Cluster statistics of thin current sheets in the Earth magnetotail: Specifics of the dawn flank, proton temperature profiles and electrostatic effects

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi: /2011ja016801, 2011 Cluster statistics of thin current sheets in the Earth magnetotail: Specifics of the dawn flank, proton temperature profiles and electrostatic effects A. V. Artemyev, 1,2 A. A. Petrukovich, 1 R. Nakamura, 3 and L. M. Zelenyi 1 Received 3 May 2010; revised 1 June 2011; accepted 6 July 2011; published 28 September [1] In this paper we use the statistics of 70 crossings by the Cluster mission to study and compare properties of thin current sheets observed at the dawn and dusk flanks of the Earth magnetotail. Special attention is devoted to the current sheet embedding: we define the degree of the current sheet embedding as b e = B ext /B 0 (B 0 and B ext are magnetic field magnitudes at the thin current sheet boundary and in the lobes). We determine the current density by curlometer technique and calculate the current sheet thickness. We demonstrate that the current sheets at the dawn flank have larger b e, smaller magnitude of the current density and larger relative thicknesses in Larmor radii than the current sheets at the dusk flank. Protons in thin current sheets are divided into two populations (the current carrying particles and the background) and the temperatures of these populations have been estimated. The distribution of the proton temperature ^T p inside typical current sheet is approximated as ^T p T p (1 a T (B x /B ext ) 2 ), where T p is the ^T p value in the central region of the current sheet. The average value ha T i 0.8. The proton current density (flow velocity in Y) is positive at the dusk flank and negative at the dawn flank, while the electron current density is positive at both flanks. This difference of the proton current density at two flanks is explained by the E B drift due to the presence of the earthward electrostatic field E x. We develop a simple model of the earthward electrostatic field to incorporate the influence of the embedding and the dawn dusk magnetic field component. Citation: Artemyev, A. V., A. A. Petrukovich, R. Nakamura, and L. M. Zelenyi (2011), Cluster statistics of thin current sheets in the Earth magnetotail: Specifics of the dawn flank, proton temperature profiles and electrostatic effects, J. Geophys. Res., 116,, doi: /2011ja Introduction [2] Thin current sheet (TCS) in the Earth magnetotail are the subject of a high interest, because such structures are closely associated with the substorm development [Baker et al., 1996; Angelopoulos et al., 2008]. Since the first direct TCS observations by ISEE mission [Mitchell et al., 1990; Sergeev et al., 1993] and up to the present Cluster and THEMIS projects TCS properties [Runov et al., 2006; Nakamura et al., 2006] and dynamics [Baumjohann et al., 2007] are very actively investigated. [3] The modern approach to TCS studies is based on a combination of the multispacecraft observations and the theoretical models. From the theory point of view, TCS is a structure in which MHD approximation is violated and kinetic effects, in particular the existence of the transient population of protons with open trajectories, should be taken 1 Space Research Institute, Russian Academy of Sciences, Moscow, Russia. 2 Nuclear Physics Institute, Moscow State University, Moscow, Russia. 3 Space Research Institute, Austrian Academy of Sciences, Graz, Austria. Copyright 2011 by the American Geophysical Union /11/2011JA into account [Kropotkin et al., 1997; Zelenyi et al., 2000; Sitnov et al., 2000]. Cluster studies reported TCSs with thickness about proton gyroradius [Artemyev et al., 2010; Petrukovich et al., 2011] in agreement with thickness expected from theoretical estimates [Zelenyi et al., 2000; Sitnov et al., 2000]. The observed current density profiles can be well approximated by the TCS models [Artemyev et al., 2008]. The transient proton population is found to provide 10 20% of the observed plasma density in TCS [Artemyev et al., 2010]. The Cluster mission demonstrates that the majority of observed TCS are embedded [Asano et al., 2005; Artemyev et al., 2010], i.e. the ratio between the magnetic field at the lobes, B ext, and that at the TCS boundary, B 0, is on average hb ext /B 0 i 2.5. [4] Although, the main properties of TCS could be described by one dimensional models, some observed effects can be explained only in a frame of a two dimensional approximation. For example, one of the unexpected properties of the observed TCS is the dominance of the electron current over the ion one [Asano et al., 2003;Runov et al., 2006; Israelevich et al., 2008; Artemyev et al., 2009]. This effect can be described by the particle E B drift due to the presence of the earthward electric field [Podgorny et al., 1988; Zelenyi et al., 2010a; Artemyev et al., 2010]. The formation of the earthward electric field is related to the 1of9

