Adiabatic acceleration of suprathermal electrons associated with dipolarization fronts

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2012ja018156, 2012 Adiabatic acceleration of suprathermal electrons associated with dipolarization fronts Qingjiang Pan, 1,2 Maha Ashour-Abdalla, 1,2 Mostafa El-Alaoui, 1,2 Raymond J. Walker, 1,3,4 and Melvyn L. Goldstein 5 Received 23 July 2012; revised 12 October 2012; accepted 26 October 2012; published 19 December [1] Recent observations in the inner magnetotail have shown rapid and significant flux increases (usually an order of magnitude of increase within seconds) of suprathermal electrons (tens of kev to hundreds of kev) associated with earthward moving dipolarization fronts. To explain where and how these suprathermal electrons are produced during substorm intervals, two types of acceleration models have been suggested by previous studies: acceleration that localizes near the reconnection site and acceleration that occurs during earthward transport. We perform an analytical analysis of adiabatic acceleration to show that the slope of source differential fluxes is critical for understanding adiabatic flux enhancements during earthward transport. Observationally, two earthward propagating dipolarization fronts accompanied by energetic electron flux enhancements observed by the THEMIS spacecraft have been analyzed; in each event the properties of dipolarization fronts in the inner magnetosphere (X GSM 10R E ) were well correlated with those further down the tail (X GSM 15R E or X GSM 20R E ). Coupled with theoretical analysis, this enables us to estimate the relative acceleration that occurred as the electrons propagated earthward between the two spacecraft. During the two events studied, the differential fluxes of supra thermal electrons had steep energy spectra with power law indices of 4 to 6.These spectra were much steeper than those at lower energy, as well as those of the supra thermal electrons observed before the fronts arrived. A compression factor of 1.5 as the electrons propagated earthward induced a flux increase of suprathermal electrons by a factor of 7 to 17. Provided these steep spectra, we demonstrate that adiabatic acceleration from the betatron and Fermi mechanisms simultaneously operating can account for these flux increases. Since both analytical analysis and data from the two events show that adiabatic acceleration during earthward transport does not significantly change the power law indices, the steep spectra were likely to be traced back to their source region, presumably near the reconnection site. Citation: Pan, Q., M. Ashour-Abdalla, M. El-Alaoui, R. J. Walker, and M. L. Goldstein (2012), Adiabatic acceleration of suprathermal electrons associated with dipolarization fronts, J. Geophys. Res., 117,, doi: /2012ja Introduction [2] Rapid increases in the north-south component of the magnetic field (B z ) called dipolarization fronts are frequently observed in the near-earth tail during magnetospheric 1 Institute for Geophysics and Planetary Physics, University of California, Los Angeles, California, USA. 2 Also at Department of Physics and Astronomy, University of California, Los Angeles, California, USA. 3 Also at Department of Earth and Space Sciences, University of California, Los Angeles, California, USA. 4 Now at the National Science Foundation, Arlington, Virginia, USA. 5 NASA Goddard Space Flight Center, Greenbelt, Maryland, USA. Corresponding author: Q. Pan, Institute for Geophysics and Planetary Physics, University of California, Los Angeles, CA , USA. (chaseidea@ucla.edu) American Geophysical Union. All Rights Reserved /12/2012JA substorms [Schmid et al., 2011; Ohtani et al., 2004;Fu et al., 2012]. Large increases in the energy flux of suprathermal electrons, sometimes reaching 100 s of kev, are frequently reported in association with dipolarization fronts [e.g., Runov et al., 2009;Asano et al., 2010]. For most of these events, the energy fluxes of suprathermal electrons increases significantly (tens of kev to hundreds of kev), while the energy fluxes decrease for lower energy electrons (a few kev or less) [e.g., Deng et al., 2010;Hwang et al., 2011]. For some dipolarization front events, the energy fluxes of suprathermal electrons increase as the fronts arrive, while in other events the suprathermal electron energy fluxes decrease just before the dipolarization is observed and then increase. Finally, for some events the suprathermal electron pitch angle distributions peak near 90, while others peak at smaller pitch angles (<45 ). Both types of distributions can appear in either the inner magnetosphere or in the near-earth plasma sheet, depending on the particular event [e.g., Deng et al.,2010;fu et al.,2011]. 1of9

