Favorable conditions for energetic electron acceleration during magnetic reconnection in the Earth s magnetotail

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi: /2011ja016576, 2011 Favorable conditions for energetic electron acceleration during magnetic reconnection in the Earth s magnetotail S. Imada, 1 M. Hirai, 2 M. Hoshino, 2 and T. Mukai 1 Received 17 February 2011; revised 9 May 2011; accepted 17 May 2011; published 16 August [1] We have studied favorable conditions for energetic electron acceleration during magnetic reconnection in the Earth s magnetosphere using the Geotail data. We have found the strong energetic electron acceleration in some reconnection events. On the other hand, the other reconnection events show weak electron acceleration. To discuss what reconnection characteristics determine energetic electron acceleration efficiency, we have studied the reconnection characteristics for 10 events in which the Geotail satellite observed the vicinity of the diffusion region. We have classified the relationship between the reconnection characteristics and the electron acceleration efficiency into three types: (1) good correlation (absolute value of correlation coefficient r > 0.6); (2) ambiguous correlation (0.6 > r > 0.3); and (3) no correlation (0.3 > r ). We found that ion heating, electron heating, current sheet thickness, reconnection electric field, and converging normal electric field could be categorized into good correlation. Ion/electron temperature ratio, total amount of reconnected magnetic energy, and reconnection rate were classified in ambiguous correlation. We could not find any correlation between energetic electron acceleration efficiency and absolute value of outflow velocity, current density parallel to magnetic field (Hall current system), and satellite location in the Earth s magnetosphere. From our analysis we claimed that the electrons are efficiently accelerated in a thin current sheet during fast reconnection events. Citation: Imada, S., M. Hirai, M. Hoshino, and T. Mukai (2011), Favorable conditions for energetic electron acceleration during magnetic reconnection in the Earth s magnetotail, J. Geophys. Res., 116,, doi: /2011ja Introduction [2] Magnetic reconnection has been discussed as one of the important mechanisms for plasma heating and particle acceleration in space. One of major aspects of magnetic reconnection is rapid energy conversion of stored free magnetic energy to kinetic, thermal, and nonthermal particle energy. These energy conversions are fundamental and essential to understand dynamical behavior of plasma in the Earth s magnetosphere [e.g., Hones, 1979; Angelopoulos et al., 1994; Mukai et al., 1996; Nagai et al., 1998, 2001; Nakamura et al., 2002; Øieroset et al., 2002; Imada et al., 2005, 2007, 2008]. The fundamental and important question of magnetic reconnection is what determines the energy distribution rate from magnetic field energy to plasma particle energies. Especially, it is important to understand what conditions control particle acceleration efficiency during magnetic reconnection. Some reconnection events in the Earth s magnetosphere clearly show strong particle acceleration. On the other hand, particle acceleration is not clear in other similar events. Recently, Gosling et al. [2005] 1 Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Sagamihara, Japan. 2 Department of Earth and Planetary Science, University of Tokyo, Tokyo, Japan. Copyright 2011 by the American Geophysical Union /11/2011JA discussed the energetic particle acceleration during magnetic reconnection in the solar wind, and they concluded there are no evidence for any substantial increase in energetic particle intensity associated with magnetic reconnection. It seems that particle acceleration is relatively sensitive to some reconnection characteristics. So far lots of studies in not only the Earth s magnetosphere but also solar, astro, or laboratory plasmas have challenged to answer the question. It is still not clear. [3] In the Earth s magnetosphere, the energetic particles are often observed in the plasma sheet associated with substorm activities. Pioneering observations showed that energetic ions and electrons bursts in the range of several 100 (kev) to 1 (MeV) are often observed in the plasma sheet, and it was suggested that those are related to formation of a neutral line [e.g., Sarris et al., 1976; Terasawa and Nishida, 1976; Baker and Stone, 1977]. It is generally believed that energetic particles are accelerated by the interaction with an inductive electric field at the X type neutral line. Later, Øieroset et al. [2002] confirmed this interpretation by showing the indication of significant electron acceleration up to 300 (kev) around the X type neutral line with the Wind satellite observation. Meanwhile some study showed that the energetic electrons are generated not only at the X type neutral line but also in the wider region surrounding the X type neutral line [e.g., Imada et al., 2007; Asano et al., 2008]. A statistical study by 1of13

