Fermi and betatron acceleration of suprathermal electrons behind dipolarization fronts

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 38,, doi: /2011gl048528, 2011 Fermi and betatron acceleration of suprathermal electrons behind dipolarization fronts H. S. Fu, 1 Y. V. Khotyaintsev, 1 M. André, 1 and A. Vaivads 1 Received 14 June 2011; revised 14 July 2011; accepted 15 July 2011; published 20 August [1] Two dipolarization front (DF) structures observed by Cluster in the Earth midtail region (X GSM 15 R E ), showing respectively the feature of Fermi and betatron acceleration of suprathermal electrons, are studied in detail in this paper. Our results show that Fermi acceleration dominates inside a decaying flux pileup region (FPR), while betatron acceleration dominates inside a growing FPR. Both decaying and growing FPRs are associated with the DF and can be distinguished by examining whether the peak of the bursty bulk flow (BBF) is co located with the DF (decaying) or is behind the DF (growing). Fermi acceleration is routinely caused by the shrinking length of flux tubes, while betatron acceleration is caused by a local compression of the magnetic field. With a simple model, we reproduce the processes of Fermi and betatron acceleration for the higher energy (>40 kev) electrons. For the lower energy (<20 kev) electrons, Fermi and betatron acceleration are not the dominant processes. Our observations reveal that betatron acceleration can be prominent in the midtail region even though the magnetic field lines are significantly stretched there. Citation: 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,, doi: /2011gl Introduction [2] The dipolarization front (DF), the earthward leading edge of the re configurated magnetic field after reconnection in the magnetotail, has been extensively studied recently together with the co existing wave activity (lower hybrid, whistlers, and electron cyclotron harmonic mode) and plasma dynamics [e.g., Runov et al., 2009; Zhou et al., 2009; Apatenkov et al., 2007; Sergeev et al., 2009; Nakamura et al., 2009; Asano et al., 2010; Khotyaintsev et al., 2011; Ge et al., 2011; Birn et al., 2011; Hwang et al., 2011]. The DF usually appears with the reconnection jet, which is sometimes called bursty bulk flow (BBF) [Angelopoulos et al., 1992]. Behind the DF, the magnetic field strength is elevated suddenly to a high level. This region is named as magnetic flux pileup region (FPR) [e.g., Zhang et al., 2007; Khotyaintsev et al., 2011]. One important but not well understood issue about DF is the acceleration of suprathermal electrons inside the FPR. [3] During the dipolarization process, the electrons can be energized to a few hundred kev inside the FPR. This energization was suggested to be associated with the inductive electric field including the contributions from betatron and 1 Swedish Institute of Space Physics, Uppsala, Sweden. Copyright 2011 by the American Geophysical Union /11/2011GL Fermi acceleration [e.g., Williams et al., 1990; Birn et al., 2004]. Betatron acceleration works when the first adiabatic invariant m v 2? /B is conserved, while Fermi acceleration is effective only when the second adiabatic invariant J = R L 0 v k dl is conserved. Wu et al. [2006] suggested that Fermi acceleration dominates in the midtail region due to the shrinking length of the flux tubes. In the near Earth region, however, betatron acceleration may be more important since the gradient of the magnetic field is much larger there. Sharber and Heikkila [1972] drew a similar conclusion when studying the auroral particles precipitation at the ionosphere altitude. They pointed out that, for the auroral particles, the change from a field aligned pitch angle distribution at high latitudes to a trapped distribution at low latitudes reflects a change from Fermi acceleration on the distant taillike field lines to betatron acceleration on the more dipolar field lines closer to the Earth. Smets et al. [1999] examined the pitch angle distributions of the 10 kev electrons behind the DF and got a similar conclusion as well. A different conclusion, however, can be inferred from the recent observation reported by Deng et al. [2010, Figure 4]: During the propagation of a DF from X GSM 20 R E to X GSM 11 R E, betatron acceleration of electrons is more prominent in the midtail region, while Fermi acceleration appears in the near Earth region. This indicates that the energization of electrons behind the DF may involve some other mechanisms in addition to the large scale (midtail to near Earth) process. [4] In this paper, we compare two events showing respectively the feature of Fermi and betatron acceleration behind the DF and then reveal the mechanisms responsible for the different processes. 