2 [3] Several mechanisms have been proposed to accelerate electrons to suprathermal energies in the Earth s magnetotail. Local acceleration mechanisms, either adiabatic or nonadiabatic, involving the reconnection electric field and stochastic processes associated with turbulence and plasmoids, are believed to be viable candidates [e.g., Shinohara et al., 1998; Drake et al., 2005, 2006; Kowal et al., 2009; Hoshino, 2012]. On the other hand, non-local acceleration mechanisms operating far from the reconnection site, including adiabatic acceleration and non-adiabatic waveparticle scattering also have been suggested as effective acceleration mechanisms [e.g., Sharber and Heikkila, 1972; Hoshino et al., 2001; Imada et al., 2007; Deng et al., 2010; Khotyaintsev et al., 2011; Fu et al., 2011; Ashour-Abdalla et al., 2011a]. However, these processes are usually investigated separately. The global scenario of where and how suprathermal electrons are generated in the outer magnetosphere during periods of geomagnetic activity remains unclear. In particular, it is unclear how much of the acceleration occurs as the dipolarization front propagates toward the Earth and how much occurs near the source, which presumably is not far away from the reconnection site. Recent studies using data from the four Cluster satellites indicate that electrons can be accelerated by multistep processes near the site of magnetic reconnection as well as far away from the diffusion region in the same events [Asano et al., 2010; Vaivads et al., 2011]. [4] This paper quantitatively explores non-local adiabatic theory and presents key features of adiabatic acceleration. Based upon the quantitative analysis of adiabatic acceleration, we attempt to qualitatively clarify the roles of magnetic reconnection and adiabatic acceleration in producing suprathermal electrons associated with dipolarization fronts in the inner magnetosphere (X GSM 10R E ). In section 2 we discuss adiabatic acceleration mechanisms. In section 3 we present a comparison with theory using data from the THEMIS spacecraft during two geo-active intervals (March 11, 2008 and February 27, 2009). In section 4 we discuss these observations in terms of what we would expect for acceleration as the dipolarization fronts propagate earthward and use those inferences to consider what may be happening nearer the reconnection site. 2. Adiabatic Acceleration Theory [5] When the time scales of changes in the magnetic and electric fields are much larger than time periods of the gyromotion of a particle about a magnetic field line, the bounce motion between mirror points, or the azimuthal drift of a particle about the Earth, there are three adiabatic invariants corresponding to these three types of motion, respectively [Northrop, 1963; Roederer, 1970; Schulz and Lanzerotti, 1974; Green and Kivelson, 2004]. The first invariant, the one associated with gyromotion is given by m ¼ P? 2. where P? is the relativistic momentum perpendicular to the magnetic field and B is the magnitude of the total magnetic field. The increase in P? due to a varying B is known as betatron acceleration. The second adiabatic invariant B ; ð1þ involves the parallel momentum integral along the bounce motion between mirror points Z J ¼ P == ds; ð2þ where P // and ds are the relativistic momentum parallel to the magnetic field and the distance along a field line, respectively. An increase in P // due to a decrease of the distance between mirror points is usually referred to as Fermi acceleration. [6] The azimuthally integrated differential flux j(e, a, r, t) and distribution function f(e, a, r, t) are functions of kinetic energy E, pitch angle a, position r and time t. The relation of differential flux and distribution function is [Schulz and Lanzerotti, 1974; Lyons and Williams, 1986] fðe; a; r; tþ ¼ je; ð a; r; t Þ P 2 ; ð3þ where P is the relativistic momentum. [7] From Liouville s Theorem, which states that the oneparticle distribution function in phase space is constant along the particle trajectory without collisions or wave-particle interaction, the differential flux along a particle trajectory in phase space is [Schulz and Lanzerotti, 1974; Lyons and Williams, 1986] j 1 ðe 1 ; a 1 ; r 1 ; t 1 Þ ¼ j 2ðE 2 ; a 2 ; r 2 ; t 2 Þ ¼ constant: P 2 1 The subscripts 1 and 2 indicate that the