2 Imada et al. [2005] discussed plasma heating and acceleration in and around magnetic reconnection region. They concluded that the electrons are first energized at the X line and further accelerated in the magnetic flux pileup region. The other important recent findings for particle acceleration are the relationship between small magnetic islands and the enhancement of energetic electrons. Chen et al. [2008] showed that energetic electron fluxes peak at sites of compressed density within islands. Retinò et al. [2008] also found the energetic electron flux enhancement within a small scale flux rope which may be associated with flux rope coalescence. They discussed the three dimensional energetic electron distribution function and claimed the importance of thin current sheets during magnetic reconnection for production of energetic electrons. Until now the proposed energetic particle acceleration regions from in situ observation are typically those three, such as X type neutral line, magnetic flux pileup region, and small magnetic islands. Although there are clear evidences for energetic electron acceleration in each region during magnetic reconnection, it is still unclear which region and when it dominates. [4] As for numerical simulation of energetic electron acceleration, a test particle approach has been used in early stage [e.g., Sato et al., 1982; Scholer and Jamitzky, 1987; Birn and Hesse, 1994]. From their results, energetic particles are accelerated by the interaction with an inductive electric field at the X type neutral line and further acceleration have been taken place in the whole plasma sheet. In recent years, self consistent particle in cell (PIC) simulation have much improved the understanding of particle acceleration during magnetic reconnection [e.g., Drake et al., 2003; Pritchett, 2005]. Hoshino et al. [2001b] discussed the origin of suprathermal electrons by using full particle simulation. They proposed that the electrons are initially energized inside the diffusion region, and then further energized in the outflow region. Acceleration in and around small magnetic islands is also discussed with PIC simulation [e.g., Oka et al., 2010; Karlicky, 2010]. Drake et al. [2006] discussed the effect of dynamical contracting motion of island for the production of high energy electrons. They concluded that the first order Fermi acceleration effectively works during island contraction. The mechanism by which particles gain energy during the reflection off the end of a contracting island is through the curvature drift along the reconnection electric field. Recently, the importance of guide field for acceleration region is pointed out by Pritchett [2008]. They studied energetic electron acceleration during multi island coalescence with and without guide field, and found that the energetic electrons are preferentially produced near the X line for the strong guide field (comparable to lobe magnetic field) case, while without guide field case they are produced mainly in the flux pileup region through the curvature drift along the reconnection electric field. [5] So far various observations and numerical studies have been done to understand the origin of energetic particles during reconnection. In this paper, we analyzed ten of magnetic reconnection events, and discuss the relationship between energetic electron acceleration efficiency and reconnection characteristics (current sheet thickness, reconnection electric field, and so on). The aim of our paper is to determine the preferential condition for energetic electron acceleration during magnetic reconnection in the Earth s magnetotail. 2. Observations of Energetic Electrons: Case Study 2.1. Instrumentation [6] In this study we have used the data from comprehensive measurements onboard the Geotail satellite, including the low energy particles (LEP/EAi, EAe)[Mukai et al., 1994], the energetic particles (EPIC/ICS) [Williams et al., 1994], and the magnetic fields (MGF) [Kokubun et al., 1994]. As for the thermal plasma moments, we calculated electron and ion temperature (T e,i ), density (N e,i ), and bulk velocity (v e,i ) from the distribution functions obtained from the LEP instrument. We used 12 s time resolution data to obtain ion moments. Although we also used 12 s data for calculation of electron moments, we averaged them to 60 s time resolution after moment calculation to reduce the statistical uncertainty. As for the energetic electrons, we used the integrated electron flux of >38 (kev) measured by the EPIC instrument with 90 s time resolution. EPIC measures distribution of electrons in 2 energy channels integrating electron flux with energies higher than 38 and 110 kev. We used only lower energy channel which can obtain enough particle counts during magnetic reconnection. The energetic electrons flux were integrated over pitch angle by assuming an isotropic velocity distribution function, because generally high energy electrons are isotropic in a current sheet [e.g., Smets et al., 1998]. [7] We transformed the coordinate into the current sheet normal system using the Minimum Variance Analysis (MVA) [Sonnerup and Cahill, 1967], where N is the estimated current sheet normal, L is in the direction of maximum variation ( X GSM ), and M completes a right hand system. The current density j is calculated directly from the ion and electron velocity difference [e.g., Asano et al., 2003]. We can calculate the current density as j = ne(v i v e ) by assuming that ion and electron densities are equal. With pressure balance between tail lobe and plasma sheet, magnetic field intensity in tail lobe is derived as B lobe = (B 2 + 2m 0 nk B (T i + T e )) 1/2, where B, n, T i, and T e are local magnetic field intensity, plasma density, ion, and electron temperatures observed by Geotail in the current sheet, respectively. Using j M and B lobe, a half thickness of current sheet d is calculated from the Amperefs law assuming the homogeneity of current density in a current sheet, d = B lobe /m 0 j M. A time scale of current sheet crossing by spacecraft might be very short when a thin current sheet is formed. We should carefully check whether a current sheet structure is resolved with our time resolution or not. The electric fields are calculate from v B with frozen in assumption. Actually ions are not frozen in inside the ion diffusion region. Especially, the electric field in N direction (the bipolar Hall electric fields) are enhanced inside the ion diffusion region [e.g., Wygant et al., 2005]. Therefore we calculated the electric fields from both of electron and ion velocities. [8] We defined the energetic electron rate by the ratio between the integrated electron flux >38 and 38 (kev). We have used EPIC and LEP data for >38 and 38 (kev) integrated flux, respectively. Note that in our definition 2of13

3 energy spectrum by kappa distribution only in the case that EPIC integrated flux is larger than 10 3 (cm 2 s 1 str 1 )to reduce the statistical uncertainty. Note that power law index is represented by + 1 in our definition. Thus smaller means harder spectrum and vice versa. Figure 1 shows the example of kappa distribution fitting. The vertical and horizontal axes show phase space density and electron energy, respectively. The solid and dashed lines are kappa and Maxwellian distribution function fitting results, respectively. Electrons often do not obey kappa distribution function inside the diffusion region. For example, in the vicinity of the X line it is frequently observed that the electron flat top distribution (Figure 1c) which shows a constant phase space density in the low energy part (< a few kev) yet a steep decrease in the high energy part [e.g., Asano et al., 2008]. Further our fitting method may not represent suprathermal component appropriately in the case that the electrons are extremely hot ( 5 kev, Figure 1b). We cannot distinguish whether nonthermal component are there or not far above 38 kev, because we used only EPIC integrated flux (>38 kev). The fitting by kappa distribution function is often failed inside the diffusion region (Figures 1b and 1c), and those distributions are represented by =11in our definition. We used both of energetic electron rate and kappa value to discuss energetic electron acceleration in and around reconnection region. Figure 1. Examples of electron energy distribution in and around the reconnection region: (a) kappa distribution, (b) Maxwellian distribution, and (c) flat top distribution. energetic electron rate depends on not only amount of nonthermal electron but also electron temperature. Therefore, we also use power law index of energetic electron. To obtain the power law indices, we fitted the LEP energy spectrum and EPIC integrated flux (>38 kev) by kappa distribution function as follows: f e ðv e Þ ¼ A 1 þ m ev 2 1 e ; ð1þ 2E Te where v e and m e are electron velocity and mass, respectively. Here there are two parameters E Te and characterizing the distribution. E Te is closely related to electron temperature, and characterizes power law distribution. The way to fit an energy spectrum by kappa distribution is as follows: (1) fit the LEP energy spectrum by kappa distribution with = 11; (2) change in the 1 to 11 range to meet EPIC integrated flux (>38 kev) with fixed E Te and A; (3) change E Te and A to fit the observed energy spectrum by LEP with fixed ; and (4) do 2 and 3 iteratively. We fit the 2.2. Strong Acceleration Case: 10 December 1996 [9] Figure 2 shows the magnetic reconnection event observed by Geotail on 10 December From the top to bottom, three component of magnetic field (B L,M,N ), plasma density, three components of bulk velocity (V L,M,N ), temperature (T i,e ), ratio between ion and electron temperature (T i /T e ), and energetic electron (>38 kev) flux are plotted for the period from 1700 to Ion and electron data are plotted by red and blue lines, respectively. The spacecraft was located in the midnight magnetotail of 26 (R E ) during the time interval and crossed the current sheet several times. After 1745 Geotail observed the flow reversal of high speed (>1000 km s 1 ) proton bulk flow from tailward to earthward with a changing N component of the magnetic field from negative to positive, which is the indication of passing an X type neutral line. The vertical dotted lines show the transition from tailward to earthward plasma flow without leaving