Magnetospheric Boundary Layer Structure and Dynamics as Seen From Cluster and Double Star Measurements

Transcription

1 /2013/33(6) Chin. J. Space Sci. Ξ ΛΠΠ Y V Bogdanova, C J Owen, M W Dunlop, M G G T Taylor, A N Fazakerley. Magnetospheric boundary layer structure and dynamics as seen from Cluster and Double star measurements. Chin. J. Space Sci., 2013, 33(6): Magnetospheric Boundary Layer Structure and Dynamics as Seen From Cluster and Double Star Measurements Y V Bogdanova 1 CJOwen 2 M W Dunlop 1 MGGTTaylor 3 A N Fazakerley 2 1(Space Science and Technology Department, RAL, Chilton, Didcot, Oxfordshire, OX11 0QX, UK) 2(Mullard Space Science Laboratory, University College London, Holmbury St.Mary, Dorking, Surrey, RH5 6NT, UK) 3(Science and Robotic Exploration Directorate, ESA/ESTEC, Noordwijk, The Netherlands) Abstract In this review, we discuss the structure and dynamics of the magnetospheric Low- Latitude Boundary Layer (LLBL) based on recent results from multi-satellite missions Cluster and Double Star. This boundary layer, adjacent to the magnetopause on the magnetospheric side, usually consists of a mixture of plasma of magnetospheric and magnetosheath origins, and plays an important role in the transfer of mass and energy from the solar wind into the magnetosphere and subsequent magnetospheric dynamics. During southward Interplanetary Magnetic Field (IMF) conditions, this boundary layer is generally considered to be formed as a result of the reconnection process between the IMF and magnetospheric magnetic field lines at the dayside magnetopause, and the structure and plasma properties inside the LLBL can be understood in terms of the time history since the reconnection process. During northward IMF conditions, the LLBL is usually thicker, and has more complex structure and topology. Recent observations confirm that the LLBL observed at the dayside can be formed by single lobe reconnection, dual lobe reconnection, or by sequential dual lobe reconnection, as well as partially by localized cross-field diffusion. The LLBL magnetic topology and plasma signatures inside the different sub-layers formed by these processes are discussed in this review. The role of the Kelvin-Helmholtz instability in the formation of the LLBL at the flank magnetopause is also discussed. Overall, we conclude that the LLBL observed at the flanks can be formed by the combination of processes, (dual) lobe reconnection and plasma mixing due to non-linear Kelvin-Helmholtz waves. Key words Magnetopause and boundary layers, Magnetic reconnection, Kelvin-Helmholtz waves, Solar wind /magnetosphere interactions Classified Index P 353 Received August 12, Revised September 06, yulia.bogdanova@stfc.ac.uk

2 578 Chin. J. Space Sci. Ξ ΛΠΠ 2013, 33(6) 0 Introduction The Low-Latitude Boundary Layer (LLBL), located just inside the magnetosphere and adjacent to the magnetopause, plays an important role in the transport of magnetosheath plasma into the magnetosphere across the magnetopause boundary. The LLBL is characterized by a mixture of the magnetospheric and magnetosheath plasma distributions (e.g., Ref.[1 3]) and is observed in 90% of magnetopause crossings [4]. This boundary layer is observed during both southward and northward Interplanetary Magnetic Field (IMF) conditions. However it was shown that during northward IMF the LLBL becomes thicker [2]. The LLBL was extensively studied for two decades prior the Cluster mission(see, for example, AGU monograph Low-Latitude Boundary Layer, published in 2003 [5] ). However a number of central questions remained open. These include: (1) What mechanism or what mechanisms are responsible for the formation of the LLBL; (2) Does the LLBL have consistent sub-structure, and if so, what are the observational signatures of different parts of the LLBL and how they can be explained; (3) What is the magnetic topology of the LLBL, does it exist on open or closed field lines; (4) What is the role of the LLBL in the overall magnetospheric dynamics? These questions are interconnected and have been addressed prior and during the Cluster and Double Star missions (see, for example, a recent review by Hasegawa [6] ). In this review, we discuss results from previous studies which are related to these questions, however we will concentrate and discuss in more detail the results of studies performed in the last decade, especially those by the authors of this review. It is important to note that before Cluster and Double Star missions, most of the studies of the LLBL were based on single or dual spacecraft measurements and only after the launch of Cluster did the era of multipoint satellite measurements in space truly flourished, bringing many benefits to the investigation of different magnetospheric regions, including the LLBL and cusp regions. The paper is structured as follows: in Section 2 we will briefly discuss the Cluster and Double Star missions, in Section 3 we will discuss the LLBL, its structure and formation during the southwardimf,andinsection4wewilldiscussthellbl structure and formation during the northward IMF. 1 The Cluster and Double Star Missions The Cluster mission is ESA s first magnetospheric multi-spacecraft mission, launched in 2001, comprising four identical spacecrafts arranged in a tetrahedron configuration. The Cluster spacecrafts were initially injected into an orbit with a perigee of 4 R E and an apogee of 19.7 R E, an inclination of 90, and an orbital period of 57 h [7]. However during the lifetime of the mission this orbit has evolved due to lunar and solar perturbations [8 9]. The tetrahedron configuration provides, for the first time, the ability to probe the dynamics of space plasma structures, including estimation of gradients, and the motion, size and orientation of the plasma structures and boundaries, as well as estimation of the directions of waves propagation. Each Cluster satellite has 11 instruments onboard, measuring plasma particle populations, electric and magnetic fields, and field fluctuations in different frequency ranges. In this review, we discuss measurements from some of the Cluster instruments. Plasma measurements are derived from the Plasma Electron and Current Experiment (PEACE) [10], and from the Hot Ion Analyser (HIA) and Composition and Distribution Function (CODIF) sensors, which are parts of the Cluster Ion Spectrometry (CIS) experiment [11].TheHIA sensor employs an electrostatic analyser to measure ions of all species with high angular and high energy resolution. The CODIF sensor combines a top-hat analyser with an instantaneous 360 field of view, with a time of flight section to measure the complete 3-D distribution functions of the major ion species, H +,He ++,He +,ando +. The sensor covers the en-

