Evidence for the dissipation region in magnetotail reconnection



[1] Signatures of the dissipation region of collisionless magnetic reconnection are investigated by the Geotail spacecraft for the 15 May 2003 event. The energy dissipation in the rest frame of the electron's bulk flow is considered in an approximate form De*, which is validated by a particle-in-cell simulation. The dissipation measure is directly evaluated from the plasma moments, the electric field, and the magnetic field. UsingDe*, a compact dissipation region is successfully detected in the vicinity of the possible X-point in Geotail data. The dissipation rate is 45 pWm−3. The length of the dissipation region is estimated to 1–2diloc (local ion inertial length). The Lorentz work W, the work rate by Lorentz force to plasmas, is also introduced. It is positive over the reconnection region and it has a peak around the pileup region away from the X-point. These new measuresDe* and W provide useful information to understand the reconnection structure.

1. Introduction

[2] Magnetic reconnection is one of the most important processes in many plasma systems. It drives various explosive events such as solar flares, substorms in the Earth's magnetosphere, and disruptions in laboratory devices. It is well known that the reconnection process is crucially influenced by the dissipation physics near the reconnection point (X-point). The structure of the dissipation region as well as the accommodated physics is of critical importance for the understanding of the reconnection mechanism. Significant efforts have been made on this subject by theories, numerical simulations, and in situ satellite observations.

[3] In a collisionless kinetic plasma, typically at a distance of the ion inertial length from the X-point, ions decouple from magnetic field lines while electrons remain magnetized. As a consequence, Hall physics plays a role inside the ion-decoupling region. Signatures of Hall physics such as quadruple magnetic field, bipolar normal electric field, and the relevant current loops [Sonnerup, 1979] were confirmed by in situ observations in the terrestrial magnetosphere [Nagai et al., 2001; Øieroset et al., 2001].

[4] Deep inside the ion-decoupling region, there is a thin layer where electrons depart from field lines. A compact dissipation region is located in a close vicinity of the X-point. In addition, recent simulation works suggest that narrow electron jets extend from there, stretching the nonideal layer in the outflow directions [Karimabadi et al., 2007; Shay et al., 2007]. These signatures were recently confirmed by satellite observations. Nagai et al. [2011]found a compact region with an intense cross-tail current and neighboring electron jets at a super-Alfvénic speed in a magnetotail reconnection event.

[5] Until recently it was not clear how to identify the dissipation region inside the electron nonideal layer. Taking the energy transfer into account, Zenitani et al. [2011a, 2011b]have proposed a general measure of the dissipation region. Using particle-in-cell (PIC) simulations, they distinguished the dissipation region from the outer electron jet, which turned out to be an oblique projection of a non-dissipative current sheet [Hesse et al., 2008; Klimas et al., 2012].

[6] In this Letter, we show in situ observational evidence for the dissipation region in a magnetotail reconnection event.

2. Observation and Analysis

[7] On 15 May 2003, Geotail detected a reconnection event in the premidnight tail. This event was extensively analyzed by Nagai et al. [2011] and so we only repeat important features here. Figure 1 shows key properties from 1053:00 UT to 1058:30 UT on 15 May 2003. All data are presented in the spacecraft (SC) coordinates, because the electric field data are available only in the SC coordinates. During the period of our interest, the SC coordinates are virtually the same as the GSE and GSM coordinates. The rotation angle to the GSE coordinates is less than 2.4° and the angle to the GSM is less than 5°. The satellite position was (XGSMYGSMZGSM) = (−27.8, +3.3, +3.5 RE) at 1056 UT.

Figure 1.

Geotail observation from 1053:00 UT to 1058:30 UT on 15 May 2003. (a) Normal magnetic field Bz [nT], (b) electric field Ex, Ey [mV/m], and (c, d) plasma perpendicular velocities [km/s] in the XSC and YSCdirections. A potential X-point (red dotted line) and a characteristic interval from 1055:07 to 1056:44 UT (shadow) are overplotted.

[8] Figure 1a shows magnetic field Bz at 16 Hz, measured from the magnetic field experiment (MGF) [Kokubun et al., 1994]. It suddenly turned from southward (Bz < 0) to northward (Bz > 0) at 1055:44 UT, as indicated by the red dotted lines. Judging from this and many other signatures [Nagai et al., 2011], Geotail encountered a potential X-point (hereafter X-point) at this time.