2. Observations [5] Data from Cluster instruments FGM, RAPID, PEACE, CIS, and EFW, are used in this study [Escoubet et al., 2001, and references therein]. Geomagnetic solar magnetospheric (GSM) coordinates are used throughout the paper unless noted otherwise. [6] Two events, showing respectively the field aligned and perpendicular energization of electrons behind the DF, were observed on 1 October 2007 and 3 September Figure 1 is an overview of these two events. In case (left) parameters are primarily measured by Cluster 4 (C4). In case (right) parameters are measured by C1. The spacecraft locations are shown in Figures 1a and 1b. In both cases, the spacecraft are located at X GSM 15 R E with small Y GSM and Z GSM. The X component of magnetic field is small (Figures 1d and 1k, black lines), and the plasma beta is larger than 0.5 most of the time (Figures 1d and 1k, blue lines). Thus the spacecraft should be inside the midtail plasma sheet in both cases. The 1of5

2 Figure 1. Two cases showing, respectively, the feature of Fermi and betatron acceleration behind the dipolarization front. (left) The parameters measured by C4 on 1 October (right) The parameters measured by C1 on 3 September Figures 1 (left) and 1 (right) have the same format. Parameters from top to bottom are: (a and b) locations of SC in the X Z and X Y plane, (c and j) Z component of the magnetic field, (d and k) X component of the magnetic field and the plasma beta, (e and l) omnidirectional differential flux of the kev electrons, (f and m) omnidirectional differential flux of the kev electrons, pitch angle distribution of the (g) kev and (n) kev electrons, (h and o) X component of the ion flow velocity, (i and p) plasma density derived from the spacecraft potential. The ion velocity in Figure 1h is measured actually by C3 but can represent the measurements of C4 due to the small separation between C3 and C4 ( 30 km). The shadowed areas indicate the FPR, which may be decaying (Figure 1, left) or growing (Figure 1, right). 2of5

3 criteria for identifying the plasma sheet are consistent with that given by Cao et al. [2006]. [7] For case , C4 measures a steady geomagnetic environment (B Z 5 nt) from 07:14:00 to 07:16:38 UT in the quiet plasma sheet (Figure 1c). Then a DF characterized by the jump of Bz from 2 to 10 nt is detected around 07:16:41 UT. Ahead of the DF is observed a short duration ( 2 s) dip [Sergeev et al., 2009]. Behind the DF, Bz is larger than in the quiet plasma sheet. The FPR is identified as the region between 07:16:41 UT and 07:18:00 UT (shadowed area), after which Bz becomes relatively steady. Using the timing analysis between C3 and C4 in combination with minimum variance analysis, we can estimate that the DF propagates along X GSM with a speed of V X 85 km/s and a thickness of d 220 km. This thickness is about 1.5 times as large as the local ion inertia length l i 150 km. Before the arrival of the DF, the electrons with energy from 3.5 kev to 20 kev dominate the plasma sheet (Figure 1f) and the plasma density, which is derived from the EFW measurements of the spacecraft potential, is almost a constant (Figure 1i). In Figure 1f, the systematic jump at 2.2 kev is due to a channel change of the PEACE instrument. When the DF arrives (vertical dashed line), the omnidirectional differential fluxes of energetic electrons ( kev) enhance suddenly (Figure 1e) and the plasma density decreases. Figure 1g shows the pitch angle distribution of the kev electrons. We notice that the enhancement of energetic electrons fluxes appears mainly in the parallel (Pitch angle, PA 0) and anti parallel (PA 180 ) direction. This is a typical cigar distribution [Baker et al., 1978] and is usually attributed to Fermi acceleration [e.g., Williams et al., 1990; Wu et al., 2006]. The cold electrons (<3.5 kev) behind the DF are determined to be field aligned (not shown); they may originate from the ionosphere. [8] In Figure 1h, the blue line represents the X component of the ion bulk velocity measured by CIS on C3, while