quantities are evaluated at different positions and time. [8] We will assume that particles undergo slow magnetic field compression given by P 2 2 B 2 B 1 ¼ g; where g is the magnetic field compression factor. Since the first adiabatic invariant is conserved and P? = P sin a, we have P 2?;2 P 2?;1 ¼ g P 2 2 sin2 a 2 P 2 1 sin2 a 1 ¼ g: The effect of Fermi acceleration on particles due to contraction of mirror distance is P ==;2 P ==;1 ¼ b; where P // = P cos a. b is the ratio of the distances between mirror points for a particular particle on different mirror bounces, which we call the contraction factor. b should vary for particles with different pitch angles, energies and positions; however, in this paper it is assumed to be uniform in ð4þ ð5þ ð6þ ð7þ ð8þ 2of9

3 order to obtain analytic estimates (see discussion section). Hence, P 2 cosa 2 P 1 cosa 1 ¼ b: With betatron and Fermi acceleration operating simultaneously, a particle trajectory in phase space is given by equations (7) and (9): P2 2 ¼ P2 1 ðb2 cos 2 a 1 þ g sin 2 a 1 Þ sin 2 g sin 2 a 1 a 2 ¼ b 2 cos 2 a 1 þ g sin 2 : a 1 Combining (4) and (10), we have ð9þ ð10þ j 2 ðe 2 ; a 2 ; r 2 ; t 2 Þ ¼ b 2 cos 2 a 1 þ g sin 2 a 1 j1 ðe 1 ; a 1 ; r 1 ; t 1 Þ; ð11þ where the relationship of the pitch angles and energies indicated by the subscripts follow from equation (10) after noting that P 2 =(E 2 +2m 0 c 2 E)/c 2, where m 0 is the particle rest mass. [9] To quantify the spectra of particles, we assume that the differential flux of energetic particles varies as a power law in energy [Øieroset et al., 2002; Imada et al., 2007]; that is je; ð a; r; tþ ¼ CW; ð a; r; tþe n ; ð12þ where W is kinetic energy range with E W. The exponent n is the power law index, which quantifies the slope of differential flux as a function of energy. If we insert the power law into (11) and use non-relativistic approximation P 2 =(E 2 +2m 0 c 2 E)/c 2 2m 0 E, we obtain: j 2 ðe 0 ; a 2 ; r 2 ; t 2 Þ ¼ðb 2 cos 2 a 1 þ g sin 2 a 1 Þj 1 ð b 2 cos 2 a 1 þ g sin 2 ; a 1 ; r 1 ; t 1 Þ a 1 ¼ðb 2 cos 2 a 1 þ g sin 2 E n 0 a 1 ÞCðW 0 ; a 1 ; r 1 ; t 1 Þ b 2 cos 2 a 1 þ g sin 2 : a 1 ¼ðb 2 cos 2 a 1 þ g sin 2 a 1 Þ nþ1 n CðW 0 ; a 1 ; r 1 ; t 1 ÞE 0 E 0 ¼ðb 2 cos 2 a 1 þ g sin 2 a 1 Þ nþ1 j 1 ðe 0 ; a 1 ; r 1 ; t 1 Þ Thus, ð13þ j 2 ðe 0 ; a 2 ; r 2 ; t 2 Þ j 1 ðe 0 ; a 1 ; r 1 ; t 1 Þ ¼ b2 cos 2 a 1 þ g sin 2 nþ1: a 1 ð14þ ThedifferentialfluxatenergyE 0 with E 0 W 0 is larger than its source flux at E 0 by a factor of (b 2 cos 2 a 1 + g sin 2 a 1 ) n+1. An important implication of this is that adiabatic enhancement of the differential flux depends strongly on the power law index of the source flux. For example, if the power law index of suprathermal (10 kev 100 kev) electrons associated with dipolarization fronts is in the range 4 to 6 and the compression factor is 1.5 when transported from the outer magnetosphere to the inner magnetosphere, the differential flux can increase by a factor of about 7 to 17. However, if the power law index is, say, between 0 and 1 in low energy range, the differential flux will increase only by a factor of about 1 to 2 under the same compression. Most importantly, adiabatic acceleration does not change the power law index because j 2 ðe 0 ; a 2 ; r 2 ; t 2 Þ¼ðb 2 cos 2 a 1 þ g sin 2 a 1 Þ nþ1 CðW 0 ; a 1 ; r 1 ; t 1 ÞE 0 n ; ¼ CðW 0 ; a 2 ; r 2 ; t 2 ÞE 0 n ð15þ where CW ð 0 ; a 2 ; r 2 ; t 2 Þ ¼ b 2 cos 2 a 1 þ g sin 2 nþ1c a 1 ð W0 ; a 1 ; r 1 ; t 1 Þ ð16þ 3. Comparison With Observations [10] We have selected two dipolarization front events observed by the THEMIS satellites. The first event was on March 11, The second event was on February 27, 2009 and has been studied extensively [Runov et al., 2009; Deng et al., 2010; Ge et al., 2011]. Our approach is to use differential flux data at a spacecraft in the near-earth tail (usually, THEMIS P1 or P2) to calculate the resultant adiabatic accelerated flux at a spacecraft closer to Earth usually P4, and then compare the result with the data at P4. The method assumes that the electrons at the distant spacecraft are the same set of electrons that are observed closer to Earth. With that assumption, we can determine if the electron flux observed nearer to the Earth is consistent with adiabatic acceleration of the flux observed at the more distant satellite. Note that electrons also drift mainly in the y direction due to magnetic field curvature and gradient. However, the large convective electric field drives electrons earthward from P1 (or P2) to P4 within 1 2 min. The width of fast flow channels