2 Table 1. The List of TCS Crossings Date j curl (na/m 2 ) B 0 (nt) B ext (nt) Y(R E ) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : a : a : : : a : : a : : : : a : a : : : : a : a : a : a : a : : : a : a : : a : : : : : : : : : : : : : : : separation of the motion of magnetized electrons and transient protons in the weakly two dimensional magnetic field configuration [Zelenyi et al., 2010a]. [5] Dawn and dusk flanks of the magnetotail are different in many aspects. In particular, the statistics of Geotail [Hori et al., 2000; Kaufmann et al., 2001; Wang et al., 2009] and Interball [Petrukovich and Yermolaev, 2002] demonstrated that proton flows are directed oppositely at the dawn and dusk flanks. The statistics of Cluster [Runov et al., 2005] and Geotail [Sergeev et al., 2006] observations show that flapping waves propagate to the flanks of the magnetotail. Thus, at the dawn flank the direction of plasma convection and flapping waves propagation are opposite to the direction of the electric current. Such dawn dusk asymmetry of the magnetotail should manifest itself in TCS properties. In this paper we compare TCS observed at different flanks using as a base the statistics of Cluster observations. We determine temperatures of current carrying and background protons. The dawn dusk distributions of TCS parameters are incorporated in the model of the earthward electrostatic field. 2. The Data and Methods [6] In this paper we use the statistics of 70 thin currents sheet crossings by Cluster mission at 2001, 2002 and 2004 years (the list of dates and the main parameters of current sheets can be found in Table 1). We use the magnetic field data from FGM instrument [Balogh et al., 2001], the moments of protons and electrons from CODIF instrument [Rème et al., 2001] and PEACE instrument [Owen et al., 2001]. All data are obtained from Cluster Active Archive ( All vectors are in GSM coordinate system. [7] For each current sheet crossing the current density j =(c/4p) curlb is determined with the curlometer technique [Runov et al., 2006]. We obtain the proper coordinate system following Runov et al. [2006]: l is directed along the maximum variation of the magnetic field, m =(j l(j l))/ j and n =[l m] is the normal vector. All used TCSs are almost horizontal with (n e z ) > 0.8. In this paper we use the magnitude j curl = max(j m) max j y for each crossing. The magnitude of the magnetic field at the TCS boundary is B 0, where TCS boundary is determined from curlometer data, [see Artemyev et al., 2010, Appendix A]. The magnetic field magnitude in the lobes B ext is found assuming the 2 vertical pressure balance B ext =8pp (B l) 0, where p is the total plasma pressure. The TCS thickness L is estimated as the ratio cb 0 /(4p j curl ). The general scheme of embedded TCS included observed parameters is presented in Figure 1. [8] The central region of TCS is defined as B l < 5 nt, where B l =(B l) B x. In the central region of TCS we determine average values of proton densities (n p ), proton and electron current densities (j p = en p (v p m) and j e = en e (v e m)), temperatures (T p and T e ) and electron temperature anisotropy (T ke /T?e ). Notes to Table 1: a The Cluster tetrahedron is so large that j curl can not be directly determined. For these events we estimate j curl by observations of two spacecraft with the similar positions in X and Y. 2of9

3 current carriers (which are present only in TCS) and the background plasma temperature. Figure 1. sheet. Scheme of TCS embedded into background [9] We include in our statistics only TCS with a small value of the magnetic shear B m =(B m) B y (B y B 0 ) and the normal magnetic field B n =(B n) B z (B n B 0 ), however the ratio B y /B z can be larger than unity. One of the significant characteristics of TCS is the curvature of the magnetic field lines in the central region [Büchner and Zelenyi, 1989]. If B y 0, the curvature radius of magnetic field lines is proportional to (B z /B 0 )(1 + (B y /B z ) 2 ) and curvature is proportional to (B 0 /B z )B z 2 /(B y 2 + B z 2 )[Büchner and Zelenyi, 1991]. [10] To obtain distributions of some plasma parameters across TCS one can approximate them as a