Current sheet structure near magnetic X-line observed by Cluster

Authors


Abstract

[1] During the interval 0947–0951 UT on 1 October 2001, when Cluster was located at XGSM = −16.4 RE near ZGSM = 0 in the pre-midnight magnetotail, the Cluster barycenter crosses the neutral sheet four times. High speed proton flow, with reversal from tailward to Earthward, was detected during the crossings. Using a linear gradient/curl estimator technique we estimate current density and magnetic field curvature within the crossings. These observations exhibit the tailward passage of an X-line over the Cluster tetrahedron. These current sheet has a bifurcated structure in the regions of tailward and earthward flows and a flat and/or slightly bifurcated thin current sheet in between. A distinct quadrupolar Hall magnetic field component was observed.

1. Introduction

[2] Detection of a reconnection region and studying its current/plasma sheet structure is difficult using single spacecraft measurements. Cluster, being a four spacecraft constellation, offers a possibility to study the spatial structure of the plasma sheet near and/or within the reconnection region.

[3] The standard macroscopic picture of magnetic reconnection includes an X-type magnetic neutral line, cold plasma inflow toward the neutral line and high speed accelerated plasma outflow. The outflow region is bounded by branches of a bifurcated current sheet. This scheme is supported by MHD simulations [e.g., Ugai and Tsuda, 1977; Sato and Hayashi, 1979] and analytical solutions [e.g., Semenov et al., 1998].

[4] As it was proposed by Sonnerup [1979], ions and electrons move differently around the X-line, and this decoupling results in a Hall current system near the X-line. Terasawa [1983] found the Hall component of the magnetic field in a tearing mode stability analysis. It was also shown in Hall-MHD [e.g., Lottermoser and Scholer, 1997], hybrid [e.g., Lottermoser et al., 1998; Nakamura et al., 1998] and PIC [Hesse et al., 2001; Pritchett, 2001] simulations that a magnetic reconnection produces a quadrupolar out-of-plane component of the magnetic field. The characteristic scale of this structure is of the order of the ion inertial length. Measurements on-board the Geotail [Nagai et al., 2001] at X ∼ 25–30 RE and Wind [Øieroset et al., 2001] (X ∼ 60 RE) showed the quadrupolar Hall magnetic field near the magnetic reconnection region. But it was not possible to estimate the characteristic scale of the Hall region using single spacecraft measurements.

[5] The purpose of this paper is to present multi-point observations of the magnetic reconnection region, detected by Cluster on 1 October 2001. Four-point measurements allow analyzing the current sheet structure in the reconnection region and estimating the characteristic scales for different parts of this region.

2. Observations and Data Analysis

[6] At 0947-0951 UT on 1 October 2001, Cluster was located at [−16.4; +8; 0.5] RE, GSM coordinates are used overall this paper. The Cluster tetrahedron configuration is shown in Figures 1a and 1b. During a half-hour long interval 0930–1000 UT Cluster repeatedly crosses the neutral sheet, located approximately in the ZGSM = 0 plane. FGM [Balogh et al., 2001] 1-s resolution data for 0947–0951 UT are shown in Figures 1c–1e. It is seen from FGM data and from the relative Cluster positions that during 0947–0951 UT Bx from s/c 1 is larger than Bx from the more southern s/c. Except for a short-time perturbation at ∼0947:40–0947:45 UT, the southernmost s/c 3 detects the smallest Bx. The magnetic field gradient is thus mainly directed along ZGSM, and the GSM system is suitable for studying this event.

Figure 1.

Cluster tetrahedron configuration (a,b) and measurements: GSM-components (c–e) of the magnetic field from Cluster/FGM, 1-s resolution, XGSM (f) and ZGSM (g) components of perpendicular proton bulk velocity vector from Cluster/CIS-CODIF, spin resolution, versus UT.