in magnetosphere is typically a few R E [e.g., Sergeev et al., 1996; Nakamura et al., 2004], we estimate electron drift in the y direction to be about one R E, which is smaller than the flow channel width, hence electrons tend to stay in the same fast flow channel as they transport earthward. [11] To more easily estimate the effects of betatron and Fermi acceleration we selected quasi-perpendicular electrons to evaluate the effects of betatron acceleration and quasiparallel electrons for Fermi acceleration. Thus, for betatron acceleration, we selected electrons such that a 1 90 a 2 90 so that P 2 2 = gp 1 2 E 2 g E 1 for energy up to 100 kev. Then the equation relating the differential flux of quasiperpendicular electrons at different locations becomes j 2 ðge 1 ; 90 ; r 2 ; t 2 Þ ¼ gj 1 ðe 1 ; 90 ; r 1 ; t 1 Þ: ð17þ For Fermi acceleration, the criteria were a 1 0 a 2 0 so that P 2 2 = b 2 P 2 1 E 2 b 2 E 1, and j 2 b 2 E 1 ; 0 ; r 2 ; t 2 ¼ b 2 j 1 ðe 1 ; 0 ; r 1 ; t 1 Þ: ð18þ 3.1. Event #1 March 11, 2008 [12] THEMIS P2 (position vector r GSM =( 14.7 R E,5.4R E, 1.8 R E )) and P4 (r GSM =( 10.4 R E,5.3R E, 1.6 R E )) probed similar structures and they were on the same flow channel in an MHD simulation [Ashour-Abdalla et al., 2011b]. The first three panels in Figure 1 are data from P2 showing in the top 3of9

4 Figure 1. Magnetic field, electron differential energy flux and suprathermal electron power law index at P2. The first three channels of energy flux are measured by the Electrostatic Analyzer (ESA), and the other channels by the Solid State Telescope (SST). panel 128 Hz resolution magnetic field observations from the Fluxgate Magnetometer (FGM) [Auster et al., 2008] in GSM coordinates. The differential energy fluxes observed on P2 are presented in the second panel. The lowest three energy channels of the flux plotted were measured by the Electrostatic Analyzer (ESA) instrument [McFadden et al., 2008], and other channels in the energy range from 26 kev to 113 kev were observed by the Solid State Telescope (SST) instrument [Angelopoulos, 2008]. Median values giving the approximate energy of each of the energy channels are summarized in the legend on the right. Notice that in the theoretical section we discussed the differential flux as a function of energy just like the distribution function; the differential flux sometimes will be abbreviated as flux; it is different from the differential energy fluxes plotted by channel in the second panel, which will be called energy fluxes. The power law index of electron differential flux (bottom panel) from SST data (26 kev to 113 kev) was calculated by using a least squares fit to the differential flux as a function of energy on a log-log scale. Red and green lines plotted along with the power law index are plus or minus one standard deviation and provide upper and lower limits. The standard deviation of the power law index was stable. The dipolarization front of interest observed by P2 was characterized by sudden intensification of B z at 06:22:58 UT after modest bumps and dips. The front was followed by large transient fluctuations. Starting from 06:20:00, concomitant with a bump/dip in the magnetic field, the energy fluxes gradually decreased to their minima just before the front arrived. At the end of this decrease, the energy fluxes were about half of those at 06:20:00. This decrease was followed by a significant but gradual increase (by a factor of 5 6 in about 2 min) associated with the fronts. The power law index decreased and reached a minimum of 3.5 as the front passed by. This change in power law index means that flux increments at different energies were different, which indicated that the energization of electrons was dispersive. After the transient fluctuations in the magnetic field, the power law index returned to 2.5 after 06:26 although the energy fluxes stayed at higher levels. [13] Figure 2 shows data from P4; the format is the same as Figure 1. The magnetic field fluctuations and trends were similar to those seen at P2. The dipolarization front arrived at P4 at 06:23:53. The energy fluxes increased by almost an order of magnitude and did so more abruptly than at P4 as the front passed by. After the dipolarization front passed (06:28) the energy fluxes at P4 returned to approximately the levels before the front s arrival. The power law index was roughly anti-correlated with the energy fluxes. It decreased to 4.5 at the front and increased to 2.5 as the energy fluxes decreased to previous levels. The large magnitude of the power law index at the front indicates the differential flux was steep. The flux of suprathermal electrons at P4 is larger than that at P2 by a factor of 6 to 7 in the fronts. The power law index during the fluctuation period at P4 was smaller than that at P2 by about 0.8. [14] Figure 3 (top) shows the differential flux of electrons. The blue, green lines show the fluxes observed by P2 and P4, respectively. The red line is the predicted flux at P4 assuming betatron acceleration using the flux at P2 as the source. The data points of electron fluxes shown are picked 4of9

