Evidence of deflected super-Alfvénic electron jet in a reconnection region with weak guide field



Recent numerical simulations demonstrated that electron diffusion region develops into two-scale structure, i.e., the inner electron diffusion region and the outer electron diffusion region. The outer diffusion region is manifested as super-Alfvénic electron jet embedded in central current sheet. However, the electron jets are deflected from neutral sheet with a weak guide field. In this paper we present the in situ evidence of deflected super-Alfvénic electron jet in a reconnection region with a weak guide field in the Earth's magnetotail. The electron-scale jet was detected at about 37 ion inertial lengths from the X line. There was a strong electric field at the jet. The strong electric field at the jet was primarily balanced by Hall electric field, as the intense current was mainly carried by magnetized electrons. Another event in the magnetosheath also supports our conclusion that guide field deflects the electron jet away the neutral sheet.

1 Introduction

Magnetic reconnection is a universal energy transfer process in astrophysical and laboratory plasmas. Hall effect has been considered as the essential mechanism mediating fast reconnection. It was suggested that the reconnection rate is controlled by ion dynamics in the ion diffusion region, while the mechanism that breaks the electron frozen-in condition in the electron diffusion region, which has a size on the order of the electron inertial length (c/ωpe), does not form a bottleneck to fast reconnection [Birn et al., 2001]. Recent kinetic simulations showed that the electron diffusion region develops a distinct two-scale structure: the inner diffusion region and the outer diffusion region [Daughton et al., 2006; Fujimoto, 2006; Karimabadi et al., 2007; Shay et al., 2007]. The inner diffusion region is several c/ωpe along the outflow direction while the outer diffusion region is manifested as super-Alfvénic electron jet that can extend to tens of ion inertial length (c/ωpi) downstream of the X line. The tearing instability causes the elongated electron diffusion region to form secondary islands/plasmoids [Daughton et al., 2006]. This elongation makes it possible for current spacecraft mission to detect the electron diffusion region. Phan et al. [2007] reported the existence of outer electron diffusion region in a fast reconnection event in the magnetosheath. The electron jet was embedded in the center of a much broader current sheet. They suggested that the jet extended at least 60 c/ωpi downstream of the X line. Wang et al. [2012] also provided evidence of ejected electron jet by analyzing electron distribution within the Hall electromagnetic region.

Recent kinetic simulation employing realistic mass ratio found that electron jet is strongly deflected, and the outer electron diffusion region is broken under a very weak guide field [Goldman et al., 2011; Le et al., 2013]. It thus contradicted with the results of Phan et al. [2007] as the observed reconnection region had a nonnegligible guide field. Le et al. [2013] put forward a partial solution to this issue. They found that not only the guide field strength but also the upstream electron β determine the type of electron diffusion region in the hydrogen-electron plasma. On the event studied by Phan et al. [2007], the upstream electron β is about 0.1, and the guide field strength is 0.14 B0. These parameters are in the regime 3 in Le et al.'s [2013] simulation, thus permit the jet to extend far away from the X line. Nevertheless, one discrepancy remains: In the simulation, the jet is oblique to the neutral sheet whereas in the observation, the jet was collimated with the neutral sheet.

In this paper, we solve this discrepancy by presenting one magnetotail reconnection event observed by Cluster spacecraft and revisiting the event reported by Phan et al. [2007]. We demonstrate that on both events, the super-Alfvénic electron jets were deflected from the neutral plane, consistent with theoretical predictions [Goldman et al., 2011; Le et al., 2013].

2 Observation

The first event we introduced was on 29 July 2003. We used the data from instruments on board the Cluster spacecraft, including the fluxgate magnetometer instrument [Balogh et al., 2001], the Cluster Ion Spectrometry experiment [Rème et al., 2001], the Plasma Electron and Current Experiment (PEACE) [Johnstone et al., 1997], the Research with Adaptive Particle Imaging Detectors [Wilken et al., 2001], and the Electric Field and Waves (EFW) instrument [Gustafsson et al., 2001]. Between 18:15 and 18:45 UT, Cluster was located at −14.78, −11.08, and 1.95 RE in geocentric solar magnetospheric (GSM) coordinates in the Earth's magnetotail. The four spacecraft formed a regular tetrahedron with an interdistance of about 200 km, which is smaller than the ion inertial length in the central plasma sheet (c/ωpi ~600 km given the plasma density ~0.15/cm3).