function of the magnetic field B x (this method was used for the electron pressure by Zelenyi et al. [2010a] and for the electron temperature by Artemyev et al. [2011]). In this paper we approximate the profile of the proton temperature ^T p by the following simple expression ^T p = T p (c T a T (B x /B ext ) 2 ). Constants c T and a T are determined by the least squares method. We use a T to distinguish the temperature of the 3. The Distribution of TCS Parameters Along Dawn Dusk Direction [11] The distribution of a number of TCS crossings with respect to the coordinate Y is presented in Figure 2a. Figure 2b shows that the temperature ratio for all Y is in the range t = T p /T e 2 [3,5]. These values are smaller than average value T p /T e 7, reported by Baumjohann et al. [1989]. The electron temperature anisotropy a k = T ke /T?e (Figure 2c), in agreement with the observations by Zelenyi et al. [2010a]. The values of B z 2 /(B z 2 + B y 2 ) at the dawn flank are larger than at the dusk flank 0.4 (Figure 2d). This difference could be related to the dependence of B y on Y (as was shown by Petrukovich [2009], B y is smaller at the dawn flank) and to the growth of B z towards the flanks. Here we have to point out, that the dependence of B z 2 /(B z 2 + B y 2 )ony is obtained only for the statistics of TCS crossings and can differ substantially from the general distribution of B z 2 /(B z 2 + B y 2 ) in the magnetotail. [12] In Figure 3 we present data on particle currents and TCS parameters obtained by Cluster multipoint observations. The distribution of amplitudes of the curlometer current density j curl is shown in Figure 3a. TCS at the dawn flank are less intense, than TCS at the dusk flank. Very important is the fact that the ratio of (j e + j p )/j curl 1 independently on Y (Figure 3b). This result agrees with the previous publications [Artemyev et al., 2009; Zelenyi et al., 2010a] and demonstrates the statistical reliability of the used particle data. The y component of the proton bulk velocity v py has the opposite directions at the dawn and dusk flanks (Figure 3c). The general statistics of plasma parameters in the plasma sheet also demonstrates such a difference in v py Figure 2. The distribution of TCS parameters along the dawn dusk coordinate Y. (a) The number of crossings. (b) The temperature ratio t = T p /T e. (c) The electron temperature anisotropy a k = T ke /T?e. (d) The ratio B 2 z /(B 2 y + B 2 z ). 3of9

4 Figure 3. The distribution of TCS parameters along the dawn dusk coordinate Y. (a) Amplitude of the current density j curl. (b) The ratio (j p + j e )/j curl. (c) The proton bulk velocity v py = j p /(en p ). (d) The electron bulk velocity v ey = j e /(en e ). [Kaufmann et al., 2001; Petrukovich and Yermolaev, 2002]. Kaufmann et al., [2001] and Wang et al. [2009] attributed this difference to the E B drift. Electron bulk velocity v ey is negative for all Y (Figure 3d). [13] Less intense TCS at the dawn flank have larger values of the embedding parameter: b e = B ext /B 0 3.3, for Y 10R E and b e 2.5, for Y 5R E (Figure 4b). Figure 4a shows that the ratio of the TCS thickness and r p (r p is the proton gyroradius in the field B 0 ) is larger at the dawn flank (L/r p 4.5, if Y 10R E ), than at the dusk flank (L/r p 3.0, if Y 5R E ). Thus, TCSs at the dawn flank differ from the TCS at the dusk flank by the typical thicknesses, intensities, value of the embedding parameter and the magnetic field lines curvature. 4. Temperature of Current Carriers and Background Protons [14] The proton temperature ^T p decreases towards the TCS boundaries and has a symmetric profile [Hoshino et al., 1996; Runov et al., 2006]. Here we use the following approximation of observations: ^T p /T p = c T a T (B x /B ext ) 2. Several examples of the observed profiles ^T p (B x ) and the corresponding approximation profiles are shown in Figure 5. For the majority of observed TCS obtained c T is close to 1. The distribution of a T for all observed TCS is presented in Figure 6a. The mean value ha T i 0.8 ± 0.1 and for the majority of observed TCS a T > 0. The statistics of a T along Y demonstrates that the proton temperature decreases with increase of B x at the dawn flank more substantially than at the dusk flank (Figure 6b). [15] The obtained dependence of ^T p on B x can be described using the assumption of multicomponent plasma content in TCS [Artemyev et al., 2009; Liu et al., 2010; Artemyev et al., 2010]. The main part of the proton current in TCS is carried by the transient population (or Speiser particles) with the small density n sp