5 Figure 2. Similar to Figure 1 but for P4. from the positions when the magnetic field reached its peak during the dipolarization fronts. Those times are 06:22:59 at P2 and 06:23:55 at P4. Quasi-perpendicular electrons were selected for the betatron acceleration calculation. The compression ratio of the total magnetic field was g = 1.3 due to either a global change of magnetic field or a local compression inside the growing pileup region [Fu et al., 2011]. Pitch angle ranges of P2, a 1 and P4, a 2 are selected to be a 1 = a 2 = The calculated flux of electrons at high energy (3 kev 200 kev) at P4 agrees with the data at P4. The flux at P4 significantly increases (by a factor of 6 to 7) in the high energy range although the compression of magnetic field from P2 to P4 was just a factor of 1.3. Because the magnitude of the power law index of the electron flux was large, a slight shift in the x axis on the log-log plot of flux as function of energy generated a large flux increase. [15] The observed flux of electrons below 3 kev at P4 was half an order smaller than the calculated one. Several possible explanations could lead to this discrepancy. First, whistler mode waves with electric wavefield 5 mv/m were detected by P4 from 06:23:55.6 to 06:23:56.4 (not shown); those waves might well scatter electrons at large pitch angles to small pitch angles within seconds due to pitch angle scattering near the resonant energy, which was a few kev in this case [Khotyaintsev et al., 2011]; this is consistent with the data that, in this time period, electrons in the low energy range are predominantly in the parallel direction. Second, B x and B y were about 10 nt, which indicates that the satellites were not exactly in the center of plasma sheet, leading to the variation of electron density. [16] Figure 3 (bottom) shows the differential flux of electrons assuming Fermi acceleration. Again the blue, green lines give observations from P2 and P4, The red line is the predicted flux at P4 assuming Fermi acceleration using the flux at P2 as the source. Quasi-parallel electrons were used (a 1 = a 2 =0 20 ).b = 1.5 from P2 to P4 gave the best fit. For suprathermal electrons, the calculated flux fits the observations very well and the discrepancy at low energy is modest Event #2 February 27, 2009 [17] We applied our theory to this well studied event. The figures of this event are in the same format as those for the March 11, 2008 event. THEMIS P1, P2, P3 and P4 observed similar dipolarization front signatures and were in the same flow channel in an MHD simulation [Ge et al., 2011, Figure 12d]. As seen in Figures 4 6, significant flux increments of high energy electrons were associated with dipolarization fronts and were consistent with predicted fluxes from adiabatic acceleration. The electron fluxes shown in Figure 6 were from 07:51:29 at P1 and 07:54:15 at P4. The compression ratio of the total magnetic field from P1 to P4 was g = 1.6 and contraction factor was b = 2.0. In addition, there are several differences in this event. First, the energy fluxes of suprathermal electrons increased immediately when the fronts arrived at both spacecraft (Figures 4 and 5). Unlike the event on March 11, there was no decrease in the energy fluxes before the increase. Second, the calculated differential fluxes from betatron and Fermi acceleration are consistent with the observed ones (Figures 6); the discrepancy between the observations and theory for quasi-perpendicular electrons at lower energy is much smaller than on March 11. This might be because P1 and P4 were both in the central plasma sheet. More importantly, the dipolarization front captured by P1 5of9

