Energetic electron acceleration in the downstream reconnection outflow region

Energetic electron acceleration in the downstream

reconnection outflow region

S. Imada,1,2 R. Nakamura,3 P. W. Daly,4 M. Hoshino,1 W. Baumjohann,3 S. Muhlbachler,4

A. Balogh,5 and H. Reme6

Received 15 May 2006; revised 17 October 2006; accepted 9 November 2006; published 3 March 2007.

[1] Energetic electrons in an earthward reconnection outflow region have been observedby Cluster/Research with Adaptive Particle Imaging Detectors. We found a goodcorrelation between the energetic electron enhancement and a normal magnetic field (Bz)enhancement within a 0.25-s time resolution. The large normal magnetic field is thought tobe associated with magnetic reconnection because the negative/positive Bz reversalobserved during the fast proton tailward/earthward flow reversal is a good indicator ofmagnetic reconnection. Using the four-spacecraft Cluster, we can clearly see that thislarge positive Bz structure propagates in the earthward direction. Furthermore, we find thatthe energy spectrum of the energetic electrons becomes harder toward the downstreamregion. A negative Bz enhancement is also observed. The intensity of energetic electronenhancement associated with the negative Bz enhancement is weaker than thatassociated with the positive one. To discuss the temporal and spatial profile of energeticelectron acceleration in the magnetic reconnection region, we determined the spacecraftposition in the temporally evolving magnetic structures of reconnection. Ourobservation clearly indicates second-step acceleration, in addition to X line acceleration,of energetic electrons in the downstream reconnection outflow region.

Citation: Imada, S., R. Nakamura, P. W. Daly, M. Hoshino, W. Baumjohann, S. Muhlbachler, A. Balogh, and H. Reme (2007),

Energetic electron acceleration in the downstream reconnection outflow region, J. Geophys. Res., 112, A03202,

doi:10.1029/2006JA011847.

1. Introduction

[2] The origin of energetic particles is an unresolvedproblem of long standing in the Earth’s magnetosphere.Magnetic reconnection has been discussed as one of theimportant mechanisms producing energetic particles in themagnetotail, because the magnetic field energy can berapidly released to the particles during reconnection. Inearly satellite observations, energetic ions and electronsbursts in the range of several 100 keV to 1 MeV are oftenobserved in the magnetotail, and it was suggested that theobserved energetic particle bursts are related to magneticreconnection and the formation of a neutral line [e.g., Sarriset al., 1976; Terasawa and Nishida, 1976; Baker and Stone,1977]. Recently, Øieroset et al. [2002], by using the Windsatellite, showed the indication of significant electron

acceleration up to 300 keV in and around the diffusionregion of reconnection.[3] So far various mechanisms have been proposed for

the origin of energetic particles during reconnection.Generally it is believed that energetic particles are acceler-ated by the interaction with an inductive electric field at theX-type neutral line. In the earliest exploration of particleacceleration, a test particle motion was studied by integrat-ing the Lorentz equation in time on the basis of theprescribed electric and magnetic fields obtained by resistiveMHD simulations [e.g., Sato et al., 1982; Scholer andJamitzky, 1987; Birn and Hesse, 1994]. Particle accelerationseems to occur not only in the X-type neutral region but alsoin the whole plasma sheet. Ambrosiano et al. [1988]suggested that MHD turbulence generated in the plasmasheet plays an important role in particle acceleration.[4] Further developments of particle acceleration are

promoted by recent kinetic simulations and modern satelliteobservations. Hoshino et al. [2001a, 2001b] discussed theorigin of hot and suprathermal electrons by comparing afull-particle simulation with Geotail observations, and con-cluded that the electrons are initially energized inside thediffusion region, and then further energized in the outflowregion. Drake et al. [2003] explored electron accelerationduring magnetic reconnection with a guide field using fullparticle simulation and showed that multiple interaction ofelectrons with low-density acceleration cavities can provideenergetic electrons. A statistical study by Imada et al.

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112, A03202, doi:10.1029/2006JA011847, 2007ClickHere

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1Department of Earth and Planetary Science, University of Tokyo,Tokyo, Japan.

2Now at National Astronomical Observatory of Japan, Tokyo, Japan.3Space Research Institute, Austrian Academy of Sciences, Graz,

Austria.4Max Planck Institute for Solar System Research, Katlenburg-Lindau,

Germany.5Space and Atmospheric Physics, Imperial College, London, UK.6Centre d’Etude Spatiale des Rayonnements, Centre National de la

Recherche Scientifique, Toulouse, France.