the reconnection region. Hot (> a few kev) and tenuous ( 0.05/cc) plasma were observed associated with the flow reversal. The ratio between electron and ion temperature shows <2 during the period, although the ratio is usually 5 in the plasma sheet [e.g., Baumjohann et al., 1989]. This result may indicate that strong electron heating took place in this region. The energetic electron flux is enhanced up to (cm 2 s 1 str 1 ) associated with the flow reversal. The energetic electronflux was slightly decreasing in the center of the flow reversal (roughly ten times). It seems that there are a gradient of energetic electron from the center to outer edge of reconnection region which is consistent with Imada et al. [2005, 2007]. [10] At 1804 Geotail encountered the sharp tangential discontinuity. This region seemed to be so called magnetic flux pileup region or dipolarization front. In this region plasmas are slow (<100 km s 1 ), dense ( 0.5/cc), and relatively cold (T e 1 kev) compared with the flow reversal 3of13

4 Figure 2. Summary plot of the 10 December 1996 event observed by Geotail. From top to bottom: three components of the magnetic field, density, three components of the velocity, temperature, temperature ratio between ions and electrons, and energetic electron flux. Ion and electron data are plotted by red and blue lines, respectively. region. Geotail observed sharp enhancement of N component of magnetic field up to 7 (nt) at 1807 (30% of tail lobe magnetic field). The ratio between ion and electron temperature show the marginal value (T i /T e 3). The energetic electron flux was increasing and reached up to (cm 2 s 1 str 1 ) again. Further the Geotail encountered the strong dipole like magnetic field (7 nt) after [11] To estimate the reconnection characteristics, we have calculated the other physical values moreover. Estimated tail lobe magnetic field (B Lobe ), ratio between L component of magnetic field and tail lobe magnetic field (B L /B Lobe ), M component of current density (j M ), current density parallel to magnetic field (j k ), M and N component of electric field (E M,N ), inflow velocity, half thickness of current sheet, energetic electron rate, and kappa value are plotted from top to bottom in Figure 3. Ion and electron data are plotted by red and blue lines, respectively. We also plots the upper limit of kappa value in our fitting method with solid line in Figure 3. The kappa value 11 means that the energetic electron flux (>38 kev) are lower than that expected from single Maxwellian distribution. The tail lobe magnetic field (B Lobe ) was roughly 30 (nt) before the flow reversal. 4of13

5 Figure 3. Summary plot of the 10 December 1996 event observed by Geotail. From top to bottom: the lobe magnetic field, B L /B Lobe, M component of current density, current density parallel to magnetic field, M and N components of electric fields, inflow velocity, current sheet thickness, energetic electron rate, and kappa. Ion and electron data are plotted by red and blue lines, respectively. The solid line in kappa shows the upper limit in the fitting. During the flow reversal, the tail lobe magnetic field was reduced down to 15 (nt), and the current density in the current sheet (j M ) was positive and enhanced up to 10 (na/m 2 ). The enhancement of j M is caused by the thinning of current sheet locally. The thickness of the current sheet was reduced to 1500 (km), which is order of ion inertia length. The current density parallel to magnetic field in this reconnection event ( 10 na/m 2 ) was well discussed with kinetic view points by Nagai et al. [2001], and it is consistent with the Hall current system scenario in the magnetic reconnection region. The M component of electric field (E M ) which may be related to reconnection electric field was also enhanced up to 5 mv/m during the flow reversal. Strong converging electric fields toward the neutral sheet (E N 15 mv/m), which is negative in the north lobe and positive in the south lobe of plasma sheet, were also observed. This converging electric field may be related to the strong Hall electric field which is often observe near the reconnection region [e.g., Wygant et al., 2005] because the ion motional electric field (v i B) N was enough small compare with that of electron (v e B) N in Figure 3. Therefore it is better to discuss the reconnection condition with E N = (v e B) N = (v i B) N + 5of13