6 propagation from P1 to P4. In Figure 6 the predicted betatron and Fermi acceleration fluxes at high energy increased by factors of 5 and 10 respectively. Figure 3. Differential flux of (top) quasi-perpendicular and (bottom) quasi-parallel electrons. The blue and green lines are observations from P2 and P4, respectively, and the red line is the predicted flux at P4 using the flux at P2 as the source assuming (top) betatron acceleration and (bottom) Fermi acceleration. (Figure 4) had a dispersive spectrum of suprathermal electrons concurrent with the energy flux increase. These were the same signatures observed in the inner magnetosphere by P2 at 15R E (not shown) and P4 at 10R E (Figure 5). P1 was at 20R E, which was close to the location of the reconnection site in the MHD simulation [Ge et al., 2011]. The data suggest these suprathermal electrons were produced by magnetic reconnection. After these electrons were ejected from the tail region, their fluxes were further enhanced during earthward 4. Discussion [18] Particle transport and non-local acceleration associated with dipolarization fronts is complicated in part because of structures and channels embedded within the fronts. As a result there is coupling between processes on multiple spatial and temporal scales [e.g., Sergeev et al., 2009; Deng et al., 2010]. Analysis is further complicated because we have observations at only a limited number of points. Despite this complexity we believe that THEMIS observed suprathermal electrons that originated near the outer satellites (P1 or P2) and subsequently were detected in the inner tail region near P4. This interpretation seems reasonable because of similarities in the observed dipolarization fronts and because they were in the same flow channel in the MHD simulations. Our analysis of the data, in combination with theory, reveals that adiabatic enhancement of flux strongly depends on the slope of the source differential flux. In particular, for suprathermal electrons large increases in flux can be induced by small magnetic field compression and small contraction of distance between mirror points provided steep spectra. [19] Adiabatic acceleration theory predicts invariance of the power law index during adiabatic transport. In the observations, the power law indices during the dipolarization fronts changed within 0.8 from P2 (or P1) to P4. The fluxes had essentially the same power law indices. They were roughly anti-correlated with the energy fluxes at different positions. Thus, the large power law indices in the high energy range associated with dipolarization most likely can be traced back to the source regions of dipolarization fronts, which is near the reconnection site. Indeed, the magnitude of power law indices tends to increase immediate downstream of the reconnection site [Øieroset et al., 2002; Imada et al., 2007]. This suggests large power law indices associated with dipolarization fronts are generated near the reconnection site. Because adiabatic acceleration enables significant increases in flux if the power law index is large, a steep electron spectrum in the high energy range generated near the magnetic reconnection site provides a favorable condition for further adiabatic enhancement of flux far from the neutral line. Consequently, we suggest that a combination of local processes near the magnetic reconnection site and non-local adiabatic acceleration during earthward transport is responsible for the high flux of suprathermal electrons associated with dipolarization fronts in the inner magnetosphere. [20] We simplified the effect of Fermi acceleration by setting the contraction factor b to be uniform for electrons with different energies and pitch angles, which is determined by contraction of mirror point distance during earthward propagation. However, a more detailed analysis would need to take into account of the non-uniformity of the parameters that describe Fermi acceleration because electron trajectories in non-dipole and dynamic magnetic fields are expected to be complicated, which makes it difficult to assign a simple contraction factor to account for the effect of Fermi acceleration in the variation of the electron flux. In addition, immediately downstream of reconnection outflow, electrons are expected to behave non-adiabatically because of the 6of9

7 Figure 4. Similar to Figure 1 but for P1 in the event of February 27, small radius of curvature of magnetic field lines and large magnetic gradient [e.g., Lyons, 1984; Büchner and Zelenyi, 1989; Schriver et al., 1998; Imada et al., 2007]. This part of the process cannot be addressed by the methods in this paper because it is not clear exactly how far P1 (or P2) is from the diffusion region and how to quantify the nonadiabatic effects. Consequently, in future work, we will refine this calculation using a large scale kinetic (LSK) Figure 5. Similar to Figure 1 but for P4 in the event of February 27, of9