Copyright 2007 by the American Geophysical Union.0148-0227/07/2006JA011847$09.00

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[2005] discussed the energetic and thermal electron profilein and around the X-type neutral line and the O-typemagnetic island on the basis of Geotail satellite observationsin the magnetotail. The study showed that the energeticelectrons are generated not only at the X-type neutral linebut also in the wider region surrounding the X-type neutralline.[5] Energetic particle acceleration is discussed not only in

the framework of the Earth’s magnetosphere, but also inother space environments [e.g., Zelenyi et al., 1990; Erakerand Simpson, 1986]. In the solar flare context, wheremagnetic reconnection is also believed to be important,Masuda et al. [1995] reported a hard X-ray source abovethe soft X-ray loop structure, concluding that the loop tophard X-ray source indicated electron acceleration at the sitewhere the downward plasma stream collided with theunderlying closed magnetic loop. Tsuneta and Naito[1998] proposed that these nonthermal electrons are effi-ciently accelerated by the first-order Fermi process at a fastoblique shock. The scale size of the Masuda flare is muchlarger than the simulation study by Hoshino et al., but bothMasuda et al. [1995] and Hoshino et al. [2001b] suggestthat the energization occurs around a sort of a magnetic wallwhere the reconnection jet is decelerated.[6] These observations and simulation results suggest that

electron acceleration can take place at different locationsand at different times in the course of reconnection. There-fore simultaneous observations covering different regions ofreconnection by multiple satellites are the key to under-standing the acceleration mechanism. The purpose of thispaper is to present the multipoint view of energetic electronsnear the magnetic reconnection region in a thin currentsheet.

2. Observations of Energetic Electrons

[7] In this study we used the data from comprehensivemeasurements on board the Cluster satellites, includinghigh-energy electrons measured by Research with AdaptiveParticle Imaging Detectors (RAPID) [Wilken et al., 2001],magnetic field from the Fluxgate Magnetometer (FGM)[Balogh et al., 2001], and low-energy ions from the ClusterIon Spectrometry (CIS) experiment [Reme et al., 2001]. Ourobservations were made during the crossing on the dusksidenear-Earth magnetotail from 0947 to 0951 UT on 1 October2001. The position of the Cluster spacecraft was [�16.4, 8,0.5] RE in GSM coordinates. This event was identified byseveral previous studies as crossing the X line from tailwardto earthward [e.g., Runov et al., 2003; Cattell et al., 2005;Wygant et al., 2005].[8] An overview of this observation is shown in Figure 1

using spin resolution (4 s) data. In the top plots, X and Zcomponents of the magnetic field [nT] in GSM, protonperpendicular velocity [km/s], and high-energy electron flux[/(cm2 str s keV)] are shown. For proton velocity, we usedthe CIS data from the Composition and Distribution Func-tion (CODIF) analyser and calculated the perpendicularcomponents to the magnetic field. All the RAPID data usedin this paper include time offset correction. The energyranges of the high-energy electron flux are 35.34–50.5 keV(darkest curve, highest value), 50.5–68.1 keV (second-darkest curve, second-highest vakue), 68.10–94.5 keV

(second-lightest curve, third-highest value), and 94.5–127.5 keV (lightest curve, lowest value), respectively.During this event, Cluster 3 (C3) was closest to the Earthand to the neutral sheet. Cluster 4 (C4), the most tailwardsatellite, was �2000 km tailward from C3, and Cluster 1(C1) was the most northern spacecraft. The Cluster tetrahe-dron configuration is also shown at the top of Figure 1. TheX component of the magnetic field shows that C1 tended toremain in the lobe or the plasma sheet boundary from 0948to 0949, while the other three spacecraft had multipleencounters with the current sheet.[9] After the passing of a plasmoid from 0947 to 0948,

Cluster observed the reversal of high-speed proton bulkflow from tailward to earthward with a changing Z compo-nent of the magnetic field from negative to positive during0948–0949, which is the indication of passing an X-typeneutral line. The event on 1 October 2001 was well studiedconcerning the fine reconnection structure such as Hallmagnetic field or double peaked current sheet by Runov etal. [2003]. According to their analysis, Cluster was locatednear the magnetic diffusion region at 0948:20 UT, becausethe curvature of the magnetic field changed from negative topositive during the neutral sheet crossing. Furthermore, theyshow the Y component of the magnetic field curvature isquite smaller than the X component of the curvature in GSMcoordinate. This result implies that the tilt of the currentsheet is small in GSM coordinate. We also check the tilt ofthe current sheet by using minimum variance analysis nearthe diffusion region, and we find small tilt of the currentsheet with respect to the ZGSM = 0 plane. Therefore theGSM system is suitable for studying this event and we useGSM coordinate overall this paper. After passing thevicinity of the magnetic diffusion region, C2, C3, and C4observed a sharp energetic electron enhancement up to127.5 keV. Furthermore, C3 detected a strongly steepenedmagnetic field (Bz > 10 nT) during the energetic electronenhancement. Those electron enhancements are not simul-taneous among C2, C4,and C3. C3 detected the electronenhancement a few seconds later when C2 and C4 detectedthe electron enhancement. These differences of timing couldreflect the position of each spacecraft: C2 and C4 arelocated tailward of C3. Unfortunately, in Figure 1 thereare hardly any differences to discuss in the temporal profileof the energetic electron enhancement and magnetic fieldsignature among the spacecraft. The reason seems to be thatthe signature is averaged over a spin period (4 s) with aCluster tetrahedron scale of 2000 km and an outflowvelocity of 500 km/s. To discuss the time profile of theenergetic electrons, we need the high time resolution data ofthe energetic electron and the magnetic field during thistime interval.[10] Figure 2 shows the two dimensional energetic elec-

tron data in the spacecraft spin plane from 0948 to 0949. Weused the energy range to obtain the electron flux between50.5 and 127.5 keV. We can clearly see that the electronenhancements occur within a few spin periods. One spinperiod is 4 s and there are consecutive observations from16 sectors in the azimuthal direction. These observations ofazimuthal direction are taken using the spacecraft spin[Wilken et al., 2001]. During this time interval, these threespacecraft, C2, C3, and C4, are located in the plasma sheetwith earthward flow. The time variation of enhancement