the black line represents the convection velocity calculated from the C3 measurements of E B. Here it is necessary to point out that, on 1 October 2007, the separation between C3 and C4 ( 30 km, not shown) is much smaller than the local ion inertia length (l i 150 km). Therefore, in principle, the ion parameters measured by C3 and C4 should be the same. We indeed compared all the available data between C3 and C4 for case and cannot find distinct discrepancies. In this way, the blue line in Figure 1h can also represent the measurements of C4. As can be seen, the flow velocities obtained from CIS and E B are roughly consistent with each other. When the DF arrives at 07:16:41 UT, the flow velocity increases suddenly from 0 to 85 km/s (from E B), which is consistent with the propagation velocity of the DF derived from the multi satellite timing. This strong convection flow should be a BBF. We notice that the peak of the flow is co located with the DF (vertical dashed line). Inside the FPR, the flow velocity decreases especially for the region between 07:16:41 UT and 07:17:15 UT. [9] For case (Figure 1, right), the DF structure is detected at 21:56:20 UT and has been reported by Asano et al. [2010] and Khotyaintsev et al. [2011]. The propagation velocity of this DF is determined as V 450 [0.91, 0.41, 0.08] km/s. Seen from Figure 1j, Bz jumps at the DF from 0 to 15 nt and then decrease gradually. Before the DF, C1 is located in the quiet plasma sheet and measured a steady magnetic field. The FPR is identified as the region between 21:56:20 UT and 21:56:35 UT (shadowed area). When the DF arrives, the differential flux of energetic electrons increases (Figure 1l) and the plasma density decreases, as the situation in case The energization characteristics of electrons inside the FPR, however, are quite different from that case. Figure 1n shows the pitch angle distribution of the kev electrons. We see that the energization of electrons almost concentrates at PA 90. This is the pancake distribution and was suggested as a consequence of betatron acceleration [e.g., Wu et al., 2006; Khotyaintsev et al., 2011]. Behind the DF, the flow velocity (Figure 1o) increases gradually from 0 to more than 900 km/s (at 21:56:35 UT). Betatron acceleration occurs inside the FPR. [10] The acceleration of suprathermal electrons is observed behind the DF in both cases. Now we compare the difference between them. In case , Fermi (field aligned) acceleration is observed inside the FPR. This is the normally expected situation in the midtail region (X GSM 15 R E ) and can be interpreted by the shrinking length of flux tubes. Because the FPR is behind the peak of the BBF, the flux tubes inside the FPR will not be compressed in the direction perpendicular to B and thus there is no local betatron acceleration. In fact, these flux tubes can even expand and will lead to a local betatron deceleration, which is beyond the scope of this paper. We define the FPR behind the peak of BBF as a decaying FPR due to the expanding flux tubes. In case , the FPR is located in front of the peak of the flow. In such a situation the leading part of the FPR moves slower than the rear part of the FPR. The tailward flux tubes are running into the earthward flux tubes and then lead to the compression of the local magnetic field, which subsequently causes the betatron acceleration of electrons. When the flow velocity decreases, the betatron acceleration disappears. This FPR in front of the BBF peak is recognized as a growing FPR. It is necessary to point out that, in case , there also exists Fermi acceleration although it is not as prominent as the betatron acceleration. [11] We investigate the evolution of the electron phasespace density (PSD) for these two cases in Figure 2 (solid lines). In case (Figure 2, top), we consider only the suprathermal electrons with energy >3 kev, which is the typical range of the plasma sheet electrons (see Figure 1f). In case (Figure 2, bottom), the kev electrons are considered in order to compare with case The gaps of PSD profiles in case are due to the unavailability of the PEACE data. The PSDs in both cases have been averaged along the azimuthal direction. In case , the PSDs are almost isotropic and show a typical kappa distribution [Christon et al., 1988] before the DF at 07:15:42.79UT. After the DF, a cigar like distribution is observed at 07:16:53.40UT. In case , an isotropic distribution is observed before the DF (21:56:16.20UT), while a pancake distribution is found after the DF (21:56:24.49UT). [12] We are able to reproduce the processes of Fermi and betatron acceleration by assuming that the electrons in the quiet plasma sheet (Figures 2a and 2c) can represent the electrons in the ion diffusion region and can be treated as the source population for the acceleration processes. Results from the acceleration model are plotted in Figures 2b and 2d as dashed lines in order to compare with the observations 3of5

