Geophysical Research Letters

Electron acceleration in the reconnection diffusion region: Cluster observations


Corresponding author: S. Y. Huang, School of Electronic and Information, Wuhan University, Wuhan 430072, China. (


[1] We present one case study of magnetic islands and energetic electrons in the reconnection diffusion region observed by the Cluster spacecraft. The cores of the islands are characterized by strong core magnetic fields and density depletion. Intense currents, with the dominant component parallel to the ambient magnetic field, are detected inside the magnetic islands. A thin current sheet is observed in the close vicinity of one magnetic island. Energetic electron fluxes increase at the location of the thin current sheet, and further increase inside the magnetic island, with the highest fluxes located at the core region of the island. We suggest that these energetic electrons are firstly accelerated in the thin current sheet, and then trapped and further accelerated in the magnetic island by betatron and Fermi acceleration.

1. Introduction

[2] Magnetic reconnection is a fundamental mechanism in space and laboratory plasma that enables reconfiguration of magnetic field topology and converts magnetic energy into plasma kinetic and thermal energies. Formation of a thin current sheet (CS) is a necessary condition for magnetic reconnection [Priest and Forbes, 2000]. When the CS becomes comparable to the ion inertial length, ions become unmagnetized, whereas electrons are still frozen in to the magnetic field. This region is called the ion diffusion region. The relative motion between unmagnetized ions and magnetized electrons in the ion diffusion region causes the Hall effect [e.g., Sonnerup, 1979; Deng and Matsumoto, 2001; Vaivads et al., 2004]. At scales below the electron inertial length, electrons also become unmagnetized, and both ions and electrons can move across the magnetic field lines. This region is called the electron diffusion region [e.g., Sonnerup, 1979; Priest and Forbes, 2000; Vaivads et al., 2006].

[3] It is believed that magnetic islands or flux ropes (both referred to as magnetic islands below) play an essential role in the physics of magnetic reconnection and can be formed by multiple X-lines reconnection [e.g.,Slavin et al., 2003; Deng et al., 2004]. Recent kinetic simulations show that smaller scale secondary islands can be formed in the diffusion region due to the unstable tearing mode during reconnection with or without guide field [Daughton et al., 2006; Drake et al., 2006b]. Such magnetic islands have been observed inside or near the ion diffusion region in the Earth's magnetosphere [e.g., Eastwood et al., 2007; Chen et al., 2008; Retinò et al., 2008; Khotyaintsev et al., 2010; Wang et al., 2010], but also have been detected far away from the reconnection site [e.g., Slavin et al., 2003; Zong et al., 2004].

[4] Energetic electrons are important consequences of magnetic reconnection [e.g., Hoshino et al., 2001; Drake et al., 2006a; Pritchett, 2006], and have been observed associated with reconnection [e.g., Øieroset etal., 2002; Imada et al., 2007; Retinò et al., 2008; Huang et al., 2012]. Magnetic islands are closely related to electron acceleration during reconnection. Recently, direct correlations between the islands and acceleration of electrons were observed in the magnetotail [Chen et al., 2008; Retinò et al., 2008; Wang et al., 2010]. Drake et al. [2006a]put forward a scenario that electrons gain kinetic energy by reflecting from the ends of contracting islands due to the Fermi acceleration. The electrons can be also accelerated during multi-island coalescence [Tanaka et al., 2010] or trapped in the islands and energized by the reconnection electric field [Oka et al., 2010]. Nevertheless, there still remain many open questions related to the physics of magnetic islands (such as how electrons are accelerated in the island, etc.), mainly because of the very limited number of in-situobservations. Multi-spacecraft observations allow us to study in detail the complicated structure of the diffusion region, including the structure of magnetic field in this region and particle energization there. In this letter, we use the Cluster multi-spacecraft observations to study electron acceleration and magnetic islands in the reconnection diffusion region.

2. Observations

[5] We present Cluster observations during the time period from 23:24 to 23:36 UT on September 19, 2003 when the spacecraft observed a reconnection event [Borg et al., 2005; Huang et al., 2010; Zhou et al., 2009, 2011]. Cluster was located at (−17.4, 3.7, 0.5) RE(the Earth's radius) in Geocentric Solar Magnetospheric (GSM) coordinates with an inter-spacecraft separation of ∼200 km (much smaller than ion inertial length in the magnetotail). Such small separation provides a good opportunity to study small-scale structures. Measurements of magnetic field (FGM), spacecraft potential (EFW), ions (CIS), electrons (PEACE and RAPID) [Escoubet et al., 1997] are used in this study.