6 Table 1. Reconnection Characteristics Observed by Geotail a Event Date Time [X, Y] Velocity Density T i T e T i /T e A :00 20:00 [ 96,7] 1567(1948) 0.01(0.01) 6.9(8.5) 2.4(3.5) 2.9(2.5) B :45 15:45 [ 29,5] 1032(1347) 0.06(0.04) 4.7(6.0) 1.6(2.5) 3.0(2.4) C :00 12:00 [ 18,2] 1207(1507) 0.03(0.03) 9.2(10.5) 5.6(7.0) 1.6(1.5) D :00 19:00 [ 26,1] 1241(1310) 0.05(0.06) 7.4(9.0) 3.5(5.3) 2.2(1.7) E a 13:30 15:30 [ 29,10] 838(1051) 0.02(0.02) 9.0(9.7) 4.5(5.9) 2.0(1.6) F b 15:30 17:30 [ 29,9] 1089(1557) 0.02(0.02) 10.0(10.9) 7.2(10.8) 1.4(1.0) G a 09:20 11:20 [ 27,6] 1078(1376) 0.05(0.05) 5.8(6.4) 1.6(2.7) 3.5(2.4) H b 14:00 16:00 [ 26,3] 660(1073) 0.02(0.02) 3.5(4.9) 1.8(2.4) 2.0(2.0) I :00 17:00 [ 24,7] 1098(1320) 0.02(0.02) 4.3(6.3) 2.5(3.5) 1.7(1.8) J :00 10:00 [ 17,9] 564(703) 0.03(0.03) 6.8(7.6) 3.6(4.3) 1.9(1.8) a Reconnection characteristics determined by 12 s average data are provided in parentheses. (j B) N /ne. Inflow speed toward the center of current sheet are calculated by E M /B lobe. Positive inflow indicates that the flow toward the center of current sheet, and negative inflow means that the flow outward to the lobe. The inflow during the flow reversal was roughly a few 100 (km/s) which is roughly 10 percent of Alfven velocity in the lobe. All of our reconnection characteristics are estimated in not the X line but the spacecraft reference frame. The reconnection electric field or reconnection inflow should be measured in the X line reference frame. However it is difficult to estimate how fast the X line is moving by single spacecraft observation. Some multisatellite observations indicate that the X line is moving with 100 km s 1 [e.g., Imada et al., 2007]. Therefore there are roughly 100 km s 1 ambiguity in our velocity estimation. The error in electric fields are 0.2 mv m 1, because the electric fields are estimated by v e B (B a few nt). The energetic electron rate was enhanced up to at 1747, and it was almost constant all the time after entering flow reversal region (>1747UT). Although the kappa value is 11 during the flow reversal due to the presence of extremely hot or flat top distributions, the low kappa values are observed just after flow reversal. We can clearly see the continuous low kappa value after the flow reversal, and gradually the kappa value is increasing with time. [12] To discuss the relationship between the energetic electron acceleration efficiency and the reconnection characteristics, we need comparison among some reconnection events. Therefore we have to determine the typical reconnection conditions and the energetic electron acceleration efficiency in each event. To reduce arbitrariness we used the maximum or minimum of 1 min average value (±30 min from flow reversal) for reconnection characteristics. In Figures 2 and 3, the typical values of reconnection characteristics and electron acceleration efficiency are shown by dashed horizontal line (red: ion, blue: electron). These values in the reconnection event on 10 December 1996 are summarized in Tables 1 and 2 (Event D). The fourth column in Table 1 shows the Geotail location (R E ). The column Velocity, Density, T i, T e, T i /T e in Table 1 shows maximum value of outflow velocity V L (km s 1 ), minimum value of density (cm 3 ), maximum value of ion and electron temperature (kev), and minimum value of the ratio between ion and electron temperature in the reconnection region, respectively. In Table 2, the column Flux, Rate, and shows the maximum value of energetic electron flux (cm 2 s 1 str 1 ) and energetic electron rate, and the minimum value of, respectively. The columns E M, E N, and d represents the maximum value of reconnection and normal electric field (mv m 1 ), and the minimum value of the current sheet thickness (km), respectively. We can estimate how much energies are totally released during reconnection (DB 2 nt 2 ) from the difference in lobe magnetic field between before and after reconnection. pffiffiffiffiffiffiffiffiffiffiffi We also calculated the reconnection 2 rate from E M 0 nm/b Lobe, where m is the proton mass. The maximum value of reconnection rate R and current density (na/m 2 ) parallel to magnetic field (j k ) are shown in the last two columns in Table 2. Note that in our definition the reconnection characteristics and the energetic electron acceleration efficiency are not necessarily observed simultaneously. The minimum current sheet thickness ( 1800 UT) and the minimum kappa value ( 1815 UT) are observed different timing in Figure Weak Acceleration Case: 13 March 1997 [13] Figure 4 shows a plot of the magnetic reconnection event observed by the Geotail on 13 March The format is the same as Figure 2. The spacecraft was located slightly dusk side (7 R E ) in the magnetotail of 24 (R E ). In Table 2. Reconnection Characteristics Observed by Geotail a Event Flux Rate E M E N d DB 2 R j k A (8.1) (193) 0.16(0.43) 5.0 B (7.1) (323) 0.19(0.25) 5.1 C (8.7) (1371) 0.13(0.17) 19.8 D (10.4) (545) 0.23(0.42) 9.4 E (13.9) (465) 0.16(0.25) 9.3 F (21.0) (1035) 0.34(0.48) 9.5 G (4.9) (244) 0.11(0.22) 7.5 H (5.6) (184) 0.11(0.12) 10.8 I (7.3) (527) 0.12(0.19) 16.8 J (3.4) (162) 0.11(0.14) 5.4 a Reconnection characteristics determined by 12 s average data are provided in parentheses. 6of13

