Current carriers in the bifurcated tail current sheet: Ions or electrons?

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113,, doi: /2007ja012541, 2008 Current carriers in the bifurcated tail current sheet: Ions or electrons? P. L. Israelevich, 1 A. I. Ershkovich, 1 and R. Oran 1 Received 15 May 2007; revised 29 October 2007; accepted 17 December 2007; published 17 April [1] We have studied statistical distributions of the current density in the geomagnetic tail current sheet for different sets of local plasma parameters using Cluster data. It is shown that the electric current density calculated from 4-point magnetic field measurements exhibits no correlation with the number flux of ions. We conclude that main current carriers in the magnetospheric system of reference are electrons. Citation: Israelevich, P. L., A. I. Ershkovich, and R. Oran (2008), Current carriers in the bifurcated tail current sheet: Ions or electrons?, J. Geophys. Res., 113,, doi: /2007ja Introduction [2] The geomagnetic tail is the main reservoir of the energy and, hence, one the key regions of the Earth s magnetosphere. Therefore it has been extensively studied since its discovery in 1964 [Ness, 1965]. The average configuration of the magnetic tail [e.g., Behannon, 1970; Fairfield, 1979] contains two lobes of magnetic field lines with opposite polarity, separated by the plasma sheet with dawn-to-dusk electric current. Being a part of the magnetosphere, the geomagnetic tail also exhibits highly variable dynamical behavior, which depends on the randomly varying parameters of the solar wind plasma and regular diurnal and seasonal changes because of the Earth s rotation axis and magnetic dipole tilts. Studies of the magnetosphere (and geomagnetic tail) are often based on the assumption, either explicit or implicit, on the existence of the steady state. In other words, it is assumed that if the external parameters (of the solar wind, ionosphere and magnetic dipole) do not change for sufficiently long time the magnetosphere reaches a certain equilibrium configuration which does not change with time. This approach is explicit in some works on numerical simulations of the solar wind interaction with the planets [cf., Walker et al., 1993; Gombosi et al., 2003], and it is the basis for creation of experimental parametrized models obtained as an averaged configuration of the geomagnetic tail (magnetosphere) for given values of external parameters [cf., Tsyganenko, 1990]. It remains valid (however, being not so evident), for the case studies and theoretical analysis of individual processes in the geomagnetic tail, which are usually considered to occur on the background of the steady state configuration. [3] Conversion of the magnetic energy stored in the tail lobes to the plasma energy (both to the heating and acceleration) occurs in the cross-tail current sheet separating the lobes. The energy conversion arises because of magnetic 1 Department of Geophysics and Planetary Sciences, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Israel. Copyright 2008 by the American Geophysical Union /08/2007JA field reconnection and/or development of variety of plasma instabilities. The thickness of this sheet is of the order of ion gyroradius, so it is a discontinuity in MHD sense, and thus requires a kinetic treatment. The model of steady state ( background ) geotail current sheet dates back to the classical paper by Harris [1962], who has obtained (in simple analytical form) one possible self-consistent solution of Vlasov s equation describing the one-dimensional layer of plasma confined between two regions of oppositely directed magnetic field. For forty years this solution was the basis for study of the processes in the geomagnetic tail [cf., Schindler, 1972; Birn et al., 1975; Kan, 1973, 1979]. [4] Evidence for the current sheet profile, substantially different from that of the Harris model, was obtained by [Sergeev et al., 1993]. Using ISEE dual satellite system, they found a case of current sheet profile with minimum of the electric current density near the point of the B x -component reversal and two off-centered maxima of the current density ( splitted or bifurcated current sheet). Such a current sheet structure was derived statistically from the magnetic field measurements in the distant geomagnetotail ( R E ) tail [Hoshino et al., 1996]. More precise Cluster multipoint measurements of magnetic field and current density in the plasma sheet have shown