4 Figure 2. Phase space density (PSD) plotted as a function of pitch angle. (a and c) PDS before the DF; it has been treated as the source. (b and d) PSD behind the DF, i.e., inside the decaying (Figure 2b) or growing (Figure 2d) FPR. Solid lines represent the observations of Cluster, while dashed lines show the modeling results. (solid lines). The modeling is achieved with the formulas E 1k =(L 0 /L 1 ) 2 E 0k = F f E 0k and E 1? =(B 1 /B 0 ) E 0? = F b E 0?, where E, L and B represent, respectively, the electron energy, the length of flux tube and the magnetic field strength; The subscripts 0 and 1 denote, respectively, the quantities before and after the acceleration; F f and F b are the factors of Fermi and betatron acceleration. They reflect the increase of electron energy, but not the velocity. For the best fit, the factor of Fermi acceleration in case is obtained as F f = The factor of Fermi and betatron acceleration in case are obtained as F f = 1.13 and F b = 1.6. Because the magnetic field lines at X GSM < 15 R E are significantly stretched, we can estimate the reconnection sites with a simple model R 2 /R 1 L 2 /L 1, where R and L represent, respectively, the radial distance to the Earth and the length of the magnetic field line. In these two cases, the factors of Fermi acceleration correspond roughly to the reconnection X line at X GSM 21 R E (case ) and X GSM 17 R E (case ); the factor of betatron acceleration indicates a local compression of magnetic field by a factor of 1.6 in case The locations of reconnection sites estimated in these two cases are reasonable according to the previous statistical studies [e.g., Nishida and Nagayama, 1973]. In case , X line is close ( 2 R E ) to the observed DF. This is consistent with the large velocity of the BBF ( 900 km/s), which may only decelerate slightly during the short propagation distance ( 2 R E ) after the ions leave the diffusion region where the typical Alfvén velocity is 1000 km/s (assuming a background with B 0 20 nt and n i 0.2 cm 3 ). We can also estimate whether the compression factor 1.6 in case is reasonable or not. Assuming the leading part of the FPR moves with V km/s and the rear part of the FPR moves with V km/s, the duration of the FPR (15s) corresponds roughly to a width of D 1 10,000 km. The local compression of magnetic field by a factor of 1.6 indicates that the initial width of the FPR should be D 0 16,000 km. In this way, the time required for the compression is t = D D/D V =(D 0 D 1 )/(V 0 V 1 ) 13s. During the period of 13s, the FPR propagates approximately 1.4 R E which is less than the suggested distance ( 2 R E ) to the X line and thus in reasonable agreement with the proposed scenario. [13] In Figure 2 (right), the modeling results agree well with the higher energy (>40 kev) electron PSDs in both cases, confirming the feasibility of Fermi and betatron acceleration. The betatron acceleration of higher energy (>40 kev) electrons is more effective than that of lowerenergy (>40 kev) electrons (Figure 2d), consistent with the simulations results of Birn et al. [2004]. For the lowerenergy (<20 kev) electrons, there exist some differences between the modeling and observations. These differences may stem from the assumption of the source population for the acceleration processes. In the plasma sheet, electrons are usually described by the kappa distribution [Christon et al., 1988], while in the ion diffusion region, electrons are described by the flat top distribution [Asano et al., 2008], which usually shows a shoulder at 2 14 kev. In this way, the electrons with energy <20 kev in the ion diffusion region may be different from that in the plasma sheet. In addition, the dynamics of electrons can be affected by the non adiabatic wave particle interaction. In case , the wave particle interaction behind DF