Dynamics of Thin Current Sheets : Cluster Observations




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Dynamics of Thin Current Sheets : Cluster Observations


W. Baumjohann , A. Roux, J. Birn, R. Nakamura, O. Le Contel, M. Hoshino, A.T.Y. Lui, C. Owen, J.A. Sauvaud, A. Vaivads, D. Fontaine, A. Runov


3. Description of events

Thin current sheets with a thickness comparable or less than the Cluster tetrahedron scale are observed under different conditions. Here we describe two current sheet observations from the Cluster 2001 tail period when the tetrahedron scale was about 2000 km and the spacecraft were near apogee in the premidnight sector (Figure 7). The first event, between 2040 and 2200 UT on September 7, 2001, consists of two different types of current sheet: (a) a thin current sheet during a quiet interval, (b) a current sheet during a small substorm. The second event shows (c) a current sheet with a flow reversal and hence a possible X-line signatures during a storm-time substorm between 0920 and 0955 UT on October 1, 2001., In the following we briefly describe the global context of the events in subsection 3.1 and highlight the specific observed features for these events in 3.2, and - 3.4. fFinally, summarize the key points of the observations are summarized in 3.35.




Figure 7: Cluster location for the September 7 and October 1 events (a-c) and tetrahedron configuration for September 7 (d-f) and October 1 event (g-i).


3.1. Description Overview of the selected events


3.1.1. September 7th 2001


The September 7th event occurred just before a change from a northward to a southward solar wind Bz component, which happened at the end of the selected time interval, around 22:00 UT. The Image and Polar spacecraft (data not shown) give evidence for an auroral bulge developing near Cluster footprint, at about 21:29. This bulge has a small extension in latitude, around 70° MLT. Hence event 1 is not a fully developed substorm; it corresponds to a localized (in latitude) perturbation propagating eastward at ~50km/sec.

Figure 8 shows spin averaged field and particle data. Three components of the magnetic field in GSM coordinates obtained by the FGM magnetometer [Balogh et al., 2001] are shown in Figures 8a–8c. The DS2 component of the electric field data from EFW [Andre et al., 2001] is shown in Figure 8d (the DS2 component is approximately parallel to -Y in GSE coordinates). Here we changed the sign of the DS2 component so that it is close to the dawn-to-dusk electric field Ey). X and Y components of the proton bulk flow from the CIS/CODIF experiment [Rème et al., 2001] are shown in Figures 8 e and f. X and Y components of the current density calculated from the linear curl estimator technique [Chanteur, 1998] using FGM data are shown in Figure 8g. It should be kept in mind that Cluster estimates the current density on the averaged scale of the tetrahedron, i.e., 2000 km. Finally, panels h and i show the parameter b for protons and oxygen, respectively. Values of b up to 100 are measured for protons and b>1, for oxygen. Yet, in spite of this high b, thin CS remains stable and quiet.

Quiet CS crossing

Between 2040-2130 UT, the Bx components vary from ~ -15 nT to +18 nT (panel a), hence the 4 S/C cross the magnetic equator. During this crossing, the CS is relatively quiet; the dawn-dusk electric field (panel d) and the ion flows in the x direction (panel e) are weak and magnetic fluctuations are small (panel a, b, and c). The most rapid variation is along the z direction. Then the CS thickness can be estimated from the difference between the values of Bx, measured at the 4 S/C locations; this is done in section 3.2.2. Around 2100 UT S/C3, which is at a lower Z than its 3 companions, is located at the CS boundary, while S/C1,2 and 4 are located close to the magnetic equator. Hence the half-thickness of the current sheet should be of the order of the distance, projected along Z, between S/C3 and the others: ~1500 km. Knowing CS thickness one can estimate the current density, Jy~DBx/m0H ~10 nA/m², consistent with the value calculated from curlB (panel g). For this event, however, the characteristic spatial scale of the current sheet is comparable to the distance between the satellites. Therefore, the current density obtained from the curlometer method can only be considered as a rough estimate (in fact an underestimate). During this quiet CS crossing the ion flow velocity is sufficient to account for the estimated Jy. Indeed for N~1/cm³, and Vy~50km/sec. (estimated from CIS) we find Jy~8nA/m². Hence during this quiet CS crossing the current is essentially carried by ions.