that at least 17% of current sheet crossings correspond to current density distribution with two off-centered maxima [Asano et al., 2005]. A number of bifurcated current sheet crossings have been reported in the past few years [Nakamura et al., 2002; Runov et al., 2003, 2004, 2005a, 2005b, 2006; Sergeev et al., 2003]. Current sheet splitting also takes place in Jovian magnetosphere [Israelevich and Ershkovich, 2006]. [5] The existence of bifurcated current sheets has been predicted by Cowley [1978], who has shown (in the framework of fluid theory) that if perpendicular plasma pressure exceeds the parallel one, a broad region of depressed current arises near the center of the current sheet, terminated at its boundaries by spikes in the current density. The electric current density profile with two off-centered maxima was observed in 1D kinetic simulations by Harold and Chen [1996]. Recent Cluster observations of bifurcated current sheets put a new challenge for further theoretical studies of the geomagnetic tail current sheet and thereby stimulated 1of8

2 theoretical and model studies of the current sheet structure and possible causes of its bifurcation [e.g., Mottez, 2003; Sitnov et al., 2003; Zelenyi et al., 2003; Karimabadi et al., 2003a, 2003b; Birn et al., 2004; Daughton et al., 2004; Ricci et al., 2004; Genot et al., 2005; Camporeale and Lapenta, 2005; Israelevich et al., 2007; Greco et al., 2007]. [6] One of the ways to check the validity of the theoretical models of the current sheet splitting (bifurcation) is to elucidate the question about the carriers of the electric current in the geomagnetic tail. Models considering different kind of particles for the role of current carriers result in different geophysical consequences. For example, the electron current dominated current sheets may undergo the lower-hybrid drift instability, whereas modified two stream instability may develop for the currents transferred by ions [Yoon and Lui, 2004]. [7] Of course, the electric current is the relative motion of ions and electrons, so the answer to this question depends on the choice of the frame of reference. The electrons are always the current carriers in the frame moving with plasma. However, all the models as well as measurements correspond to the magnetospheric system (where the magnetosphere is, so to say, at rest ). Solar ecliptic or solarmagnetospheric systems are examples. Sometimes, another choice can be made for convenience, but the final result is always presented (or, at least, may be presented) in the magnetospheric system. It is worth mentioning that the spacecraft reference system is close to magnetospheric system in sense that the spacecraft velocity is much less than the plasma and current velocities. Here we will use the term current carriers in this sense, i.e., we consider the velocities of electrons and ions, V e and V i, in magnetospheric system, and speak about dominant current carriers in cases when one of these velocities is significantly larger than the other. Using this terminology, we can say that for the Harris model (and its further modifications) the main carriers of the electric currents are ions. [8] The difficulties in determining the electric current density (and the main current carriers) from the distribution function are obvious: the current velocity for the electric current density 10 na/m 2 is 60 km/s, whereas the thermal velocities of ions and electrons in the current sheet are 1000 and 20,000 km/s, respectively. Nevertheless, at least strong currents may be measured this way [Frank et al., 1984; Patterson et al., 1998; Mukai et al., 1998; Kaufmann et al., 2001]. [9] Although in the Harris model the main carriers of the current are ions, observations show that current sheets are often dominated by the electron current [McComas et al., 1986; Mitchell et al., 1990; Mukai et al., 1998; Kaufmann et al., 2001; Asano et al., 2003]. However, ions may become dominant current carriers in certain regions of the plasma sheet or at certain stages of substorm development [Mitchell et al., 1990; Kaufmann et al., 2001]. It is interesting, that in the work of Kaufmann et al. [2001] one can find some evidence for bifurcation of the electron current, at least in the center of the geomagnetic tail (Y = 0) with the maximum current density at b = 3 10 (i.e., at the place where the magnetic field in the plasma sheet reaches approximately half of its value in the lobe) (see Figure 2b therein). In this paper we will try to determine which kind of particles is predominantly responsible for the charge transfer in the geomagnetic current sheet, using magnetic field and ion measurements by Cluster satellites. 