and the relatively large temperature T sp [Artemyev et al., 2010]. The remaining population of background protons has the density n bg and the temperature T bg. One can assume that both the temperature and density of background protons are not changing on the scale of TCS. The resulting decrease of proton temperature towards the TCS boundary corresponds to the decrease of the density of transient protons. [16] The proton temperature in the TCS central region is defined as T p =(T bg n bg + T sp n sp )/(n bg + n sp ). We take c T 1 Figure 4. The distribution of TCS parameters along the dawn dusk coordinate Y. (a) The relative thickness L/r p. (b) The embedding parameter b e = B ext /B 0. 4of9

5 of TCS the main role is played by the drift v E B E x /B z.to redistribute currents in TCS so that j e becomes larger than j p, in a rest frame coordinate system one needs v E B < 0 and E x > 0. Electrostatic field E x is caused by the difference of motions of transient protons and magnetized electrons [Zelenyi et al., 2010a]. The drift of a cold and dense background plasma in E x electrostatic field is dramatically manifested in the measured ion bulk velocity [Artemyev et al., 2010]. In this section we develop the model of E x generator including the presence of B y 0 and effects of TCS embedding. For our estimates we will use the observed parameters of TCS discussed in the previous sections. We will apply this model to understand the redistribution of currents in the TCSs, observed in different segments of magnetotail. [19] TCSs thicknesses as a rule are much larger than the electron scales (the only exception are electron TCSs [Nakamura et al., 2006], which are beyond the scope of this paper). For the description of electron dynamics we apply the fluid approximation. Electron pressure balance in a stationary system has the following form [Shkarofsky et al., 1966]: r^p e ¼en e E þ c 1 ½j e BŠ ð2þ [20] Here r^p e = r? p?e + r k p ke + L[(Br)B 2b(Br)B], B = B, b = B/B, L =(p ke p?e )B 2. The projection of equation (2) onto the b direction allows to obtain the equation for the scalar potential (here we assume that the quasi neutrality condition n e n p is satisfied): en p r k ¼r k p ke LBr k B ð3þ Figure 5. The dimensionless proton temperature ^T p /T p as a function of the dimensionless magnetic field B x /B ext for the selected TCS crossings (grey crosses). The black curves show the approximation ^T p = T p (c T a T (B x /B ext ) 2 ). [21] Here for simplicity we assume that electron component could be considered as an ideal gas (p ke = a k T e n e, and write the conditions of the pressure balance in the TCS central region and at the boundary: 8 T bg n bg þ T sp n sp ¼ Bext 2 8 >< T bg n bg þ B0 2 8 ¼ B 2 ext 8 >: T bg n bg þ n sp ¼ Tbg n bg þ T sp n sp 1 T b 2 e [17] The solution of this system is T bg /T p =1 a T b e 2, T sp /T p =(1 a T b e 2 )/(1 a T ). The ratio T sp /T bg = 1/(1 a T ) does not depend on the TCS embedding level b e. Corresponding ratios of the densities n bg/ n sp = t bg (b e 2 1), n bg/ n p = t bg (b e 2 1)/(1 + t bg (b e 2 1)) and n sp /n p =1/(1 + t bg (b e 2 1)). For the mean value of a T 0.8 the parameter t bg = T sp /T bg 5. ð1þ 5. Electrostatic Effects in TCS [18] The cross field drift v E B = c[e B]/B 2 can redistribute currents in TCS. In the system with v E B the proton and electron currents are modified: j py = j py + en p v E B and j ey = j ey en p v E B (the quasi neutrality condition n p n e is satisfied). Due to the presence of B z 0 in the central region Figure 6. The statistics of a T values and the distribution of a T along Y. 5of9

6 Figure 7. The maps of j m p */j m p values depending on embedding b e and t: dark grey color is used for the regions with j m p */j m p > 0 and light grey color is used for the regions with j m p */j m p <0. p?e = T e n e, a k = const > 1 and T e = const). The solution of equation (3) is ¼ k ln n p Bð 1 k Þ= k Here = e /T e. The drop D from the TCS boundary to the central region is approximately equal to 2 D k ln4 1 þ n sp nbg 1 þ B 2 0 B 2 z þ B2 y k1 2 k ð4þ 3 5 ð5þ [22] Taking into account the pressure balance we rewrite equation (5) in the new form: " # D k ln 1 þ bg 1 b 2 e þ b 2 n þ 1 k1 b2 2 k m [23] Here we introduce the dimensionless parameters b n = B z /B 0 and b m = B y /B 0. The magnitude of E x E z L z /L x D /L x, ð6þ where L x is the spatial scale of TCS along the Earth Sun direction [Zelenyi et al., 2010a; Artemyev et al., 2010]. The drift velocity v E B has the following form: jv EB E x B z b j ¼ c B 2 0 b2 n þ 2 n ¼ v T b2 m b 2 n þ b2 m D b e ; bg ; k ; b n ; b m pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi [24] Here l =2b n L x /r p and v T = 2T p =m p. Current carrying protons are on transient trajectories and their bulk velocity along current direction is about the thermal velocity v D v T (see [Artemyev et al., 2010] and references therein). The model proton current density in TCS including the effect of v E B < 0 can be written as jp m * ¼ en spðv D jv EB jþþen bg v bg jv EB j [25] Here v bg is the rest frame bulk velocity of the background plasma. To estimate v bg = j bg /(en bg ) we assume that j bg c(b ext B 0 )/(4pL bg ), where L bg is the background current sheet thickness. Taking into account the second ð7þ ð8þ 6of9

7 Figure 8. The same as in the Figure 7, but depending on b n and b m. equation of the system (1) we obtain v bg =2cT bg /(el bg (B ext + B 0 )) and, as a result v bg v T ¼ 1 T bg sp 1 1 T sp L bg ðb e 1Þ ¼ bg b 2 e ð9þ ðb e 1Þ L bg = sp [26] Substituting equations (7) and (9) into equation (8) we obtain j m p * v jebj n p ¼ 1 n sp v D þ n bg v bg j m p b2 n ¼ 1 b 2 m þ b2 n D 1 þ bg b 2 e 1 1 þ bg b 2 e 1 ð10þ vbg =v T [27] Here j p m = ev T n sp + ev bg n bg is the model proton current density in the TCS without E x. [28] The ratio j p m */j p m as a function of various parameters is presented in Figures 7 and 8. We set l = 5 according to the empirical model by Artemyev et al. [2011], L bg /r p =20in agreement with the observations by Zelenyietal.[2010b] and t bg = 5 (see the previous section). The component B y substantially influences the proton current density decrease (for small values of b m the ratio j p m */j p m could be even negative). The dependence of j p m */j p m on b e is not monotonous. The drop of plasma density between TCS boundaries and the central region is large for TCS with small b e (B 0 B ext ). However, TCS with large b e have the small value of n sp and even small v E B drift creates relatively strong negative current v E B n bg > v T n sp. We use parameters of observed TCS from Figures 2, 4, and 6 to obtain the distribution of j p m */j p m over Y (Figure 9). The model ratio j p m */j p m is positive for Y > 5R E and negative for Y < 5R E in agreement with the observations (see Figure 3c). This suggests that, the observed difference of TCS parameters at the dawn and dusk flanks allows to reproduce qualitatively the surprising effect of the opposite direction of proton flows. 6. Discussion [29] We obtain the large values of the ratio T sp /T bg. However, in the observed TCS the current carrying component can not be distinguished from the plasma background by the temperature difference only (an exception is the TCS observation with a very small value of B z component [Zhou et al., 2009]). Typically observed ratio n sp /(n sp + n bg ) and T sp 2T p [Artemyev et al., 2010]. This contradiction could be solved by taking into account the three 7of9

8 Figure 9. The ratio j p m */j p m as a function of Y. proton components. The first transient component is present mainly in TCS and carries the most part of the proton current density. The second population is the part of the background with the temperature close to T sp. The third population is the cold dense core with the temperature less than 1 kev [Artemyev et al., 2009]. In such a case the ratio T sp /T bg may be large due to the presence of a cold background, but the separation of the hot background and the transient particles could not be performed visually. The theory of proton dynamics in TCS [Büchner and Zelenyi, 1989] predicts that these three populations are related to each other due to scattering and resonances. However, the three component distribution possesses a large number of free parameters, which cannot be determined by using only the observed proton densities and temperatures. The problem could be solved in the future by the direct comparison of the model and observed velocity distributions [Ball et al., 2005; Zhou et al., 2009; Artemyev et al., 2009]. [30] The obtained difference of the proton flow directions at the dawn and dusk flanks (Figure 3) allows to propose a new explanation of TCS flapping waves. The first statistical studies based on Cluster observations demonstrated that flapping waves propagate to the flanks of the magnetotail [Runov et al., 2005]. This result is confirmed also by the Geotail statistics [Sergeev et al., 2006]. Thus, at the dawn flank flapping waves propagate oppositely to the electric current direction. Theories of drift instabilities use the reference frame with drift E B = 0, in which the current density is in the