JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 118, 674–684, 10.1029/2012JA018323, 2013
Cluster observations of kinetic structures and electron acceleration within a dynamic plasma bubble Meng Zhou,1,2 Xiaohua Deng,1 Maha Ashour-Abdalla,3,4 Raymond Walker,4,5 Ye Pang,1 Chaoling Tang,6 Shiyong Huang,7 Mostafa El-Alaoui,4 Zhigang Yuan,7 and Huimin Li7 Received 25 September 2012; revised 16 November 2012; accepted 12 December 2012; published 11 February 2013.
[1] Fast plasma flows are believed to play important roles in transporting mass,
momentum, and energy in the magnetotail during active periods, such as the magnetospheric substorms. In this paper, we present Cluster observations of a plasmadepleted flux tube, i.e., a plasma bubble associated with fast plasma flow before the onset of a substorm in the near-Earth tail around X = 18 RE. The bubble is bounded by both sharp leading (@bz/@x < 0) and trailing (@bz/@x > 0) edges. The two edges are thin current layers (approximately ion inertial length) that carry not only intense perpendicular current but also field-aligned current. The leading edge is a dipolarization front (DF) within a slow plasma flow, while the trailing edge is embedded in a super-Alfvénic convective ion jet. The electron jet speed exceeds the ion flow speed thus producing a large tangential current at the trailing edge. The electron drift is primarily given by the E B drift. Interestingly, the trailing edge moves faster than the leading edge, which causes shrinking of the bubble and local flux pileup inside the bubble. This resulted in a further intensification of Bz, or a secondary dipolarization. Both the leading and trailing edges are tangential discontinuities that confine the electrons inside the bubble. Strong electron acceleration occurred corresponding to the secondary dipolarization, with perpendicular fluxes dominating the field-aligned fluxes. We suggest that betatron acceleration is responsible for the electron energization. Whistler waves and lower hybrid drift waves were identified inside the bubble. Their generation mechanisms and potential roles in electron dynamics are discussed. Citation: Zhou, M., X. Deng, M. Ashour-Abdalla, R. Walker, Y. Pang, C. Tang, S. Huang, M. El-Alaoui, Z. Yuan and H. Li (2013), Cluster observations of kinetic structures and electron acceleration within a dynamic plasma bubble, J. Geophys. Res. Space Physics, 118, 674–684, doi:10.1029/2012JA018323.
1. Introduction [2] Earth’s magnetotail is full of transient and localized phenomena [Sharma et al., 2008]. Fast plasma flows are important transient phenomena commonly observed in the 1
Institute of Space Science and Technology, Nanchang University, Nanchang, China. 2 State Key Laboratory of Space Weather, Chinese Academy of Sciences, Beijing, China. 3 Department of Physics and Astronomy, University of California, Los Angeles, California, USA. 4 Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California, USA. 5 Department of Earth and Space Science, University of California, Los Angeles, California, USA. 6 School of Space Science and Physics, Shandong University at Weihai, Weihai, China. 7 School of Electronic and Information, Wuhan University, Wuhan, China. Corresponding author: M. Zhou, Institute of Space Science and Technology, Nanchang University, Nanchang, China. (
[email protected]) ©2012. American Geophysical Union. All Rights Reserved. 2169-9380/13/2012JA018323
Earth’s magnetotail. Such flows are known as bursty bulk flows (BBF) because of their transient nature [e.g., Angelopoulos et al., 1992, 1994]. Statistically, the duration of a BBF is about 10–20 min, and the flow channel is about 2–4 RE in the dawn-dusk and Z directions [Angelopoulos et al., 1994; Cao et al., 2006]. It is commonly believed that BBFs play significant roles in magnetosphere activities because of their importance in the transport of mass, momentum, and energy in the magnetotail, especially during magnetospheric substorms. It is shown that they provide a dominant (70–80%) contribution to the total plasma sheet transport [Sharma et al., 2008]. BBF is one intrinsic ingredient of the present substorm models [Baker et al., 1996; Lui, 1996]. In particular, the near-Earth neutral line (NENL) model suggests that fast flow braking causes the near-Earth dipolarization and the formation of substorm current wedge, which induces the auroral substorm onset [e.g., Shiokawa et al., 1997]. [3] One candidate model describing the BBF involves the plasma depleted flux tube, i.e., bubble in the plasma sheet. The introduction of bubble is to explain the “pressure catastrophe” in the magnetosphere, whereby the adiabatic transport of magnetic flux and plasma earthward from the mid-tail results in plasma pressures in the near-tail which are far too high to
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2. Instrumentation [6] A series of instruments onboard the Cluster spacecraft were utilized in this study: (1) FGM provides 22.5 Hz resolution magnetic fields [Balogh et al., 2001], (2) CIS-CODIF provides spin resolution ion moment data [Rème et al., 2001], (3) PEACE provides spin resolution pitch angle distributions of thermal electrons with energy under 30 keV [Johnstone et al., 1997], (4) RAPID provides proton/electron omnidirectional flux and three-dimensional distribution above 30 keV [Wilken et al., 2001], (5) EFW provides 25 Hz resolution electric fields [Gustafson et al., 1997], and (6) STAFF-SA provides power spectral density (PSD) and the polarization parameters of electromagnetic fields in the frequency range of 8–4000 Hz [Cornilleau-Wehrlin et al., 2001]. The EFW instrument measures only two components of electric field in the spin plane. The third component Ez is derived by the assumption that E B = 0, which is valid is this study. To avoid ambiguity, Ez is calculated only when the following requirements are satisfied: |B| > 2 nT, tan1(bz/√(bx2 + by2)) > 15 , i.e., the elevation angle of the magnetic field with respect to the spin plane should be larger than 15 . Values of Ez used in this paper were calculated by the EFW team. The three-dimensional electric fields were directly downloaded from the Cluster Active Archive (http://caa.estec.esa.int).