[7] Data from the CIS experiment [Rème et al., 2001] in the time interval 0947-0951 UT show a reversal of the proton bulk flow from tailward to earthward. Figures 1f, g show the XGSM and ZGSM components of the perpendicular velocity vector Vp = b × (Vp × b), where b = B/∣B∣, and Vp is proton bulk velocity from CIS/CODIF. Spin-averaged (∼4, s) resolution data are used. Maximum (minimum) proton bulk velocity value from s/c 1, 3, 4 are ∼900 (−700) km s−1 for the Earthward and tailward flows, respectively, which is ∼0.5 VA, with VA the Alfvén speed in the lobe (B ∼ 25 nT, Np ∼ 0.1 cm−3, according to Cluster 1).

[8] During the interval 0947–0951 UT Cluster 2, 3, 4 cross the neutral sheet four times. Cluster 1 stays in the northern hemisphere (NH) in close vicinity of the neutral sheet. During the first crossing (denoted as “A”) Cluster 2, 3 and 4 traverse the neutral sheet from NH into the southern hemisphere (SH). They detect fast tailward proton bulk flows concentrated near Bx ∼ 0. This tailward flow follows a large amplitude bipolar variation of Bz, which is the signature of a plasmoid. The value of Bz measured by s/c 2, 3 and 4 during the tailward flow interval A are mostly negative with minima of −9, −22, −13 nT, respectively.

[9] During the next crossing, marked “B”, s/c 2, 3 and 4 return from SH to NH. It is clearly seen from the Bx traces of the spacecraft that the current sheet becomes thinner during the traversal from A to B. During interval B, the X-component of V is about zero. Cluster 1, staying in NH, detects a negative Z component Vz, while s/c 4 in SH sees a positive Vz in between A and B. The Bz components at s/c 1, 2, and 4 are about zero. In contrast, Bz ∼ 5 nT at s/c 3 with a peak value of 16 nT at 0948:50 UT.

[10] During interval C all four Cluster spacecraft cross the neutral sheet from NH to SH and detect fast Earthward proton bulk flows, focused at Bx ∼ 0. The Bz-components are all positive with a tendency to grow. The maximum value of Bz is ∼5 nT. The Z-component of the proton bulk velocity s/c 1 and 4 changes from negative to positive. The next SH → NH crossing (D) is characterized by a large positive Vx and significant negative Vz, and Bz ∼ 5–8 nT.

[11] The correlation between the magnetic field measurements of the four spacecraft was high (correlation coefficient 0.82 < R < 0.95). Hence all spacecraft stay in the same physical region, and the linear gradient and curl estimator technique [Chanteur, 1998] can be applied. Figure 2 shows the magnetic field components in the tetrahedron barycenter (upper panel), the curl B components, X and Y GSM components of the magnetic field curvature vector curv B = (b · ∇)b, magnetic field divergence div B, and X- and Z-components of the bulk proton flow from the mean value of the s/c 1, 3 and 4 CIS/CODIF measurements. The y-component of curl B has a maximum value of ∼16–20 nT/103 km (jy ∼ 12–15nA m−2) in the transition region between the tailward and earthward flow regions. There are significant peaks of in-plane (X and Z) components of the curl B over crossings A and B, which may be interpreted as Hall-current branches: positive X- and negative Z-components in the NH → SH crossing during tailward flow (A) and negative X, and weak positive Z components of the current density in the crossings C and D associated with strong earthward ion flow (see the schematic representation of the Hall current system by Nagai et al. [2001]). It should be noted that div B, which is a measure of the accuracy of the calculation, ranges between ±5 nT/103km, except for a peak up to −10 nT/103 km at 0948:40 UT.

Figure 2.

Cluster measurements at the tetrahedron barycentre. From top to bottom: components of the magnetic field, components of curl B vector, the magnetic field divergence, X and Y components of the magnetic field curvature vector, and proton bulk velocity as a mean value of s/c 1, 3 and 4 measurements versus UT.