[6] Figure 1displays an overview of the event. During this event, the CS is titled by 10° off the GSM-z direction [Borg et al., 2005]. From the electron spectrogram (Figure 1a) one can see that the Cluster spacecraft are in the plasma sheet (where plasma β is larger than 0.5 (not shown)) with red bar with energy from several to tens keV in this spectrogram except for the time interval between 23:32:26 and 23:32:42 UT when they are in the lobe. Reversal of the plasma flow (Figure 1c) from tailward to earthward is detected around 23:29:35 UT. The Cluster spacecraft stay in the northern hemisphere during the observation of the tailward flow, then they cross the CS several times and finally stay mostly in the southern hemisphere during the observation of the earthward flow. Accompanying this flow reversal, magnetic field Bzchanges from negative to positive, which implies that an X-line passed the Cluster spacecraft.Borg et al. [2005]identified the interval of 23:25:15–23:34:00 UT as a diffusion region crossing owing to a Hall quadrupolar structure of the out-of-plane magnetic fields and bipolar Hall electric fields pointing toward CS in the normal direction.Figure 1d shows two examples of the proton distributions in the Vx − Vz plane within the vertical yellow band during which magnetic islands are observed. One can notice that these distributions consist of two beams with positive and negative Vz, and positive Vx, consistent with proton distributions within diffusion region seen in hybrid simulations [Aunai et al., 2011]. Hence, all these give strong evidence for that the Cluster spacecraft are located in the ion diffusion region.

Figure 1.

Overview of Cluster observations: (a) PEACE/HEEA electron differential energy flux dEF, (b) magnetic field, and (c) plasma flow measured by C1 between 23:24 and 23:36 UT on September 19, 2003, and two examples of proton distributions (d) measured by C1 and C4. The vertical yellow band marks the time interval of observations of magnetic islands.

[7] Figure 2 shows the detailed observations of two magnetic islands and a thin CS detected within the diffusion region from 23:31:10 to 23:31:50 UT. We transform the magnetic field into the LMN coordinate system (Figures 2b–2d) where N is the normal to the CS found from timing analysis of Bx during the CS crossing, M is the core field direction for the second island, and L = M × N. Bipolar signatures (−/+) in Bn (grey shadowed regions of Figure 2d) with corresponding peaks of total magnetic field (Figure 2a) are observed around 23:31:18 UT and 23:31:40 UT, consistent with crossing of two magnetic islands [Slavin et al., 2003; Zong et al., 2004]. These two islands with strong core field (|Bm|) peaks can be clearly seen in two grey shadowed regions in Figure 2c. C3, the most tailward spacecraft, observes the bipolar structures first, and then the other spacecraft observe them, indicating that magnetic islands are moving earthward, most probably embedded in the plasma flow. The X component of plasma flow (Figure 1c) is positive during the first island and small, but slightly positive, for the second island. Negative to positive bipolar signatures in Bn embedded in the earthward plasma flow are the typical feature of earthward moving magnetic island [e.g., Slavin et al., 2003].

Figure 2.

Detailed observations of magnetic islands and the thin CS. (a–d) The magnitude and three components of magnetic field in LMN coordinates (L = [0.81, −0.52, 0.20], M = [0.56, 0.75, −0.31], N = [0.01, 0.37, 0.93] in GSM coordinates); (e) electron density; (f, g) current density in the field aligned coordinate (FAC) and LMN coordinates, respectively; and (h) electron pitch angle distribution. The four yellow shaded regions mark the time intervals for which the electron pitch angle distribution is shown in Figure 2h. The two bipolar structures and the thin CS are marked with grey shadows.

[8] The electron density deduced from the spacecraft potential measured by the EFW instrument [Pedersen et al., 2008] shows depletions in the core region of both islands (Figure 2e). Figures 2f and 2g present the current density calculated by the curlometer method [Dunlop et al., 2002]. There are intense currents associated with both islands having a large component in the M direction (Figure 2g). The large Jm indicates intense axial current in the magnetic islands. The parallel component of the current is dominant in the islands (Figure 2f), however, there is still significant perpendicular component of the current indicating that the islands are not in a force-free magnetic field configuration.

[9] During the time period from 23:31:32 to 23:31:35.6 UT, between the two islands, the Cluster spacecraft encounter a thin CS, with the thickness below ion inertial length. This can be seen both as a large increase in perpendicular current (Figure 2f) but also as a large difference in the observed value of Bl between the spacecraft in Figure 2b (marked in grey shadow). In the thin CS, C1 is located in the center of the CS, and C4 is at the southern edge of the CS. The separation between C1 and C4 is ∼200 km in the N direction, which indicates that the width of thin CS is about 400 km (∼0.6 di, where di is the ion inertial length for plasma sheet density of 0.1 cm−3).