[9] Other quantities are shown at 12 s time resolution. Figure 1b shows electric field data, obtained from the electric field detector (EFD) [Tsuruda et al., 1994]. Technically, they were measured every 3 s and then averaged over 12 s. We note that the average electric field during 1057:45–1057:58 UT (the arrow in Figure 1b) is represented by one during 1057:45–1057:52 UT, because EFD had violent, high-frequency noises of ΔE ∼ 50 mVm−1 during 1057:52–1057:58 UT. One can see that Exhas a bipolar signature across the X-point. This is a well-known signature of kinetic reconnection [e.g.,Hoshino, 2005].

[10] Figures 1c and 1dshow the ion and electron bulk velocities. Plasma moments are calculated from distribution functions that are measured by the low-energy particle experiment (LEP) [Mukai et al., 1994]. Due to the low time-resolution of 12 s, these moments contain field-aligned flows along the separatrices from 1055:30 UT to 1057:00 UT. To rule out the field-aligned Hall currents, transverse velocities are presented (vive). The veyis distinctly fast near the X-point (Figure 1d). As seen in Figure 1c, both vix and vexchange their signs across the X-point. Note thatvex overshoots vixon both two sides of the X-point. The outward electron velocity is even faster than the typical upstream Alfvén velocity. The upstream magnetic field (10 nT) and density (0.01 cm−3) give 2200 km/s. Such bi-directional, super-Alfvénic electron jets are consistent with previous simulations [Karimabadi et al., 2007; Shay et al., 2007].

[11] The shadows indicate a characteristic interval from 1055:07 to 1056:44 UT, surrounded by sudden spikes in Bz (Figure 1a). This interval features super-Alfvénic electron jets (Figure 1c), an intense duskward electron flow (Figure 1d), and a low plasma density (not shown). Nagai et al. [2011]referred to this interval as the “ion-electron decoupling time.”

[12] Next we introduce several measures to discuss the reconnection region from Geotail data. We consider the energy transfer in the rest frame of the electron's bulk flow. This measure, the electron-frame dissipation measureDe, is formally defined in Zenitani et al. [2011a, equation (7)].

[13] In a nonrelativistic neutral plasma, it can be reduced to

display math

where math formula is the nonideal electric field and

display math

is the work rate per unit volume by the Lorentz force to the ion fluid or the electron fluid. Since this Lorentz work W (/sec /unit volume) stands for the energy transfer in the ideal MHD, equation (1) reads the total energy transfer minus the ideal transfer, i.e., the nonideal energy transfer from fields to plasmas [Birn and Hesse, 2005; Zenitani et al., 2011a]. We further assume Ez = 0 to obtain the following approximate form,

display math

The two measures De* and W are shown in Figure 2. The current density is directly calculated from the plasma moments, j = eni(vi − ve). The dissipation De*(gray histogram) has a peak near the X-point. Its peak rates are 39 and 45 pWm−3 during 1055:32–1055:44 UT and 1055:44–1055:56 UT (two 12 s intervals), respectively. The Lorentz work W (dashed histogram) has a peak during 1054:31–1054:43 UT.

Figure 2.

The approximate dissipation measure De* (gray histogram) and the work rate by the Lorentz force W(dashed histogram). The X-point (red dotted line) and the interval (shadow) are the same as those inFigure 1.

3. PIC Simulation

[14] We validate our observations with a 2D PIC simulation [Zenitani et al., 2011b]. We employ a Harris-like initial model, math formula and n(z) = n0[0.2 + cosh−2(z/L)], where B0 and n0 are the reference magnetic field and density. The current sheet thickness is set to L = 0.5di, where di is the ion inertial length. Other simulation parameters are mi/me = 100, ωpece = 4, Ti/Te = 5, and 2400 × 1600 cells with 2.2 × 109 particles. The computational domain is xz ∈ [0, 76.8] × [−19.2, 19.2] in units of di with periodic (x) and reflecting (z) boundaries. Velocities are normalized by the typical Alfvén velocity cA = B0/(μ0n0mi)1/2.

[15] Figure 3shows snapshots in the well-developed stage. In this case, judging from the sign ofDe, the dissipation region is located around 34.7 < x < 41.5 and −0.38 < z < +0.38. Its thickness is limited by that of an electron current layer. The layer thickness is comparable with the local electron inertial length, deloc ∼ 0.31. There are also weak dissipative regions at x = 28 and x = 48, where the magnetic field lines suddenly flip. Surprisingly, both De and De* give almost identical pictures, as shown in Figures 3a and 3b. There are minor differences near the vertical dissipative regions but it is hard to recognize them in the figures.

Figure 3.