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could not be caused by anisotropy because high-energyelectrons are expected to be isotropic by multiple interactionwith neutral sheet, especially in the thin current sheet [Smetset al., 1998]. We assume that these electrons remainisotropic, although the flux varies with time. In this waythe energetic electrons flux data are obtained with a timeresolution of (1spin)/sector = 4/16[s], which is the time tocollect data within one azimuthal sector.[11] We check the validity of our isotropic assumption of

energetic electrons by comparing the electron enhancementpeak direction at C2, C3, and C4 (Figure 2). The peak at C2is in sector 12. Note that the sector 12 corresponds to datawhen the sensor is looking toward the Sun as illustrated inthe top plot of Figure 2, where the looking direction of

RAPID sensor is shown for the azimuthal sectors. The peakat C3 is in sector 5 which is in tailward looking, and thepeak at C4 is in sector 9 which is the duskward lookingsector. It seems that there is no systematic asymmetry,because the three spacecraft observed the electron enhance-ment peak by looking different directions. Unfortunately,the three-dimensional RAPID data are not available on thisevent. By using only spin plane data, we also check therelationship between energetic electrons and pitch angle,and there is no systematic relationship between both.[12] Figure 3 shows the relationship between the X (top)

and Z (middle) components of the magnetic field with 1/22-stime resolution and the omnidirectional energetic electronflux in the energy range between 50.5 and 127.5 keV,

Figure 1. Overview of Cluster data behavior of 0947–0951 UT on 1 October 2001: (top to bottom) Xand Z components of the magnetic field (nT) in GSM, proton perpendicular velocity (km/s), and high-energy electron flux (/(cm2 str s keV)). The energy ranges of the high-energy electron flux are 35.34–50.5 keV (darkest curve, highest value), 50.5–68.1 keV (second-darkest curve, second-highest value),68.1–94.5 keV (second-lightest curve, third-highest value), and 94.5–127.5 keV (lightest curve, lowestvalue). The Cluster tetrahedron configuration is also shown at the top of the figure.

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Figure 2. Two-dimensional energetic electron flux (/(cm2 str s keV)) behavior from 50.5 to 127.5 keV.The vertical axis shows azimuthal sectors, and the horizontal axis gives UT. Orientation of the RAPIDazimuthal sectors relative to the Sun is also at the top of the figure.

Figure 3. Relationship between the (top) X and (middle) Z components of magnetic field (nT) with1/22-s time resolution and (bottom) omnidirectional energetic electrons flux (energy range is from 50.5 to127.5 keV) (/(cm2 str s keV)) with 0.25-s time resolution on Cluster 2 from 0948:30 to 0949:00.

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assuming isotropic distribution (bottom), on C2 from0948:30 to 0949:00. At 0948:41, C2 observed a largeBz (�8 nT) reversal at short time. This reversal is thoughtto indicate that C2 is in the vicinity of the X line. During thereversal time, the energetic electron level is �102/(cm2 str skeV). We can see the clear relationship between the ener-getic electron enhancement and the enhancement of the Zcomponent of the magnetic field in the middle and bottomof Figure 3. There are two peaks of energetic electronenhancement with large positive Bz, and the intensity ofthe first peak is larger than the second one. The peak time ofthe first electron enhancement is 0948:43.051, and the valueof the energetic electron flux is 515/(cm2 str s keV). A smallenhancement of energetic electron with large negative Bz

can also be seen. This enhancement, however, is weakerthan the enhancement with positive Bz. Figures 4 and 5

show the relationship between the magnetic field andenergetic electron flux of C3 and C4, respectively. In theboth cases of C3 and C4 enhancement, the energeticelectron flux level exceeds �102/(cm2 str s keV). We canalso see the good correlation between energetic electronenhancements with Bz enhancements both at C3 and C4.The peak times of electron enhancement of C3 and C4 are0948:49.508 and 0948:41.45, respectively, and the maxi-mum values of the energetic electron flux are 3310 and 838/(cm2 str s keV), respectively. The value of Bz detected by C3and C4 is �16 and 6 nT, respectively. Furthermore, bycomparing the peak time of electron enhancement amongC2, C3, and C4, the energetic electron enhancements areobserved in order from tailward to earthward: C4 waslocated the most tailward, and C3 was located the mostearthward.

Figure 4. Relationship between the (top) X and (middle) Z components of magnetic field (nT) with1/22-s time resolution and (bottom) omnidirectional energetic electrons flux (energy range is from50.5 to 127.5 keV) (/(cm2 str s keV)) with 0.25-s time resolution on Cluster 3 from 0948:30 to0949:00. The figure scales are the same as in Figure 3.

Figure 5. Relationship between the (top) X and (middle) Z components of magnetic field (nT) with1/22-s time resolution and (bottom) omnidirectional energetic electrons flux (energy range is from50.5 to 127.5 keV) (/(cm2 str s keV)) with 0.25-s time resolution on Cluster 4 from 0948:30 to0949:00. The figure scales are the same as in Figure 3.

