet. It is shown that mirror-mode structures of ion gyroradius scale develop within the pileup region due to the observed ion temperature anisotropy (Ti > Ti). We suggest that the growth of these mirror modes is driven by the perpendicular total pressure perturbation (Δp) generated by the braking jet. When Δp becomes too large, the mirror-mode structure cannot maintain pressure balance any longer, and consequently a shocklet is formed in the pileup region ahead of the jet front. We present the first evidence for such a kinetic shocklet in the flow-braking region.

1. Introduction

[2] The near-Earth flow-braking region is defined as the part of the magnetotail where intermittent fast earthward plasma jets (often referred to as bursty bulk flows), which are generally attributed to outflows from reconnection regions [Baumjohann, 2002], are significantly decelerated and/or diverted by the more dipolar magnetic field and the denser ambient plasma of the near-Earth plasma sheet [Shiokawa et al., 1997]. This region is also known as the near-Earth dipolarization region, since the stretched tail-like magnetic field changes to a more dipole-like configuration in this part of the magnetotail. Statistical studies of GEOTAIL and Wind observations revealed that the occurrence probability of rapid earthward flux transport strongly decreases between −15 and −10 RE [Schödel et al., 2001] and the occurrence rate of dipolarization events also drops significantly at about −10 RE in the magnetotail [Sigsbee et al., 2005]. Although near-Earth dipolarization events have been studied extensively in connection with substorm dynamics, the kinetic processes of flow braking are addressed only by a few recent studies [Sergeev et al., 2009; Zhou et al., 2010; Khotyaintsev et al., 2011; Ge et al., 2011; Runov et al., 2011].

[3] The aim of the present paper is to reveal the small-scale kinetic processes involved in the interaction between a fast earthward plasma jet and the temperature anisotropic ambient plasma sheet. We show for the first time that braking jets can generate ion-scale mirror-mode structures and shocklets in the magnetic pileup region ahead of the jet front.

2. Observations

2.1. Event Overview

[4] The fast plasma jet at ∼9:14 UT, 27 October, 2007 of our case study is imbedded in a multiple dipolarization event between 9:00 and 9:30 UT [Nakamura et al., 2009; Asano et al., 2010]. The location and configuration of the Cluster spacecraft were ideal for observing multi-scale processes in the near-Earth flow-braking region at ∼−10 RE. C1, C3, and C4 were approximately aligned in radial direction with a separation of ∼10,000 km between C1 and C4 and a very close separation of ∼30 km between C3 and C4. C2 was ∼10,000 km off from C3 and C4 in the YGSM direction. Since we focus on the braking of an earthward propagating jet, which is localized in the Y direction, we will restrict our discussion to observations from C1, C3 and C4, of which C1 was the most tailward and C3 was the most earthward. For more detailed information about the spacecraft configuration, the reader is referred to Nakamura et al. [2009].

[5] Figure 1 provides an overview of the event from C1 and C3 between 9:10 and 9:22 UT. During this 12-minute interval, the most tailward spacecraft C1 observed three fast jets exceeding an earthward velocity of 1000 km/s (Figure 1c). All of these jets are associated with a significantly hotter (Te > 4 keV) plasma population than the ambient plasma sheet plasma (Te ∼ 2 keV) observed before the first jet (see electron temperature in Figure 1d). Unfortunately, ion moments could not be obtained from CIS during the fast flow intervals, because the corresponding hotter ion distribution is not covered by the limited energy ranges of the HIA and CODIF instruments. Nevertheless, ion moments are available for the ambient plasma sheet before the fast jets, where the density and convection velocity from CIS agree very well with corresponding estimates from other instruments (see Figures 1b and 1c). In Figure 1d, we plotted CODIF proton temperature from C4 because the HIA instrument underestimates the ion temperature (the highest energy channel is 32 keV for HIA and 40 keV for CODIF). Since the separation between C3 and C4 is merely 30 km, observations at C3 and C4 are practically identical in spin-resolution data.

Figure 1.

Fluid-scale overview of the event: (a) magnetic field intensity B from the FGM instrument, (b) number density n obtained from EFW spacecraft potential (solid lines) and from CIS HIA ion moments (dots), (c) earthward plasma convection velocity vx calculated from three-component electric and magnetic field vectors (solid lines), from CIS HIA ion moments (dots), and from PEACE electron moments (circles), (d) ion and electron temperatures from CIS CODIF and PEACE moments (dots and solid lines, respectively), and finally (e) the ion temperature ratio Ti/Ti from CIS HIA (dots).