Active CS crossings

From 2130 to 2142UT, the averaged value of Bx, for S/C3, varies from positive to negative. Large amplitude oscillations on By and Bz are superimposed; hence the current density structure is three-dimensional. On the other hand, the fluctuations in Bx , detected by S/C1, 2 and 4, are weaker, and Bx remains close to the lobe value (~20 nT). Therefore S/C1, 2 and 4 are located outside the CS, or close to CS boundary layer, at least till 2146. Thus, between 2130 and 2146, the CS thickness must be smaller than the distance between SC3 and its companions projected along Z (~1500 km). After 2145 Bx(1,2,3) decrease, in average, and oscillate, while Bx(3) becomes negative. Hence the CS thickness becomes comparable to the distance between the S/C. Using the value of Bx, normalized by the lobe value (~20nT), as a proxy, to estimate how far is a given S/C from the center of the CS, we find that large ion flow velocities (Vx) are found close to the equator. The converse is not true; being at equator does not warrant the observation of a fast ion flow.

Notice that large amplitude variations in Ey (figure 8, panel d) are also observed.

Surprisingly the ion velocity in the y direction, which was positive (as expected) before 2130 UT, becomes negative (eastward) around 2135 UT, and sometimes reaches -200 km/s. The westward current must be carried by electrons moving eastward, faster than ions; this is further discussed in subsection 3.2.2. Asano et al (200?) have also given evidence for westward currents carried by electrons, in the case of a GEOTAIL event.

Thick CS

After 21:52 UT, all s/c measure almost the same Bx~0 indicating that the spatial scale of the CS is now much larger than the distance between the satellites. During this period, the current density Jy (panel g) is smaller than before. Note that after 21:55 UT, a short lasting thinning of the CS occurs again, while enhanced Vx are detected.




Figure 8: (a,b,c): spin resolution data from GSM components of the magnetic field, (d) DS2 component of the electric field, (e,f) GSM X,Y components of the proton bulk velocity, (g) current density determined from the magnetic field, (h,i) proton and oxygen beta. For the particle and field plots, profiles for Cluster 1, 2, 3, 4 are plotted with black, red, green, and blue lines. Black and red lines in the current density plots correspond to X and Y components.


3.1.2. October 1 event

Between 6 and 16 UT on October 1 a series of semi-periodic substorms took place. The interval has been identified as a "saw-tooth" event [Henderson et al., reference ????] during a large storm with a minimum SYM-H of –150 nT at 0830 UT. The interplanetary magnetic field (IMF) was directed southward during the whole interval and ranged between Bz = -15 and -2 nT. In this study we examine Cluster observations during the second substorm interval when a LANL geosynchronous satellite (1991-080) detected multiple dispersionless electron and ion injections starting at 0926 UT and a large substorm with AE >1000 nT took place. As shown in Figures 7a-c, Cluster was located at XGSM = -16.4 RE, near ZGSM = 0 in the pre-midnight magnetotail. The Cluster tetrahedron configuration at 0920 UT is shown in Figure 7g-i.

Figure 9 shows spin average field and particle data in same format as Figure 8 except for the two bottom panels. The sum of particle and magnetic pressure is shown as a thick line and magnetic pressure is shown as thin line in Figure 9h. Here the particle pressure was calculated using both proton and oxygen. We converted the pressure value into an equivalent magnetic field value, in nT, so that the likely lobe field strength can be inferred from the total pressure. The ratio between oxygen and hydrogen pressure is shown in Figure 9i.