Figure 1 shows the overview of the Cluster 4 (C4) observations from 18:15 to 18:45 UT. The C4 was mainly located in the plasma sheet during the entire interval except between 18:20 and 18:26 UT, when it was outside the plasma sheet, where Bx was larger than 30 nT, proton density dropped, and ~keV electron fluxes were significantly low while electron fluxes below 100 eV increased significantly. We see that Bz changed from negative to positive at around 18:29 UT. Plasma flow Vx reversed sign when Bz changed polarity. There are multiple energetic electron flux increases during the flow reversal, at around 18:29:30, 18:30:20, and 18:35 UT, respectively. The correlated flow Vx and Bz reversal and energetic electron acceleration are typical signatures of the X line passage [e.g., Deng et al., 2004; Huang et al., 2012]. The flow changed from negative to positive, implying that a tailward retreating the X line passed the spacecraft. The retreating speed is estimated as −150 km/s by multispacecraft timing analysis based on the Bz profile, which is close to the simulation results that the X line retreating speed is 0.1 VA [Oka et al., 2008], where VA~2100 km/s is the upstream Alfvén speed determined by the upstream magnetic field strength |B|~33 nT and plasma density n~0.12/cm3.

Figure 1.

Overview of C4 observations between 18:15 and 18:45 UT. (a) Magnetic field Bx, (b) By and (c) Bz, (d) plasma flow Vx, (e) proton density, (f) differential energy fluxes of energetic electrons, and (g) thermal electrons.

The shaded area in Figure 1 marks the time interval when the spacecraft crossed the current sheet twice. By minimum variance analysis (MVA) [Sonnerup and Scheible, 1998], we constructed the current sheet normal coordinate, with L = (0.901, 0.426, 0.082), M = (−0.372, 0.663, 0.649), and N = (0.222, −0.616, 0.756) in GSM coordinate, where N indicates the normal direction of the current sheet, L points earthward and contains the main magnetic field reversal, and M = N × L. Moreover, the normal direction of the current sheet derived from the multispacecraft timing analysis is consistent with the N obtained from the MVA. We found that the normal speed of the current sheet was about 280 km/s for the first crossing and 250 km/s for the second crossing. For both crossings, the current sheet normal motions are relatively stable as timing analysis based on different values of BL gives consistent speeds.

Figure 2 shows the magnetic field, electric field, and electron density around the first current sheet crossing. The electron density was inferred from the spacecraft potential at a time resolution of 0.2 s [Pedersen et al., 2008]. We derived a 3-D electric field assuming that E · B = 0, which is, in general, invalid only in the following three regions: the inner electron diffusion region, where E|| is required for magnetic field lines break and reconnect [Mozer, 2005]; density cavities around the separatrix region, where patchy parallel electric field was observed [Wang et al., 2013]; the core region of secondary island during the initial phase after the generation [Zhou et al., 2012]. None of the above regions were encountered by the spacecraft during this X line crossing, so E · B = 0 can be employed to derive the third electric field component. We put further restrictions, |B| > 2 nT and math formula > 6°, on deriving Ez [Eastwood et al., 2007]. The electric field was then transformed to the X line frame, which consists of the current sheet motion along +N and X line movement in the −L direction. We noted that there was a weak guide field in the reconnection region. The guide field strength is about −5.2 nT by averaging magnetic field BM during the flow reversal interval between 18:26 and 18:38 UT. Magnetic and electric field perturbations across the current sheet are consistent with the signature of Hall electromagnetic fields [Eastwood et al., 2007]. The magnetic field (BM − Bg) reverses sign across the current sheet, coincident with the reversal of BL. The EN changes from negative to positive across the current sheet, which means that EN points toward the midplane near the neutral sheet. One noticeable feature is that the point where (BM − Bg) changes sign is above instead of at the neutral sheet where BL = 0. This asymmetry is also evident for EN, as the region of positive EN extends to above the neutral sheet, where BL > 0. This feature agrees with the recent observation that guide field distorts the symmetrical Hall electromagnetic field across the current sheet [Eastwood et al., 2010; Wang et al., 2012], which further proves that the reconnection region had a negative guide field.

Figure 2.

Observation of a neutral sheet crossing by C4. (a) Magnetic field in the LMN coordinate, (b) electric field in the LMN coordinates in the X line frame, (c) electron density, and (d) schematic illustration of the spacecraft trajectory through the reconnection region.

Two BN bipolar structures were observed at 18:31:44 and 18:31:49 UT, respectively, between the two current sheet crossings. These two structures are commonly recognized as the secondary magnetic islands in the reconnection region [Drake et al., 2006; Eastwood et al., 2007; Huang et al., 2012; Nakamura et al., 2006; Teh et al., 2010; Wang et al., 2010, 2012]. The BN changes from negative to positive, consistent with the polarity change of an earthward moving island/plasmoid. Both islands have local density peaks coincident with the BN reversal, but they did not show any magnetic field enhancements, similar to the island observed in the magnetopause current sheet [Teh et al., 2010]. The former island was detected when C4 was in the neutral sheet, while the latter was detected when C4 was located far away from neutral sheet, where BL ≈ 20 nT.