7 Figure 4. Figure 2. Summary plot of the 13 March 1997 event observed by Geotail. The format is the same as this event, the Geotail first observed positive N component of the magnetic field with tailward flow around 1545, and then negative B N were also observed with tailward flow. This may indicate that the plasmoid was passing the Geotail. After passing plasmoid, the Geotail observed the flow reversal with a changing N component of the magnetic field from negative to positive during , which is the indication of passing an X type neutral line. Hot (> a few kev) and tenuous ( 0.01/cc) plasmas were observed associated with the flow reversal. The ratio between electron and ion temperature shows <2 during the period. The energetic electron flux is not clearly enhanced associated with the flow reversal ( 10 3 cm 2 s 1 str 1 ). In the outer edge of earthward reconnection outflow, the energetic electron fluxes were slightly enhanced up to (cm 2 s 1 str 1 ). After 1622, Geotail observed slow (<100 km s 1 ), dense ( 0.5/cc), and relatively cold (T e 1 kev) plasma compared with the flow reversal region. The ratio between ion and electron temperature shows 5 which is the typical value in the plasma sheet. The energetic electron flux was decreasing from the outer edge of the flow reversal region to the further outer region. The dipole like magnetic field was also decreasing with time. [14] Figure 5 shows the other physical values calculated in the same way as the previous event. The lobe magnetic field (B Lobe ) was roughly 22 (nt) before the flow reversal. During 7of13

8 Figure 5. Figure 3. Summary plot of the 13 March 1997 event observed by Geotail. The format is the same as the flow reversal, the lobe magnetic field was reduced down to 12 (nt). The current density in the current sheet (j M ) enhanced up to 10 (na/m 2 ), and the thickness of the current sheet was also reduced to 3000 (km) during the flow reversal. The current density parallel to magnetic field was 10 (na/m 2 ), and the reconnection electric field (E M ) was also enhanced up to 5 (mv/m) during flow reversal. The converging normal electric fields (E N 5 mv/m) which were smaller than the previous event were observed. The inflow during the flow reversal in this event was also roughly a few 100 (km/s). The energetic electron rate were almost constant (10 3 ) in and around flow reversal region. We can clearly see the low kappa value ( 4.5) just after the flow reversal, and gradually the kappa value was increased with time. The reconnection characteristics and energetic electron acceleration efficiency which was estimated in the same way as the previous event are summarized in Tables 1 and 2 (Event I). 3. Statistical Property of Energetic Electron Acceleration [15] In section 2 we discussed two reconnection events to clarify what reconnection characteristics control the ener- 8of13

9 Figure 6. Correlation between energetic electron rate and reconnection characteristics. Energetic electron rate was defined as the ratio between the integrated electron flux >38 and 38 (kev). getic electron acceleration efficiency. Let us discuss what is the major difference between the 10 December 1996 and 13 March 1997 events. The column Flux, Rate, and in Table 2 represents energetic electron acceleration efficiency. All of three show that the electrons are clearly much accelerated in event D than event I. We can find ion and electron are efficiently heated in event D than event I from Table 1. Further, we can clearly see the large difference between event D and I in both of electric fields (E M and E N ), current sheet thickness (d), and reconnection rate (R) in Table 2. Therefore, at least within these two events, it seems that the electrons are efficiently accelerated and strongly heated in a thin current sheet during fast reconnection event. By using ten of reconnection event, we will discuss the generality of the point in section 3. [16] We have statistically studied favorable conditions for energetic electron acceleration during magnetic reconnection. We surveyed the reconnection events in which the Geotail satellite observed the vicinity of diffusion region. The surveying period is from January 1994 through July 1997, during which the LEP electron data was carefully calibrated. We have used only the data for which 3 D distribution functions are available, because our analysis is relatively sensitive to the electron moments. We identify the events by the following conditions: (1) X GSM < 15 R E, (2) the presence of fast bulk flow ( V x > 500 km s 1 ), and (3) the presence of hot electron (>2 kev). After the data selection, we have found 10 individual events totally [e.g., Nagai et al., 2001]. The way to determine the reconnection characteristics is the same as section 2. The summary of our analysis in ten of the reconnection events are shown in Tables 1 and 2. To clarify the relationship between the energetic electron acceleration efficiency and the reconnection characteristics, we carried out correlation analysis among them. Figure 6 shows the relationship between the energetic electron rate and the reconnection characteristics. 9of13