3. Event Overview [7] Figure 1a shows the Auroral Electrojet (AE) index from 01:00 UT to 04:00 UT on 1 September 2003. There are two substorm onsets, which are denoted by rapid (a)
400 350
AE (nT)
300 250 200 150 100 50 0 01:00
01:30
02:00
02:30
03:00
03:30
04:00
01−Sep−2003
(b) C1 C2 C3 C4
−1.62 −1.61 −1.6 −1.59 −1.58
−0.06
Z−gsm (RE)
−1.63
Y−gsm (RE)
be confined by magnetic fields that are consistent with observed values [Chen and Wolf, 1993, 1999]. A plasma bubble is an entropy-depleted flux tube with a small dawndusk cross-section. Possible models for the formation of plasma bubbles include being a direct consequence of reconnection, or being generated by the interchange instability at the interface between hot fast plasma flow and ambient plasmas [Nakamura et al., 2002a; Birn et al., 2004; Guzdar et al., 2010]. The bubble can propagate earthward under the Lorentz force as long as its entropy is lower than that of the background flux tubes [Birn et al., 2004]. The cross-tail current is disrupted in the bubble because the low-entropy flux tube cannot support as much gradient/curvature drift as surrounding plasmas. This diverts the cross-tail current into the ionosphere, flowing into the ionosphere at the dawn edge of bubble and out of the ionosphere at the dusk edge, in a manner similar to the substorm current wedge [Birn et al., 2004]. The bubble is also considered as a building element of substorm particle injections because previous simulations found that the energetic particle injection boundary is well coincident with the earthward boundary of the plasma bubble [Yang et al., 2011]. [4] Observational evidence of plasma bubble was reported by Sergeev et al. [1996] using ISEE data. They found that the magnetic field becomes dipolarized inside the bubble. Other observations showed that most fast plasma flows are associated with magnetic field dipolarization [Ohtani et al., 2004]. Behind the dipolarization, the plasma density and pressure decrease, similar to the properties of the bubble. The leading edges of some bubbles are characterized by a sharp increase in the magnetic field Bz, called a sharp dipolarization front (DF) [Nakamura et al., 2002b]. The DFs are thin boundary layers separating distinct plasmas. The thicknesses of the DFs are close to the local ion inertial length, or ion Larmor radius [Runov et al., 2009; Zhou et al., 2009b]. DF is also a vertical current layer with intense cross-tail current, which is several times larger than the current in the horizontal cross-tail current sheet [Zhou et al., 2009b; Sergeev et al., 2009; Runov et al., 2011]. There are frequently particle energizations around or behind the front [Deng et al., 2010; Ashour-Abdalla et al., 2011; Fu et al., 2011; Zhou et al., 2011; Huang et al., 2012a]. Associated with the particle energization, plasma wave enhancements from below the lower hybrid frequency to above the electron cyclotron frequency have also been observed [Zhou et al., 2009b; Deng et al., 2010; Hwang et al., 2011; Khotyaintsev et al., 2011; Huang et al., 2012a]. [5] In this paper, we use Cluster observations to study the kinetic structures in a plasma bubble, accompanied by fast convective flow in the plasma sheet. Strong electron acceleration occurred inside the bubble. The bubble has two features that were seldom reported previously. First, the bubble is characterized by not only a sharp leading boundary but also a sharp tail boundary. Second, the interaction between the leading and trailing boundaries leads to the formation of a secondary DF. We found that the secondary DF is associated with strong electron acceleration. The structure of this paper is as follows. In section 2, we introduce the instruments and data used in the paper. In section 3, we present the event overview. In section 4, we show the structure of the bubble in detail. Electron acceleration and evolution are studied in section 5. Our observations are discussed in section 6 and summarized in section 7.
−0.07 −0.08 −0.09 −0.1 −0.11
−1.57 −18.59 −18.6 −18.61 −18.62 −18.63
X−gsm (RE)
−18.5 9 −18.6 −18.6 1 −18.62 −18.63
X−gsm (RE)
Figure 1. (a) AE index between 01:00 UT and 04:00 UT on 01 September 2003. (b) Positions of the Cluster spacecraft. They were around (18.6, 1.6, 0.08) RE, with the interdistance between each spacecraft being about 200 km.
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increases in the AE index. The first onset occurred at around 01:25 UT. The AE index increases from 130 to 260 nT in less than 15 min and then decreased starting at around 01:40 UT. The recovery of the AE index continued for about 30 min. The second onset occurred at around 02:11 UT, when the AE index started to increase from 150 to 370 nT over 30 min, and then gradually decreased to 270 nT at about 03:20 UT. [8] During the time interval of interest, the Cluster spacecraft was located at approximately (18.6, 1.6, 0.1) RE in the Geocentric Solar Magnetospheric (GSM) coordinates. This is just post-midnight sector in the Earth’s magnetotail (Figure 1b). The four spacecraft formed a regular tetrahedron with interspacecraft distances of ~200 km, which is smaller than the ion inertial length in the central plasma sheet (c/opi ~ 360 km given that ni ~ 0.4/cm3). The small separation of spacecraft enables us to study the sub-ion scale structures of the bubble. [9] Figure 2 shows the event overview observed by C4 between 01:55 UT and 02:10 UT. Because the four spacecraft were close to each other, their observations were very similar. Therefore, we show only the C4 observations as representative of all four in the following discussions. GSM coordinates are utilized in the rest of the paper unless otherwise noted. Overall, there were six magnetic field dipolarizations (01:56:20 UT, 01:58:30 UT, 01:59:35 UT, 02:02:50 UT, 02:04:45 UT, and 02:07:00 UT, respectively) observed between 01:55 and 02:10 UT. During that period, the spacecraft was in the central plasma sheet where plasma b is much greater than 1 and the ion and electron energy fluxes are high. Each of the dipolarizations is associated with a decrease in both plasma density and plasma b, and an earthward plasma flow. Plasma flow was mainly in the (a)
Bx By Bz
(b)
Vx Vy Vz
(c)
4. Structure of the Bubble
(d)
(g)
keV/(s-str-cm2-keV)
(e)
(f)
x and y directions. Vx was earthward during the first three dipolarizations, but changed to tailward between 02:00 UT and 02:02UT. Vx changed back to earthward at 02:02 UT and had a slight excursion to tailward for a short time period, and then turned earthward again for the rest of the interval (Figure 2b). There was a large short-lived flow burst between 02:07 UT and 02:09 UT, with the maximum magnitude exceeding 1000 km/s. In this paper, we focus on the dipolarization observed at around 02:07 UT, a few minutes before the second AE index intensification. [10] The plasma entropy PVg (g = 5/3 is the ratio of specific heat, P is the plasma pressure, and V is the volume per unit magnetic flux of the flux tube integrated along the tube’s length) is displayed in Figure 2e. The value of V is estimated based on the single spacecraft measurements in the plasma sheet, using the formula given by Wolf et al. [2006]. Plasma pressure P includes both ion pressure and electron pressure and was provided by the CIS-CODIF and PEACE instruments, respectively. As shown in Figures 2f and 2g, there are probably high fluxes above the upper energy limits of the CIS-CODIF and PEACE instruments. Thus, in order to take into account the contribution from these energetic particles, we incorporated data from RAPID (ion: 30–1000 keV, electron: 40–240 keV) when calculating plasma pressure. Discontinuities in the PVg profile are present because PVg is not calculated when Bz is negative or Bz is significantly smaller than the equatorial magnetic field. We see that the value of PVg drops rapidly in correlation with each of dipolarizations mentioned above. Inside these plasma-depleted flux tubes, the entropy is lower than the background plasma, which is consistent with the definition of the plasma bubble [Chen and Wolf, 1993, 1999]. We should note that the formula given by Wolf et al. [2006] suffers from the overestimation of the entropy by a factor of 2–3 in rapid earthward flow. For the structure observed between 02:07:00 UT and 02:07:40 UT, the estimated entropy in the fast flow is already lower than the background, so reducing the estimated entropy by a factor of 2–3 leads to an even more entropy-depleted bubble.
Figure 2. Event overview of C4. (a) Three components of the magnetic fields. (b) Three components of the plasma flow. (c) Ion density. (d) Ion plasma beta. (e) The entropy parameter PVg. (f) Ion and (g) electron differential energy fluxes in units of keV/(cm2 str s keV). Dipolarizations are marked by vertical dashed lines.