2. Data Analysis [10] Here we compare the results of electric current calculations as a curl of the magnetic field measured by FGM instruments aboard four Cluster [Balogh et al., 2001] satellites with measurements of ion density and velocity by CIS instruments [Reme et al., 2001] aboard Cluster satellites 1, 3, and 4. We use current sheet crossings in August- October 2001 (see the list in Table 1) when the separation between the satellites was 2000 km. [11] CIS consists of two different instruments: Hot Ion Analyzer (HIA) sensor and Ion Composition and Distribution function sensor (CODIF) which provide independent sets of calculated moments of the ion distribution function. HIA sensor performs measurements in the energy range 5 ev/q to 32 kev/q, whereas the upper energy limit for CODIF sensor is somewhat higher, up to 38 kev/q. Figure 1 shows the moments of the ion distribution function (density and velocity components) calculated from HIA measurements versus simultaneous moments from CODIF sensor. Thick lines show the best fits and thin lines correspond to dependencies y = x. HIA and CODIF moments correlate rather well. The absolute values of HIA and CODIF moments also correspond to each other except for V z component of the velocity and the number density. The HIA number density is, in average, 2/3 of the number density calculated from CODIF measurements. In order to choose which set of moments is preferable for the statistical comparison with the magnetic field data, we have considered which plasma data set (either CODIF or HIA) satisfies the pressure balance better. [12] The total pressure P across the current sheet is Pt ðþ¼p mag ðzt ðþþþp plasma ðzt ðþþ ð1þ where P mag = B 2 /8p is the magnetic field pressure and P plasma = n i T i + n e T e, and z is the distance from the plasma sheet center (B x = 0). In general, the time variation of the total pressure P(t) is much slower that the time variation of the satellite position z(t) due to the tail flapping motion. Therefore dp mag dt þ dp plasma dt 0 The electron pressure in the plasma sheet is much smaller than the ion pressure, and, hence, one can check the pressure balance by comparing simultaneous changes of the magnetic field and ion pressure. Figure 2 shows the changes of the ion pressure DP i (CODIF momenta, upper panel; HIA momenta, lower panel) versus the changes of the magnetic field pressure DP mag. The changes of the pressure are averaged over 1 min. One can see that the ion pressure as measured by HIA accounts only for 30% of the pressure balance in the plasma sheet, whereas CODIF data set ensures at least 60% of the pressure balance. The correlation coefficient for CODIF pressure (0.32) is smaller than that for HIA pressure (0.5). This fact is associated with the difference in noise levels, but absolute value of measured parameters is more important for further analysis. Therefore it is reasonable to use the moments of CODIF ion ð2þ 2of8

3 Figure 1. Momenta of 3D ion distribution function measured by CIS-HIA (number density and ion velocity components) versus the same momenta from CIS-CODIF measurements. Thick solid lines show best fits, thin solid lines correspond to the dependence y = x. distribution for the statistical comparison between the electric current density calculated directly from the magnetic field measurements and the ion electric current en i V i. The other 40% of the pressure balance is supported by the electron pressure and, possibly, by the pressure from ions whose energy is higher than the upper limit of CODIF sensor (38 kev/q). Estimating the electron pressure as 15% of the ion pressure, we arrive at the conclusion that the high energy ions (38 kev/q) may account for less than 30% of the pressure balance, i.e., less than 15% of the electric current flowing across the tail. [13] The 1-s averaged electric current density was calculated for the barycenter of satellites system. The z-coordinate of the neutral sheet (i.e., the point where B x = 0) varies continuously because of tail flapping. Therefore we use the value of the B x -component as the measure of the distance of the barycenter (or satellite) from the neutral sheet. We consider only points where jb x j < 20 nt in order to eliminate strong currents in the tail lobes from the analysis. All measurements of the electric current density were averaged over 1 nt bins of B x. The result is shown in Figure 3a by solid line. Two double off-centered maxima of j y are clearly seen. Thus the averaged distribution of the electric current shows the bifurcated current sheet as well as individual distributions of electric current density for some of geotail current sheet crossings. This is not surprising as clear double-peak current sheet crossings constitute at least 17% of the total number of crossings [Asano et al., 2005]. Because of averaging, the maximum value of the electric current density is 3 na/m 2, i.e., it is 3of8