3 Y V Bogdanova, et al.: Magnetospheric Boundary Layer Structure and Dynamics as Seen From Cluster ergy range between 0.02 and 38 kev/e with a time resolution of 4 s. Each PEACE package consists of two sensors, i.e. the HEEA (High Energy Electron Analyser) and the LEEA (Low Energy Electron Analyser), mounted on the diametrically opposite sides of the spacecraft. They are designed to measure the three dimensional velocity distributions of electrons in the range of 0.6 ev to 26 kev, with a time resolution of 4 s. To estimate a reliable electron density and velocity, the photoelectron population should be removed from the moments calculations. This is done by making an estimate of the spacecraft potential derived from the Electric Fields and Waves (EFW) instrument [12]. The magnetic field data from the Fluxgate Magnetometer (FGM) [13] is also used in the data analysis. The Double Star mission was the first magnetospheric mission launched by China, and was the first joint effort between the European Space Agency (ESA) and the Chinese National Space Administration. The mission consisted of two satellites, TC-1 and TC-2, and was designed to complement the Cluster observations. The TC-1 satellite was launched in 2003 into an equatorial orbit at 28.2 inclination, with a perigee of 577 km, an apogee of 13.4 R E, and an orbital period of 27.4 h [14]. The second spacecraft, TC-2, was launched in 2004 into a polar orbit with a perigee of 700 km and an apogee of 6 R E. Double Star TC-1 re-entered the atmosphere in October 2007 and TC-2 ceased operations in late The orbits of TC-1 and TC-2 satellites were complimentary to that of Cluster, providing many possibilities for conjugate studies of magnetospheric dynamics. Some instruments near-identical to Cluster were installed on the Double Star satellites such as the PEACE [15],CIS [16] and FGM [17] although operated in a different manner due to different interfaces and other restrictions. The common time resolution of data coming from TC-1 and TC-2 was 4 s. On both Double Star spacecrafts, the PEACE instrument consisted of one sensor, which usually ran in alternating sweep pre-set mode. This meant that every spin the sensor coverage alternated between different (high and low) energy ranges. The PEACE instruments on the Double Star satellites were allocated enough telemetry for 3-D data to be available for every spin, unlike Cluster. While investigating plasma dynamics inside the magnetosphere, it is important to have knowledge of the external solar wind and IMF conditions. In the papers discussed in this review this was most commonly provided by the ACE spacecraft mission. ACE orbits the L 1 libration point about 1.5 million km from the Earth and million km from the Sun. The IMF data come from the Magnetic Field Experiment (MAG) [18] andthesolarwinddensityandvelocity come from the Solar Wind Electron Proton Alpha Monitor (SWEPAM) [19]. In addition, OMNI data [20], which are derived from a number of upstream monitors and have their epoch mapped to the bow shock nose, are also used in some studies. 2 LLBL Structure and Formation During Southward IMF During southward IMF, the LLBL is most likely to be formed by the reconnection process and lies on the field lines which have undergone a recent reconnection between terrestrial and magnetosheath field lines at the dayside magnetopause [21]. During such reconnection processes, the field lines forming the LLBL become open, with one end connected to the ionosphere and another end connected to the solar wind. Due to the constant solar wind flow and a magnetic stress force created during the reconnection process, these LLBL field lines will convect anti-sunward from the dayside to the nightside. A number of papers deal with the structure of such a recently reconnected boundary layer, both from theoretical (e.g. Ref.[22 26]) and observational (e.g., Ref.[27]) perspectives. A widely accepted but slightly simplified (from a theoretical point of view) picture of the LLBL formation and structure was presented by Gosling et al. [28]. These authors suggested that due to different and

4 580 Chin. J. Space Sci. Ξ ΛΠΠ 2013, 33(6) definite time of flights of the ions and electrons, the LLBL has a well-defined sub-structure. This further was discussed by Bogdanova et al. [29], based on observations made by Cluster inside and around the mid-altitude cusp region. They adapted the picture of the LLBL formation and sub-structure [28] for the mid-altitude observations and discussed how the observations are consistent with this picture. Figure 1 shows a simplified schematic view of the evolution of the magnetic field line following reconnection and the corresponding different plasma regions, which can be observed in the ionosphere, or at mid-altitudes, or close to the magnetopause, depending on the spacecraft trajectory. In this picture, the magnetopause is represented by a vertical black line; the ionosphere by a horizontal black line; and the location of the reconnection process is indicated by a star. The right-hand side of the vertical black line shows the magnetic Fig. 1 A simplified schematic view of the evolution of magnetic field lines following reconnection, and the corresponding plasma regions at mid-altitudes or in the ionosphere. In this figure, all field lines have been straightened so that the magnetopause is represented by the vertical black line towards the left of the figure, and the ionosphere by the horizontal black line towards the top. The blue star shows the location of the reconnection at the magnetopause. The red line represents a newly reconnected field line with time history since reconnection t = 0. This line is the separatrix between closed and open field lines and also represents the electron equatorward boundary of the LLBL/cusp. The green line represents an older reconnected field line with time history since reconnection t = t 1 along which the most energetic magnetosheath ions have arrived at mid-altitudes. The trajectory of these energetic ions is indicated by the dashed green line. This line represents ion equatorward boundary of the LLBL/cusp. Due to the magnetic tension, this line will convect away from the reconnection site, as indicated by the green solid line. The blue line represents an even older field line, with time history since reconnection t = t 2 along which the bulk plasma flow accelerated at the magnetopause up to the local magnetosheath Alfvén velocity will arrive at mid-altitudes. The trajectory of the plasma bulk flow is indicated by the dashed blue line. This line marks the equatorward boundary of the cusp proper. The region between the electron and ion boundaries of the LLBL/cusp is named the electron edge of the LLBL and contains only magnetosheath-like electrons but still with magnetospheric ions. The region between the ion boundary of the LLBL/cusp and equatorward boundary of the cusp proper is the LLBL proper, containing both accelerated magnetosheath-like electrons and ions. The region poleward of the equatorward boundary of the cusp is the cusp proper [29].