As can be seen from Bx (Figure 9a) and from the relative Cluster positions (Figures 7e and f), the ordering of decreasing Bx values, i.e., Cluster 1, then 2, then 4, and finally 3, is consistent with the relative order of the Cluster positions from north to south most of the time, except for a short-time perturbation lasting less than a minute. The tail current sheet orientation is therefore approximately perpendicular to ZGSM and BX gives a good indicator of the location relative to the equator on longer time scales. Cluster was initially located close to the northern lobe. Because of the high solar wind pressure and larger flux in the tail during a storm, the lobe field value during the initial interval is expected to be larger than 40 nT, as can be seen in the BX component 0930 and 0933 UT when Cluster enters the lobe between 0930 and 0933 UT. After 0937UT, Cluster experienced several neutral sheet crossings until 0953 UT, when all the spacecraft stayed in the plasma sheet. The first signatures of substorm disturbance at Cluster are the magnetic field fluctuations accompanied by tailward proton flow and encounter of the plasma sheet starting at 0926UT, which corresponds to the time of the geosynchronous injection. After the plasma sheet encounter the total pressure started to decrease with some fluctuations and became 30 nT by 0950 UT and stayed nearly the same value afterwards. This negative trend in the pressure is a typical manifestation of unloading in the midtail region during substorm expansion phase. As is often the case for a storm, the oxygen contribution is significant, as shown in Figure 9i. Particularly after 0944UT the pressure is dominated by oxygen. This corresponds to the time interval of the thin current sheet as will be described later.




Figure 9: Same format as Figure 8 except for the bottom two panels, which are: (h) total and magnetic pressure, and (i) ratio between Oxygen and hydrogen pressure. In the pressure plot the total and the magnetic pressures are plotted with thick and thin lines, respectively.


There were mainly two periods of enhanced tailward/Earthward proton flows during the interval (Figure 9e).

The first one is the tailward flow between 0926 and 0930 UT near the geosynchronous injection time. Associated with this first tailward flow period (~0927), a sharp enhancement is BY and a positive, then negative disturbance in BZ of about 30 s is observed, which is a typical signature of a flux rope. The disturbance is accompanied by a large spike in the current density. This current is directly parallel to the ambient field flowing out from the ionosphere. Such <30 s structures with BZ reversals and BY perturbations are identified also during the next flow enhancement interval such as at 0936, 0939, 0942, 0947 UT.

The second flow interval is from 0937 UT and continues until 1004 UT (not shown) with several flow reversals from tailward to Earthward and vice versa on a timescale of >10 minutes containing also rapid fluctuations. The BZ profile in Figure 9c also shows corresponding sign reversals on longer and shorter time scales: i.e., negative values on average, during predominantly tailward flow period and positive value mainly during Earthward flow periods, overlapped with faster fluctuations. The overall relationship between BZ and flow, on greater than 10-min scale, is in a sense of producing dawn-to-dusk –VxB electric field. Consistently, the dawn-to-dusk electric field from EFW (Figure 9d) became enhanced during the flow intervals exceeding several mV/m (up to 10 mV/m). Between 0943 and 0958 UT, even stronger electric fields were observed associated with neutral sheet crossings. Detailed field and plasma signatures between 0946 and 0951 UT, when strong electric fields, flow reversals and neutral sheet crossings were observed, will be discussed in section 2.2.1.

Starting around 0937 UT, when Cluster encountered the plasma sheet and observed tailward flow, persistent oscillations also started in the Bx profile (Figure 9a) with a time scale of about 2 min. Based on minimum variance analysis of each crossing and timing analysis of the four spacecraft, these oscillations are due to a wavy current sheet. Assuming that the vector identified from the current sheet crossings represents the motion of the current sheet, it is expected that the motion of the wavy current sheet is mainly duskward with a speed of 100-300 km/s. From this speed and the time scale of 2 min recurrence it is estimated that these wavy structure has a spatial scale of 2-6 RE. It should be also noted that the interspacecraft difference in Bx stands out during this period (Figure 9a). The profile shows that the half thickness of the current sheet is expected to be smaller than the Cluster tetrahedron. Duskward current density obtained from the Cluster increases up to 20 nA/m2. .