10 Figure 7. Correlation between kappa and reconnection characteristics. The all of vertical axes show the energetic electron rate in logarithmic scale, and the horizontal axes show the each parameter in logarithmic scale. The squares/diamonds show the result of 1 min/12 s average results, respectively. The fitted results with squares/diamonds are presented by solid/ dashed lines, respectively. The correlation coefficients are also shown. [17] We have classified the relationship between reconnection characteristics and electron acceleration efficiency into 3 types: (1) good correlation (absolute value of correlation coefficient r > 0.6); (2) ambiguous correlation (0.6 > r > 0.3); and (3) no correlation ( r 0). We found that ion heating, electron heating, current sheet thickness, reconnection electric field, and electric field normal to the neutral sheet can be categorized into good correlation. Ion/electron temperature ratio, total amount of reduced magnetic energy, and reconnection rate are classified in ambiguous correlation. We cannot find any correlation with absolute value of outflow velocity, current density parallel to magnetic field (Hall current system), satellite location in the Earth s magnetosphere. [18] To ensure the result in Figure 6, we carried out the same correlation analysis between the reconnection condition and the kappa value in Figure 7. Figure 7 (top left) shows the correlation between the kappa value and the energetic electron rate. The correlation efficiency is almost 1, thus it seems that both of them are well reproduce of the energetic electron characteristics. The other eight panels show the correlation between the kappa value and the reconnection condition which are categorized good or ambiguous correlation in Figure 6, and the result is almost the same as Figure 5. Therefore, our claim is confirmed in ten of the reconnection events. 4. Discussion and Summary [19] We have studied favorable conditions for energetic electron acceleration during magnetic reconnection in the Earth s magnetosphere using the Geotail data. We have found both of the strong and weak energetic electron acceleration in the reconnection events. To discuss what reconnection characteristics determine the energetic electron acceleration efficiency, we have studied the reconnection conditions for ten events in which the Geotail satellite observed the vicinity of diffusion region. We found that ion heating, electron heating, current sheet thickness, reconnection electric field, and electric field normal to neutral sheet can be categorized into good correlation ( r > 0.6). Ion/electron temperature ratio, total amount of reconnected magnetic energy, and reconnection rate are classified in ambiguous correlation (0.6 > r > 0.3). We could not find any correlation between energetic electron acceleration efficiency and absolute value of outflow velocity, current 10 of 13

11 density parallel to magnetic field (Hall current system), satellite location in the Earth s magnetosphere (0.3 > r ). [20] To ensure our results, let us briefly review the past observations which are related to the reconnection characteristics. There are numerous studies about the current sheet thickness in the late growth phase of substorm by modern satellites, such as ISEE or Cluster [e.g., Mitchell et al., 1990; Sanny et al., 1994; Pulkkinen et al., 1994; Nakamura et al., 2002]. According to their study, the thickness of the current sheet can be as thin as the ion inertial length ( a few 1000 km), and the bifurcated current sheet is often observed during substorm. In Table 2, minimum/ maximum thickness of thin current sheet is 800/5300 (km), respectively. The average of observed thin current sheet in our study is 2500 (km). Therefore our estimation of the current sheet thickness during magnetic reconnection is consistent with the past observations. Eastwood et al. [2010] discuss the average properties of the magnetic reconnection ion diffusion region in the Earth s magnetotail by the Cluster observation. Their study is especially concentrated on the electric and magnetic field measurements which are related to the Hall effect. According to their study, the peak E N is in the range 5 30 (mv/m). The maximum, average, and minimum value of the peak E N in our events are 29.2, 14.0, and 1.9 (mv/m), respectively. They also discuss the peak E M, and its range is also 5 15 (mv/m). Retinò et al. [2008] also showed the similar value for E M with the Cluster observation. Asano et al. [2008] statistically studied the flat top electron distribution by the Cluster observation, and they found that the shoulder energy of the flat top distribution is in the range 4 10 (kev). The shoulder energy of the flat top distribution represents the maximum electron temperature in the reconnection region (see Figures 1 and 2), though they are not exactly the same. Roughly, most of our estimated electron temperature in the reconnection region is also in the range. Therefore, the reconnection characteristics estimated by the Geotail data are consistent with the results from the other in situ observations. One may think that the normalization of reconnection characteristics by tail lobe condition is useful for understanding a particle acceleration process. We have estimated tail lobe conditions to normalize the reconnection electric field. In Figure 6, we showed the result of correlation analysis between energetic electron rate and reconnection rate, and found that the energetic electron rate correlates well with reconnection electric field but less well with reconnection rate. It is useful to answer which is more important for energetic electron acceleration, reconnection rate or reconnection electric field normalized by the other values (e.g., thermal velocity and tail lobe