[11] In this section, we describe in detail the bubble structure observed between 02:07:00 and 02:07:40 UT. The leading edge of the bubble is a DF (02:07:09–02:07:16 UT) characterized by a sharp increase of Bz. Plasma flow accompanied with the DF is smaller than 200 km/s. There is a large earthward and duskward flow around the trailing edge of the bubble, characterized by a sharp decrease of Bz between 02:07:29 and 02:07:35 UT. The large flow is mostly a convective flow because the magnetic field mainly points in the Z direction. The fast flow persists for about 90 s, and then gradually drops below 200 km/s. [12] We calculated the convective and parallel flow speeds and compared them with the local ion Alfven speed, i.e., VA = B/√(nimi), where B is the magnetic field strength, ni is the plasma density, and mi is the proton mass. The convective velocity is calculated by V⊥ = b (V b), where b is the unit vector of the local magnetic field. The parallel velocity is given by V|| = V•b. As shown in Figure 3c, the flow is dominated by a convective component, while the parallel flow component is small. Convective flow speed exceeds the local Alfvén speed between 02:07:22 and 02:07:42 UT. V|| is
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B (nT)
10
(b)
Vp (km/s)
(c)
Vconv (km/s)
1000 500 0 −500 1500 1000 500 0 1
(d)
(10 −18 N/m3 ) P (nPa)
(a)
F
(e)
0
0.5 0 200 0 −200 02:06:40
02:07:20
02:08:00
02:08:40
Figure 3. Plasma parameters associated with the bubble observed around 02:07:00 UT. (a) Three components of magnetic fields. (b) Three components of plasma flow in GSM coordinates. (c) Convective flow speed (black), parallel flow speed (green) and local Alfvén speed (red). (d) Total pressure (black), plasma pressure (red), and magnetic pressure (green). (e) Pressure gradient force (red), Lorentz force (green) and the total force (black). To take into account the contribution by particles exceeding the energy coverage of CIS-CODIF and PEACE, we incorporated the data from RAPID in calculating plasma pressure. positive inside the bubble. We noted that the parallel flow starts to increase at the trailing edge of the bubble, which leads to V|| > VA. [13] We calculated plasma pressure and magnetic field pressure in order to investigate the pressure variation across the bubble. Figure 3d shows that the plasma pressure decreases and the magnetic field pressure increases inside the bubble. Decreases in the plasma density and pressure, and an increase in the magnetic field pressure are typical characteristics of a plasma bubble [Sergeev et al., 1996]. The total pressure also decreases inside and after the passage of the bubble. The pressure ahead of the bubble is higher than that behind the bubble, indicating the presence of a tailward pressure gradient. We will discuss the force balance around the bubble later. [14] Because the spacecraft separation was about 200 km, we assume that both the leading and trailing boundaries passed the spacecraft as planar structures. Hence, multispacecraft timing analysis can be used to estimate the normal direction and velocity of both boundaries. We found that the trailing edge moved in the direction n = [0.86,0.51,0.11] with a speed of approximately 170 km/s, and the leading edge moved in the direction n = [0.81,0.55,0.18] with a speed of about 85 km/s. The normals of the two boundaries point mainly earthward and dawnward. The angle between the normals of the leading and trailing edges is only 4 .
Minimum variance analysis (MVA) also was used to re-examine the normal direction of both edges [Sonnerup and Scheible, 1998]. For the leading edge, the ratio between the intermediate eigenvalue (l2) and the minimum eigenvalue (l3) is about 9. The normal direction of leading edge obtained from the MVA is consistent with the timing analysis. The angle difference inferred from both methods is only 6 . The normal direction of the trailing edge obtained from the MVA (l2/l3 6) is also consistent with the timing analysis, with an angle difference of only 16 . The duration of the leading edge was about 7 s. Thus, the width of the leading edge is about 600 km, which is approximately 1.3 local ion inertial lengths based on the local ion density of 0.25/cm3. Similarly, the thickness of the trailing edge is about 1100 km, which is equivalent to 1.5 local ion inertial lengths based on the local ion density of 0.1/cm3. The above parameters are summarized in Table 1. [15] One noticeable feature is that the trailing edge moves faster than the leading edge, which implies a shrinking of the bubble along the normal direction. Because of the speed imbalance between the leading and the trailing edges, the thickness of the bubble along the normal direction is reduced during its propagation. The width of the bubble along the normal direction at the observation time can be roughly estimated as follows. We assume the velocity of the structure decreases linearly from the trailing edge to the leading edge. Thus, the size of the bubble along the normal direction can be estimated as (Vlead + Vtrail)/2 Tduration = 3750 km ~ 0.6 RE, which is much smaller than that determined by previous observations and simulations [Sergeev et al., 1996; Birn et al., 2004]. There is a further intensification of Bz slightly ahead of the trailing edge, at around 02:07:25 UT. The value of Bz increases from 15 to 20 nT in less than 5 s and then decreases rapidly. The profile of the Bz increase resembles a DF, so we call it a secondary DF as compared to the main DF at the leading edge. We found that the secondary DF is coherently tied to the trailing edge because the normal direction and speed of the secondary DF is close to that of the trailing edge. The thickness of the secondary DF is estimated as 160 km/s 4 s = 640 km ~ 0.9c/opi given that the local ni 0.1/cm3. [16] High resolution electron density is inferred from the spacecraft potential [Pedersen et al., 2008]. Similar to the ion density, electron density decreases inside the bubble. It shows a slight enhancement ahead of the front, which suggests a compression of the background plasma due to the arriving of the bubble. The density ahead of the bubble is higher than that after the passage of the bubble. [17] A strong electric field is localized at the trailing edge, as displayed in Figures 4c–4 e. The Ex and Ey components are much larger than Ez. Because the magnetic field mainly points in the Z direction, the electric fields are primarily in the perpendicular direction. The large electric field corresponds to the large convective flow. Thus, we compared
Table 1. Summary of Parameters About the Bubble
Leading edge Trailing edge Secondary DF
Time (UT)
Normal
l2/l3
Propagation Speed (km/s)
Thickness (local c/opi)
02:07:09–02:07:16 02:07:29–02:07:35 02:07:25–02:07:29
[0.81,0.55,0.18] [0.86,0.51,0.11] [0.84,0.52, 0.12]
9.2 6.3 8.1
85 170 160
1.3 1.5 0.9
677
(a)
Bz (nT)
(b)
J J Ey |∇× B| Ne Ex Ez 2 2 /|∇⋅ B| (nA/m ) (nA/m ) (mV/m) (mV/m) (mV/m) (cm−3 )
ZHOU ET AL.: OBSERVATION OF A DYNAMIC BUBBLE C1 C2 C3 C4
20 10 0
(c) (d) (e) (f) (g) (h)
0.3 0.2 0.1 0 −20 −40 30 20 10 0 −10 4 2 0 −2 −4 −6 −8 40 20 0 −20 40 20 0 −20 1
E -(V ×B)
Jx Jy Jz J J J
1
0.5 0
02:06:40
02:07:20
02:08:00