same direction as the proton drift [Lapenta and Brackbill, 1997; Daughton, 1998; Büchner and Kuska, 1999] and TCS flapping oscillations could propagate only in the same direction as the proton drift. This contradiction of flapping observations and their interpretation as propagating (duskward) drift mode results in the appearance of the alternative theories of TCS oscillations: the balloon instability [Golovchanskaya and Maltsev, 2005] and the double gradient instability [Erkaev et al., 2009]. Our results concerning the proton flow direction nevertheless allow to solve this contradiction in the frame of a drift mode model: at the dawn flank protons bulk flow is opposite to the current density, but occurs in the same direction as the flapping waves. Therefore, flapping at the both flanks can be described as the drift mode of TCS [Zelenyi et al., 2009]. [31] We demonstrated that the presence of an electrostatic field E x in TCS is caused by the difference of the electron and proton motion. However, another mechanism of E x formation can be also suggested and can intensify the dawndusk asymmetry of proton flows. The component B z is decreasing during stretching of the magnetotail and formation of TCS [Petrukovich et al., 2007]. Evolution of B z with time is related to the inductive electric field with (curle) e z = E x / y E y / x = c 1 B z / t.weassume E y / x 0 according to the model of Wang et al. [2001]. If B z does not depend on Y, the drift velocity v E B = ce x /B z = Y( B z / t)/b z. We use the expression ( B z / t)/b z 1/t 0, where t 0 is the time scale of the current sheet thinning. The corresponding drift velocity v E B Y/t 0 is directed to the flanks (v E B <0if Y < 0 and v E B >0ifY > 0). We estimate v E B 35 km/s for Y 10R E and t 0 30 min. This value of v E B is comparable to the observed proton bulk velocity. Therefore, the process of TCS formation (the magnetotail stretching) could also provide the dawn dusk asymmetry of proton flows at the flanks. [32] In this paper we stress the difference between dawn and dusk flanks. However, it would be more correct to say, that the dawn flank (Y < 5R E ) is an exceptional region different from the dusk flank and the near midnight zone. We could explain this difference by the variation of the transient proton population along the dawn dusk direction. At the dawn flank the density of the transient population could be assumed to be smaller than at the dusk flank, because the decrease of the current density magnitude (Figure 3a). In addition, we obtain the increase of plasma density towards the dawn flank (hn p i Y< 5RE /hn p i Y 5RE 1.4) in agreement with estimates by Wing and Newell [1998]. One more signature of asymmetry is the distribution of B y field (see Figure 2c), which is smaller at the dawn flank. 7. Conclusions [33] In this paper we compare the main parameters of TCS at the dawn and dusk flanks. We demonstrate that at the dawn flank (in comparison with the dusk flank) (1) the ratio B ext /B 0 is larger, (2) the current density j curl is weaker and the relative TCS thickness L/r p is larger, and (3) the curvature radius of magnetic field lines (the parameter 1 + (B y /B z ) 2 )is smaller. [34] Vertical distributions of the proton temperature across TCS obtained above demonstrate that the drop of proton temperature between the central region and the TCS boundary is about 50 80%. This variation of proton temperature is described by the model of multicomponent proton population in TCS. [35] We have shown that protons flows in TCS in Y direction are opposite at the dawn and dusk flanks (i.e. in both cases protons are flowing to the flanks). We demonstrate that this effect can be described qualitatively by the magnetotail model taking into account the presence of the large scale electrostatic field E x after one will include the observed dawn dusk asymmetry of the TCS parameters into calculations. [36] Acknowledgments. Authors would like to acknowledge Cluster Active Archive and Cluster instrument teams, in particular FGM, PEACE and CIS for excellent data. The work of A.V.A., A.A.P. and L.M.Z. was supported in part by the RF Presidential Program for the State Support of Leading Scientific Schools (project NSh ), the Russian Foundation for Basic Research (projects , ). The work of R.N. was supported by Austrian Science Fund (FWF) I429 N16. A.V.A. would like to acknowledge hospitality of IWF, Graz, Austria. [37] Masaki Fujimoto thanks Xiaogang Wang and the reviewers for their assistance in evaluating this paper. 8of9

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