4 and of the averaged y-component of the measured ion velocity hv y i. Again, there is no sign for off-centered maxima of hv y i. Moreover, the hv y i is almost everywhere smaller than hj y i/ehn i i and even has an opposite sign for large jb x j (far from the neutral sheet). The fact that two curves coincide for small values of B x (i.e., close to the neutral sheet) does not allow us (as we will check later) to conclude that the electric current near the neutral sheet is transferred by ions. [14] Another way to check whether the ions are the main carriers of the electric current in the geomagnetic tail is to investigate the correlation between the electric current density and the ion fluxes. Figure 4 shows j y plotted versus corresponding values of n i V y. The solid line shows the best fit, and the dashed line is j y = n i V y. There is no correlation between the two quantities. Ion fluxes may have both a positive and a negative y-component and their presence, obviously, does not affect directly the electric current Figure 2. Top: 1-min averaged changes of the ion pressure as measured by CIS-CODIF versus 1-min averaged changes of the magnetic pressure. Bottom: Same for CIS-HIA measurements. 5 times smaller than those for some individual crossing of bifurcated sheet, but it is still large enough in order to be measured by ion detectors: The velocity of ions (if they are the primary carriers of the current and their number density is 1 cm 3 ) should be 20 km/s. However, no double-peak structure is seen in averaged distribution of n i V y (see dashed line in Figure 3a which shows values of n i V y averaged over the same 1 nt bins of B x ). The lowest panel, (Figure 3b) shows the dependencies (versus B x ) of the ion velocity relative to electrons calculated as hj y i/hn i i (solid line) Figure 3. From top to bottom: (a) averaged j y -component of the current density (solid line), averaged y-component of ion flux (dashed line), and (b) calculated velocity of current carriers (solid line) and averaged V y -component of the ion velocity (dashed line) versus B x -component of the magnetic field. 4of8

5 Figure 4. Local values of the electric current density j y versus ion flux n i V y. Solid line shows the best fit, dashed line represents j y = n i V y. Figure 6. Histogramm of ion velocity V y. Dashed line corresponds to the whole set of data, solid line represents a distribution for the points with jb x j <1nT. density. Moreover, the strongest currents are observed for small n i V y, that is for cases when plasma motion in the y- direction is absent, and the electron fluxes are significant. The same conclusion is true not only for the plasma sheet as a whole, but for the region of the neutral sheet where B x -component of the magnetic field changes its sign. This may be seen from Figure 5 (which shows in the same format as Figure 4) the data points only for jb x j <1nT.The Figure 5. Same as Figure 3, but only for the points in the vicinity of neutral line (jb x j < 1 nt). correlation between j y and n i V y is also absent in the neutral sheet. [15] As it is known, the y-component of ion velocity may reach very high values, up to hundreds km/s, but it does not exhibit any preferential sign (positive or negative). Figure 6 shows the probability distribution for given values of V y. The dashed line represents the whole set of measurements, and the solid line corresponds only to the points in the closest vicinity of the neutral sheet (jb x j < 1 nt). Average velocity is close to zero (0.7 km/s for the whole distribution and 3.4 km/s for the neutral sheet). Therefore we tentatively conclude that in an average steady state magnetosphere the ion fluxes are absent. However, strong variability of the magnetosphere results in a large standard deviation (100 km/s) from the average velocity. This