magnetic field). However, the estimation of tail lobe plasma characteristics by a single satellite observation has relatively large ambiguity. Generally, the tail lobe plasma is tenuous ( 0.01 /cc) and cold (<100 ev). Further the plasma measurement in tail lobe is often affected by a contamination of photoelectrons. Therefore in this paper we restrict ourself not to discuss it. [21] We now discuss the energetic electron observations in the reconnection region. The power law index which is represented by + 1 is in the range 4 to 6 in our results. Øieroset et al. [2002] reported the electron distribution inside the ion diffusion region by using the Wind observation, and found that the power index is 4.8 near the center of the diffusion region. Imada et al. [2007] discussed the second step acceleration, in addition to X line acceleration, of energetic electron in the downstream reconnection outflow region by using the Cluster data. They showed the hard electron energy spectrum which the power index was 5. Those two observations by the Wind and Cluster satellite are consistent with our results in the spectral index of electron energy distribution. Our previous study [Imada et al., 2005] focused on the acceleration region of the energetic electrons with the same Geotail data set. They discussed the relationship between the energetic electron flux and the reconnected magnetic field (B N ), and they concluded that the large normal magnetic field causes the energetic electron enhancement. They also claimed that the acceleration region was located far from the center of reconnection region in most case. [22] In Figures 2 and 3, the enhancement of energetic electron flux with the minimum kappa value was observed just after the flow reversal period. On the other hand, the hot electrons are observed during the flow reversal. It seems that the energetic electrons and the hot electrons cannot be observed simultaneously. Asano et al. [2008] also discuss the relationship between the energetic electrons and the hot electrons (flat top type) by Cluster observation. They conclude that the electron acceleration processes for the flattop type distributions are different from the suprathermal components, because the flat top distributions are not simultaneously observed with increase of the high energy electrons. Further, they claim that the energetic electrons are produced in the downstream of the flat top distribution. It does not necessarily means that the flat top distribution has no contribution to producing the energetic electron. It is plausible that those highly heated electrons are seeds of energetic electron. The relationship between guide field and acceleration region which is claimed by Pritchett [2008] is not clear in our study (not shown), because in most case guide field is weak and not spatially uniform. Therefore we restrict ourself not to discuss it. [23] Let us discuss the plausible scenario of the energetic electron acceleration from our observation. It is crucial to produce strongly heated electrons in and around the diffusion region for energetic electron acceleration at the down stream of reconnection outflow region [Imada et al., 2007] because most of acceleration mechanisms effectively work on high energy electron which has relatively large Larmor radius. It is well established that the current sheet thinning causes strong electron heating or produces the flat top electron distribution. There are largely three kind of the mechanism to produce the strongly heated electron. One is that the hot electrons are produced by the wave particle interaction with obliquely propagating lower hybrid waves which is exited in a thin current sheet [Shinohara et al., 1998; Shinohara and Hoshino, 1999]. Another possibility of producing hot electrons is by the thermalization process of the highly accelerated beams component during the neutral sheet crossing or wave scattering [Smets et al., 1998; Hoshino et al., 2001a]. Third mechanism is related to the electric field point toward the neutral sheet which is known to be produced associated with Hall electric current. Hoshino [2005] discussed the effect of polarization electric field in a thin current sheet which is strongly enhanced in an 11 of 13

12 externally driven reconnection system. They concluded the polarization electric field also effectively work for preacceleration to produce energetic electrons. Either process effectively works in a thin current sheet which produces the strong Hall electric field. Therefore, we conclude that a thin current sheet formation during magnetic reconnection is essential to produce energetic electron acceleration. It is still unclear what reconnection characteristics determine the thickness of current sheet during magnetic reconnection. This is for future work. Another important unresolved issue for energetic particle acceleration is the relationship between energetic ion and electron in magnetic reconnection region. Some observations show the strong energetic electron acceleration without energetic ion during magnetic reconnection [e.g., Øieroset et al., 2002]. 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