[6] We focus on the fast plasma jet between 9:14 UT and 9:15 UT (Figure 1c). The jet was observed first by C1 (9:14:42 UT) and then by the more earthward C3/C4 spacecraft (9:14:56). The earthward plasma convection velocity dropped to less than one third from C1 to C3 (black and green lines in Figure 1c) and even turned negative (tailward) at C3, indicating strong deceleration and reflection of the flow. This direct measurement provides evidence of being in the flow-braking region, as discussed by A. Retinò et al. (Energetic electron acceleration in the near-Earth flow braking region: Cluster multi-scale observations, submitted to Journal of Geophysical Research, 2011). The velocity peak is preceded by a large peak in the total magnetic field, and the magnetic peak is preceded by a significant density enhancement at each spacecraft (see the locations of peaks in Figures 1a1c for C1 and C3, respectively). Both the magnetic peak and the density peak increased from C1 to C3 (compare black and green lines in Figures 1a and 1b), indicating the compression of magnetic field and plasma ahead of the jet, the former usually referred to as magnetic pileup region. On the other hand, an extended rarefaction region with n < 0.2 is observed at C1 (black line in Figure 1b) trailing the fast jet at 9:14:42 UT (black line in Figure 1c).

[7] The mean ion temperature anisotropy Ti/Ti in the ambient plasma observed before the arrival of the jets (between 9:10 and 9:14 UT) is 1.01 at C1 and 1.09 at C3 (see horizontal lines in Figure 1e), which means that the ambient plasma can be mirror-instable if the effective plasma β becomes sufficiently high. After the fast jets the temperature anisotropy became somewhat higher (see Ti/Ti in Figure 1e from 9:17 UT to 9:22 UT), which suggests perpendicular ion heating at jet fronts. In the following sections, we will use high-resolution (sub-spin) data to reveal the kinetic structure of the jet front.

2.2. Mirror-Mode Structure Within the Pileup Region

[8] The selected plasma jet events are plotted in high time resolution in Figure 2 as observed by C1 (Figures 2a, 2c, and 2e) and C4 (Figures 2b, 2d, and 2f), where the latter was located 8400 km earthward from C1. The three components of the FGM magnetic field in GSM coordinates are plotted in Figures 2a and 2b. Figures 2c and 2d show the total magnetic field B (red line) with a resolution of 0.045 s and number density n (blue line) obtained from the EFW spacecraft potential with a resolution of 0.2 s. Figures 2e and 2f depict the Y component of the electric field EY (green line) in GSM coordinates with a resolution of 0.04 s, and the smoothed earthward convection velocity vx (blue line) obtained from high resolution magnetic and electric field data (E × B/B2). A 4-second running average was applied to vx in order to remove the high-frequency fluctuations caused by plasma waves.

Figure 2.

Ion-scale mirror-mode structures ahead of the fast plasma jet at (a, c, and e) C1 and (b, d, and f) C4. Vertical dashed lines mark local minima in the total magnetic field. B* is the mirror instability threshold.

[9] The two spacecraft observations have many common features. The main velocity peak of the jet is preceded by a pileup region with deep depressions (often referred to as magnetic holes) superimposed on it. Density fluctuations are generally anticorrelated with the total magnetic field within the pileup region (Figures 2c and 2d) except for a brief interval between 9:14:50 UT and 9:14:55 UT at C4 (see Figure 3), which we discuss further in section 2.3. The plasma convection velocity profile (blue lines in Figures 2e and 2f) has a long foot with gradually increasing velocity. The velocity of the plasma sharply increases where the magnetic field and the density drops to a significantly lower value, indicating the typically hot and tenuous plasma population of a fast jet. We call this interface as “jet front”. Such a jet front was observed at 9:14:39 UT and 9:14:55 UT at C1 and C4, respectively (see Figure 2).

Figure 3.

Shocklet (S) and tangential discontinuity (TD) at C4. Red line is the best-fitting density perturbation assuming local pressure balance, and vx* is the earthward velocity from timing between C3 and C4.

[10] We identify the magnetic perturbation within the pileup region (troughs are marked with vertical dashed lines in Figure 2) as small scale mirror-mode structures. The first evidence is the regular coincidence of magnetic depressions and density peaks (compare red and blue lines in Figures 2c and 2d). The second evidence is provided by the timing analysis between C3 and C4. Here we make use of the fact that the normal of the magnetic structures is very close to X (GSM) and the flow is predominantly earthward (for more details see A. Retinò et al., submitted manuscript, 2011). The magnetic structures travel with more or less the same velocity as the convection velocity of the ambient plasma, except the magnetic discontinuity S (see Figure 3c) next to the jet front (TD), which is discussed in the next section. Thus the observed magnetic structures do not propagate in the plasma frame, as required for mirror modes. Finally, the ion temperature anisotropy Ti/Ti > 1 observed in the ambient high-β plasma ahead of the jet (see Figure 1e) strongly suggests the existence of mirror-mode structures.