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[13] Let us discuss the structure of energetic electronenhancement which propagates earthward in the XGSM �YGSM plane by using both the energetic electron peak timeand position of each spacecraft. First, C4 observed anenergetic electron enhancement at 0948:41.450. C2 andC3 observed the enhancement 1.501 and 8.058 s later,

respectively. If the enhancement region were uniform inthe YGSM direction and propagated with constant speed, thetiming differences among C2, C3, and C4 are proportionalto the difference of XGSM position. However, these timingdifferences are not proportional to the difference in XGSM

position: C2 and C4 are located 634 and 2124 km tailwardof C3, respectively (see Figure 1). Therefore we think thatthis enhancement region is tilted in the X-Y plane. Figure 6shows the schematic view of energetic electron enhance-ment region inclined in the X-Y plane, which is calculatedfrom the position and enhancement time of each spacecraft.In this estimation, we assume that the energetic electronregion is uniform in the Z direction. The assumption seemsvalid for this analysis, because all magnetic x componentsdetected by C2, C3, and C4 are small in comparison withthe normal magnetic field (Bz) (Figures 3–5).

3. Analysis of Reconnection Structure

[14] To discuss the energetic electron acceleration region,we place the spacecraft position in the magnetic reconnec-tion region. It is useful to transform the magnetic field dataof (Bx, Bz) into the relative position of (X, Z) from theX-type neutral line. Imada et al. [2005] describe thedistance by a nondimensional unit and is normalized by acharacteristic scale length for X and Z direction by using the

Figure 6. Schematic view of energetic electron enhance-ment region inclined in the X-Y plane which is calculatedfrom position and enhancement time of each spacecraft. Thearrow gives the change of enhancement region between4841.450 and 4849.

Figure 7. Best fit parameters for magnetic reconnection from 0948:30 to 0949:00 (see text for details).

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relationship between the magnetic field and the spatialcoordinate with some assumption of parameters. In thispaper, we calculate the scale length by using the four-spacecraft data instead of any assumption of scale lengthor a. As the coordinate transformation for this reconnectionevent, we use the relationship of

B ¼ Blobe ax

lx

ez þ tanhz

lz

� �ex

� �; ð1Þ

where B and Blobe are the local magnetic field observed byCluster and the lobe magnetic field, respectively. Thereconnection rate, which is represented by a, is believed tobe �0.2 for a steady state reconnection model [Shay et al.,2001]. Our only assumption is the 2-Dmagnetic field model inthe reconnection region, which is described by equation (1). Ingeneral, there are some y dependences in the current sheetsuch as kink-mode waves. The typical observed wave-length in the y direction is 2�3 RE [e.g., Sergeev et al.,2003]. However, the maximum distance between thespacecraft in our observation is �1700 km which is quitesmaller than the wavelength. Thus the spatial variationcaused by kink mode in the Y direction is thought to bequite small. Indeed, the normal vectors of current sheetwhich calculated by using C2, C3 and C4 is almost same.

Thus we assume that reconnection take place in twodimensions. How to estimate the parameters such as a, lxand lz is shown in Appendix A.[15] Figure 7 shows the best fit parameters of this

magnetic reconnection between 0948:30 and 0949:00. Fromtop to bottom, Blobe, lz, lx/a, lx and a are shown. Duringthis time interval, Blobe is almost constant between 24 to28 nT. From 0948:30 to 0948:40, lz stays near 1200 km.After 0948:40, the current sheet gets thicker, and at0949:00, lz is almost 2200 km. Recently, thin current sheetstructures have been well studied [e.g., Nakamura et al.,2002; Asano et al., 2003; Nakamura et al., 2006] and thehalf thickness of the current sheet is often of the order of theproton inertia length. In this event, Runov et al. [2003]argued that the current sheet thickness is roughly 500–600 km from 0948:07–0948:40. In our analysis, the thin-nest current sheet is 743 km at 0948:16 (not shown here).Therefore it seems that our analysis of the current sheetthickness is consistent with Runov et al. [2003]. Theparameters of lx/a and lx show the same trend as lz. Thevalue of lx is almost 4000 km from 0948:30 to 0948:40 andgrows thicker up to 7500 km at the end of this interval. Theratio of scale length, a, is almost constant near 0.3 duringthis interval, and the value is consistent with recent kineticsimulation [e.g., Shay et al., 2001]. We may thereforeconclude that reconnection structure self-similarly expandstoward both the x and z direction with the same a � 0.3.[16] To calculate the spacecraft position, we use the 30-s

moving average value of the magnetic field among C2, C3,and C4. We put lz, lx/a, and center-averaged Bx and Bz intoequation (1), and derive the center position of the three-spacecraft triangle in the reconnection region. We know therelative position of C2, C3, and C4 from the center of thetriangle. Figure 8 shows the relative position of C2, C3, andC4 in the magnetic reconnection region. From the top, theresults at 0948:32, 0948:40, 0948:48, and 0949:56 areshown. C1 is located more than 1000 km away fromequatorial plane in the northern lobe region during thisinterval (not shown here). The curves show the contour ofthe magnetic vector potential.[17] C2 is located near the plasma sheet boundary layer