[10] Figure 2h displays the phase space density (PSD) of electron pitch angle distribution combined from PEACE/HEEA and PEACE/LEEA detectors for the four periods marked by yellow bars in Figure 2g. The first and the second correspond to the thick CS and show bidirectional field-aligned distribution, i.e., intensification of the PSD at 0° and 180°, which is a typical signature around the X-line [e.g.,Egedal et al., 2010]. One electron beam in anti-parallel direction is detected in the thin CS (III ofFigure 2h). An anti-parallel beam is also found in the second magnetic island (IV ofFigure 2h), suggesting that the electrons in the thin CS and in the second island are more closely related.

[11] Figure 3 shows the observations of energetic electrons. The energetic electron fluxes (Figure 3b) increase in the region of thin current and the second magnetic island. Figures 3c and 3ddisplay the sub-spin resolution (0.25 s) energetic electron fluxes of two energy channels, 29.9 keV and 68.1 keV. One can see that there is no enhancement of energetic electron fluxes prior to the encounter of the thin CS. The energetic fluxes increase in the thin CS and then further increase in the second magnetic island. The highest fluxes are in the core region of magnetic island, co-located with the density depletion. C1, which is located close to the center of the thin CS, observes the highest energetic electrons fluxes, while C4, at the edge region of the thin CS, detects the lowest fluxes, which indicates that energetic electrons are more effectively accelerated in the center of the thin CS.Figure 3e shows PSD of energetic electrons measured by C1 in the second magnetic island, thin CS, and thick CS. The grey dots present the approximation noise level of RAPID instrument when C1 was in the lobe region for the same day. We can see that all dots of our event are far above the noise level. We fit the power law distribution as ∝ Eγ to data from the four lowest energy channels.

Figure 3.

Detailed observations of energetic electrons: (a) Blcomponent of magnetic field; (b) RAPID omni-directional electron differential flux; (c, d) electron flux at time resolution of 0.25 s in the energy channels 29.9 keV and 68.1 keV; (e) PSD of energetic electrons in the different region (red dots: the second magnetic island; blue dots: thin CS; black dots: thick CS) with a power law function fitted to the four lowest energy channels. The grey dots are the RAPID measurement in the lobe region on 19 September 2003 which approximates the noise level of RAPID instrument. (f) Cartoon of the crossings of the CS inLMN coordinates. The green dashed line presents the Cluster trajectory. The color bars in the top of first panel show the first island, the thin CS, and the second island. The black bar in Figure 3f denotes the thin CS.

3. Discussion

[12] We observe two magnetic islands with density depletions in the core region in the ion diffusion region. This feature is similar to the previous observations [Retinò et al., 2008; Wang et al., 2010], but in contrast with the report of Chen et al. [2008] where density peaks were found. A density depletion in the core region of island could be explained by pressure balance with the surrounding plasma, with the high magnetic pressure inside the magnetic island expelling the electrons out of the core region [Wang et al., 2010] or as a result of coalescence of two magnetic islands [Retinò et al., 2008]. In contrast, some recent 2D simulation show density peaks in the secondary islands [Daughton et al., 2006; Drake et al., 2006b]. The difference may arise because the core field completely confines the magnetized electrons within the island in the 2D simulations, whereas in three dimensions the electrons can escape from the ends. The thin CS observed in the vicinity of the magnetic islands is possibly an electron diffusion region, as the thin CS is very narrow (about 0.6 di) where the ion flow is much slower than the reconnection outflow observed around, and the nearby electron distribution (II of Figure 2h) is highly anisotropic, characteristic for the vicinity of the electron diffusion region [Egedal et al., 2010]. In addition, the thin CS is also favorable for generation of secondary islands [e.g., Daughton et al., 2006]. Considering the situation that the first magnetic island is observed within the thick CS and the second magnetic island is observed in close vicinity of the thin CS, we suggest that the first one is far away from the electron diffusion region, and the second is a secondary island associated with the thin CS and is close to the electron diffusion region.

[13] Energetic electrons with energies of hundreds of keV have been observed in the reconnection diffusion region [Øieroset et al., 2002; He et al., 2008; Retinò et al., 2008], outflow region [Imada et al., 2007; Huang et al., 2012], and within magnetic islands [Chen et al., 2008; Retinò et al., 2008; Wang et al., 2010]. Recently, Imada et al. [2011] have studied favorable conditions for energetic electron acceleration using 10 reconnection events observed by Geotail, and found that the electrons are efficiently accelerated in a thin CS during magnetic reconnection. In our event, we observe high fluxes of energetic electrons within the thin CS, and much lower fluxes in the thick CS, which is consistent with the conclusion of Imada et al. [2011]. However, they did not consider another important factor for electron acceleration: magnetic island. Chen et al. [2008] presented the observations of correlation between the energetic electrons and magnetic islands and found that the highest energetic electron fluxes coincide with density peaks in the magnetic islands. Retinò et al. [2008] reported that energetic electrons were detected mostly at the edges of a magnetic island while lower fluxes were found in the density depletion in the center of the island. Here, we observed energetic electrons within the magnetic island located in the ion diffusion region, and the highest fluxes of energetic electrons fluxes coincided with density depletion of core region of magnetic island.