[11] The mirror-instability condition is satisfied if

equation image

The perpendicular plasma-β is defined as the ratio of the perpendicular plasma and magnetic pressures

equation image

where k is the Boltzmann constant and μ0 is the permeability of free space. For simplicity, we use the cold electron approximation in equation (2), which means that the electrons' contribution to the plasma pressure is neglected. The latter is justified by the observed large ion-to-electron temperature ratio (Ti/Te ∼ 5) of the ambient plasma (see Figure 1d).

[12] From equations (1) and (2) we can get a mirror instability threshold for B:

equation image

Inserting the mean ion temperature from CIS CODIF (Ti = 9.8 keV) and the mean ion temperature ratios Ti/Ti (1.01 for C1 and 1.09 for C3/C4) of the ambient plasma ahead of the jet into the inequality of equation (3), we obtain the critical magnetic field B* plotted as black lines in Figures 2c and 2d. It is seen that the mirror-instability condition is marginally satisfied in all but one magnetic trough at C1 and satisfied in all three magnetic troughs at C4.

[13] The polarization of the mirror-mode structure is close to linear with predominant variations in the BZ GSM component (Figures 2a and 2b), which indicate that the mirror-mode structures are more or less perpendicular to the plasma flow. The width of the magnetic troughs can be roughly estimated from single spacecraft data by integrating the observed plasma convection velocity in time domain over the structure [Ge et al., 2011]. This simple method yields an average spatial width of 2480 km for the magnetic troughs at C1, and a comparable average spatial width of 1890 km for the magnetic troughs at C4. As a benchmark, the gyroradius of a 10 keV proton in the pileup region with an average background magnetic field of 20 nT is not more than 510 km. Thus the observed mirror modes have a typical spatial width of about 4–5 ion gyroradii. The reduced spatial width of the magnetic troughs between C1 and C4 implies that the mirror-mode structures are still growing.

[14] The amplitude of the mirror-mode perturbation in the magnetic field reaches and even surpasses 50% of the background field (see Figure 3a) at C4, which indicates that the mirror instability is in the nonlinear stage [Kivelson and Southwood, 1996].

2.3. Kinetic Shocklet

[15] Although the general structure of the jet front, as well as the spatial size of mirror modes in the pileup region, is very similar at C1 and C4, we would like to point out a key difference. At about 9:14:50 UT, a peculiar thin boundary was detected within the pileup region at C4 (discontinuity S in Figure 3) with no equivalent at C1. This discontinuity is characterized by large positive gradients in magnetic field and plasma density, associated with unusually large electric field (see EY in Figure 2f). The expected jump in the total pressure across the discontinuity cannot be verified directly because ion moments in the pileup region are not available. However, we can find indirect evidence for a step-like change in the total pressure at 9:14:50 UT using the pressure balance assumption for the mirror-mode structure, as described below. Assuming that the thermal pressure perturbation is balanced by the magnetic pressure perturbation Δpmag within the pileup region so that the total pressure remains constant, one gets the following relationship between the density perturbation Δn and the magnetic field perturbation ΔB

equation image

where B0 is the unperturbed magnetic field intensity. Since B0 is comparable to ΔB (see Figure 3a) we cannot neglect the second-order term in equation (4) as done in the linear theory of mirror instability [Hasegawa, 1969].

[16] We extracted Δn and ΔB from the observed data through high-pass filtering with a cutoff frequency of 1/20 Hz. Similarly, the unperturbed density n0 and the unperturbed magnetic field B0 were obtained from the observed data through low-pass filtering. A linear regression between Δn and Δpmag yields an observational estimate of the ion temperature Ti within the pileup region that is substantially higher (Ti = 23.1 keV) than the observed temperature in the ambient plasma sheet before the arrival of the fast jets (Ti = 10 keV at C4). This is a clear evidence for the heating of ions in the mirror-mode structure.

[17] Substituting the ion temperature estimate for the pileup region to equation (4), we can readily calculate the best fitting density perturbation expected from pressure balance, which is plotted in Figure 3b (red line) along with the observed density perturbation (black line). The local pressure balance of mirror modes is generally verified, except between 9:14:50 UT (discontinuity S) and 9:14:55 UT (discontinuity TD), where the observed density variation is inconsistent with the constant total pressure assumption. Thus the sharp density gradients at these boundaries cannot be explained with mirror instability.

[18] The magnetic boundary at 9:14:55 UT is the jet front, which is assumed to be a tangential discontinuity (TD) separating the cold and dense ambient plasma from the hot and tenuous plasma population of the fast jet. This explains the step-like jump of density at this boundary. The timing analysis shows that the jet front (TD) propagates with the same velocity as the plasma (Figure 3c), which is a necessary condition for a tangential discontinuity.