on the earthward side during these time intervals. C3 islocated in the central plasma sheet on the earthward side,and C4 is located very near to the X line during these timeintervals. We can clearly see that the reconnection regionexpands toward both the x and z directions with time. Wecan also see that the neutral line propagates tailward (atroughly 100 km/s).[18] Let us check the validity of our calculation of

spacecraft position. It is useful to compare the magneticfields observed by each spacecraft with the magnetic fieldscalculated by our analysis. Figure 9 shows both observedand calculated magnetic field. From top to bottom, Bx2, Bz2,Bx3, Bz3, Bx4 and Bz4 are shown, respectively. Subscriptsgive spacecraft numbers. The thick curves are the magneticfields calculated by our magnetic field model, and the thincurves are the observed magnetic field with 1/22-s timeresolution. The arrows give the energetic electron enhance-ment time as discussed before. More rapid variations of themagnetic field can be seen, but the trends are consistentbetween observation and estimation. Especially, normalmagnetic field reversal of C2 is delayed from our model.

Figure 8. Relative position of C2, C3, and C4 in themagnetic reconnection region. The vertical axis gives Z (km),and the horizontal axis gives X (km). The curves showcontours of the magnetic vector potential. The results at (topto bottom) 0948:32, 0948:40, 0948:48, and 0948:56 areshown. C1 is located more than 1000 km away from theequatorial plane in the northern lobe region during thisinterval (not shown here). The square, triangle, and invertedtriangle show the spacecraft position of C2, C3, and C4,respectively.

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Reasons for the discrepancies with C2 might be that the finereconnection structure is not as simple as the structuredescribed by equation (1). In spite of these discrepanciesin transient features, we think that the averaged trends of thereconnection, such as tailward motion of the X line ordevelopment of the entire current sheet, are well reproducedwith the model.

4. Energetic Electrons in the ReconnectionRegion

[19] In this section, we try to determine the accelerationregion for energetic electrons in the structure of the mag-netic reconnection which is calculated in the previoussection. The first enhancement of energetic electrons hasbeen observed at 0948:41 by C4 (see Figure 5). At this time,we can see that C4 is located earthward and in the vicinityof the X line in the second plot of Figure 8. The timevariation of the magnetic field in the bottom two plots ofFigure 9 shows that C4 moves to the inner central plasmasheet and observes Bz � 5 nT around the enhancement time

indicated by an arrow. This normal magnetic field is largerthan we expected from the model.[20] The second energetic electron enhancement has been

observed at 0948:43 by C2 (see Figure 3). At this time, C2is located earthward of the X line and almost 500 km awayfrom the equatorial plane (cf. second plot of Figure 8). Wecan also see that C2 and C4 are located along almost thesame magnetic field line in Figure 8. The top two plots inFigure 9 show that at the enhancement time, C2 moves fromthe boundary layer (Bx � 10 nT) to the inner central plasmasheet (Bx � a few nT) and observes the strong Bz � 8 nT.The energetic electron flux of second positive and negativeBz peaks are weaker than those of the first positive Bz peak.At these weak enhancement times, C2 is located more in theouter plasma sheet than during the first enhancement time.[21] The latest and most energetic enhancement of elec-

tron fluxes has been observed at 0948:50 by C3. At thistime, in the third plot of Figure 8, we can see that C3 islocated on the earthward side in the central plasma sheet andmore than 3000 km away from the X line. During theenhancement time, C3 is located in the central plasma sheetand observes strong Bz � 16 nT. This large normal magneticfield is 60 percent of the lobe magnetic field.[22] To discuss whether these electron enhancements are

caused by an adiabatic or a nonadiabatic process, we analyzethe electron energy spectrum at the enhancement peak time ofeach spacecraft. Figure 10a shows the electron energy spec-trum integrated over pitch angle for the electron enhancementpeak times (C2 0948:40, C3 0948:48, C4 0948:39). Thesquares show the peak energy spectrum of C2, the trianglesshow the energy spectrum of C3, and the inverted trianglesshow the energy spectrum of C4. The value of energeticelectrons observed by C1 is approximately the backgroundlevels during this time interval (not shown here). The verticalaxis gives the phase space density (logarithmic scale), and thehorizontal axis shows the energy. We fit the power lawdistribution as / E�g with the energy range from 43 to111 keV by logarithmic least squares fit, because the valueof other energy channels are approximately the backgroundlevel. Fitted g of C2, C3, and C4 are 6.3, 5.0, and 6.5,respectively. Comparing the energy spectra of these intervals,the spectrum of C3 at 0948:52, which is denoted by triangles,is the hardest one. The power of C3 is almost the same value asthe power in theWind observation discussed byØieroset et al.[2002]. We also carry out single-spacecraft analysis of energyspectra to check the consistency of four-spacecraft result.Figure 10b shows the evolution of the electron distributionwhich observed byC3. The power law indexes, g, are 6.7, 6.3,and 5.0 at the time of 0948:40, 0948:44, and 0948:48,respectively. Both of the analyses using four and singlespacecraft indicate that the spectrum of C3 at 0948:52 is thehardest one.[23] All energetic electron enhancements are observed

during a large normal magnetic field. It seems that thereare also the correlation between Bx and energetic electronexcept C3. Energetic electrons are preferentially observed inthe inner plasma sheet where jBxj is small. This correlationis reasonable, because in general the center of plasma sheetis more energetic than the outer plasma sheet. Note howeverthat C3, which is continuously staying in the inner plasmasheet, observes the energetic electron enhancement with

Figure 9. Observed and modeled magnetic field showing(top to bottom) Bx2, Bz2, Bx3, Bz3, Bx4 and Bz4 (nT)(subscripts give spacecraft number). The thick curves arethe magnetic fields calculated by our magnetic field model,and thin curves are observed magnetic field with 1/22-s timeresolution. The arrows show the energetic electron en-hancement time.