[12] The X-component of the magnetic field curvature dominates all four neutral sheet crossings. Moreover, the tailward flow (A) is associated with a large negative X-component in the magnetic field curvature, while during the crossings B, C and D the X-component of the curvature is positive. Thus, the magnetic field loop associated with tailward proton flow is open in the tailward direction, and the loop associated with earthward flow is open toward Earth. These observations can be interpreted as the tailward passage of an X-line region over Cluster. The nonzero Y component of the magnetic curvature vector probably results from the small tilt of the current sheet with respect to the ZGSM = 0 plane. The Z-component of the curvature vector (not shown) is negligibly small.

[13] CIS/CODIF onboard s/c 1, 3 and 4 detected tailward moving protons of energy 1–10 keV (s/c 1) and ∼10 keV (s/c 3 and 4) during crossing A, 0.1–1 keV for s/c 1, which stays at the level of Bx ∼ 20 nT, and ∼1 keV for s/c 3 and 4 during crossing B, and ≥10 keV during crossings C and D (not shown). These observations conform to ion flow in the vicinity of an X-line: cold (lobe) plasma inflow (B) and accelerated plasma outflow (A, C, D).

[14] Using the calculated curl B, we analyzed the current sheet structure near the X-line. Figure 3 shows the y-component of curl B, which results mostly from the magnetic field gradient along ZGSM, versus Bx in the tetrahedron barycenter (Bxc). During crossing A, the Y-component of the current density associated with the tailward ion flow tends to decrease when Bxc → 0. After jumping to a large value, which probably is a temporal effect, jy ∼ (curl B)y has a local minimum near Bxc ∼ 0–5 nT in crossing B (Figure 3, thick curve, marked by bullets). It should be noted that the estimate of curl B during the interval 0948:25–0948:35 UT, when s/c 2, 3, and 4 are in SH, and s/c 1 stays in NH, is of minimum accuracy. The linear estimate of the magnetic field divergence for this interval yields absolute values of 1–5 nT/103km, an order of magnitude less then the estimate of curl By, but comparable with the difference between the maximum and minimum values of jy in crossing B. Thus, the current density during this interval has a rather flat distribution with a tendency to decrease when Bx → 0.

Figure 3.

Current sheet structure in the vicinity of the X-line: the Y-component of curl B (cross-tail current density) versus Bx in the tetrahedron barycentre.

[15] The value of jy drops to a smaller value between crossings B and C and exhibits a flat profile (curve marked by “+” sign) during crossing C. This is associated with earthward proton flow. In crossing D (curve marked by “x”) the jy profile has a pronounced minimum at Bxc ∼ 0.

[16] Figure 4 shows scatter plots of the out-of-plane By component versus Bx for crossings A, C and D. During the NH → SH crossing A, By changes from being positive at Bx > 0 (NH) to negative at Bx < 0 (SH). The crossings C (NH → SH) and D (NH → SH) are characterized by positive By at Bx > 0 and negative By at Bx < 0. These results are consistent with the presence of Hall currents. A sketch of the reconnected current sheet structure including the Hall magnetic field near the X-line is given in the bottom panel of Figure 4.

Figure 4.

The out-of-plane Hall magnetic field component By versus Bx over neutral sheet crossings A, C and D (upper panel), and a sketch of reconnected current sheet structure with Hall currents. ⊙ and ⊕ denote the By direction; dotted line shows schematic representation of the Cluster barycentre trajectory.

3. Discussion

[17] We interpret the Cluster observations of 1 October 2001 at 0947–0951 UT in terms of an X-line in tailward motion past the spacecraft. The Cluster four-point measurements allow us to calculate the magnetic field curvature and curl and to analyze the current sheet structure near the X-line. The actual value of the current density j = μ0−1curl B may be underestimated because the inter-spacecraft separations are too large in order to detect any small-scale current structures.