Another important observation for this is the ion composition. During the thin current sheet interval, 0945- 0955UT, pressure as well as density was dominated by O+ than H+ (Kistler et al., 2005), which was interpreted as being due to storm-time ion outflow. In this O+ ions dominated thin current sheet, the O+ were observed to execute Speiser-type serpentine orbits across the tail and were found to carry about 5-10\% of the cross-tail current (Kistler et al., 2005). Detailed analysis of the distribution function showed separate O+ layers above and below the thin current sheet (Wilber et al., 2004).


3.2. Specific Crossing of a quiet CSperiods; September 7th, 2001, ~2100 UT

3.2.1. September 7: crossing of a quiet CS

Figure 10 (panels a,b, and c), shows that Bx changes from ~-20nT to +20nT, while By and Bz (plotted here with a different scale) and their fluctuations, are small (few nT). The current densities Jy, estimated by various methods are shown in panel d. We have fitted the Bx component of the magnetic field measured by S/C 1 and 3 with a “Harris sheet model” (Harris, 1962) defined by Bx = BL tanh ((z-z0)/H) where z0 and H represent the center and the half-thickness of the current sheet, respectively. BL is obtained either from direct measurement in the lobe region (if the S/C happens to be located in the lobes) or by assuming the equilibrium of the vertical pressure within the plasma sheet (see also Kivelson et al. 2005). Once these parameters are determined, we compute and plot the Harris current density at the equator (thick pink line), and at the location of S/C 3 (thick green line). We also plot the current density estimated from curlB (thin pink line) and the contribution of the ions computed from CIS measurement on S/C 3 (thin green line).

We find that Jy is maximum near the center of the CS and that Jymax ~10 nA/m². The ion current is also quite close to the other estimates, which suggests that during the quiet crossing most of the current is carried by ions. The contribution of electrons to the current (not shown here) is indeed small. Jx (not shown here) is much smaller than Jy (panel d).

The fit with a Harris sheet has also been used to estimate the half-thickness of the CS (H). Figure 10e shows that, around 2100, H~2000km. During this period all the S/C are located inside the CS, hence the fit is good. The increases in H found around 2050 and 2120 are probably not reliable, because the S/C get too close to the CS boundary. Figure 10f shows the position of the CS center (z0), and the estimated location of its lower (z0-H) and upper (z0+H) boundaries, deduced from the same fitting procedure. It tells us that the CS moves southward at ~5.5km/sec, in the S/C frame. Cluster spacecraft move slowly southward (~2km/sec.); thus the CS moves at ~7.5km/sec.. The motion of the CS can also be inferred from the time (~10mn) it takes to cross the CS (2x2000km). With these numbers we find that the CS center moves southward at ~7km/sec; consistent with previous estimate. Noticing that C1, C2, and C4 are approximately at the same ZGSM, the delay between the crossing of the center of the CS can be used to characterize the flapping of the CS; we find that this flapping oscillation moves radially tailward at about 200km/sec.

In summary a relatively thin CS (half thickness~2000 km) can be stable over long time periods. For N~1/cm³, Vthi~10³ km/sec, and FH+~0.15 Hz (lobe field), we get the H+ ion Larmor radius and ion inertial length i~L~10³ km; twice smaller than the CS half thickness. As already mentioned, while describing Figure 8, magnetic fluctuations are weak and no fast flow is observed during the crossing of this quiet but relatively thin CS. the slow flapping oscillation does not affect the stability of the CS.




Figure 10: Quiet CS crossing. Notice that By and Bz are not at the same scale as Bx; most of the magnetic field variations are on Bx, as expected for a 1D CS. Panel d shows Jy estimated by 3 different methods (see text) . Panel e and f show the half thickness (H) of the CS and the location of its center (Z),see text.