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normal magnetic field (Bz) enhancement. The electronenhancement observed in C3 therefore cannot be due tothe spatial profile across the plasma sheet. The order ofdetected timing of the enhancement starts from the space-craft nearest to the X point. The electrons are accelerated upto more energetic energy far from the X point toward thedownstream region of earthwardside. From these results, wecan conclude that the acceleration region that has a largenormal magnetic field Bz is created near to the X point andpropagates to the downstream region while producingfurther high-energy electrons.

5. Discussion and Summary

[24] We have studied the behavior of the high-energyelectrons in the vicinity of the near-Earth neutral line by themultispacecraft Cluster observation. We found that the high-energy electron flux enhancement is associated with largenormal magnetic fields (Bz). These energetic electrons areconfined in the magnetic field associated with reconnection

and propagate earthward with the fast plasma flow. Further-more, energetic electrons are preferentially observed in theinner plasma sheet. We also found that the energy spectrumbecomes harder with the time evolution of reconnection.[25] Let us discuss the large normal magnetic field region

that propagate earthward in the course of energetic electronacceleration. C3 observed the energetic electron enhance-ment 8 s after C4 observed the enhancement. The propaga-tion velocity can be estimated at 312 km/s for XGSM

direction from Figure 6. The time duration of the electronenhancement is almost 3 s at C2, C3, and C4; therefore thethickness of the electron enhancement for XGSM direction is3 (s) 312 (km/s) � 1000 km, i.e., about the proton inertialength. At first, C4 observed four peaks of large normalmagnetic field (6 nT) with 1 s duration each; next C2observed two peaks (8 nT) with 3 s duration; and at last C3observed a single peak (16 nT) with 3 s duration. Thereforewe think that these large normal magnetic field regions aretime-dependent and enlarging their normal magnetic fieldintensity. The number of peaks, differ at each spacecraft, isthought to be the product of an oscillation of the magneticreconnection, and those bundles of magnetic field aretogether with time. One of the interpretations of theseoscillation is that magnetic islands are produced [e.g.,Horiuchi et al., 2001; Drake et al., 2003].[26] We now discuss the energetic electron acceleration

process in the course of magnetic reconnection under a thincurrent sheet (lz � ion inertia length). It seems that there aretwo different acceleration regions in the magnetotail. One isnear the X-type diffusion region and the other is the piled-up magnetic field region. Hoshino et al. [2001b] proposed atwo-step acceleration mechanism for reconnection. Theunmagnetized electrons in the vicinity of the X-type diffu-sion region can be accelerated by strong inductive electricfield during the meandering/Speiser motion [e.g., Shay etal., 2001]. Zelenyi et al. [1990] discussed the energyspectrum of particles accelerated near X point of themagnetic field with finite normal magnetic field effect inthe course of the tearing instability development in thecurrent sheet. They conclude that the inductive electric fieldis able to generate energetic electrons and the power lawindex of these electrons is 4�10 in the case of Earth’smagnetosphere. Another important agent of the electronpreacceleration is surfing acceleration [Hoshino, 2005]. Elec-trons can be trapped by the polarization electric fields whichare strongly enhanced in an externally driven reconnectionsystem and can gain their energies from the convection/inductive reconnection electric fields. Accelerated electrons,which have a large gyroradius, are then transported outwardfrom the diffusion region and are further accelerated aroundthe piled-up magnetic field region because ofrB drift and/orcurvature drift under the nonadiabatic motion of k � 1 witheffective wave scattering [e.g., Buchner and Zelenyi, 1989;Delcourt et al., 1996]. Our Cluster observation gives evi-dence of the second-step acceleration at the downstreamreconnection outflow region, and we think that the energiza-tion around the strongBz region plays an important role on thereconnection downstream region.[27] Let us discuss a mechanism of the pileup magnetic

field. The fast reconnection outflow is colliding with thepreexisting stationary plasma, and the pileup of the mag-netic field is formed at the downstream of fast flow [e.g.,

Figure 10. (a) Electron energy spectrum integrated overpitch angle for the electron enhancement peak time (C2,0948:40; C3, 0948:48; and C4, 0948:39). Squares show thepeak energy spectrum of C2, triangles show the energyspectrum of C3, and inverted triangles show the energyspectrum of C4. Vertical axis shows logarithmic scale ofphase space density (s3/m6), and horizontal axis showslogarithmic scale of energy (keV). We fitted the power lawcurves as / E�g with energy range from 43 to 111 keV.(b) Time series of energy spectra obtained by C3. Solid,dotted, and dashed curves show the energy spectra fitted bypower law at 0948:48, 0948:44, and 0948:40, respectively.The power law indices, g, are 6.7, 6.3, and 5.0 at 0948:40,0948:44, and 0948:48, respectively.