Figure 4. (a) Bz profile recorded by all four spacecraft. (b) Electron density inferred from the spacecraft potential. (c–e) The three components of measured electric fields in 25 Hz resolution (black) and the convective electric field given by (vi B) (red). (f) Electric current density in GSM coordinates. (g) Electric current density in MFA coordinates. (h) The absolute ratio between the divergence and curl of the magnetic field. E and (Vi B), as displayed in Figures 4c–4e. It is apparent that E and (Vi B) are mostly equivalent to each other at the leading edge and inside the bubble. However, there is an obvious discrepancy between E and (Vi B) at the trailing edge. This discrepancy is mostly evident in the Ex and Ey components, since the maximum amplitudes of Ex and Ey are about 10–20 mV/m larger than the maximum amplitude of (Vi B). The discrepancies in Ex and Ey might be caused by the ion velocity being underestimated by neglecting highenergy ions that exceed the energy range of the CIS-CODIF instrument. However, we cannot incorporate the RAPID data to adjust the ion flow as we did for pressure due to the lack of ion measurements in the central head of the instrument and the need for a 3D distribution in the velocity calculation [Wilken et al., 2001]. This discrepancy might also be due to the Hall effect at the thin boundary layers [Zhou et al., 2009b; Fu et al., 2012], which we will discuss further in section 6. [18] Figures 4f and 4g show the electric current density in GSM and magnetic field aligned (MFA) coordinates. Because the four spacecraft formed a regular tetrahedron (geometric parameters: elongation 0.2 and planarity 0.3), we used the curlometer method based on magnetic field measurements to estimate the current density [Dunlop et al., 2002]. The uncertainties of the estimated current density are shown in Figure 4h. It is determined by the ratio between the divergence and curl of the magnetic field, i.e., |r • B/r B|, which statistically indicates the error of the estimated current density, i.e., |dJ/J|. We can see that the value of |r • B/r B| is
relatively small in the bubble during most of the time, especially at the two edges where the ratio is less than 0.4. The current density is larger at the edges than inside the bubble, which is consistent with the prediction that cross-tail current is reduced in the bubble [Chen and Wolf, 1993]. As shown in Figure 4g, the field-aligned current (FAC) at the trailing edge is mainly anti-parallel, while at the leading edge there is a FAC shear. The FAC exhibits a fine tri-polar structure around the leading edge, initially parallel to the magnetic field, and then changes to the anti-parallel direction and then back to the parallel direction in a short time period. The perpendicular current is also enhanced at both edges. [19] Knowing the electric current, we estimated the Lorentz force and compared it with the plasma pressure gradient force. Figure 3e depicts the force along the normal of the bubble. The Lorentz force is given by j B, where j is the electric current density and B is the magnetic field. The pressure gradient force is given by –@P/@n = @P/vn/dt, where P is the plasma pressure and vn is the moving speed of the bubble along the normal. The total force is the sum of Lorentz force and the plasma pressure gradient force. We see that the Lorentz force points outward from the bubble, whereas the gradient force points inward. Because the gradient force is larger than the Lorentz force, the net force is in the same direction as the gradient force. Thus, the effect of the net force is to compress the bubble, which explains the fact that the bubble is shrinking along the normal. Moreover, the leading edge is under decelerating while the trailing edge is under accelerating. [20] It was suggested that a DF is a tangential discontinuity [Khotyaintsev et al., 2011; Fu et al., 2012]. One fundamental feature of the tangential discontinuity is that the net flow normal to the boundary is zero, which means that the plasma bulk flow should be tangential to the boundary. One important implication is that the tangential discontinuity separates two flux tubes without plasma exchange, such as the subsolar magnetopause under the northward interplanetary magnetic field. We found that the normal electric current is close to zero at the leading edge, implying that the current is flowing tangentially to the boundary. This is also true for the trailing edge. Furthermore, the average magnetic fields normal to the boundary bn are about 2 nT at the leading edge and about 1 nT at the trailing edge, which are much smaller than the total magnetic field. The bulk flows in the normal direction in the reference frame moving with the boundary (Vn Vbn) are approximately 0 and 100 km/s at the leading and trailing edges, respectively. Both of these are much smaller than the tangential flow speed. The above evidences suggest that both the leading and trailing boundaries are tangential discontinuities. However, we have to mention that even though the bulk flow speed at the thin layer is close to zero, ions may be able to penetrate through the boundary because of the finite Larmor radius effect. While electrons, with much smaller gyroradius, are likely frozen-in to magnetic fields and cannot transport across the boundary.
5. Electron Acceleration [21] Figure 5 shows the characteristics of electron fluxes inside the bubble. There is a tendency for the high energy electron fluxes to increase inside the bubble, whereas lower energy electron fluxes decrease. The transition occurs at about 3 keV. This is similar to the variations of electron
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(c)
20
Bx By Bz
10 0 0
−100 −200 4 10
40.7-50.5keV 50.5-68.1keV 68.1-94.5keV 94.5-127.5keV 127.5-244.1keV
2
10
0
(d) (e)
DPflux 1/(cm2⋅s⋅str⋅keV)
10
10 10 10
16915-21043eV 6977-8712eV 1844-2305eV 757-945eV 201-251eV
7 6 5
20000 E=(40.7-50.5)keV 10000
(f)
0 90 180
0 4000 E=(50.5-68.1)keV 2000 0
02:06:40
02:07:20
02:08:00
Figure 5. Electron acceleration inside the bubble. (a) Magnetic field. (b) J ∙ E, (c) Spin resolution electron flux from RAPID. (d) Spin resolution electron flux from PEACE. The different colors beside each panel represent different energy channels. (e–f) Subspin resolution (0.25 s) electron fluxes with energies of 40.7–50.5 and 50.5–68.1 keV inferred from RAPID data. Details about deducing the subspin resolution electron fluxes are described in the text. fluxes associated with DFs observed in the near-Earth region [Ashour-Abdalla et al., 2011], as well as the characteristics of electron injection observed at the geosynchronous orbit [Birn et al., 1998]. [22] The 3D distributions help reveal the details of the energetic electrons within the bubble. In this event, the RAPID instrument provides 16 azimuthal distributions in three given polar angles for two energy channels during every spin period. One polar angle is always perpendicular to the ambient magnetic field, and the other two polar angles are 0 and 180 relative to the spin axis. In a region dominated by Bz, the spin axis is approximately parallel to the Z direction. Thus, the two polar angles are approximately 0 and 180 relative to the ambient magnetic field. Assuming that the electrons are gyro-tropic, the flux differences between the different azimuthal angles can be viewed as a temporal change of the flux. Hence, the subspin resolution electron fluxes can be inferred from the azimuthal distribution. This is similar to the method for inferring subspin resolution electron fluxes around DFs using the THEMIS spacecraft [Sergeev et al., 2009]. From Figures 5e and 5f we see that, corresponding to the leading edge, the fluxes show weak fluctuations and are almost isotropic with small magnitude. The perpendicular flux has a transient increase between 02:07:17 and 02:07:20 UT. Then fluxes decrease, but show a major increase at around 02:07:25 UT corresponding to the secondary DF. Fluxes reach their peak when the magnetic field Bz reaches its maximum. Fluxes in the perpendicular direction are greater than those in the field-aligned direction. This anisotropy starts at approximately 02:07:16 UT (behind the leading edge) and ends at 02:07:33 UT (at the trailing edge). There is no apparent dispersion between the fluxes increase in the two different energy channels.