5 Y V Bogdanova, et al.: Magnetospheric Boundary Layer Structure and Dynamics as Seen From Cluster field lines inside the magnetosphere and the left-hand side corresponds to the magnetosheath. The most recently reconnected field line is shown in red. This line marks the separatrix, or the boundary between the closed, magnetospheric, field lines, and open field lines, connected to the magnetosheath. This Open- Closed Boundary (OCB) also maps back to the active neutral line. Along this field line, the magnetosheath electrons moving with very high velocity [28] will arrive in the ionosphere almost immediately after field line become open. At the same time, magnetospheric electrons will escape from the magnetosphere into the magnetosheath. The electron boundary of the LLBL, identified by the first open field line associated with magnetosheath electrons, is topologically very close to the separatrix and thus a good marker of the OCB. Due to the speed difference between even the most energetic ions and energetic electrons, the energetic magnetosheath ions will propagate towards the ionosphere with a time delay, and can be observed arriving at mid-altitudes ( 6 R E ) with the time delay up to 12 min compared to electrons [30]. The region between the electron and ion boundaries of the LLBL is called the electron edge of the LLBL and is populated by the energetic magnetosheath electrons and by the pre-existing magnetospheric ions. The layer with mixed energetic ions and electrons with energies above those typical for an accelerated magnetosheath population yet with fluxes below a typical magnetosheath population is the LLBL proper [31 32] and maps into the cleft region at the mid-altitudes. This layer is on older open field lines, where some time has passed since reconnection of those field lines. The source of these energetic LLBL ions is still a subject of debate in literature. According to Lockwood et al. [33] and Lockwood and Moen [25], ions forming the LLBL region can be generated on open field lines by reflection of the preexisting magnetospheric population by an interior Alfvén wave. The interior Alfvén wave is launched from the reconnection site into the inflow region in the magnetospheric side of the boundary, and due to the difference in the plasma density inside and outside the magnetosphere, this wave propagates faster than the exterior Alfvén wave which is launched from the reconnection site into the magnetosheath and contains the major rotation of the magnetic field. The ions which form the LLBL will be accelerated to the local interior Alfvén wave. Fuselier et al. [34] suggested an alternative explanation for the energetic LLBL ions. They showed that the distribution of the magnetosheath ions already has 20% higher energy ions and proposed that the LLBL forms due to the arrival of this high-energy part of the magnetosheath distribution. Finally, a sub-layer with the bulk of the magnetosheath plasma population accelerated up to the exterior Alfvén velocity, forms the inner part of the LLBL and can be mapped into the cusp region at the mid-altitudes. Therefore, in the case of dayside reconnection, the LLBL consists of several different sub-layers, all of which can be topologically mapped into the low-altitudes and ionosphere and thus can also be studied using data from the low- and mid-altitude satellites. Bogdanova et al. [29] studied the properties of the LLBL, particularly the properties of the electron edge of the LLBL using 3 years of Cluster mid-altitude cleft and cusp crossings. Figure 2 shows a typical observation from this study, made on 10 September 2002, 13:45 14:10 UT, under stable southward IMF. Panels (a) (c) show the electron energy-time spectrograms in the anti-parallel, perpendicular and parallel directions respectively; panels (d) (g) show the H + energy-time spectrogram, the O + energy-time spectrogram, the pitch-angle-time spectrogram for the low-energy protons (< 800 ev) and the pitch-angle spectrogram for high-energy protons (> 800 ev); panel (h) shows the electron density (black) and ion density (red); panel (i) shows the electron temperature anisotropy; panels (j) (l) show components of the ion (red) and electron (black) velocities: parallel, and X-andY-components of the perpendicular velocity. The two vertical lines are two boundaries of the

6 582 Chin. J. Space Sci. Ξ ΛΠΠ 2013, 33(6) Fig. 2 PEACE and CIS data for the mid-altitude cusp crossing with the prominent electron edge of the LLBL on 10 September 2002, 13:45 14:10 UT. From top to the bottom: electron energy-time spectrograms in the antiparallel (panel a), perpendicular (panel b) and parallel (panel c) directions; the energy-time spectrogram of protons H + (panel d); the energy-time spectrogram of oxygen O + ions (panel e); the pitch-angle (0 180 )-time spectrograms for lowenergy (20 < E < 800 ev) and high-energy (0.8 < E < 38 kev) protons (panels f and g, respectively); the electron (black trace) and the ion (red trace) density (panel h); the electron anisotropy, defined as T /T, (panel i); the parallel velocity of plasma (panel j) and X- andy -components of the perpendicular plasma velocity (panels k and l). Black traces correspond to electron data and red traces correspond to ion data, and plasma velocities are shown in the same scale for inter-comparison. The ephemeris data for SC1 are presented under the plot: X-, Y -, Z-components of position in the GSE coordinate system, magnetic local time (MLT) and invariant latitude (ILAT) of observation [29].

7 Y V Bogdanova, et al.: Magnetospheric Boundary Layer Structure and Dynamics as Seen From Cluster electron edge of the LLBL. As one can see, this region is populated by the low-density, magnetosheath-like electrons, with some occasional electron beams [29]. At the same time, the proton population is still of magnetospheric origin. The explanation of why this region contains such low fluxes of electrons was offered by Wing et al. [35 36]. It has been shown that a parallel electric field between the magnetopause and low-altitudes must exist in order to explain and adequately model the observed electron population with magnetosheath-type energies but very low fluxes. This electric field prevents the penetration of the electrons originating from the solar wind along the field lines ahead of the ions and therefore conserves the quasi-neutrality of the plasma. However the suprathermal halo population of the solar wind will not be fully retarded by the parallel electric field and will penetrate to the low altitudes ahead of magnetosheath ions. Bogdanova et al. [37] showed that the electron beams inside the electron edge of the LLBL are of magnetosheath energy and similar to the magnetosheath flux, and that they strongly correlate with O + and H + ionheatingandwith localized extra low frequency (1 10 Hz) electromagnetic waves with broadband spectra. It was also suggested that inside the electron edge of the LLBL, the suprathermal electron bursts are most likely an energy source for the wave destabilization. Bogdanova et al. [29] performed a statistical study of the electron edge size and defined what external parameters can influence the size of this LLBL sub-layer. In that study, three years of the mid-altitude cleft and cusp crossings were used. The boundaries of the electron edge region for every crossing were defined based on the electron and ion plasma signatures, and only events with the clear boundaries were used. The external parameters were estimated based on the solar wind and IMF observations from the ACE satellite. A method of size estimation based on the multi- SC observations was introduced; in this method the authors used measurements of both boundaries of the electron edge by three Cluster spacecraft and reconstructed (under assumption of constant motion) the dynamic of the boundaries over the four spacecraft crossing time, and then used these reconstructed data for the electron edge size estimation. It was shown that the majority of the events have the electron edge of a size of 0 1 invariant latitude (ILAT), with a mean value of 0.3 ILAT and a median value of 0.2 ILAT. It was shown that the size of the electron edge of the LLBL depends on the combination of many external factors, but some individual trends were found: it was shown that the size of this region anti-correlates with the strength of the IMF, the absolute values of the IMF B Y -andb X -components, and the solar wind dynamic pressure. Such dependencies in the LLBL electron edge size are expected from a simple reconnection model for the origin of this region, confirming that the electron edge of the LLBL is formed during, and connected to, the reconnection process at the magnetopause. More recently, the structure of the LLBL was investigated using THEMIS observations near the magnetopause under the north-dawnward IMF conditions [38]. In this case, observations showed a clear transition through the reconnected layers when the satellite flew from the magnetosphere to the magnetosheath across the dayside magnetopause. Observations showed a clear mixture of the plasma populations from the different sources inside the LLBL. It was shown that inside the reconnection layer there are two plasma boundaries, close to the inferred separatrixes on the magnetospheric and magnetosheath sides of the magnetopause, and two boundaries associated with the Alfvén waves (similar to the interior and exterior Alfvén waves discussed previously by Lockwood et al. [33] ). The uniqueness of this event is that the spacecraft trajectory performed a clear cut through the reconnected boundary layers (both LLBL and magnetosheath boundary layer) observing plasma distributions which are well-ordered according to the time elapsed since reconnection of the field line, including a velocity dispersion effect in the electron anisotropy.