(a) The dissipation measure De (equation (1)) in unit of J0cAB0 with magnetic field lines superposed, (b) the approximate dissipation measure De* (equation (3)) in the same unit, (c) vixvex at z = 0, and (d) the dissipation measure De and the Lorentz work W at z = 0.

[16] Figure 3c presents plasma outflow velocities along the outflow line (z = 0). The electron jet substantially overruns the ion flow [Karimabadi et al., 2007; Shay et al., 2007] until it reaches a shock-like transition region atx ≈ 28 and x ≈ 48. The electrons are magnetized further downstream. Note that vix and vex are still different in the downstream, because the ions remain unmagnetized.

[17] Figures 3d shows the dissipation measure De and the Lorentz work W. The De measure is almost identical to De* along the outflow line, where jzEz ≈ 0. Outside the central dissipation region, De exhibits a weak undershoot in the downstream, indicating energy transfer from plasmas to the electromagnetic fields in the comoving frame of plasmas. This is a signature of the fast electron jet region [Zenitani et al., 2011b]. The Lorentz work W is usually positive over the reconnection region, because the Lorentz force continuously drives plasmas in the outflow directions. Further downstream, it has a local peak at x ≈ 16.5 (outside the domain in Figure 3), where the reconnected flux (Bz) hits the initial current sheet.

4. Discussion

[18] Let us examine the validity of the approximate measure (equation (3)). Since EFD does not measure Ez along the spin axis, we have to reconstruct Ez in equation (1). We consider the following three ways.

[19] 1. A popular way is to assume E · B = 0. However, since there are strong parallel electric field near the dissipation region, E ≠ 0 [Pritchett, 2001; Wygant et al., 2005], and since Bz is usually weak, this does not work.

[20] 2. The second is to assume Ez = 0. This gives a different picture that emphasizes separatrices. Physically, this assumption drops the energy transfer jzEz but leave the ideal part jz(ve × B)z in equation (1). In other words, the ideal part contaminates the nonideal dissipation measure De. Thus we should not assume Ez = 0.

[21] 3. The third is to set Ez = 0. This is our choice. Despite strong Hall electric field Ez near the dissipation region [Shay et al., 1998; Wygant et al., 2005], the Ez ≈ 0 condition is fairly satisfied outside the electron current layer, and so jzEz is a minor contributor to De along the inflow line [see Zenitani et al., 2011b, Figure 5a]. The ideal condition is also violated Ez ≠ 0 along the separatrices but this does not involve significant energy transfer. In general, jzEz is negligible due to weak jz. Thus De* approximates De quite well. Note that this choice is specific to a magnetotail configuration without a guide field. In other configurations jzEz could be important and equation (3) may not be useful.

[22] In Figure 2, the De*measure has a peak near the X-point during 1055:44–1056:08 UT. This is evident for the dissipation region. Let us evaluate the dissipation rate. The reconnection electric fieldEyis fairly uniform over the reconnection region, except for the magnetic pile-up region near the outflow jet front. From PIC simulations, we empirically know that the reconnection rate remains constant,Ey ≈ 0.1cA,upBup. Here, Bup and cA,up are the magnetic field and the Alfvén velocity in an upstream region, typically a few diupstream from the X-point. It is empirically known that the half width of the electron current layer is approximated by the local electron inertial lengthdeloc up to the case of a realistic mass ratio [Pritchett, 2010]. The current density inside the dissipation region is j ∼ Bd/(μ0deloc), where Bdis the magnetic field at the upstream edge of the dissipation region. After the initial current sheet plasma moves out, the plasma density is roughly uniform over the reconnection region. Assuming a uniform density, one can estimate typical dissipation at the X-point,

display math

From simulations, we know that the upstream magnetic field is typically a half of the asymptotic lobe field : math formula. In this event, the lobe field is estimated to B0 = 20 nT, while Bx occasionally hits 10 nT near the separatrices. Thus, it would be reasonable to assume Bup = 10 nT. Meanwhile, it is very difficult to estimate Bd, because the electron-scale dissipation region is embedded in a thick reconnection layer of the order of the ion meandering width. From simulation we obtain (Bd/Bup) ≈ 0.5. However, this ratio could be smaller in a real system, because the electron skin depth with mi/me = 1836 is 4.3 times smaller than one with mi/me = 100. Using Bup = 10 nT and (Bd/Bup) < 0.5, we obtain De* < 163 pWm−3. In addition, our data are averaged over a time interval of 12 s. Geotail resolves the spatial structure rather coarsely. Using spatially averaged quantities, their product De* could be underestimated by a factor of two or three. Considering this, the observed rates, 39 and 45 pWm−3 (1055:44–1056:08 UT), are reasonable.