[23] Furthermore, we calculated the value of J•E across the bubble, as shown in Figure 5b. The value of J•E determines the amount of energy transferred between the plasma and the electromagnetic fields. Electromagnetic energy is converted to plasma energy when J•E > 0, while plasma energy is converted to electromagnetic energy when J•E < 0. We see that J•E is mostly positive with magnitude less than 50 pw/m3 inside the bubble, except for a strong negative pulse (approximately 150 pw/m3) at the trailing edge, which corresponds to the decrease of the energetic electron fluxes. [24] Figure 6 shows the high-energy electron particle differential fluxes as a function of energies at four different times during the bubble crossing. It is clear that the power law index of the electron spectrum is smallest (g = 3.5) around the time when the fluxes reach their peak, which means that the electron spectrum is the hardest at that time. Energetic electron spectra are softer (g > 4) outside the bubble and at the leading edge of the bubble than those corresponding to the secondary DF. [25] Electron distributions are displayed in Figure 7 in order to understand the evolution of electron dynamics. At the leading edge of the bubble (Figure 7g), the electrons are almost isotropic below 2 keV. Above 2 keV, the parallel phase space density (PSD) drops below the PSD in the antiparallel and perpendicular directions. Inside the bubble, during the intensification of Bz (Figures 7h and 7i), electrons are anisotropic with PSD in the perpendicular direction being greater than that in the field-aligned direction above 1 keV. Below 1 keV, the PSD in the field-aligned direction is greater than that in the perpendicular direction. In addition, the electron temperature is highly anisotropic, with Te⊥ > Te|| inside the bubble (Figure 7b). This anisotropy persists for about 10 s. Before that, the electron temperature is weakly anisotropic, with Te|| > Te⊥, corresponding to the leading edge. The electron distribution inside the bubble is similar to that in the flux pileup region [Khotyaintsev et al., 2011], where the electrons are anisotropic with the PSD in the perpendicular direction being greater than that in the field-aligned direction. Khotyaintsev et al. [2011] suggested 5
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Figure 7. The evolution of electron temperature and pitch angle distributions (PADs) inside the bubble. (a) Three components of magnetic fields. (b) Electron parallel (black) and perpendicular (red) temperature recorded by C2. (c–f) Electron PADs as a function of time at four different energy channels. (g–i) Electron PSDs as a function of energy for different pitch angles at four different times indicated by the vertical dashed lines through Figures 7a–7f). Pitch angles of 0 , 90 , and 180 are represented by black, red, and green traces, respectively. 680
6. Discussion [26] A plasma bubble was observed in the central plasma sheet by the Cluster spacecraft. This bubble is bounded by sharp leading and trailing edges. The leading edge is a DF associated with a relatively slow plasma flow, while the trailing edge is embedded in a super-Alfvénic flow. Interestingly, the normals of the leading and trailing edge are in the same direction while the speed of the trailing edge is faster than the leading edge, which leads to the shrinking of the bubble along the normal direction. The interaction between the leading and trailing edge causes a flux pileup and the resultant growth of the magnetic field inside the bubble: the secondary DF. This process represents a local flow braking or flux pileup, as the main DF (the leading edge) resembles the Earth’s dipole field, while the secondary DF results from the interaction between the fast flow and the dipolarized magnetic field behind the main DF. The observation of secondary dipolarization inside a bubble or after a main dipolarization may provide new clues on the formation of multiple DFs observed in the near-Earth region [Zhou et al., 2009b; Guzdar et al., 2010]. [27] The normal distance between the leading and trailing edge is about 0.6 RE, which is only 10 ion inertial lengths given that ni = 0.4/cm3 in the central plasma sheet. This is much smaller than the previously reported bubbles in the near-Earth region [Birn et al., 2004; Pang et al., 2012]. We are unable to estimate the dawn-dusk width of the bubble due to the limited inter-distance between the spacecraft. These small-scale bubbles may be able to propagate to the flow braking or transition region around X = 10 RE, and possibly play crucial roles during substorm particle injection. We should mention that a bubble with sharp leading and trailing boundaries is not unique. Similar structures were recently reported by Pang et al. [2012] using Cluster observations. They found that the interaction between the leading and trailing edge causes the deformation of bubbles, which leads to the generation of a FAC system. [28] Convective flow speeds in the magnetotail are occasionally larger than VA, as recently reported by Parks et al., 2007. They found nonlinear electromagnetic pulse in super-Alfvénic convective flow. We suggest that the formation of the sharp trailing boundary may be closely related to the intense flow. Figure 8 shows the magnetic fields, electric fields, and electric current at the trailing edge in boundary normal coordinate. The boundary normal coordinates are defined as follows: N is the boundary normal, M is the cross product of N and the unit vector of the ambient magnetic field, and L completes a right-handed coordinate system, i.e., L = M N. M represents the tangential direction in the plane perpendicular to the ambient magnetic field. The electric field is dominated by EN at the trailing edge, reaching up to 50 mV/m. EN is negative, and thus points tailward, which is probably the Hall electric field or the polarization electric field at the thin boundary layer [Zhou et al., 2009b; Fu et al., 2012]. The current jM at the trailing edge is positive while the ion flow
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by assuming that the pressure is isotropic, which is valid since the temperature anisotropy disappears at the trailing edge. The first term on the right-hand side of the above equation is the E B drift, while the second term is the diamagnetic drift in the presence of pressure gradient. The third term, which is the inertial drift, can be ignored here because in order to produce a 100 km/s inertial drift, the dve/dt term must be as large as 250,000 km/s, which is too high. The E B drift mainly points in the M direction because E is dominated by EN and B is dominated by BL. The E B drift in the M direction is about 2200 km/s. On the other hand, the diamagnetic drift is also primarily in the M direction, because B points in the L direction while the pressure gradient is opposite to the boundary normal N. Its magnitude can be roughly estimated as follows. The electron pressure gradient along the normal @Pe/@n can be estimated from (Pe(t0 + dt) Pe(t0))/Vn/dt ~ 2 105 nPa/km and B ~ BL ~ 16 nT, n ~ 0.1/cm3. Thus, Vd ~ 80 km/s, which is much smaller than the E B drift. Therefore, intense electron flow at the trailing edge is due to the E B drift. [29] There is an equatorial current reversal within the bubble (see Figure 4f). Jx reverses from earthward to tailward, which is associated with the simultaneous reversal of Jy from duskward to dawnward from 02:07:10 to 02:07:35 UT. As we mentioned before, these currents are tangential to the two boundaries. However, the current at the leading edge points earthward and duskward, while the current at the trailing edge points tailward and dawnward, so there is an obvious current