8 584 Chin. J. Space Sci. Ξ ΛΠΠ 2013, 33(6) Thus, the structure of the LLBL during the southward IMF is believed to be controlled by the reconnection process at the magnetopause: the LLBL is topologically open, and consists of a mixture of plasma populations from the different origins, with some sub-structure, related to time of flight of energetic electrons, energetic ions, and the propagation of the interior and exterior Alfvén waves from the reconnection site. More recently a number of papers (e.g., Ref.[39 41]) reported observations of multiple X-lines and a sequential magnetic reconnection process at the magnetopause. As every reconnection process creates the set of associated reconnected layers, we expect that a sequential reconnection process would create a boundary layer with complex sub-structure and magnetic topology. Such boundary layers should be the subject of future observations and analysis. 3 LLBL Structure and Formation During Northward IMF The structure of the LLBL and its topology during northward IMF is more complex than in the case of the southward IMF and mechanism or mechanisms responsible for the LLBL formation are still under investigation. Previous studies [42 46] suggested that the LLBL exhibits complicated structure and a few sub-layers are often visible in the data. Song et al. [42] distinguished two sub-layers: the Outer Boundary Layer (OBL), which is dominated by magnetosheathlike particles with very stable, plateau-like, characteristics of the density and temperature, and the Inner Boundary Layer (IBL), which is dominated by the magnetospheric population, which shows smooth variations of density and temperature across the layer. In these observations, plasma within the layers is homogeneous and sharp boundaries exist between the two layers, suggesting little or no diffusion present. Le et al. [44] presented observations of the ion populations inside the LLBL, showing that the OBL consists of heated magnetosheath plasma with little or no magnetospheric population while inside the IBL a mixture of magnetospheric and magnetosheath plasma is observed. Observations presented in Ref.[45] agreed with these previous observations. They again demonstrated that the LLBL consists of two regions, separated by a thin boundary, and that the density profile is monotonic across the sharp boundaries. Vaisberg et al. [45] also note that the IBL is a mixture of two populations, and while the trapped magnetospheric population is always observed inside the IBL, it also may be observed sometimes inside the OBL. Bauer et al. [46] performed a large statistical study of the plasma characteristics inside both the outer and inner layers. They showed that while the plasma of the solar wind origin is dominant inside the OBL, the partial densities of the solar wind and magnetospheric populations are comparable inside the IBL. They also showed that the counterstreaming electron beams at magnetosheath energies are a characteristic feature of the LLBL, and that they often overlap with the magnetospheric population inside the IBL. Their observations also showed a density plateau inside the OBL and that the plasma density exhibits step-like profiles inside the outer and inner boundary layers. There are a number of suggested mechanisms responsible for the formation of the LLBL and plasma transfer across the boundary layer during the northward IMF. As the LLBL has a complex sub-structure, we also can expect that more than one mechanism may contribute towards the formation of the LLBL and its different sub-layers. Some previous studies suggested that plasma diffusion occurs across the magnetopause and contributes to plasma mixing inside the LLBL. For example, the plasma diffusion rate can be enhanced due to localized wave activity and turbulence (e.g., Ref.[47]). However, it was shown that in general the diffusion coefficients are not high enough to explain the formation of the LLBL [48]. Bauer et al. [46] estimated the diffusion efficiency caused by lower hybrid drift instability, gyroresonant pitch-angle scattering and kinetic Alfvén wave turbulence and argued that the cross-field diffu-

9 Y V Bogdanova, et al.: Magnetospheric Boundary Layer Structure and Dynamics as Seen From Cluster sion is not sufficient to form outer and inner boundary layers with the observed thickness. These authors also pointed out that diffusion can only explain formation of the boundary layers with smooth gradients in plasma density, and not the formation of the layers with the density plateaus. The authors also considered other mechanisms, such as curvature drift, gradient drift and polarization drift and argued that these mechanisms can always contribute towards the formation of the boundary layer at some extent. The other suggested mechanisms which can be responsible for the LLBL formation and plasma mixing is large-scale waves at the flank magnetopause, plasma may be transferred across the magnetopause at the flanks via Kelvin-Helmholz instability [49 50]. Mixing of plasma from different sources has been observed in the presence of the K-H waves by Cluster (e.g., Ref.[51]) and it was suggested that localized reconnection can happen inside the rolled-up vortices (e.g., Ref.[52]). This mechanism operates only at the flank magnetopause, and will be discussed in more detail later in the review. 3.1 LLBL Structure and Formation for Northward IMF: Observations at the Dayside Magnetopause It is widely accepted that the main mechanism responsible for the formation of LLBL near the dayside magnetopause is a merging or reconnection process between the terrestrial and magnetosheath magnetic field lines. Under northward IMF, reconnection is more likely to occur in the lobe sector of the magnetopause, poleward of the cusp, near the location of maximum shear between magnetosheath and magnetospheric field lines (e.g., Ref.[53 54]). Cowley et al. [55 56] described all possible reconnection geometries during northward IMF, which include single lobe reconnection, dual lobe reconnection, and sequential merging. Single lobe reconnection occurs poleward of one of the magnetospheric cusps, only depending on the combination of the influence of the IMF B X -component and dipole tilt effect (e.g., Ref.[57]). During this process, a relatively thick LLBL on open field lines may be formed across the dayside magnetopause, which can slowly convect across the magnetopause from the dayside and around the flanks towards the nightside, under the influence of solar wind/magnetosheath convection (e.g., Ref.[58]). During dual lobe reconnection, which may occur under strong northward IMF, open field lines from both lobes reconnect with part of the magnetosheath field lines, creating LLBL on newly closed field lines which capture accelerated magnetosheath plasma inside them [59 61]. Thus, the field lines creating the LLBL in this case are closed, and are disconnected from the solar wind/magnetosheath. With time, they sink into the magnetosphere and under the action of an interchange instability may move anti-sunward around the flanks, contributing to the formation of the cold dense plasma sheet (e.g., Ref.[62]). The sequential merging process is similar to the dual lobe reconnection scenario, but the reconnection processes in two hemispheres does not occur simultaneously, creating a boundary layer with one sub-layer on open field lines, and another sub-layer on closed field lines. Le et al. [44] adapted the idea of sequential merging in order to explain formation of the Outer and Inner boundary layers. It was suggested that the outer boundary layer is formed by the single lobe reconnection and is on open field lines. The inner boundary layer is formed by a dual lobe sequential reconnection andisonclosedfieldlines. Themixtureofthemagnetosheath and magnetospheric populations inside the inner boundary layer was then explained by the drift of hot magnetospheric plasma on these closed field lines [63]. While this explanation is in agreement with theplasmadatapresentedinleet al. [44], it cannot explain some other observed LLBL crossings where the sub-layers have various density profiles. One example of the dual lobe reconnection with the sequential merging scenario was discussed by Bogdanova et al. [58], based on the plasma observations inside the exterior cusp region and in the ionosphere. The illustration of this scenario is presented on Figure 3. On this figure, panel (a) shows a view from the