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Ugai, 1995; Nagai et al., 1998; Hoshino et al., 2001b].Plasma sheet field lines are at first reconnected, and then thereconnection proceeds to tail lobe field lines. The outflowspeed of magnetic reconnection is approximately the Alfvenvelocity. The outflow velocity of plasma sheet reconnectionis slower than that of tail lobe reconnection, because theplasma mass density is quite small in the tail lobe. Thisdifference in the velocity of reconnection outflow might bean important role on the pileup of the magnetic field, anddecide whether additional acceleration at the downstreamcan take place. Furthermore, especially in the near-Earthreconnection, the earthward flow collides with the strongerintrinsic dipole-like magnetic field which is one of thecandidates of an obstacle in the downstream region. Imadaet al. [2005] also mentioned that the intensity of energeticelectrons flux is much higher in the earthward flow regionthan in the tailward flow region in the near-Earth reconnec-tion. They also mentioned that this difference is probablyunderstood by the dipole field effect of the earth. In ourCluster observation, the velocity gap at neutral sheet is500 km/s (�ion sound speed) and the pileup region isobserved �10 s before the peak of fast earthward flow.This result indicates that the pileup region exist in the frontof fast flow and is consistent with our scenario. Further-more, the abundance of oxygen in the plasma sheet isextremely high (70 percent) [Wygant et al., 2005]. The richoxygen may support to produce large normal magneticfield. Although second-step acceleration with large Bz wasobserved in some cases, additional acceleration was notobserved in other cases [e.g., Øieroset et al., 2002]. Toexplain the absence of additional acceleration, two reasonscan be considered according to the discussion above. Thefirst reason is the effect of the intrinsic dipole-like magneticfield, which is one of the candidates of an obstacle in thedownstream region. It is plausible that second-step acceler-ation is not observed in the deep tail region where theintrinsic dipole-like magnetic field is negligible. The secondreason is the difference in outflow velocity between plasmasheet reconnection and tail lobe reconnection. The outflowvelocity may have important role to produce a large pileupmagnetic field. There might also be other reasons such asrich oxygen or spatial variation along the Y direction. Wecannot decide what control the production of large pileupmagnetic field by only one event. This is unresolved issue.[28] In Figure 4, C3 observed almost constant magnetic

field (Bx � 0 nT, Bz � 5 nT) after C3 observed a largenormal magnetic field (0948:52). The pileup magnetic fieldregion is located in the front of the reconnection outflowregion. Therefore it seems that C3 was located between alarge normal magnetic field region and an X-type neutralline, because C3 observed the large normal magnetic field at0948:50 with fast earthward plasma flow. We can find thatthe energetic electron flux behind the pileup region is higherthan that in the normal plasma sheet. This result indicatesthat there is preacceleration between a large normal mag-netic field region and an X-type neutral line, although wecannot directly find the energetic electron acceleration in thevicinity of X line. The preacceleration in the vicinity of Xline is discussed in many past studies [e.g., Øieroset et al.,2002]. From our study, we can deduce the preaccelerationlevel as the one observed after 0948:52 (Figure 4, dashedcurve). However, it is difficult to determine whether these

accelerated electrons are made by meandering/Speiser mo-tion or by surfing acceleration in the vicinity of X line.[29] In Figure 10, the power law indexes vary with time

and location. This is one of the evidence that these electronsare caused by a nonadiabatic process, because adiabaticbetatron acceleration cannot change the power law index.Let us estimate the energetic electron energy of nonadia-batic motion k � 1 in our model, which is described byequation (1). k value is one of the important agents fornonadiabatic motion in the reconnection downstream re-gion. In the neutral sheet where Bx is 0, nonadiabatic energy(k � 1) can be expressed with our parameters by

Eele ¼e2

2mec2

� �lz

2 alx

� �4

Blobe2x4; ð2Þ

where e is the electric charge and me is the electron mass. Atthe energetic electron enhancement time of C3 (0948:50),lz, lx/a, and Blobe are 1500 km, 20000 km, and 28 nT,respectively. Note that at this time the half thickness of thecurrent sheet (lz) is relatively thicker than the thicknessobserved by Nakamura et al. [2002] or Asano et al. [2003].When we put x = 3000 km and the parameter values of lz,lx/a and Blobe into equation (2), we get Eele � 150 keV.These estimations of nonadiabatic energy (k � 1) includesome uncertainty, such as lz or lx/a. However, at theenhancement time (Bz � 16 nT), the gradient of Bz (�10/1000 [nT/km]) is larger than that estimated by our model.Therefore it seems that energetic electrons observed by C3around the peak time are highly magnetized.[30] One of the candidates which breaks the adiabatic

motion of energetic electron is the interaction between theturbulent current sheet and energetic electrons. In recentwave observations of the reconnection region [e.g., Cattellet al., 2005], large-amplitude solitary waves (�0.1 fpe) thatwere polarized primarily parallel to the magnetic field orwaves near the lower hybrid frequency [e.g., Shinohara etal., 1998] that were predominantly perpendicular to themagnetic field have been observed. These waves may havean important role in the scattering during the course ofenergetic electron acceleration.