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shear between the leading and trailing edge. The current shear is mainly attributed to the electron flow since ion flow is always earthward and duskward through the bubble. At the leading edge the tangential current is about 20 nA/m2, which exceeds the ion current of ~8 nA/m2. Hence the electron flow should be opposite to the ion flow in order to provide the measured electric current. This is confirmed by the electron moment data (not shown). The flow shear might indicate the existence of a small scale clockwise (viewed above the equatorial plane) electron flow vortex, which probably resulted from the local flow braking and bouncing. This is similar to the generation of large scale flow vortex observed near the transition region [Keiling et al., 2009; Tang, 2012]. However, the flow vortex observed here is mainly carried by electrons since ions are probably unmagnetized at the two thin boundaries. [30] The FAC system associated with the bubble is rather complex. As illustrated in section 4, the FAC has a tri-polar structure around the leading edge, while at the trailing edge the FAC is uni-polar. A FAC gradient on the scale of ion inertial length at the leading edge implies that a sub-ion scale effect is important in manipulating the FAC. It was shown previously that the cross-tail current is reduced in the bubble such that the current diverts into the ionosphere to form a FAC system in a manner similar to the substorm current wedge [Birn et al., 2004]. The FAC flows into the ionosphere on the dawn edge of the bubble, while it flows into the equatorial plane on the dusk edge of the bubble. Since the boundary normal points in the dawn direction, this means the spacecraft was located on the dawn side of the bubble. Moreover, it was shown that flow vorticity in the equatorial plane can generate a FAC [Keiling et al., 2009]. The clockwise (counterclockwise) flow vorticity corresponds to a downward (upward) FAC in the ionosphere. The FAC observed here is neither consistent with the model of FAC associated with bubble nor FAC generated by flow vortex. The relationship between the FAC associated with the bubble, the small-scale electron flow vortex, and the ionospheric response requires further study. [31] Plasma waves ranging from the ion cyclotron frequency to above the electron cyclotron frequency were observed previously in fast flows [Zhou et al., 2009b; Deng et al., 2010; Khotyaintsev et al., 2011]. The role of these waves in particle energization is still poorly understood. Figure 9 shows the wave properties around the bubble. Figures 9b and 9c show electromagnetic field power spectral density (PSD) data from the STAFF instrument, and Figure 9d shows the PSD of electric fields produced by wavelet analysis on the electric field from the EFW instrument. Figure 9e shows the ellipticity of the electromagnetic waves. A plus sign indicates that the wave is right-hand polarized, and minus sign indicates that the wave is left-hand polarized. The greater the absolute value of ellipticity, the closer the wave is to a circularly polarized wave. Figure 9f shows the propagation angle of the electromagnetic wave with respect to the main magnetic field. Ellipticity and wave angle are calculated by the single value decomposition method as applied to magnetic field data [Santolĺk et al., 2003]. [32] Looking at Figures 9c and 9d, we see there are wave enhancements throughout the bubble in a broad range around the lower hybrid frequency. This is possibly the lower hybrid drift wave driven by diamagnetic drift in the
(a) (b) (c) (d) (e) (f)
Figure 9. Waves observed by C4. (a) Magnetic fields. (b) PSDs of magnetic fields. (c) PSDs of electric fields from 8 to 4000 Hz. (d) PSDs of electric fields from 0.1–12 Hz. (e) Ellipticity. (f) Propagation angle with respect to the main magnetic field of the electromagnetic waves. Since we cannot distinguish between the parallel and anti-parallel propagation, the range of propagation angle is limited in (0 –90 ). Black dashed traces in Figures 9b–9f indicate the lower hybrid frequency and electron cyclotron frequency, respectively.
presence of large density gradient as depicted in Figure 4 [Zhou et al., 2009a, 2009b]. The lower hybrid wave is able to accelerate electrons along the field line and may be responsible for the formation of the field-aligned distribution and FAC at the two boundaries [Khotyaintsev et al., 2011]. Figures 9b and 9c demonstrate that there are enhancements in the power spectrum of both the magnetic and electric fields above 50 Hz and below the electron cyclotron frequency. The wave emissions are manifested as two isolated wave packets. Polarization analysis shows that the wave is a right-hand circularly polarized wave (red color), which is consistent with the electron whistler wave. The waves propagated parallel or anti-parallel to the main magnetic field. Whistler waves were probably excited by the temperature anisotropy, or the pitch angle anisotropy, as was demonstrated already in section 5. Whistler waves may cause the scattering of the electrons from large pitch angle to smaller pitch angle, leading to an enhancement of the electron fluxes in the field-aligned direction. [33] Electron acceleration in the near-tail is a longstanding, unsolved problem. There are numerous studies demonstrating that reconnection in the mid- or near-tail is able to produce a large fluxes of electrons with hundreds of keV energy [e.g., ieroset et al., 2002; Huang et al., 2012b]. Thus, reconnection is probably responsible for the injection of energetic electrons into the inner magnetosphere. However, the possibility of energization by reconnection was seriously questioned by global test particle simulations [Birn et al., 1998; AshourAbdalla et al., 2011]. In particular, Ashour-Abdalla et al. [2011] found that electrons with energies higher than 100 keV are produced within the earthward moving DF, embedded in fast flow. In this study, we found intense electron acceleration within a dynamic plasma bubble. There
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is no obvious electron acceleration in the main DF. Instead, the major electron energization occurs coincident with the secondary DF. The intense electron acceleration inside the bubble is closely associated with the bubble evolution because the secondary DF is formed by the interaction between the leading and trailing boundaries of the bubble. Assuming negligible amounts of electrons losses or sources from the ionosphere, the electrons observed inside the bubble are confined in the bubble because both the leading and trailing boundaries are tangential discontinuities through which no bulk transport of plasma occurs. [34] The electron distribution inside the acceleration region is anisotropic, with perpendicular fluxes dominating fieldaligned fluxes. This is a typical signature of betatron acceleration [e.g., Asano et al., 2010]. We assume that electrons gain energy through adiabatic acceleration, because the characteristic spatial variance length is much larger than the electron Larmor radius (~70 km for 50 keV electrons), and characteristic temporal variance period is much longer than the electron gyro-period (~0.003 s). Considering a particle with its first invariant m is conserved, i.e., mv2⊥ =B = const, then the increase of magnetic field will result in the perpendicular energy gain of the particle. This is the principle of adiabatic betatron acceleration. In general, the perpendicular energy gain for an adiabatic particle is either through betatron acceleration or through pitch angle transition from field-aligned electrons. However, there is no evidence of such pitch angle transition. Furthermore, the betatron mechanism can be divided to two types. Considering a particle under guiding center approximation, the perpendicular energy gain can be expressed as dW⊥ @B ⇀ ¼ qEVrB þ m @t dt
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[35] The first term on the right-hand side of the above equation is the energy gain due to the guiding center’s gradient-B drift along the electric field, while the second term on the right-hand side is the energy gain due to electron gyro-motion along the inductive electric field [Northrop, 1963]. The first term corresponds to drift-betatron acceleration, which does not necessarily involve an inductive electric field. The second term corresponds to the gyro-betatron acceleration, which is the acceleration by inductive electric field due to the temporal change of magnetic flux. We found that these electrons were not likely drift into the observation region since the fluxes in two energy channels shown in Figure 5 do not exhibit any dispersion. In addition, at the secondary DF, the electron gradient-B drift velocity is in the M direction, which is in the same direction as the tangential electric field (not shown). Hence the perpendicular energy gain cannot be resulted from the drift motion in the electric field. Thus, the energy gain can only be caused by the second term on the right-hand side of the above equation, i.e., gyrobetatron acceleration. The source electrons probably originate from the reconnection site tailward of the spacecraft. Electrons were originally produced by reconnection and then swept away within the bubble where magnetic fields were initially weak. The evolution of the bubble leads to the gradual enhancement of magnetic field inside the bubble, and the related inductive electric field accelerated these electrons. This is similar to the mechanism proposed by Ashour-Abdalla et al. [2011]. They showed that the electrons pre-accelerated by
Figure 10. Schematic overview of the plasma bubble in the X-Y plane. The spacecraft path is shown in a frame of reference moving with the bubble. reconnection are further energized by betatron mechanism within the earthward-moving DF as the magnetic field becomes stronger. Our observations invoke the attention on the electron energization by multiple dipolarizations.