[14] Over the past several decades, several acceleration mechanisms have been proposed to interpret the production of the energetic electron during magnetic reconnection [e.g., Hoshino et al., 2001; Drake et al., 2006a; Pritchett, 2006; Oka et al., 2010; Tanaka et al., 2010], which allows us to identify with which acceleration mechanisms our observations are consistent. Following the observations, Figure 3f presents a cartoon of Cluster crossing of the CS during the event. The Cluster spacecraft first cross the thick CS, then encounter the thin CS (black bar in Figure 3f), and finally cross the second magnetic island. There is no enhancement of energetic electron flux in the thick CS, but a clear flux increase within the thin CS (highest flux in the center as expected due to Ey acceleration [Pritchett, 2006]), and further increase in the nearby magnetic island.

[15] Recently, Oka et al. [2010] suggested that electrons can be trapped inside the island, and energized continuously by the reconnection electric field prevalent in the reconnection diffusion region. In agreement with our observations, the electron energy spectrum inside the second island is higher than in the adjacent thin CS [Oka et al., 2010, Figure 1b]. From timing analysis of Bx, the width of magnetic island is estimated to be about 540 km. For the energetic electrons with ε = 127 keV, the gyroradius in the magnetic field at the edge (core region) of island B is ∼10 (22) nT, ρce ∼ 120 (56) km. Thus the gyroradius of electrons is much smaller than the estimated width of the island and therefore electrons can be trapped in the island and repeatedly interact with the reconnection electric field. Additionally, the electrons may undergo the betatron acceleration due to the increase of the magnetic field (Figure 2a) in the magnetic island. The largest relative variations of the total magnetic field within the magnetic island is δB/B ∼ 2. The observed enhancement in the perpendicular flux at intermediate energies (IV of Figure 2h) support this mechanism. Betatron acceleration has been observed in the pileup region in the magnetotail [e.g., Fu et al., 2011; Ashour-Abdalla et al., 2011; Khotyaintsev et al., 2011]. Similarly, Fermi acceleration in a contracting island [Drake et al., 2006a] is expected. Unfortunately, because there is no RAPID burst mode data available for this time interval, we cannot verify directly the pitch angle distribution of the energetic electrons. The observed power law index (Figure 3e) in the magnetic island is similar to that in the thin CS, which gives strong evidence for an adiabatic acceleration process, such as betatron and/or Fermi acceleration. Therefore, there may be a two-step acceleration process for the observed energetic electrons: electrons are first accelerated in the thin CS, and then trapped in the magnetic island and further accelerated by betatron and Fermi acceleration. When the electron gyroradius approaches the scale of thin CS/magnetic island, the adiabatic acceleration ceases. This effect can be seen inFigure 3e where the fluxes in the highest energy channel are lower than the power law fit.

4. Conclusions

[16] In this letter, we presented Cluster observations of two magnetic islands and a thin CS embedded in the earthward plasma flow in the reconnection diffusion region. The thin CS is possibly an electron diffusion region owing to its narrow width, nearby strongly anisotropic electron distribution and low ion outflow. There are density depletions in the core region of the islands and intense currents therein which are dominantly parallel to Band have a large component along the island axis. There is also non-zero perpendicular current component present which indicates that the islands are not in force-free magnetic field configuration. The first magnetic island is further away from the electron diffusion region compared to the second island. We suggest the second magnetic island as a secondary island in the vicinity of the thin CS. Energetic electrons are only observed in the thin CS (energetic electrons fluxes in the center are larger than at the edge) and in the second magnetic island. The greatest enhancement is near the core of the second island. These energetic electrons may have been first accelerated in the thin CS, and then trapped and further accelerated in the magnetic island by betatron and Fermi acceleration.


[17] We thank the FGM, CIS, PEACE, and RAPID instrument teams and the ESA Cluster Active Archive. This work was supported by the Swedish Research Council (under grants 2007–4377, 2009–3902 and 2009–4165), and the National Natural Science Foundation of China (NSFC) (under grants 40890163, 41174147 and 41004060). S. Y. Huang appreciates the China Scholarship Council for sponsoring his study at IRF.

[18] The Editor thanks Shinsuke Imada and an anonymous reviewer for assisting in the evaluation of this paper.