A steep BM change was observed by the spacecraft before it crossed the current sheet at around 18:31:43 UT, as shown in Figure 3. This sharp decrease of BM corresponds to a density dip. The profile of BM decrease lasts about 1 s, corresponding to a spatial size of 280 km, which is comparable to the interdistance of four spacecrafts; thus, we cannot use multispacecraft methods to estimate the current density. However, the current sheet normal speed is uniform through this crossing, so the current density can be estimated by single spacecraft measurements based on the 2-D discontinuity analysis [e.g., Zhou et al., 2009]. We see that there is an intense current jL coincident with the sharp BM decrease. Ion flow in the L direction is positive with a magnitude of 550 km/s, whereas the electric current density is negative with a maximum magnitude of 150 nA/m2 measured by C1 and C4. It implies that a large +L electron flow is required to provide the −L current. Given that the local plasma density is about 0.2/cm3, we derived the electron flow velocity as veL = viL − jL/nie ≈ 5200 km/s, which is twice larger than the upstream Alfvén speed VA~2100 km/s. The jet was located slightly above the neutral sheet (BL ≈ 5 nT ≈ 0.15 B0) but below the separatrix region. It was suggested that the jet deflection is due to the Lorentz force −neqVeL × Bg [Goldman et al., 2011]. In this case the guide field is negative in M, and the electron jet velocity is positive in L; the resultant Lorentz force is about 2 × 10−15 N/m2 predominantly in the positive N direction, which leads to an upward shift (corresponding to BL > 0 in the LMN coordinate). This agrees with the observation that the electron jet was observed in the northern hemisphere. We estimated the width of the super-Alfvénic jet as follows: First, we defined the boundary of the super-Alfvénic jet, which is the minimum current density required for the electron jet to be super-Alfvénic, i.e., jL = (viL − vup, A) * nie = −49.6 nA/m2. Then the width of super-Alfvénic jet is calculated as the current sheet normal speed times the duration bounded by two dashed lines in Figure 3 defined by jL = −49.6 nA/m2, which is about 98 km~7 c/ωpe. For simplicity, we assume that when Bz reversed sign at around 18:29:10 UT, the spacecraft reached the smallest distance to the X line in the L direction. At 18:31:43 UT when the jet was detected, the relative distance between the spacecraft and the X line equals the X line moving speed (150 km/s) multiplied by the time difference (150 s), which is about 22,500 km~37 c/ωpi.

Figure 3.

Observation of the electron jet by C1 (black) and C4 (blue). (a) Magnetic field BM, (b) electron density, (c–d) electric current density, (e–f) comparison of measured electric field (black), Hall electric field (red), convective electric field (green), and electric field provided by electron pressure gradient (blue).

Fortunately, Cluster was in burst mode during the interested time interval, so 3-D electron distribution is available from PEACE. Figure 4 depicts the electron distribution Vz − Vspin between 18:31:43.696 and 18:31:43.946 UT. The slice collected electrons in the azimuthal angles of −3.6° and 18.6°. It shows that, besides the core component, electrons with energy 2 keV and polar angle 90°–120° (corresponds to (Vz, Vspin)~(0–13,000 and 22,000–26000 km/s)) are also evident. The enhanced electron flux is opposite to the direction of electric current (azimuthal angle: 186.9° and polar angle: 78.4°), implying that electrons are the main carrier of the intense current.

Figure 4.

Electron distribution Vz − Vspin during 18:31:43.696–18:31:43.946 UT. The corresponding azimuthal angle is from −3.6° to 18.6°. Vz is the velocity along the spin axis, which is approximately the z axis of the geocentric solar ecliptic coordinate. Vspin is the magnitude of velocity in the plane perpendicular to the spin axis. Black arrow indicates the direction antiparallel to the electric current.

3 Discussion

Figure 2d is a sketch of the spacecraft trajectory through the reconnection region in the X line frame. The blue dashed line represents the spacecraft trajectory. The electron jet was located at the leading edge of the first island, which suggests a possible coupling between the extended electron jet and the magnetic island. The bipolar Bz observed away from the neutral sheet are usually interpreted as the spacecraft passes a magnetic island away from its center. However, this bipolar Bz could also be a signature of Kelvin-Helmholtz (KH) instability around the separatrix region. Due to the lack of spacecraft in the neutral sheet at the time when the bipolar Bz was observed, we cannot determine whether it is the remote sensing of a magnetic island or a localized phenomenon around the separatrix region. Recently, Fermo et al. [2012] suggested that secondary island can be generated by the electron KH instability instead of tearing instability. The relationship between KH instability and secondary island is worth to be further studied.