has been analyzed in detail by Khotyaintsev et al. [2011, Figure 3b]. They demonstrate that the pitch angle diffusion of lower energy electrons is much more effective than that of higher energy electrons. During the diffusion process, the distribution function at low energies will become isotropic while it will stay anisotropic at high energies. In case , the whistlers are also observed behind the DF (not shown). We have examined the gyro resonance condition and found that also in this case the whistlers can effectively scatter the lower energy (<20 kev) electrons and isotropize the distribution function at low energies. Ashour Abdalla et al. [2010, 2011] also suggested that the energizations of the high and low energy electrons are dominated by different processes. [14] We re examine the raw data of the event reported by Deng et al. [2010, Figure 4] and find that the betatron acceleration observed by THEMIS B & C in the midtail region (X GSM 20.1 R E and X GSM 16.7 R E ) is associated with a growing FPR in front of the BBF peak, while the Fermi acceleration observed by THEMIS D in the near Earth region (X GSM 11.0 R E ) is related to a decaying FPR behind the BBF peak. This event strongly supports our 4of5

5 proposition that growing and decaying FPRs lead to different acceleration processes. Betatron acceleration in the midtail is caused by a local compression of the magnetic field. 3. Conclusions [15] In this paper, we performed a comparison study of electron acceleration behind dipolarization fronts (DFs). Two events observed in the midtail region (X GSM 15 R E ) are analyzed in detail. For case , C4 observed Fermi (field aligned) acceleration inside a decaying flux pileup region (FPR). No ongoing compression of the magnetic field is found in this case. For case , C1 observed betatron (perpendicular) acceleration inside a growing FPR due to the local compression of the magnetic field. The decaying and growing FPR can be distinguished by examining whether the peak of the bursty bulk flow (BBF) is co located with the DF (decaying) or is behind the DF (growing). Assuming the electrons in the quiet plasma sheet can represent the electrons near the X line, we reproduce the processes of Fermi (case ) and betatron (case ) acceleration for the higher energy (>40 kev) electrons. For the lower energy (<20 kev) electrons, Fermi and betatron acceleration are no longer effective, indicating the contribution from other processes such as the nonadiabatic wave particle interaction. Our study reveals that the behavior and properties of electrons in the FPR can be related to different stages in the time evolution of DFs as well as can depend on locations relative to the flow/magnetic structure. The growing and decaying FPRs can lead to different acceleration processes. Betatron acceleration can be very important in the midtail region or even close to the X line. Fermi acceleration works all the time behind the DF due to the reduced length of flux tubes. The acceleration event observed by THEMIS [Deng et al., 2010] supports our conclusions. A statistical study is necessary in the future to understand this issue well. [16] Acknowledgments. We thank the Cluster Active Archive for providing the data for this study. This research is supported by the Swedish Research Council under grants , and YK and AV also acknowledge the support from ISSI. [17] The Editor thanks two anonymous reviewers for their assistance in evaluating this paper. References Angelopoulos, V., W. Baumjohann, C. F. Kennel, F. V. Coroniti, M. G. Kivelson, R. Pellat, R. J. Walker, H. Lühr, and G. Paschmann (1992), Bursty Bulk Flows in the Inner Central Plasma Sheet, J. Geophys. Res., 97(A4), , doi: /91ja Apatenkov, S. V., et al. (2007), Multi spacecraft observation of plasma dipolarization/injection in the inner magnetosphere, Ann. Geophys., 25, , doi: /angeo Asano, Y., et al. (2008), Electron flat top distributions around the magnetic reconnection region, J. Geophys. Res., 113, A01207, doi: / 2007JA Asano, Y., et al. 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Pang (2009), THEMIS observation of multiple dipolarization fronts and associated wave characteristics in the near Earth magnetotail, Geophys. Res. Lett., 36, L20107, doi: /2009gl M. André, H. S. Fu, Y. V. Khotyaintsev, and A. Vaivads, Swedish Institute of Space Physics, Box 537, SE Uppsala, Sweden. (huishan@irfu.se) 5of5