10 586 Chin. J. Space Sci. Ξ ΛΠΠ 2013, 33(6) Fig. 3 Schematic of dual lobe sequential reconnection which can form the LLBL at the dayside: magnetic field configuration with two (north and south) X-lines (NXL and SXL) and Cluster trajectory [58]. the dusk and panel (b) shows a view from the Sun. In the dual lobe sequential reconnection scenario, reconnection happens first at the dusk-northern lobe sector poleward of the northern cusp (site NXL), creating open field line (A). This field line convects across the dayside magnetopause and reconnects the second time with the lobe field lines at the dawn-southern lobe sector poleward of the southern cusp (site SXL), forming line (B). This schematic also illustrates that southern X-line can also act as a primary reconnection site and create open field lines, such as line (C), due to the MLT difference between the two reconnection sites, one being in the dusk sector, and another being in the dawn sector. The IMF conditions which are are most favourable for dual lobe reconnection have also been widely discussed. Based on ionospheric observations, Imber et al. [64] suggested that dual lobe reconnection might occur only under very strong northward IMF, with the magnitude of the clock angle less than 10. The clock angle was defined as CA = tan 1 (B Y /B Z ), where B Y and B Z are components in the GSM coordinate system. However, the statistical study by Lavraud et al. [65] examining the occurrence of the bidirectional electron beams in the magnetosheath boundary layer showed that dual lobe reconnection can occur under IMF clock angles in the range ±(0 40 ). Results presented in Bogdanova et al. [58,66] and Hu et al. [67] also showed that dual lobe reconnection can occur for IMF clock-angles larger than 10. As shown in Figure 3, for a relatively large IMF clockangle, the reconnection site can be shifted to the dawn/dusk sectors poleward of the cusp to the position of the maximum shear between lobe and magnetosheath magnetic field lines, which would depend on the B Y -component of the IMF. More recently, Watanabe et al. [68] introduce a new model of sequential and internal reconnection, suggesting for the intervals with strong northward IMF and significant dipole tilt, internal reconnection can occur in the winter hemisphere, not only between a summer lobe field line and a winter lobe field line but also between a summer lobe field line and a closed field line. Bogdanova et al. [66] presented conjugated observations of the dayside LLBL by the Double Star TC-1 satellite and inside the northern cusp region by four Cluster spacecrafts. This event was a close mag-

11 Y V Bogdanova, et al.: Magnetospheric Boundary Layer Structure and Dynamics as Seen From Cluster netic conjunction between Cluster and Double Star, as they were only separated by 1 2 hours in MLT, and occurred during very stable northward IMF, with a clock angle close to 0 for most of the time of interest and variable in the range ±40. Figure 4 shows the electron energy-time spectrogram for Cluster in the top panel and for TC-1 in the bottom panel for the event on 28 February 2004, 00:00 03:40UT. As one can see from Figure 4, Cluster, moving from the nightside to the dayside, crosses the lobe, cusp proper, equatorward boundary of the cusp with reduced magnetosheath-like population, and the boundary layer consisting of a mixture of high-energy, magnetospheric and low-energy magnetosheath-like plasma, but with very low fluxes. Thirty minutes later, the TC-1 satellite crossed from the magnetosheath to the magnetosphere via the sub-solar magnetopause, passing through a plasma depletion layer, the very structured LLBL dominated by accelerated magnetosheath particles but with some residual magnetospheric population. At the end of the period shown, TC-1 crossed an additional sub-layer with a mixture of the magnetosheath-like population (however with very low fluxes) and a magnetospheric population. This is a typical observation of the LLBL at the dayside magnetopause during northward IMF. However due to variable solar wind pressure, the magnetopause and adjacent LLBL move back and forward across the satellite, making data analysis more complicated. Figure 5 shows the same LLBL for a smaller time interval, and every sub-panel of this plot represents the pitch-angle spectrogram, with 180 on the top and 0 on the bottom of every sub-panel. The temporal variations during this LLBL crossing are more evident on this figure: the spacecraft begins in the Plasma Depletion Layer (PDL), which Fig. 4 Overview of the nearly simultaneous observations of the cusp and LLBL from Cluster and Double Star TC-1 satellites on 28 February 2004, 00:00 03:40 UT. Panel (a) shows the electron energy-time spectrogram measured at Cluster SC2. The black line at the bottom of the panel represents the spacecraft potential. Panel (b) presents the electron energy-time spectrogram from TC-1. On both panels, omnidirectional differential energy flux (averaged over all anodes) is color-coded [66].