Figure 2b shows that there is an intense electric field associated with the jet; it would be interesting to know how the large electric field be generated. Here we compare the measured electric field to different terms in the generalized Ohm's law. Figures 3e and 3f show the normal component of measured electric field, convective electric field −(Vi × B), Hall electric field (j × B)/nee, and electron pressure gradient term math formula. The inertial termmath formula in the generalized Ohm's law is not shown here. To provide an electric field of 1 mV/m, dve/dt should reach ~200,000 km/s2. This is too large, so the inertial term can be neglected. The electron pressure gradient term is assessed as follows: Assuming that the electron temperature is constant throughout the jet (Te~1800 eV), the electron pressure gradient can be expressed asmath formula; thus, we used high-resolution electron density inferred from spacecraft potential to derive the electron pressure gradient. It clearly shows that the measured electric fields are primarily balanced by the Hall electric field, while the electron pressure gradient terms are negative with magnitude less than 10 mV/m. The convective electric fields are at least 1 order smaller than the Hall electric fields. It implies that magnetic fields are frozen-in to the electron flow, and thus, energy dissipation in the electron frame is negligible at this thin layer. This strong EN was only observed at the electron jet because electric current jL reaches peak within the electron jet. In other regions, jL are relatively small.

We revisit the event studied by Phan et al. [2007]. They reported a collimated super-Alfvénic electron jet extending ~60 c/ωpi downstream of the X line. The electron jet was embedded in a much broader current sheet supporting the reversed reconnecting magnetic field component. We reached a different conclusion after revisiting the event. Figure 5 shows the magnetic field and estimated current density in the current sheet normal coordinate defined by Phan et al. [2007] between 06:11:45 and 06:12:15 UT. The super-Alfvénic electron jet was exactly coincident with the steepest change of BM profile, as marked by the yellow shadow. We noticed that the electron jet was observed at BL ≈ 20 nT, obviously away from the central current sheet where BL~0. This implies that the jet was deflected from the neutral plane, similar to the aforementioned case. The Lorentz force imposed by guide field Bg will lead to a downward shift in N (corresponds to BL > 0 in the LMN coordinate defined by Phan et al. [2007]). This is consistent with the observation that the jet was detected below the neutral sheet [Phan et al., 2007].

Figure 5.

(a–c) Magnetic fields in the LMN coordinate and (d) current density jL estimated and observed by C1 on the 14 January 2003 event. The jL is estimated by the same method we used on the 29 July 2003 event. The yellow shaded region marks the super-Alfvénic electron jet. The red line in Figure 5b indicates the guide field Bg = 7 nT.

Recent kinetic simulations demonstrated that at realistic mass ratio, there are at least four different reconnection regimes determined by the combination of guide field strength and upstream electron β [Le et al., 2013]. On the 29 July 2003 event, the upstream electron β is about 0.03, and the guide field strength is about 0.15 B0. The parameter set is in the regime 3 in Le et al.'s [2013] simulation. Moreover, the electrons are magnetized in the thin layer as the field line curvature radius, estimated by multispacecraft method [Shen et al., 2003], was on the order of 1000 km, which is much larger than the electron gyroradius (40 km for 20 keV electrons). This is consistent with simulation that in regime 3, electrons are magnetized.

4 Summary

In summary, we clarify the discrepancy between recent observation and kinetic simulation about the super-Alfvénic electron jet in reconnection. We show that with weak guide field, the super-Alfvénic electron jet can extend to tens of ion inertial length from the inner electron diffusion region; however, it was deflected from the neutral sheet owing to the Lorentz force. The jet was carried by magnetized electrons. Strong electric fields at the jet were primarily balanced by the Hall electric field, which implies that magnetic fields were frozen-in to the electron flow, and energy dissipation in the electron frame was negligible in this thin layer. A systematic study of parameters controlling the type of inner electron diffusion region and outward electron jet requires further efforts both in simulation and observation.


This work was supported by the National Science Foundation of China under grants 41174147, 41274170, and 41331070 and Science Foundation of Jiangxi Province under grants 20122BAB212002. R.X. Tang is also supported by the Specialized Research Fund for State Key Laboratories. We thank the Cluster teams and Cluster Active Archive for providing high-quality data.

Philippa Browning thanks the reviewers for their assistance in evaluating this paper.