value is larger than the expected velocity of current carriers and the latter cannot be revealed on the background of a random y-component of ion fluxes. Nevertheless, there is a way to check which kind of particles, electrons or ions, are the main current carriers in the magnetospheric system of reference. Let us consider the calculations of the electric currents density only for the points where the measured ion velocity component V y is zero. If the current carriers are ions, then the average electric current density j y also should be close to zero. On the contrary, if the electrons are the main carriers of the current, then the distribution of the electric current density should be close to those observed for all possible values of V y. [16] We have chosen the data points for which jv y j < 5 km/s. The electric current densities for these points were averaged over 2 nt bins of B x. The resulting dependence j y = j y (B x ) (i.e., the current versus the distance from the neutral sheet) is shown in Figure 7a. This distribution of the electric current density is almost identical to the distribution obtained for the whole data set (Figure 1a). It also exhibits two off-centered 5of8

6 velocity is 10 4 km/s. Nevertheless, some evidence for this can be found in electron data [cf., Kaufmann et al., 2001]. 3. Discussion and Conclusion [17] The results of the above analysis show that the electrons were the main current carriers in the bifurcated current sheet for the used data set. The electron current is simply E B drift of adiabatic electrons in this case. The electric field is E ¼ 1 c v e B ð3þ Using our conlusion that electrons are the main current carriers, we can calculate v e as hj y i/ehni shown in Figure 3b by solid line. The result hei ¼ hi j hbi cehi n ð4þ Figure 7. (a) Dependence of the electric current density j y averaged over the points with the ion velocity jv y j < 5 km/s versus B x -component of the magnetic field. (b) The velocity of current carriers calculated for the current density distribution shown in panel (a). is presented in Figure 8. The electric field is directed toward the center of the current layer and reaches, in average, mv/m near the electric current maxima. For individual events, the electric field may be as strong as 5 mv/m [Henderson et al., 2006]. Two off-centered layers of positive spatial charge with (n i n e )/n i 10 8 (similar to those observed in numerical simulation by Daughton et al. [2004]) can account for such an electric field. The appearance of such layers is explained by resonant scattering of ions in the regions of lower-hybrid drift instability development. The scattering leads to a loss of the positive charge in the center of the current layer and a gain of positive charge at the layer edges. Such a scattering, of course, modifies the ion distribution function in the plane perpendicular to the magnetic field. As a result, the maxima of j y and a decrease of the current near B x =0.In other words, the averaged distribution of the electric current density for jv y j < 5 km/s also corresponds to the splitted (bifurcated) current sheet. The relative velocity between electrons and ions is calculated as hj y i/ehn i i where hn i i is the ion number density averaged over the same 2 nt bins of B x. It happens to be much larger than our constraint for the ion velocity of 5 km/s (see Figure 7b). Thus we arrive at the conclusion that, in the magnetospheric coordinate system, electrons are the main carriers of the current, and the bifurcation of the current sheet (when it exists) is associated with two off-centered maxima of the electron velocity y-component. The velocity of electrons near the maxima may reach 60 km/s (for the reported current density strength of 10 na/m 2 in the individual crossings). Of course, it is very difficult to observe such values of the directed electron velocity when the thermal electron Figure 8. Electric field in the current sheet calculated from the current density and particle number density distributions. 6of8