[19] The magnetic discontinuity S, which is the tailward boundary of a magnetic trough within the pileup region, propagates earthward much faster than the corresponding plasma convection velocity vx, unlike the rest of the magnetic boundaries that are apparently frozen in the ambient plasma flow (see Figure 3c). The step-like jump of density and magnetic field across discontinuity S (Figures 3a and 3b) suggests a step-like jump in the total pressure. The high-resolution transverse electric field EY (green line in Figure 2f) shows a step-like local jump in the earthward plasma convection velocity at this time (9:14:50 UT), too. We identify this boundary as a small-scale shock-like discontinuity often referred to as shocklet in other space plasma environments [Hoppe et al., 1981; Le et al., 1989; Lucek and Balogh, 1997; Wilson et al., 2009]. Shocklets are usually generated by the nonlinear steepening of magnetosonic waves [Omidi and Winske, 1990]. Since the spatial scale of discontinuity S is about 70 km, i.e. of the order of several electron inertial lengths (A. Retinò et al., submitted manuscript, 2011), the discontinuity cannot be regarded as a regular MHD shock. Therefore we suggest that the sharp discontinuity detected by C4 at 9:14:50 UT is a kinetic shocklet (S).

3. Discussion

[20] As shown in section 2.1, magnetic flux pileup and plasma compression regions are observed ahead of the jet front, and an extended rarefaction region is observed trailing the jet front. These features are very similar to the interaction between fast and slow solar wind streams in corotating interaction regions (CIR) [Gosling and Pizzo, 1999].

[21] In section 2.2, we show evidence for ion gyroradius-scale mirror modes developing in the pileup region ahead of the jet front. Mirror-mode structures of comparable scale have been reported recently by Ge et al. [2011] in the near-Earth plasma sheet following the passage of dipolarization fronts. The observed non-sinusoidal shape of the magnetic field perturbation (Figure 3a) with long-lasting magnetic compressions and deep and narrow magnetic depressions suggests that heating occurs for a substantial fraction of the trapped particles, unlike in saturated mirror-mode structures where trapped particles with intermediate pitch angles are heated and trapped particles with quasi-perpendicular pitch angles are cooled [Kivelson and Southwood, 1996].

[22] Mirror modes are likely to be excited by small perpendicular total pressure perturbations in a temperature-anisotropic plasma as

equation image

where p0⊥ is the unperturbed perpendicular total pressure [Hasegawa, 1969; Southwood and Kivelson, 1993]. In our case, the kinetic pressure of the earthward propagating plasma jet provides the free energy for the perpendicular total pressure perturbation Δp required for the growth of the observed mirror modes. When Δp cannot be balanced any longer with growing mirror modes in the pileup region, the boundary of the mirror-mode structure can nonlinearly steepen into a kinetic shocklet. We suggest that the discontinuity observed by C4 at 9:14:50 UT is produced by such a mechanism.

[23] We observed a slight increase in the temperature anisotropy after the passage of the jet fronts (see Figure 1e). A series of jets or dipolarization fronts during substorm intervals, as in our case, would result in increased ion temperature anisotropy (Ti/Ti > 1) in the ambient central plasma sheet, which would provide a positive feedback for the mirror-instability. Ge et al. [2011] also found that after the dipolarization front, the local ions became more anisotropic.

[24] On fluid scale, the plasma jet loses kinetic energy through the work of compressing the ambient plasma. This is why Cluster observed a substantial decrease in convection velocity from C1 to C3/C4 and an increase in density and magnetic field ahead of the earthward propagating jet front. On kinetic scale, particles can be reflected from the jet front, heated by mirror modes, and accelerated by shocklets. We presume that it is the coupling between fluid- and kinetic-scale processes what eventually leads to the deceleration of the plasma jet.

4. Summary

[25] We have presented novel multi-scale Cluster observations in the flow-braking region providing evidence of mirror-mode structures with a scale-size of a few ion gyroradii in the pileup region ahead of jet fronts. It is shown that the density perturbation is generally anticorrelated with the magnetic perturbation, in good agreement with the density variation expected from local pressure balance. The observed temperature anisotropy of the ambient plasma before the arrival of the jets provides a necessary precondition for the mirror instability. The timing analysis between the closely spaced spacecraft C3 and C4 confirms that the observed magnetic structures are indeed spatial structures frozen in the ambient plasma. For the first time, we report a small-scale shock-like discontinuity in the flow-braking region, which we interpret as a kinetic shocklet due to the nonlinear steepening of mirror modes.


[26] Cluster data from the Cluster Active Archive and the Cluster instrument teams are gratefully acknowledged. This research was supported by the Austrian Science Fund FWF I429-N16.

[27] The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.