7. Conclusion [36] In this paper, we present a case study of a dynamic plasma bubble: its kinetic structure, evolution, and associated electron acceleration. Figure 10 displays the schematic overview of the characteristics of the bubble in the equatorial plane (GSM X-Y plane). The bubble is bounded by sharp leading (@bz/@x < 0) and trailing edges (@bz/@x > 0). The two edges are thin current layers with scale size on the order of the ion inertial length. The thin layers carry not only intense perpendicular currents but also field-aligned currents, which may be important in magnetosphere-ionosphere coupling. Both the leading and trailing edges are tangential discontinuities that confine the electrons inside the bubble. The trailing edge moves faster than the leading edge, which causes a local flux pileup inside the bubble, resulting in a further intensification of Bz, or a secondary dipolarization. Strong electron acceleration occurred at the secondary dipolarization, with perpendicular fluxes dominating the field-aligned fluxes. We suggest that betatron acceleration due to inductive electric field associated with the increase of magnetic field inside the bubble is responsible for the electron energization. Whistler waves and lower hybrid drift waves may add some additional nonadiabatic effect to the electron acceleration within the bubble. Our results appear to provide new clues on the understanding of the evolution of plasma bubble and its role in electron injection during magnetospheric substorms. To uncover the precise role of these bubbles in substorms, such as how they evolve in the transition or flow braking region, and how common are they in the magnetotail, more such bubbles needs to be studied in the future. [37] Acknowledgments. We thank the Cluster teams and Cluster Active Archive for providing high quality data. This work was supported by the National Science Foundation of China (NSFC) under grants 41004060, 40890163, 41174147, and 41274170, Scientific Research Program of Education Department of Jiangxi Province under grant GJJ11049, and Specialized Research Fund for State Key Laboratories.
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ZHOU ET AL.: OBSERVATION OF A DYNAMIC BUBBLE Meng Zhou appreciates Tony Lui, Andre Runov, E. Lee, Zuyin Pu, and Huishan Fu for valuable discussions and comments. We also thank Greg Kallemeyn for carefully reading the manuscript and correcting the English.
References Angelopoulos, V., et al. (1992), Bursty bulk flows in the inner central plasma sheet, J. Geophys. Res., 97, 4027. Angelopoulos, V., et al. (1994), Statistical characteristics of bursty bulk flow events, J. Geophys. Res., 99, 21,257. Asano, Y., et al. (2010), Electron acceleration signatures in the magnetotail associated with substorms, J. Geophys. Res., 115, A05215, doi:10.1029/ 2009JA014587. Ashour-Abdalla, M., M. El-Alaoui, M. Goldstein, M. Zhou, et al. (2011), Observations and simulations of nonlocal acceleration of electrons in magnetotail magnetic reconnection events, Nat. Phys., doi:10.1038/nphys1903. Baker, D. N., T. I. Pulkkinen, V. Angelopoulos, W. Baumjohann, and R. L. McPherron (1996), Neutral line model of substorms: Past results and present view, J. Geophys. Res., 101(A6), 12,975–13,010, doi:10.1029/95JA03753. Balogh, A., et al. (2001), The Cluster magnetic field investigation: Overview of in-flight performance and initial results, Ann. Geophys., 19, 1207–1217. Birn, J., M. F. Thomsen, J. E. Borovsky, G. D. Reeves, D. J. McComas, R. D. Belian, and M. Hesse (1998), Substorm electron injections: Geosynchronous observations and test particle simulations, J. Geophys. Res., 103(A5), 9235–9248, doi:10.1029/97JA02635. Birn, J., J. Raeder, Y. L. Wang, R. A. Wolf, and M. Hesse (2004), On the propagation of bubbles in the geomagnetic tail, Ann. Geophys., 22, 1773–1786. Cao, J. B., et al. (2006), Joint observations by Cluster satellites of bursty bulk flows in the magnetotail, J. Geophys. Res., 111, A04206, doi:10.1029/ 2005JA011322. Chen, C. X., and R. A. Wolf (1993), Interpretation of high-speed flows in the plasma sheet, J. Geophys. Res., 98(A12), 21,409–21,419, doi:10.1029/93JA02080. Chen, C. X., and R. A. Wolf (1999), Theory of thin-filament motion in Earth’s magnetotail and its application to bursty bulk flows, J. Geophys. Res., 104(A7), 14,613–14,626, doi:10.1029/1999JA900005. Cornilleau-Wehrlin, N., et al. (2001), First results obtained by the Cluster STAFF experiment, Ann. Geophys., 21, 437– 456. Deng, X., M. Ashour-Abdalla, M. Zhou, R. Walker, M. El-Alaoui, V. Angelopoulos, R. E. Ergun, and D. Schriver (2010), Wave and particle characteristics of earthward electron injections associated with dipolarization fronts, J. Geophys. Res., 115, A09225, doi:10.1029/ 2009JA015107, 2010. Dunlop, M. W., A. Balogh, K.-H. Glassmeier, and P. Robert (2002), Fourpoint Cluster application of magnetic field analysis tools: The curlometer, J. Geophys. Res., 107(A11), 1384, doi:10.1029/2001JA005088. Fu, H. S., Y. V. Khotyaintsev, M. Andre, and A. Vaivads (2011), Fermi and betatron acceleration of suprathermal electrons behind dipolarization fronts, Geophys. Res. Lett., 38, L16104, doi:10.1029/ 2011GL048528. Fu, H. S., Y. V. Khotyaintsev, A. Vaivads, M. André, and S. Y. Huang (2012), Electric structure of dipolarization front at sub-proton scale, Geophys. Res. Lett., 39, L06105, doi:10.1029/ 2012GL051274. Gustafson, G., et al. (1997), The electric field and wave experiment for the Cluster mission, Space Sc. Rev., 79, 137–156, 1997. Guzdar, P. N., A. B. Hassam, M. Swisdak, and M. I. Sitnov (2010), A simple MHD model for the formation of multiple dipolarization fronts, Geophys. Res. Lett., 37, L20102, doi:10.1029/2010GL045017. Huang, S. Y., Zhou, M., Deng, X. H., Yuan, Z. G., Pang, Y., Wei, Q., Su, W., Li, H. M., and Wang, Q. Q. (2012a), Kinetic structure and wave properties associated with sharp dipolarization front observed by Cluster, Ann. Geophys., 30, 97-107, doi:10.5194/angeo-30-97-2012. Huang, S. Y., et al. (2012b), Electron acceleration in the reconnection diffusion region: Cluster observations, Geophys. Res. Lett., 39, L11103, doi:10.1029/ 2012GL051946. Hwang, K.-J., M. L. Goldstein, E. Lee, and J. S. Pickett (2011), Cluster observations of multiple dipolarization fronts, J. Geophys. Res., 116, A00I32, doi:10.1029/2010JA015742. Johnstone, A. D., et al. (1997), PEACE: A plasma electron and current experiment, Space Sci. Rev., 79, 351–398. Keiling, A., et al. (2009), Substorm current wedge driven by plasma flow vortices: THEMIS observations, J. Geophys. Res., 114, A00C22, doi:10.1029/2009JA014114. Khotyaintsev, Y. V., C. M. Cully, A. Vaivads, M. André, and C. J. Owen (2011), Plasma jet braking: Energy dissipation and nonadiabatic electrons, Phys. Rev. Lett., 106, 165001, doi:10.1103/PhysRevLett.106.165001. Lui, A. T. Y. (1996), Current disruption in the Earth’s magnetosphere: Observations and models, J. Geophys. Res., 101, 13,067 – 13,088, doi:10.1029/96JA00079.