12 588 Chin. J. Space Sci. Ξ ΛΠΠ 2013, 33(6) Fig. 5 Overview of the TC-1 observations on 28 February 2004, 01:15 02:10UT. The bottom sub-panel shows the flow azimuth, and the other twenty sub-panels present the pitch angle distribution (0 180 )for electrons with center energy shown on the left (in the range ev). Differential energy flux is colorcoded according to the logarithmic colour bar shown on the right [66]. is characterized by fluxes lower than that of the magnetosheath, and by asymmetric electron populations: below 44 ev the electron population is mostly moving anti-parallel to a field lines, and above 85eV electrons are mostly field-aligned. While TC-1 is moving across the boundary layer, one can see at least three short-duration crossings into the PDL later on. Inside the boundary layer, the accelerated magnetosheath population is observed and electrons are mainly bi-directional. However uni-directional electron beams are sporadically observed as well. In addition, at high energies, some low fluxes of magnetospheric plasma are evident. At 01:58 UT, TC-1 crossed into a different boundary layer with sharply reduced electron fluxes, and with a mixture of the magnetospheric and magnetosheath electrons, with both populations having higher fluxes at 90 pitchangles. In such situations, it is difficult to disentangle spatial-temporal ambiguities. For such events, Hapgood and Bryant [69] suggested a method of reorganizing observations that removes temporal variations and emphasizes spatial variations. The method is based on the re-ordering observations across the reconnected layer according to the electron density and temperature. This technique, called the transition parameter technique, is based on the existence of anticorrelations of the density and temperature inside the boundary layer. Indeed, many observations show (e.g., Ref.[42, 69 70]) that inside the dayside magnetosphere the temperature is high and density is low, inside the magnetosheath, the temperature is low and density is high, and inside the boundary layer where the mixture of both populations is present, the density and temperature anti-correlate and vary from the

13 Y V Bogdanova, et al.: Magnetospheric Boundary Layer Structure and Dynamics as Seen From Cluster magnetospheric state to the magnetosheath state, depending on the position inside the boundary layer. Bogdanova et al. [66] applied this technique to the TC-1 observations at the magnetopause, assuming that the Transition Parameter (TP) equals 0 inside the magnetosheath proper and is equal to 100 inside the dayside magnetosphere proper. The data were re-ordered according to the electron density and temperature, and the transition parameter corresponding to every state of plasma mixing has been found according to a best fit curve to the scatter plot of the electron density versus the perpendicular electron temperature. Figure 6 shows a best fit of the TC-1 observations between magnetospheric and magnetosheath states. Figure 6 shows that the PDL population has high density and low temperature and the magnetospheric population has low density and high temperature. In addition, two types of boundary layer are also evident: one boundary layer, marked as BL-1, has plasma characteristics very close to the PDL population: it has similar to the PDL densities, but a more heated population, also evident in Figure 5. Another boundary layer, marked as BL-2, shows a smooth transition between a high density/low temperature state to a low density/high temperature state. This second boundary layer is also evident on Figure 5, after 01:58 UT. Using the transition parameter it is possible to re-order the observed data according to the relative position in the boundary layer instead of ordering the data as a function of time. This re-ordering of data removes temporal effects and keeps only spatial effects in the observations. Figure 7 shows the electron energy-transition spectrogram in the antiparallel, perpendicular and parallel directions for the period of interest from Bogdanova et al. [66].Thisfigure shows the same data set as in Figure 5, but ordered in terms of TP, thus showing only spatial, structural, variations of the plasma parameters through the LLBL. Fig. 6 Scatter logarithmic plot of the electron density versus the perpendicular electron temperature for the interval 01:00 02:20 UT. The solid line represents the least squares fits and is used for transition parameter re-ordering. One can see that the data can be split into four groups, according to location on the graph, representing populations inside the PDL, boundary layer dominated by the magnetosheath-like accelerated electrons (BL-1), boundary layer with mixed population from the both sources (BL-2) and magnetospheric population (MSP proper) [66].

14 590 Chin. J. Space Sci. Ξ ΛΠΠ 2013, 33(6) Fig. 7 The electron energy-transition parameter spectrograms in the anti-parallel (a), perpendicular (b), and parallel (c) directions for the period of 28 February 2004, 01:00 02:20 UT. Differential energy flux is color-coded. The red vertical dashed lines mark different sub-layers [66]. This is a good example of the LLBL at the dayside, and the different sub-layers are clearly seen. Observations start in the PDL, with Transition Parameter (TP) range being 0 7, which is characterized by anti-parallel fluxes of electrons at low energies and parallel fluxes of electrons at higher energies. The region with TP = 7 18 corresponds to a uni-directional electron sub-layer. In this sub-layer, the parallel part of the population is similar to the PDL population (only shows lower fluxes) and the anti-parallel part of the electron population shows strong energization. The region with TP = consists of more balanced electron population, with nearly the same fluxes in parallel and anti-parallel direction at similar energies (energies of heated magnetosheath population). The constant energization of the electron population also can be seen inside this sub-layer. The region with TP = consists also of an electron population with nearly equal fluxes in the parallel and anti-parallel directions. The difference of this electron population from the population observed at TP = is energy: the electron population inside this region is hotter in comparison with those from the previous sub-layer. The region with TP = shows a slow change in the plasma parameters from mostly dominated by the magnetosheath-type population to mostly dominated by the magnetospheric-type population. The authors

