Detection of a separator line that connects magnetic nulls and the determination of the dynamics and plasma environment of such a structure can improve our understanding of the three-dimensional (3D) magnetic reconnection process. However, this type of field and particle configuration has not been directly observed in space plasmas. Here we report the identification of a pair of nulls, the null-null line that connects them, and associated fans and spines in the magnetotail of Earth using data from the four Cluster spacecraft. With di and de designating the ion and electron inertial lengths, respectively, the separation between the nulls is found to be ~0.7di and an associated oscillation is identified as a lower hybrid wave with wavelength ~ de. This in situ evidence of the full 3D reconnection geometry and associated dynamics provides an important step toward to establishing an observational framework of 3D reconnection.
Deep Dive into Satellite Observations of Separator Line Geometry of Three-Dimensional Magnetic Reconnection.
Detection of a separator line that connects magnetic nulls and the determination of the dynamics and plasma environment of such a structure can improve our understanding of the three-dimensional (3D) magnetic reconnection process. However, this type of field and particle configuration has not been directly observed in space plasmas. Here we report the identification of a pair of nulls, the null-null line that connects them, and associated fans and spines in the magnetotail of Earth using data from the four Cluster spacecraft. With di and de designating the ion and electron inertial lengths, respectively, the separation between the nulls is found to be ~0.7di and an associated oscillation is identified as a lower hybrid wave with wavelength ~ de. This in situ evidence of the full 3D reconnection geometry and associated dynamics provides an important step toward to establishing an observational framework of 3D reconnection.
In general, 3D magnetic reconnection occurs on a separator line that is analogous to a two-dimensional (2D) X-line. The legs of this line, called separatrices, correspond to fans ( Σ -surfaces) bounded by spines ( γ -lines) that emerge from the nulls [1][2][3][4] . 3D reconnection models are fundamentally based on chains of A-B null pairs [1][2][3][4][8][9] . [The classification of a null depends on whether the field along the separator line converges (A) or diverges (B) from the null point, as shown in Figure 1d.] Identification of A-B null pairs and identification of the separator and associated structures such as spines and fans is a fundamental to increasing our understanding of 3D reconnection.
Identification of null-null lines and their neighbouring 3D structure and associated dynamics has been attempted for solar coronal plasmas [10][11] . Recently, Xiao et al. successfully identified an isolated magnetic null point related to a reconnection region in the magnetotail of the earth 9 . These authors made use of measurements provided by the Cluster mission 12 , which provides data from four similarly instrumented spacecraft that form a tetrahedron in space, thereby providing unique opportunities to detect small-scale 3D plasma structures. In their analysis, these authors applied the Poincaré-Index method [13][14] to infer the presence of a true magnetic null point.
Here we analyze an event on October 1, 2001 between 09:36 UT and 09:55 UT during which time the Cluster spacecraft meandered several times around a reconnection region in the magnetotail, near ~ (-16.3, 7.9, 0.9) R E GSM (in geocentric solar magnetospheric coordinates). As shown in Figure 1a, the four spacecraft were separated by less than 2250 km. Four second average data from the Fluxgate Magnetometer (FGM) 15 for the magnetic field (B) and the Cluster Ion Spectrometer (CIS) 16 , for the plasma density (N), and velocity (V) during the interval 09:45-09:51 UT are plotted for spacecraft C4 in Fig. 2a-2c. The event has previously been extensively studied assuming a two-dimensional structure for reconnection [17][18][19][20] . A tailward passage of the X-line with respect to the Cluster tetrahedron from 09:47-09:51UT is shown. The measured magnetic field and flow velocity patterns match the 2D Hall reconnection picture [21][22] .
Vector field theory 23 implies that X-lines are structurally unstable and that any small perturbation would break them apart into pairs of nulls 2 . We, therefore, considered that this X-line passage event could be a potential candidate for detecting a pair of nulls. In the interval 09:48:20-09:48:50 UT, the Cluster tetrahedron encountered the “X-line” as indicated by the observed flow reversal and the quadrupolar Hall magnetic field perturbations. In order to identify a null pair in the reconnection region during the period under consideration we apply the Poincaré Index method [13][14] , which has been successfully used in previous work for identifying magnetic nulls from its change of sign 9 . For this purpose we use high resolution (0.04s) magnetic field data from all four spacecraft and find that the Poincaré Index jumps up first to +1, then jumps down to -1, and returns afterwards to +1 again (see Fig. 2d-2g). We may, therefore, conclude that some magnetic nulls were present within the Cluster tetrahedron. We can also verify the result by linear interpolation as shown in Fig. 1a.
The total relative error in calculating δ B can be estimated from the ratio / ∇⋅ ∇× B B 9, 24-25 . In this event / ∇ ⋅ ∇× B B is a few hundredths at the times when the Poincaré Index is ±1. The types of these nulls can be identified from three eigenvalues of the corresponding δ B matrix around the nulls. If the real parts of two eigenvalues for a null are negative, we call it a negative or A-type. Otherwise, we call it a positive or Btype [1][2][3][4] . We find that the Cluster tetrahedron first encounters an A-null in the interval 09:48:24.166 -09:48:25.682UT, then a B-null in the interval 09:48:26.975 -09:48:29.830UT. Characteristics of the null pair observed are shown in Table 1.
The detailed analysis of the null-pair characteristics is consistent with a 3D reconnection configuration such as that plotted in Fig. 1d, where the A-B null line is analogous to the X-line in 2D model (as illustrated in Fig. 1c), with the legs replaced by the fan planes A Σ and B Σ that are bounded by the spines B γ and A γ respectively [1][2][3][4] .
The surfaces A Σ and B Σ are determined by the eigenvectors a 2 and a 3 , and b 2 and b 3 in Table 1 respectively; while the spines A γ and B γ are determined by the eigenvectors a 1 and b 1 . The field lines above the upper halves of the Σ surfaces and those below the lower halves merge and cross-link at the null-null line.
Theory predicts that A and B nulls that connect to form a 3D reconnection geometry, obey following features 2 : 1) a 3 corresponding to the smaller negative eigenvalue of the A-null
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