3.2.2 : Crossings of an active CS, September 7th, 2001, 2130-2155 UT

3.2.1. Magnetic fields and current densities

The four top panels (a, b, c,d and e) of figure 11 show again the Bx, By, Bz, the emodulus of B, and Ey (more precisely the -SR2) components, with an enlarged scale. Magnetic and electric field data are now displayed with full resolution (22.4 points/sec for B and 25 points/sec for Ey). The motion of the CS, as inferred from the averaged variations of Bx, is now upward. Panel i shows Jy, estimated from curlB. Till {2133} curlB cannot be estimated because all the S/C are still located outside the CS. After 2133 the current density Jy estimated from the Harris fit and the current density computed from curlB agree quite well. As discussed before (section 3.1.1), between 2133 and 2145 only S/C3 is inside the CS and detects large amplitude fluctuations of Bx (with ~1mn quasi–period). The large amplitude fluctuations observed on Bx(3) can be due (i) to a modulation of the total current Iy below the S/C, (ii) to a flapping of the CS (with amplitude of D), or (iii)to a modulation in the CS thickness (H). Bx at S/C1,2,4 (outside the CS) being almost constant, interpretation (i) is ruled out. Thus the CS thickness is modulated (symmetric mode), or the CS flaps up and down (anti-symmetric mode), or a mixture of both. Whatever the mode, the fact that Bx(3) can be negative, while Bx(1,2,4) remain approximately constant and positive, indicates that H0+H and z0-H (displayed in the last panel of Figure 11) provides a proxy for the accuracy of the estimate of z0 and H. As long as one of the edge value, z0+H here, remains constant while z0 and the location of the other edge (z0-H here) undergo large variations, z0 and H are not correctly estimated. For instance, around 2135, H is largely overestimated and the largely negative value of z0 should not be trusted. More generally, before 2145, z0+H varies much less than z0 and z0-H, which indicates that the Harris fit overestimates H. Yet we can infer that between 2133 and 2145, H0 and symmetric variations of z0+H and z0-H. Between 2145 and 2152 we find that H~ 1500-2000 km. After 2152, H rapidly increases; H>>D. At the scale of the tetrahedron, the magnetic energy has been dissipated since B is quasi-null on all spacecraft. There are no longer large flow velocities. Thus the large amplitude quasi-periodic (60sec.) fluctuations are strongly confined in the CS and they develop only when the CS is thin, or very thin (2133-2145). The thickening of the CS, and therefore the local dissipation of the magnetic energy, starts around 2145. After 2152, the CS gets very thick (~2Re); the magnetic energy has been dissipated and the transport of particles stops by 2154 UT.

When the CS is thin or very thin, the fluctuations of By and Bz are quite large, in particular (but not only) on S/C3. These fluctuations are interpreted as signatures of field aligned currents (see section 4.2), when S/C are off-equator. Panel h and i show Jx and Jy, estimated from curlB. Firstly, we observe a signature of positive parallel current (Jx>0) between 2129-2130 associated with Vx<0 (tailward) and Vy<0 (dawnward), for electrons as well as for ions (see also Le Contel et al. [2002] and references therein), which suggests that the active region is localized earthward or westward of the S/C (see discussion in section 4). In this current density structure the current is essentially parallel to B, and the spatial scale is comparable or smaller than D, as can be seen from the By and Bz profiles on S/C 3. Hence the current density (Jx~ -5 nA/m2) is probably underestimated. Thus both Jy and Jx are likely to be underestimated, at least during the first period (2133-2145). The fluctuations of Jx (panel g) are as large as the fluctuations of Jy (as expected from divJ=0). Thus, unlike the previous crossing (~2100) the structure of the CS is now 3D. The signatures of the FAC are seen on By, as expected, but also on Bz, which indicates that they have a small scale in the Y direction; they correspond to filamentary structures as will be shown in the next two figures. . . We defer further discussion to section 4.

Notice that shorter period fluctuations (T~1-10sec) are superimposed on the ~60sec fluctuations described above. Their amplitudes are quite large (~few nT, ~1-20 mV/m), but still smaller than long period oscillations, at least for the magnetic components. We do not further discuss about these “high frequency” oscillations here.
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