15 Y V Bogdanova, et al.: Magnetospheric Boundary Layer Structure and Dynamics as Seen From Cluster called this layer the transition layer. The region with TP > 87 is mostly the magnetospheric population and is defined as a magnetosphere proper. Inside this region, the plasma properties are very close to those inside the dayside magnetosphere, although some residue of magnetosheath population is still evident. Figure 8 shows examples of the electron distributions inside every LLBL sub-layer described above. In this figure, first and third rows (the panels marked by a ) show 2-D cuts of the electron distribution, in which the differential energy flux is color-coded. The horizontal axis corresponds to the perpendicular (gyration) speed and the vertical axis corresponds to the parallel component. The figures have been mirrored around V = 0 for readability. The second and fourth rows (the panels marked by b ) present 1-D cuts of the distribution, in units of differential energy flux. Cuts are in the parallel, perpendicular, and antiparallel directions. The black line corresponds to the cut at 0 pitch-angle, the red line to 90 pitch angle, and the blue line to 180 pitch angle. Panels (1a) and (1b) show the electron distribution inside the PDL: it is clear that the low-energy part of the population has strong fluxes in the anti-parallel direction, and the high-energy population has significant fluxes in the parallel direction. Panels (2a) and (2b) show an example of the distribution inside the uni-directional electron beam region, with TP = The population at 0 pitch-angle remains almost unchanged and is similar to the PDL population while 180 population is significantly heated. Panels 3a and 3b present an example of electron distribution inside the sublayer with unbalanced bi-directional electrons, TP = Inside this region, significant heating occurs in all directions. However one can see that fluxes of electrons in parallel and anti-parallel directions are not well balanced at all energies (panel 3b). Panels 4a and 4b show an example of electron distribution inside the sub-layer with TP = This sub-layer is dominated by the heated magnetosheath-like electrons, with bi-directional beams having very similar fluxes in the parallel and anti-parallel directions. Panels 5aand5bshowanexampleofelectrondistribution in the sub-layer with smooth changes in the plasma parameters, so-called the transition layer, with TP = Inside this region the electron spectra exhibit interesting behaviour and both magnetosheathtype and magnetospheric-type population have comparable fluxes. Plasma sheet electrons are trapped, with higher fluxes in the 90 direction. At low energies, there are observations of the bi-directional (0 and 180 ) population. Moreover, the electrons with magnetosheath-like energies are concentrated at pitch-angles of 45 and 135. This was interpreted as a signature of strong pitch-angle diffusion inside this region. Finally, panels (6a) and (6b) show the electron distribution inside the sub-layer which is closest to the dayside trapped magnetospheric population. Inside this layer, the magnetospheric population becomes dominant, with enhanced fluxes at 90 pitch-angle. The magnetosheath-like population still exists, and it also has mostly 90 pitch-angles. Dominance of the perpendicular fluxes indicates that inside this sublayer both populations are trapped. Bogdanova et al. [66] also investigated changes in the plasma parameters, such as electron density, temperature, temperature anisotropy and plasma velocity as observed in the data set re-binned according to the transition parameter. They showed that inside the different sub-layers the plasma moments characteristics are different. Thus, inside the sub-layer with uni-directional electron beams a density plateau was observed, the small variations of density and temperature were observed in two sub-layers with bidirectional electron beams, and smooth variations of plasma parameters (decreasing density and increasing temperature) were observed inside the transition sub-layer.

16 592 Chin. J. Space Sci. Ξ ΛΠΠ 2013, 33(6) Fig. 8 Electron distribution functions from the TC-1 satellite. The first and third rows show 2-D cuts of the electron differential energy flux. The horizontal axis corresponds to the perpendicular (gyration) speed and the vertical axis corresponds to the parallel component. The figures have been mirrored around V =0for readability. The second and fourth rows show 1-D cuts of the distribution, in units of differential energy flux. Cuts are in the parallel, perpendicular, and antiparallel directions. The distribution functions are presented at times (1) 01:22 UT (inside the PDL), (2) 01:32 UT (when uni-directional electron beam is detected), (3) 01:40 UT (when significant heating is observed, but fluxes in the parallel and antiparallel directions are not completely balanced), (4) 01:57 UT (when more heating is observed, and the counter streaming population is balanced), (5) 01:58 UT (inside the transition layer), and (6) 02:03 UT (inside the boundary layer with properties very close to the dayside magnetosphere) [66].

17 Y V Bogdanova, et al.: Magnetospheric Boundary Layer Structure and Dynamics as Seen From Cluster Based on the analysis of the plasma populations inside the different sub-layers and previous published results on the formation of the LLBL at the dayside during northward IMF, Bogdanova et al. [66] suggested the mechanism of the formation of the dayside LLBL, which we believe is a generalized mechanism which can explain most of the observations of LLBL at the dayside magnetopause. Figure 9 shows a schematic representation of the formation of LLBL with different sub-layers which can be formed by the different processes during northward IMF. This is view from dusk, and field lines with different history and properties are marked by 1 6. A dashed curve shows the magnetopause. We will discuss the different sublayers as they are crossed by the TC-1 satellite, as discussed above. The first region, marked by Line 1, is a PDL region this region is the closest upstream to the magnetopause and field lines from this region will soon participate in the reconnection process with the magnetospheric field lines on the lobe magnetopause. Field Line 2 is an open field line lying outside the magnetopause, and this field line configuration is formed due to reconnection process occurring between the draped magnetosheath (or PDL) field lines and the lobe field line poleward of the cusp in the northern hemisphere. Thus, this field line is part of the Magnetosheath Boundary Layer (MBL), and it contains the PDL electron population moving towards the reconnection site at 0 pitch-angles and electrons heated at the reconnection site and propagating away from the reconnection site at 180 pitch- Fig. 9 Schematic of the formation of the low-latitude boundary layer observed at the dayside by the TC-1 satellite. Line 1 shows the PDL field line, draped around the dayside magnetosphere. Line 2 represents a field line which is formed due to reconnection between the PDL and lobe field lines poleward of the cusp in the northern hemisphere. This field line is open and is outside the magnetopause, in the magnetosheath boundary layer. Line 3 represents an open field line which is formed due to reconnection poleward of the cusp in the northern hemisphere and which sinks inside the magnetosphere, crossing the magnetopause. Line 4 shows a field line which is formed by dual lobe reconnection. Line 5 represents field lines populated by plasma with reduced fluxes from both magnetosheath and magnetosphere sources. The process responsible for this population is diffusion across the magnetic field. Other lines show the magnetospheric field lines. The dashed line shows the magnetopause which is defined as a topological boundary [66].