7 distribution function looses its axial symmetry Daughton et al. [2004]. [18] We have shown that the bifurcation of the current layer is rather common feature of the geomagnetic tail, so that it appears in the magnetospheric field distributions averaged for a long periods of time. This enabled us to study statistical distributions of the bifurcated current density for different sets of plasma parameters in the geomagnetic tail. It was shown, that the electric current density directly calculated from four point magnetic field measurements exhibits no correlation with the flux of ions. Therefore we conclude that main current carriers in the magnetospheric system of reference are electrons. [19] Acknowledgments. Authors are grateful to A. Runov for stimulating discussions. We also appreciate Cluster Active Archive at caa.estec.int, and Cluster project FGM and CIS teams. [20] Amitava Bhattacharjee thanks Daniel Holland and another reviewer for their assistance in evaluating this paper. References Asano, Y., T. Mukai, M. Hoshino, Y. Saito, H. Hayakawa, and T. Nagai (2003), Evolution of the thin current sheet in a substorm observed by Geotail, J. Geophys. Res., 108(A5), 1189, doi: /2002ja Asano, Y., R. Nakamura, W. Baumjohann, A. Runov, Z. Vörös, M. Volwerk, T. L. Zhang, A. Balogh, B. Klecker, and H. Rème (2005), How typical are atypical current sheets?, Geophys. Res. Lett., 32, L03108, doi: / 2004GL Balogh, A., et al. (2001), The cluster magnetic field investigation: Overview of in-flight performance and initial results, Ann. Geophys., 19, Behannon, K. W. (1970), Geometry of the geomagnetic tail, J. Geophys. Res., 75(4), Birn, J., R. Sommer, and K. Schindler (1975), Open and closed magnetospheric tail configurations and their stability, Astrophys. Space Sci., 35, 389. Birn, J., K. Schindler, and M. Hesse (2004), Thin electron current sheets and their relation to auroral potentials, J. Geophys. Res., 109, A02217, doi: /2003ja Camporeale, E., and G. Lapenta (2005), Model of bifurcated current sheets in the Earth s magnetotail: Equilibrium and stability, J. Geophys. Res., 110, A07206, doi: /2004ja Cowley, S. W. H. (1978), The effect of pressure anisotropy on the equilibrium structure of magnetic current sheets, Planet. Space Sci., 26, Daughton, W., G. Lapenta, and P. Ricci (2004), Nonlinear evolution of the lower-hybrid drift instability in a current sheet, Phys. Rev. Lett., 93(10), Fairfield, D. H. (1979), On the average configuration of the geomagnetic tail, J. Geophys. Res., 84(A5), Frank, L. A., C. Y. Huang, and T. E. Eastman (1984), Currents in the Earth s magnetotail, in Magnetospheric Currents, Geophys. Monogr. Ser., vol. 28, edited by T. A. Potemra, pp , AGU, Washington, DC. Genot, V., F. Mottez, G. Fruit, P. Louarn, J. A. Sauvaud, and A. Balogh (2005), Bifurcated current sheet: Model and Cluster observations, Planet. Space Sci., 53, Gombosi, T. I., D. L. De Zeeuw, K. G. Powell, A. J. Ridley, I. V. Sokolov, Q. F. Stout, and G. Toth (2003), Adaptive mesh refinement MHD for global space weather simulations, in Space Plasma Simulation, edited by J. Buchner, C. T. Dum, and M. Scholer, Lecture Notes in Physics, vol. 615, pp , Springer, Berlin-Heidelberg-New York. Greco, A., R. De Bartolo, G. Zimbardo, and P. Veltri (2007), A threedimensional kinetic-fluid numerical code to study the equilibrium structure of the magnetotail: The role of electrons in the formation of the bifurcated current sheet, J. Geophys. Res., 112, A06218, doi: / 2007JA Harold, J. B., and J. Chen (1996), Kinetic thinning in one-dimensional selfconsistent current sheets, J. Geophys. Res., 101(A11), 24,899 24,909. Harris, E. G. (1962), On a plasma sheet separating regions of oppositely directed magnetic field, Nuovo Cimento, 23, Henderson, P. D., C. J. Owen, A. D. Lahiff, I. V. Alexeev, A. N. Fazakerley, E. Lucek, and H. Rème (2006), Cluster PEACE observations of electron pressure tensor divergence in the magnetotail, Geophys. Res. Lett., 33, L22106, doi: /2006gl Hoshino, M., A. Nishida, T. Mukai, Y. Saito, T. Yamamoto, and S. Kokubun (1996), Structure of plasma sheet in magnetotail: Double-peaked electric current sheet, J. Geophys. Res., 101(A11), 24,775 24,786. Israelevich, P., and A. Ershkovich (2006), Bifurcation of Jovian magnetotail current sheet, Ann. Geophys., 24, Israelevich, P., A. Ershkovich, and R. Oran (2007), Bifurcation of the tail current sheet in Jovian magnetosphere, Planet. Space Sci., 55(15), Kan, J. (1973), On the structure of the magnetotail current sheet, J. Geophys. Res., 78(19), Kan, J. (1979), Non-linear tearing structures in equilibrium current sheet, Planet. Space Sci., 27, 351. Karimabadi, H., W. Daughton, P. L. Pritchett, and D. Krauss-Varban (2003a), Ion-ion kink instability in the magnetotail: 1. Linear theory, J. Geophys. Res., 108(A11), 1400, doi: /2003ja Karimabadi, H., P. L. Pritchett, W. Daughton, and D. Krauss-Varban (2003b), Ion-ion kink instability