[23] It is difficult to evaluate unambiguously the size of the dissipation region in our single-satellite observation.Shay et al. [2007] predicted that the half length of the Ey > 0 region is ∼0.6di. In many mi/me = 25 runs (A. Klimas, private communication, 2012) and in our mi/me = 100 run, the dissipation region is twice longer than the Ey > 0 region. Thus the full length of the dissipation region will be 2.4di. On the other hand, Zenitani et al. [2011b] reported that the aspect ratio of the dissipation region is ∼0.1. Given that the half width of the dissipation region is ∼deloc, the full length will be ∼20deloc ∼ 0.47diloc. In these cases, the full extent of the dissipation region will be

display math
display math

Examining several clues such as the upstream distribution functions, Nagai et al. [2011] estimated that the entire structure retreats at ∼100 km/s. The above two estimates are comparable with the spatial scale of one or two sampling intervals (12–24 s), 1200–2400 km. Geotail detected the dissipation region by two or three sampling intervals (Figure 2), 2400–3600 km or 3–5di or 1–2diloc. The length of the dissipation region is on the same order.

[24] The characteristic interval from 1055:07 to 1056:44 UT (the shadow regions in Figures 1 and 2) would correspond to the full extent of the outer electron jet region in the PIC simulation (28 < x < 48 in Figure 3). One can recognize the magnetic field fluctuations in Figure 1a (indicated by arrows). It is likely that the fluctuations originate from the electron jet front region at x ≈ 28 and x ≈ 48 (Figure 3), where the fast electron jet hits the outer plasma outflow. In observation, De* is negative before the central dissipation region arrives (Figure 2). This is consistent with the weak undershoot of De in the electron jet region in the PIC simulation (Figure 3). We do not recognize a similar undershoot on the other side (1055:44–1056:44 UT). This is because the Geotail was near the separatrix, outside the central electron jet region [Nagai et al., 2011]. It is not surprising that vi still differs from ve outside the interval (Figures 1c and 1d). Electrons are magnetized there, but ions remain unmagnetized downstream of the electron jet fronts. Reconnection outflow recovers the ideal MHD approximation when ions are magnetized further downstream, but the transition to the MHD region could be ambiguous.

[25] As seen in Figure 2, the Lorentz work W is usually positive over the reconnection region. This signature is consistent with the PIC simulation (Section 3). One can recognize a peak during 1054–1055 UT. We find that Bz is compressed (Figure 1a) in this interval and that the plasma density decreased after the W-region arrived [seeNagai et al., 2011, Figure 1j]. This W-region appears to be a magnetic pile-up region behind a tangential discontinuity, where the compressedBz pushes the dense plasma sheet outward. We do not recognize similar W-region on the other side of 1057–1058 UT, because the satellite was not in the central neutral plane. In fact, we find similarW-regions associated with the pile-up regions in other reconnection events. TheW measure in reconnection deserves further investigation by theories, simulations, and observations.

[26] To our knowledge, this is the first identification of the dissipation region in magnetotail reconnection. Earlier observations focused on large-scale signatures of the reconnection site, such as the flow reversal or Hall fields. In the 15 May 2003 event, Geotail fortunately resolved a small-scale signatures of bi-directional electron jets [Nagai et al., 2011] and then the present work finally detected a compact dissipation region between the jets. Although our resolution is quite limited, this is the best possible measurement with the present instruments. In addition, this work is a step forward for reconnection theories. The dissipation measure theory [Zenitani et al., 2011a] was only tested by 2D PIC simulations with artificial mass ratio. Here we showed that the theory works in the complex real world. The theory appears to be practically useful.

5. Conclusion

[27] We analyzed Geotail reconnection event on 15 May 2003. We applied the electron-frame dissipation measureDe(De*) to the reconnection structure. Using De*, for the first time, we identified the dissipation region around the possible X-point in nature. The dissipation rate (45 pWm−3) and the length of the dissipation region (1–2diloc) are reasonable. We introduced the Lorentz work W as well. The two measures are useful for better understanding of the reconnection structure.

[28] Our approach will be applicable to next-generation in situ observations. NASA's upcoming Magnetospheric Multiscale (MMS) mission features high temporal resolution, multi-satellite observation, and measurement of all three components of the electric field. We will be able to see clearer pictures of the dissipation region.


[29] S.Z. acknowledges S. Imada, M. Hoshino, Y. Miyashita, M. N. Nishino, and M. H. Saito for useful advice.

[30] The Editor thanks two anonymous reviewers for assisting in the evaluation of this paper.