8 detailed simulation and statistical study will not fundamentally change the physics described here that is local processes near reconnection site, as well as non-local adiabatic enhancement in the downstream region contribute to the observed characteristics of suprathermal electrons in the inner magnetosphere and the former mechanisms facilitate the latter by providing steep spectra of electrons in the high energy range. [21] Acknowledgments. The research at UCLA and at the Goddard Space Flight Center was supported by a Magnetospheric Multiscale Mission Interdisciplinary Scientist grant (NASA grant NNX08AO48G at UCLA) and at UCLA was also supported by Geospace grant (NASA grant NNX12AD13G). Qingjiang Pan thanks Robert Richard and David Schriver for helpful discussions. This work was completed while R. J. Walker served at the National Science Foundation as Program Director for Magnetospheric Physics. We acknowledge V. Angelopoulos and THEMIS Science Support team for use of data and software from the THEMIS Mission, and specifically, C. W. Carlson and J. P. McFadden for the use of ESA data, D. Larson and R. P. Lin for the use of SST data, D. L. Turner for calibration of SST data, K. H. Glassmeier, U. Auster and W. Baumjohann for the use of FGM data. The MHD computations for Event #1 were carried out with the support of the NASA Advanced Supercomputing Facility at the Ames Research Center. UCLA Institute of Geophysics and Planetary Physics publication [22] Masaki Fujimoto thanks the reviewers for their assistance in evaluating this paper. Figure 6. Similar to Figure 3 but for the event of February 27, The blue line is from P1, the green line is from P4 and red line is the calculated flux. simulation, in which we follow a large number of electron trajectories in the time-dependent electric and magnetic fields derived from a global MHD simulation [Ashour- Abdalla et al., 1993]. This study will enable us to include the effects due to non-adiabatic motion in the outflow region immediately downstream from the reconnection site and demonstrate betatron and Fermi acceleration for an ensemble of particles. Power law indices of suprathermal electron flux during transport will be re-examined in the LSK simulation. A statistical study using THEMIS data should provide clues that reveal the relationship between the structures in dipolarization fronts and reconnection, and thereby help us understand the high energy particles produced in these processes. Our present analysis suggests, however, that such References Angelopoulos, V. (2008), The THEMIS mission, Space Sci. Rev., 141, 5 34, doi: /s Asano, Y., et al. (2010), Electron acceleration signatures in the magnetotail associated with substorms, J. Geophys. Res., 115, A05215, doi: / 2009JA Ashour-Abdalla, M., J. P. Berchem, J. Büchner, and L. M. Zelenyi (1993), Shaping of the magnetotail from the mantle Global and local structuring, J. Geophys. Res., 98, , doi: /92ja Ashour-Abdalla, M., M. El-Alaoui, M. L. Goldstein, M. Zhou, D. Schriver, R. Richard, R. Walker, M. G. Kivelson, and K. Hwang (2011a), Observations and simulations of non local acceleration of electrons in magnetotail magnetic reconnection events, Nat. Phys., 7, , doi: / nphys1903. Ashour-Abdalla, M., M. El-Alaoui, D. Schriver, Q.-J. Pan, R. Richard, M. Zhou, and R. Walker (2011b), Electron acceleration associated with earthward propagating dipolarization fronts, Abstract SM13C-2098 presented at 2011 Fall Meeting, AGU, San Francisco, Calif., 5 9 Dec. Auster, U., et al. (2008), The THEMIS fluxgate magnetometer, Space Sci. Rev., 141, , doi: /s Büchner, J., and L. M. Zelenyi (1989), Regular and chaotic charged particle motion in magnetotaillike field reversals: 1. Basic theory of trapped motion, J. Geophys. Res., 94(A9), 11,821 11,842, doi: /ja094ia09p Deng, X., M. Ashour-Abdalla, M. Zhou, R. Walker, M. El-Alaoui, V. Angelopoulos, R. E. Ergun, and D. Schriver (2010), Wave and particle characteristics of earthward electron injections associated with dipolarization fronts, J. Geophys. Res., 115, A09225, doi: /2009ja Drake, J. F., M. A. Shay, W. Thongthai, and M. Swisdak (2005), Production of energetic electrons during magnetic reconnection, Phys. Rev. Lett., 94, , doi: /physrevlett Drake, J. F., M. Swisdak, H. Che, and M. A. Shay (2006), Electron acceleration from contracting magnetic islands during reconnection, Nature, 443, , doi: /nature Fu, H. S., Y. V. Khotyaintsev, M. André, and