[18] The current sheet profiles in the crossings A and D are consistent with a bifurcated current structure in both reconnection outflow regions, as predicted by MHD/Hall-MHD and kinetic simulations of the reconnection process, as well as some analytical solutions. A double-peak current structure had already been detected in the distant tail by Hoshino et al. [1996] from the statistical analysis of Geotail measurements. It was interpreted there in terms of a pair of Petschek-type shock waves formed in localized reconnection. Asano [2001] showed that the cross-tail current has a bifurcated structure in the post-plasmoid plasma sheet in agreement with simulation results of Arzner and Scholer [2001]. Recently, Nakamura et al. [2002], Runov et al. [2002], and Sergeev et al. [2002] observed bifurcated current sheets in the Cluster observations. In contrast to this paper, in those cases the bifurcation could not be directly attributed to magnetic reconnection.

[19] The thick curve, corresponding to crossing B in Figure 3 indicates that the current density in this crossing is higher than during the other crossings. This intense current is localized in the Bx interval −10 nT < Bx < 12 nT. From the gradient estimate one finds a rough value of λ ∼ 500–600 km for the half-width of the current, in agreement with the estimate obtained from the fit to a Harris-type model [Nakamura et al., 2002]. We may therefore conclude that the Cluster observations support that the reconnection region at 0947–0951 UT has the structure sketched in Figure 4 and exhibits two outflow regions that are bounded by bifurcated currents, and a comparably thin current sheet in the center. The TCS was observed by Cluster during the 30 s long interval 0948:07–0948:40 UT. Referring to the average value of 〈Vx〉 ≈ −200 km s−1 during this interval we get as an estimate of the length of the TCS along X a value of ∼6000–7000 km, about 10 ion Larmor radii (calculated for 10-keV ions in a 20 nT field). It should be noted that the structure of the TCS differs from a Harris sheet. The current density profile has a local minimum at Bx ∼ 0.

[20] The Y-component of the magnetic field has a quadrupolar spatial distribution. This behavior of By near the magnetic X-line is predicted by Hall-MHD, hybrid and kinetic simulations of the reconnection process and is an indication for the magnetic X-line being detected [e.g., Nagai et al., 2001]. The observations allow for an estimate of the ion inertial length di, using the calculated gradient of the magnetic field. One finds that di ∼ 1742, 1451, and 2540 km for crossings A, C and D, respectively.

4. Concluding Remarks

[21] Magnetic reconnection relies on microscopic aspects of magnetic field and particle dynamics. In the first place it is the dynamics of the electrons that determines the reconnection process [for a recent account see e.g., Sitnov et al., 2002]. Decoupling of the electron motion from ions takes place on the ion inertial scale near the X-line. This decoupling gives rise to Hall currents and generates a Hall By field component. It thus can be detected in a comparably large volume, while the decoupling of the electrons from the magnetic field takes place on the electron inertial scale and thus usually escapes observation. One should, however, keep in mind that the Hall field is but an indication of decoupling of electron and ion dynamics. In the reconnection process itself it plays a little role as it merely rotates the total field. In this sense the characteristic ion and electron inertial lengths are the crucial parameters of the physical processes in the reconnection region. In our analysis of Cluster X-line observations on 1 October 2001, Cluster was able to resolve some of the fine structure of the reconnection region and to determine these scales. The accuracy of the estimates of characteristic lengths as well as the scales of the gradient and curl is still relatively low. It will be essentially higher with upcoming smaller inter-spacecraft separation. Nonetheless, for the event under consideration in this communication we were able to draw a consistent picture of the structure of the tail reconnection region in relation to currents, flows, and the geometry of the magnetic field.

Acknowledgments

[22] We thank H.-U. Eichelberger, G. Laky, and Y. Bogdanova for helping Cluster data analysis, and T. Terasawa, V. Sergeev, M. Sitnov, V. Semenov, T. Nagai, and M. Fujimoto for helpful discussion and comments. We acknowledge the CSDS and the World Data Center for Geomagnetism in Kyoto.

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