Nakamura, M. S., H. Matsumoto, and M. Fujimoto (2002a), Interchange instability at the leading part of reconnection jets, Geophys. Res. Lett., 29(8), 1247, doi:10.1029/2001GL013780. Nakamura, R., et al. (2002b), Motion of the dipolarization front during a flow burst event observed by Cluster, Geophys. Res. Lett., 29(20), 1942, doi:10.1029/2002GL015763. Northrop, T. G. (1963), The Adiabatic Motion of Charged Particles, Intersci. Publ., New York. ieroset, M., R. P. Lin, T. D. Phan, D. E. Larson, and S. D. Bale (2002), Evidence for electron acceleration up to 1300 keV in the magnetic reconnection diffusion region of Earth’s magnetotail, Phys. Rev. Lett., 89(19), 195001, doi;10.1103/PhysRevLett.89.195,001. Ohtani, S., M. A. Shay, and T. Mukai (2004), Temporal structure of the fast convective flow in the plasma sheet: Comparison between observations and two-fluid simulations, J. Geophys. Res., 109, A03210, doi:10.1029/ 2003JA010002. Pang, Y., M. H. Lin, X. H. Deng, M. Zhou, and S. Y. Huang (2012), Deformation of plasma bubbles and the associated field aligned current system during substorm recovery phase, J. Geophys. Res., 117, A09223, doi:10.1029/ 2011JA017410. Parks, G. K., et al. (2007), Solitary electromagnetic pulses detected with super-Alfvénic flows in Earth’s geomagnetic tail, Phys. Rev. Lett., 98(26), 265001-1–265001-4. Pedersen, A., et al. (2008), Electron density estimations derived from spacecraft potential measurements on Cluster in tenuous plasma regions, J. Geophys. Res., 113, A07S33, doi:10.1029/2007JA012636. Rème, H., et al. (2001), First multispacecraft ion measurements in and near the Earth’s magnetosphere with the identical Cluster ion spectrometry (CIS) experiment. Ann. Geophys., 19, 1303. Runov A., V. Angelopoulos, M. I. Sitnov, V. A. Sergeev, J. Bonnell, J. P. McFadden, D. Larson, K.-H. Glassmeier, U. Auster (2009), THEMIS observations of an earthward-propagating dipolarization front, Geophys. Res. Lett., 36, L14106, doi:10.1029/2009GL038980. Runov, A., V. Angelopoulos, X.-Z. Zhou, X.-J. Zhang, S. Li, F. Plaschke, and J. Bonnell (2011), A THEMIS multicase study of dipolarization fronts in the magnetotail plasma sheet, J. Geophys. Res., 116, A05216, doi:10.1029/2010JA016316. Santolĺk, O., M. Parrot, and F. Lefeuvre (2003), Singular value decomposition methods for wave propagation analysis, Radio Sci., 38(1), 1010, doi:10.1029/2000RS002523. Sergeev, V. A., Angelopoulos, V., Gosling, J. T., Cattell, C. A., and Russell, C. T.(1996), Detection of localized, plasma-depleted flux tubes or bubbles in the midtail plasma sheet, J. Geophys. Res., 101(10) 817. Sergeev, V., V. Angelopoulos, S. Apatenkov, J. Bonnell, R. Ergun, R. Nakamura, J. McFadden, D. Larson, and A. Runov (2009), Kinetic structure of the sharp injection/dipolarization front in the flow-braking region, Geophys. Res. Lett., 36, L21105, doi:10.1029/2009GL040658. Sharma, A. S., Nakamura, R., Runov, A., Grigorenko, et al. (2008), Transient and localized processes in the magnetotail: A review, Ann. Geophys., 26, 955–1006, doi:10.5194/angeo-26-955-2008. Shiokawa, K., W. Baumjohann, and G. Haerendel (1997), Braking of highspeed flows in the near-Earth tail, Geophys. Res. Lett., 24, 1179. Sonnerup, U. O., and M. Scheible, (1998), Minimum and maximum variance analysis, in Analysis Methods for Multi-Spacecraft Data, edited by G. Paschmann and P. W. Daly, Int. Space Sci. Inst., Bern, 249–270 Tang, C. L. (2012), A plasma flow vortex in the magnetotail and its related ionospheric signatures, Ann. Geophys., 30, 537-544, doi:10.5194/angeo30-537-2012. Wilken, B., et al. (2001), First results from the RAPID imaging energetic particle spectrometer on board Cluster, Ann. Geophys., 10, 1355–1366. Wolf, R. A., V. Kumar, F. R. Toffoletto, G. M. Erickson, A. M. Savoie, C. X. Chen, and C. L. Lemon (2006), Estimating local plasma sheet PV 5/3 from single-spacecraft measurements, J. Geophys. Res., 111, A12218, doi:10.1029/2006JA012010. Yang, J., F. R. Toffoletto, R. A. Wolf, and S. Sazykin (2011), RCM-E simulation of ion acceleration during an idealized plasma sheet bubble injection, J. Geophys. Res., 116, A05207, doi:10.1029/2010JA016346. Zhou, M., et al., (2009a) Observation of waves near lower hybrid frequency in the reconnection region with thin current sheet, J. Geophys. Res., 114, A02216, doi:10.1029/2008JA013427. Zhou, M., M. Ashour-Abdalla, X. Deng, D. Schriver, M. El-Alaoui, and Y. Pang (2009b), THEMIS observation of multiple dipolarization fronts and associated wave characteristics in the near-Earth magnetotail, Geophys. Res. Lett., 36, L20107, doi:10.1029/2009GL040663 Zhou, M., M. Ashour-Abdalla, X. Deng, M. El-Alaoui, R. L. Richard, and R. J. Walker (2011), Modeling substorm ion injection observed by the THEMIS and LANL spacecraft in the near-Earth magnetotail, J. Geophys. Res., 116, A08222, doi:10.1029/2010JA016391.
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