A. Vaivads (2011), Fermi and betatron acceleration of suprathermal electrons behind dipolarization fronts, Geophys. Res. Lett., 38, L16104, doi: /2011gl Fu, H. S., Y. V. Khotyaintsev, A. Vaivads, M. André, and S. Y. Huang (2012), Occurrence rate of earthward-propagating depolarization fronts, Geophys. Res. Lett., 39, L10101, doi: /2012gl Ge, Y. S., J. Raeder, V. Angelopoulos, M. L. Gilson, and A. Runov (2011), Interaction of dipolarization fronts within multiple bursty bulk flows in global MHD simulations of a substorm on 27 February 2009, J. Geophys. Res., 116, A00I23, doi: /2010ja Green, J. C., and M. G. Kivelson (2004), Relativistic electrons in the outer radiation belt: Differentiating between acceleration mechanisms, J. Geophys. Res., 109, A03213, doi: /2003ja Hoshino, M. (2012), Stochastic particle acceleration in multiple magnetic islands during reconnection, Phys. Rev. Lett., 108, , doi: / PhysRevLett of9

9 Hoshino, M., T. Mukai, T. Terasawa, and I. Shinohara (2001), Suprathermal electron acceleration in magnetic reconnection, J. Geophys. Res., 106, 25,979 25,997, doi: /2001ja Hwang, K.-J., M. L. Goldstein, E. Lee, and J. S. Pickett (2011), Cluster observations of multiple dipolarization fronts, J. Geophys. Res., 116, A00I32, doi: /2010ja 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: /2006ja Khotyaintsev, Y. V., C. M. Cully, A. Vaivads, M. Andre, and C. J. Owen (2011), Plasma jet braking: Energy dissipation and non-adiabatic electrons, Phys. Rev. Lett., 106, , doi: /physrevlett Kowal, G., A. Lazarian, E. T. Vishniac, and K. Otmianowska-Mazur (2009), Numerical tests of fast reconnection in weakly stochastic magnetic fields, Astrophys. J., 700,63 85, doi: / x/700/1/63. Lyons, L. R. (1984), Electron energization in the geomagnetic tail current sheet, J. Geophys. Res., 89(A7), , doi: /ja089ia07p Lyons, L. R., and D. J. Williams (1986), Quantitative aspects of magnetospheric physics, Geophys. J. R. Astron. Soc., 86, , doi: / j x.1986.tb01089.x. McFadden, J. P., et al. (2008), The THEMIS ESA plasma instrument and in-flight calibration, Space Sci. Rev., 141, , doi: / s Nakamura, R., et al. (2004), Spatial scale of high-speed flows in the plasma sheet observed by Cluster, Geophys. Res. Lett., 31, L09804, doi: / 2004GL Northrop, T. G. (1963), The Adiabatic Motion of Charged Particles, John Wiley, New York. Ohtani, S., M. A. Shay, and T. Mukai (2004), Temporal structure of the fast convective flow in the plasma sheet: Comparison between observations and two-fluid simulations, J. Geophys. Res., 109, A03210, doi: / 2003JA Øieroset, M., R. P. Lin, T. D. Phan, D. E. Larson, and S. D. Bale (2002), Evidence for electron acceleration up to 300 kev in the magnetic reconnection diffusion region in the earth s magnetotail, Phys. Rev. Lett., 89, , doi: /physrevlett Roederer, J. G. (1970), Dynamics of Geomagnetically Trapped Radiation, Cambridge Univ. Press, New York, doi: / Runov, A., V. Angelopoulos, M. I. Sitnov, V. A. Sergeev, J. Bonnell, J. P. McFadden, D. Larson, K.-H. Glassmeier, and U. Auster (2009), THEMIS observations of an earthward propagating dipolarization front, Geophys. Res. Lett., 36, L14106, doi: /2009gl Schmid, D., et al. (2011), A statistical and event study of magnetotail dipolarization fronts, Ann. Geophys., 29, , doi: /angeo Schriver, D., M. Ashour-Abdalla, and R. L. Richard (1998), On the origin of the ion-electron temperature difference in the plasma sheet, J. Geophys. Res., 103(A7), 14,879 14,895, doi: /98ja Schulz, M., and L. Lanzerotti (1974), Particle Diffusion in the Radiation Belts, vol. 7, Springer, New York, doi: / Sergeev, V., V. Angelopoulos, S. Apatenkov, J. Bonnell, R. Ergun, R. Nakamura, J. McFadden, D. Larson, and A. Runov (2009), Kinetic structure of the sharp injection/dipolarization front in the flow-braking region, Geophys. Res. Lett., 36, L21105, doi: /2009gl Sergeev, V. A., V. Angelopoulos, J. T. Gosling, C. A. Cattell, and C. T. Russell (1996), Detection of localized, plasma-depleted flux tubes or bubbles in the midtail plasma sheet, J. Geophys. Res., 101(A5), 10,817 10,826, doi: /96ja Sharber, J. R., and W. J. Heikkila (1972), Fermi acceleration of auroral particles, J. Geophys. Res., 77(19), , doi: /ja077i019p Shinohara, I., et al. (1998), Low-frequency electromagnetic turbulence observed near the substorm onset site, J. Geophys. Res., 103, 20,365 20,388, doi: /98ja Vaivads, A., A. Retinò, Y. V. Khotyaintsev, and M. André (2011), Suprathermal electron acceleration during reconnection onset in the magnetotail, Ann. Geophys., 29, , doi: /angeo of9