Appendix A: Calculation of ReconnectionParameters

[31] We calculate reconnection parameters such as thehalf thickness of the current sheet or the ratio of the typicalscale length between x and z to discuss the spacecraftlocation in the reconnection region. We calculate the scalelength by using four-spacecraft data instead of any assump-tion of scale length or a. As the coordinate transformationfor this reconnection event, we use the relationship ofequation (1). Our only assumption is the magnetic fieldmodel in the reconnection region which is described byequation (1). We use 30-s moving average data, a protongyroperiod at B � 2 nT, to remove a rapid oscillation, belowgyroperiod.[32] We evaluate the lobe magnetic field from pressure

balance by equating the lobe magnetic pressure to the sumof the local gas and magnetic pressures measured by C1,which was located near to the lobe region from 0948:30 to

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0949:00. The X and Z component of equation (1) can betransformed as follows:

x ¼ lx

aBz

Blobe

ðA1Þ

z ¼ lz tanh�1 Bx

Blobe

� �: ðA2Þ

To get the parameters, such as lx/a and lz, we use the leastsquares method by using the relative distances among C2,C3, and C4 calculated from equations (A1) and (A2). Weknow the distance between each spacecraft, and we alsoknow the tilt of energetic electron enhancement region inthe X-Y plane, which is discussed in Figure 6. By slidingthe spacecraft positions to the YGSM plane along theenergetic electron enhancement line (see Figure 6), weobatin the relative spacecraft position: C2(�2013, 1008),C3(0, 0), C4(�2513, 476). Using different lx/a and lz, wesurvey the minimum values of Mx and Mz:

Mx �Xi¼2;3

Xi<j

j¼3;4

xi � xj� �

�Dxi; j

� �2 ðA3Þ

Mz �Xi¼2;3

Xi<j

j¼3;4

f zi � zj� �

�Dzi; jg2; ðA4Þ

where xi and zi (i = 2, 3, 4) are the relative position from theX-type neutral line calculated by equations (A1) and (A2),Dxi,j andDzi,j (i = 2, 3, j = 3, 4, i < j) is the distance betweenCluster(i) and Cluster( j). If we assume a = lz/lx, which is aSweet-Parker like diffusion region,

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffilzlx=a

pand

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffilza=lx

prepresent lx and a, respectively. We estimate the meansquare errors of lx/a and lz by the following equation:

mlx=a � 1ffiffiffi3

p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXi¼2;3

Xi<j

j¼3;4

xi � xj� �

�Dxi;j

Bzi

Blobe� Bzj

Blobe

( )2vuut ðA5Þ

mlz �1ffiffiffi3

p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXi¼2;3

Xi<j

j¼3;4

zi � zj� �

�Dzi;j

tanh�1 Bxi

Blobe

� �� tanh�1 Bxj

Blobe

� �8<:

9=;

2vuuut ; ðA6Þ

where mlx/a and mlz

are the mean square error of lx/a andlz, respectively. Additionally, we estimate the mean squareerrors of a and lx by standard error propagation methodusing the following equation:

F lz;lx=að Þ � a ¼

ffiffiffiffiffiffiffiffiffiffilz

lx=a

sðA7Þ

ma �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi@F

@lz

mlz

� �2

þ @F

@lx=amlx=a

� �2s

ðA8Þ

G lz;lx=að Þ � lx ¼ffiffiffiffiffiffiffiffiffiffilz

lx

a

rðA9Þ

mlx�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi@G

@lz

mlz

� �2

þ @G

@lx=amlx=a

� �2s

; ðA10Þ

where ma and mlxare the mean square error of a and lx,

respectively. In this way, we estimate the best fit parameterslz, lx and a.

[33] Acknowledgments. We thank all members of the IWF Clusterteam for discussing the Cluster data. The authors are grateful to Y. Asano,T. Takada, T. Terasawa, T. Yokoyama, I. Shinohara, Y. Saito, andH. Hayakawa for fruitful discussions. This work was supported in partby the 21st COE Program of University of Tokyo, Predictability of theEvolution and Variation of the Multi-scale Earth System, and by the Grant-in-Aid for Creative Scientific Research of MEXT/Japan, the Basic Study ofSpace Weather Predication.[34] Amitava Bhattacharjee thanks LevM. Zelenyi and another reviewer

for their assistance in evaluating this paper.

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�����������������������A. Balogh, Space and Atmospheric Physics, Imperial College, London

SW7 2BZ, UK.W. Baumjohann and R. Nakamura, Space Research Institute, Austrian

Academy of Sciences, Schmiedlstr. 6, A-8042, Graz, Austria.P. W. Daly and S. Muhlbachler, Max Planck Institute for Solar System

Research, Katlenburg-Lindau, D-37191 Katlenburg-Lindau, Germany.M. Hoshino, Department of Earth and Planetary Science, University of

Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan. ([email protected])S. Imada, National Astronomical Observatory of Japan, 2-21-1 Osawa,

Mitaka, Tokyo 181-8588, Japan. ([email protected])H. Reme, CESR, CNRS, F-31028 Toulouse, France.

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