in the magnetotail: 2. Three-dimensional full particle and hybrid simulations and comparison with observations, J. Geophys. Res., 108(A11), 1401, doi: /2003ja Kaufmann, R. L., B. M. Ball, W. R. Patterson, and L. A. Frank (2001), Plasma sheet thickness and electric currents, J. Geophys. Res., 106(A4), McComas, D. J., C. T. Russell, R. C. Elphic, and S. J. Bame (1986), The near-earth cross-tail current sheet: Detailed ISEE 1 and 2 case studies, J. Geophys. Res., 91(A4), Mitchell, D. G., D. J. Williams, C. Y. Huang, L. A. Frank, and C. T. Russell (1990), Current carriers in the near-earth cross-tail current sheet during substorm growth phase, Geophys. Res. Lett., 17(5), Mottez, F. (2003), Exact nonlinear analytic Vlasov-Maxwell tangential equilibria with arbitrary density and temperature profiles, Phys. Plasmas, 10, Mukai, T., M. Hoshino, Y. Saito, I. Shinohara, T. Yamamoto, T. Nagai, and S. Kokubun (1998), Pre-onset and onset signatures for substorms in the near-tail plasma sheet: Geotail observations, in Substroms-4, edited by S. Kokubun and Y. Kamide, pp , Kluwer Acad., Norwell, Mass. Nakamura, R., et al. (2002), Fast flows during current sheet thinning, Geophys. Res. Lett., 29(23), 2140, doi: /2002gl Ness, N. F. (1965), The Earth s magnetic tail, J. Geophys. Res., 70(13), Patterson, W. R., L. A. Frank, S. Kokubun, and T. Yamomoto (1998), Geotail observations of current systems in the plasma sheet, in Geospace Mass and Energy Flow: Results from the International Solar-Terrestrial Programm, Geophys. Monogr. Ser., vol. 104, edited by J. L. Gorwitz, D. L. Galagher, and W. K. Peterson, pp , AGU, Washington, DC. Reme, H., et al. (2001), First multi-spacecraft ion measurements in and near the Earth s magnetosphere with the identical Cluster Ion Spectrometry (CIS) experiment, Ann. Geophys., 19, Ricci, P., G. Lapenta, and J. U. Brackbill (2004), Structure of the magnetotail current: Kinetic simulation and comparison with satellite observations, Geophys. Res. Lett., 31, L06801, doi: /2003gl Runov, A., R. Nakamura, W. Baumjohann, T. L. Zhang, M. Volwerk, H.-U. Eichelberger, and A. Balogh (2003), Cluster observation of a bifurcated current sheet, Geophys. Res. Lett., 30(2), 1036, doi: / 2002GL Runov, A., V. Sergeev, R. Nakamura, W. Baumjohann, Z. Vörös, M. Volwerk, Y. Asano, B. Klecker, H. Rème, and A. Balogh (2004), Properties of a bifurcated current sheet observed on 29 August 2001, Ann. Geophys., 22, Runov, A., V. Sergeev, R. Nakamura, W. Baumjohann, T. L. Zhang, Y. Asano, M. Volwerk, Z. Vörös, A. Balogh, and H. Rème (2005a), Reconstruction of the magnetotail current sheet structure using multipoint cluster measurements, Planet. Space Sci., 53, Runov, A., et al. (2005b), Electric current and magnetic field geometry in flapping magnetotail current sheets, Ann. Geophys., 23, Runov, A., et al. (2006), Local structure of the magnetotail current sheet: 2001 cluster observations, Ann. Geophys., 24, Schindler, K. (1972), A self-consistent theory of the tail of the magnetosphere, in Earth s Magnetospheric Processes, edited by B. M. McCormac, p. 200, D. Reidel, Norwell, Mass. Sergeev, V. A., D. G. Mitchell, C. T. Russell, and D. J. Williams (1993), Structure of the tail plasma/current sheet at 11 R E and its changes in the course of a substorm, J. Geophys. Res., 98(A10), 17,345 17,365. Sergeev, V., et al. (2003), Current sheet flapping motion and structure observed by cluster, Geophys. Res. Lett., 30(6), 1327, doi: / 2002GL Sitnov, M. I., P. N. Guzdar, and M. Swisdak (2003), A model of the bifurcated current sheet, Geophys. Res. Lett., 30(13), 1712, doi: /2003gl of8

8 Tsyganenko, N. A. (1990), Quantitative models of the magnetospheric magnetic field: Methods and results, Space Sci. Rev., 54, Walker, R. J., T. Ogino, J. Raeder, and M. Ashour-Abdalla (1993), A global magnetohydrodynamic simulation of the magnetosphere when the interplanetary magnetic field is southward: The onset of magnetotail reconnection, J. Geophys. Res., 98(A10), 17,235 17,249. Yoon, P. H., and A. T. Y. Lui (2004), Lower-hybrid-drift and modified-twostream instabilities in current sheet equilibrium, J. Geophys. Res., 109, A02210, doi: /2003ja Zelenyi, L. M., H. V. Malova, and V. Yu. Popov (2003), Splitting of thin current sheets in the Earth s magnetosphere, JETP Lett., 78, A. I. Ershkovich, P. L. Israelevich, and R. Oran, Department of Geophysics and Planetary Sciences, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv 69978, Israel. (peter@luna.tau.ac.il) 8of8