18 594 Chin. J. Space Sci. Ξ ΛΠΠ 2013, 33(6) angles (e.g., Ref.[71 72]). The directionality of the heated electrons inside the magnetosheath boundary layer can be an indication of the location of the reconnection site (in the northern or southern hemisphere), see e.g., Ref.[58, 73 74]. The third region, marked by Line 3, is on field lines which were open during the northern lobe reconnection process some time ago. The difference between this line and Line 2 is that this line is already partially inside the magnetosphere, and it has undergone a sinking process due to the propagation of the kink in the magnetic field, related to the Alfvén wave or slow mode wave generated by the reconnection site in the northern lobe sector. This magnetic field line is identified by significant heating of the whole electron population. In addition, the parallel and anti-parallel fluxes of electrons are comparable, but not completely balanced, indicating that these field lines are open (e.g., Ref.[75]). It was suggested that the heating of the electrons observed on these field lines happened at the high-latitude magnetopause where the shear between the terrestrial and magnetosheath field lines is high [61]. Besides, the electron heating can exist at the low-latitude magnetopause where the plasma population interacts with the kink in the magnetic field. The field line marked by Line 4 is a newlyreclosed field line resulting from the second reconnection process that occurs in the lobe sector poleward of the southern cusp. On these field lines, which are thus formed by dual lobe reconnection, the magnetosheath-like part of the electron population undergoes additional heating which could be due to additional energization at the second reconnection site [58,73]. In addition, the electron fluxes of magnetosheath-like energies in the parallel and antiparallel directions are well balanced and fluxes of the electrons with the plasma sheet energies are increased. These observational signatures in equatorial regions are both good indicators of the closed magnetic topology of this sub-layer (e.g., Ref.[58]). This region is still dominated by the magnetosheath-like plasma. The field lines inside this boundary layer are slowly convecting around the magnetospheric flanks towards the magnetotail due to the interchange instability and eventually will form a thick LLBL and cold dense plasma sheet (e.g., Ref.[62]). The field line marked by Line 5 is inside the sublayer which is formed due to plasma diffusion across the magnetic field. This layer is characterized by the mixture of the magnetosheath and magnetospheric populations with low and comparable fluxes, and with dominant 90 pitch-angle distribution. Inside this layer smooth changes of the plasma parameters are often observed. The suggested scenario is a generalization and some boundary sub-layers can be absent or show different observational signatures. Thus, for example, the boundary sub-layer on the closed field lines which is formed due to the cross-field diffusion process can be absent, depending on the conditions favorable for diffusion, such as wave-particle interactions (e.g., Ref.[46]), andthe efficiencyofthis process. The initial lobe reconnection process can occur in the southern hemisphere first, depending on the orientation of the IMF B X component and the magnetospheric dipole tilt. Finally, the boundary sub-layer with the open magnetic topology will be absent for the case of nearly simultaneous dual lobe reconnection. Such cases recently were reported by Oieroset et al. [76] and Hasegawa et al. [77]. Thus, in the event presented by Hasegawa et al. [77] the observed LLBL was mostly magnetically closed and it was suggested that comparable reconnection rates in both hemispheres would explain the closed magnetic topology of the whole LLBL. Bogdanova et al. [66] also discussed the observed sub-layers inside the cusp region in conjunction with the LLBL observations by TC-1. Comparison of the plasma populations inside the LLBL and cusp showed that the complex LLBL observed at the dayside magnetopause maps into the mid-altitude cleft/cusp region and that similar sub-layers with similar plasma properties are observed inside both regions, including

19 Y V Bogdanova, et al.: Magnetospheric Boundary Layer Structure and Dynamics as Seen From Cluster layers formed by single lobe reconnection, dual lobe reconnection, and by the diffusion process. These observations confirm that the cusp provides a snapshot of the magnetopause conditions and that reconnection at the magnetopause can be studied using observations inside the LLBL and cusp region. 3.2 LLBL Structure and Formation for Northward IMF: Flank Observations In this section we briefly discuss another process responsible for the formation of the LLBL and its complex structure when observed away from the dayside, at the magnetospheric flanks, usually under the northward IMF conditions. It has been suggested that the Kelvin-Helmholtz (K-H) instability can facilitate the plasma transport across the magnetopause and contribute towards the formation of the thick LLBL observed at the flanks (e.g., Ref.[50, 78-84]). The K-H instability is a fluid instability which can be excited at the interface of two fluids where a flow shear exists. This is applicable to the magnetospheric flanks, where the magnetopause separates two plasmas with very different parameters: the magnetosheath which consists of steady and fairly fast anti-sunward flow of relatively high density plasma and plasma sheet which consists of stagnant or slowly sunward convecting, rarefied plasma population (e.g., Ref.[85]). The excitation of the K-H instability and growth of the surface K-H waves depends on local conditions, i.e. velocity shear between two plasmas and magnetic field shear, and the condition of the wave growth (for an incompressible plasma) is defined by the following expression (e.g., Ref.[86]): [k (V 1 V 2 )] 2 > n 1 + n 2 [(k B 1 ) 2 +(k B 2 ) 2 ], µ 0 m p n 1 n 2 where n is the plasma number density, V is plasma flow velocity, B is the magnetic field vector, m p is the proton mass, k is the wave vector and µ 0 is a permeability of free space. Indexes 1 and 2 refer to two plasma regions, or in the discussed case here, to the magnetosheath and magnetospheric plasma respectively. Thus, if a flow shear is larger than some critical value, defined based on the magnetic field and plasma density inside the two regions, the K-H wave instability will grow and large-scale surface K-H waves will be developed and be observed at the flank magnetopause [87]. An example of the typical observations of the plasma and magnetic field parameters at the flank magnetopause during the time with the K-H wave activity is presented on Figure 10 [88]. From the top to the bottom: the electron energy-time spectrogram, the ion energy-time spectrogram, the magnetic field, the ion temperature, the ion density, the ion velocity, the electron density and the electron temperature. In this example, the TC-1 satellite is near the dusk flank magnetopause, moving from the magnetosheath to the magnetosphere. When encountering the magnetopause, it detects quasi-periodic ( 2min period) variations of the plasma parameters, when the bursts of heated magnetosheath-like plasma typical for the boundary layer are intermittent with intervals of magnetosheath proper (during the time interval 16:30 18:20UT). This intermittence is especially clear in the observed plasma density and temperature, with low temperature and high density intervals corresponding to the magnetosheath proper intervals and high temperature and low density intervals corresponding to the observations inside the magnetosphere, possibly of the boundary layer. These observations are interpreted as a signature of large-scale surface waves travelling along the magnetopause anti-sunward, causing the magnetopause motion back and forth over the spacecraft. After 18:20UT, TC-1 is located deeper inside the magnetosphere and does not detect the passage of the surface waves anymore. From this time, the satellite is inside the boundary layer which is characterized by the heated magnetosheath population mixed with some higher-energy population of the magnetospheric origin. This region is defined as part of the cold dense

20 596 Chin. J. Space Sci. Ξ ΛΠΠ 2013, 33(6) Fig. 10 Detail of TC-1 magnetopause crossing. (a) electron spectrogram (erg s 1 cm 2 sr 1 ev 1 ); (b) Ion spectrogram(kev s 1 sr 1 kev 1 ); (c) FGM B field GSE; (d) ion temperature; (e) ion density; (f) ion velocity; (g) electron density; (h) electron temperature [88]. plasma sheet [88]. A number of recent numerical simulations suggest that the plasma mixing and efficient transport of plasma across the magnetopause associated with K-H instability can be achieved only during the nonlinear phase of the K-H instability, when rolled-up plasma vortices are formed at the magnetopause (e.g., Ref.[79, 84, 89 90]). Hasegawa et al. [51] presented an