kelvin-helmholtz waves at the earth’s magnetopause ...apr-jun).journal... · kelvin-helmholtz...

Kelvin-Helmholtz waves at the Earth’s magnetopause: Multiscale

development and associated reconnection

H. Hasegawa,1 A. Retino,2 A. Vaivads,3 Y. Khotyaintsev,3 M. Andre,3

T. K. M. Nakamura,1 W.-L. Teh,4,5 B. U. O. Sonnerup,4 S. J. Schwartz,6 Y. Seki,1

M. Fujimoto,1 Y. Saito,1 H. Reme,7 and P. Canu8

Received 2 January 2009; revised 2 July 2009; accepted 12 August 2009; published 4 December 2009.

[1] We examine traversals on 20 November 2001 of the equatorial magnetopauseboundary layer simultaneously at �1500 magnetic local time (MLT) by the Geotailspacecraft and at �1900 MLT by the Cluster spacecraft, which detected rolled-up MHD-scale vortices generated by the Kelvin-Helmholtz instability (KHI) under prolongednorthward interplanetary magnetic field conditions. Our purpose is to address theexcitation process of the KHI, MHD-scale and ion-scale structures of the vortices, and theformation mechanism of the low-latitude boundary layer (LLBL). The observed KHwavelength (>4 � 104 km) is considerably longer than predicted by the linear theory fromthe thickness (�1000 km) of the dayside velocity shear layer. Our analyses suggest thatthe KHI excitation is facilitated by combined effects of the formation of the LLBLpresumably through high-latitude magnetopause reconnection and compressionalmagnetosheath fluctuations on the dayside, and that breakup and/or coalescence of thevortices are beginning around 1900 MLT. Current layers of thickness a few times ioninertia length �100 km and of magnetic shear �60� existed at the trailing edges of thevortices. Identified in one such current sheet were signatures of local reconnection:Alfvenic outflow jet within a bifurcated current sheet, nonzero magnetic field componentnormal to the sheet, and field-aligned beam of accelerated electrons. Because of itsincipient nature, however, this reconnection process is unlikely to lead to the observeddusk-flank LLBL. It is thus inferred that the flank LLBL resulted from other mechanisms,namely, diffusion and/or remote reconnection unidentified by Cluster.

Citation: Hasegawa, H., et al. (2009), Kelvin-Helmholtz waves at the Earth’s magnetopause: Multiscale development and associated

reconnection, J. Geophys. Res., 114, A12207, doi:10.1029/2009JA014042.

1. Introduction

[2] The Kelvin-Helmholtz instability (KHI) can growalong an interface between two plasma media streaming ata different velocity relative to each other, such as the low-latitude magnetopause situated between the magnetosheath,characterized by an antisunward flow of shocked solarwind, and the outer plasma sheet characterized by stagnantor weak sunward flows. It has been studied extensively forunderstanding various phenomena in the terrestrial magne-

tosphere, such as momentum or mass transport from thesolar wind into the magnetosphere [e.g., Miura, 1984;Fujimoto and Terasawa, 1994], and ultra low frequency(ULF) waves which may eventually accelerate electrons inthe outer radiation belt [e.g., Elkington, 2006]. The KHImay grow also along the inner edge of the low-latitudeboundary layer (LLBL) [Sonnerup, 1980; Sckopke et al.,1981], and the resulting waves or vortices are suggested tohave some relation to aurorae with spatially periodic forms[e.g., Lui et al., 1989; Yamamoto, 2008].[3] There exists substantial observational evidence of the

KHI in the form of surface waves propagating antisunwardalong the magnetopause [Sckopke et al., 1981; Chen et al.,1993; Kivelson and Chen, 1995; Fairfield et al., 2000].These Kelvin-Helmholtz (KH) waves or vortices tend to bedetected more frequently during northward interplanetarymagnetic field (IMF) conditions than during southward IMF[Kivelson and Chen, 1995; Fujimoto et al., 2003; Hasegawaet al., 2006], and are believed to be a key ingredient for theformation of the thick LLBL [Mitchell et al., 1987] and thecold and dense plasma sheet (CDPS) [Terasawa et al.,1997; Wing and Newell, 2002], both encountered predom-inantly under northward IMF. Recently, multipoint obser-

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, A12207, doi:10.1029/2009JA014042, 2009ClickHere

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1Institute of Space and Astronautical Science, JAXA, Sagamihara,Japan.

2Space Research Institute, Austrian Academy of Science, Graz, Austria.3Swedish Institute of Space Physics, Uppsala, Sweden.4Thayer School of Engineering, Dartmouth College, Hanover, New

Hampshire, USA.5Now at Laboratory for Atmospheric and Space Physics, University of

Colorado at Boulder, Boulder, Colorado, USA.6Blackett Laboratory, Imperial College, London, UK.7Centre d’Etude Spatiale des Rayonnements, Toulouse, France.8Centre d’Etude des Environnements Terrestre et Planetaires, IPSL,

CNRS, Velizy, France.

Copyright 2009 by the American Geophysical Union.0148-0227/09/2009JA014042$09.00

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vations by the Cluster spacecraft demonstrated that during aprolonged northward IMF period, the KHI grows non-linearly along the dusk-flank magnetopause to form large-scale rolled-up plasma vortices [Hasegawa et al., 2004a].[4] The generation of the LLBL and CDPS requires

efficient entry of collisionless solar wind plasma into themagnetosphere, and thus must invoke nonmagnetohydro-dynamic (non-MHD) process(es). While magnetic reconnec-tion at the poleward-of-the-cusp magnetopause in bothhemispheres [Song and Russell, 1992; Lavraud et al.,2005; Øieroset et al., 2008] has been considered as thedominant plasma entry mechanism, there are a couple ofnon-MHD processes that may become facilitated as a con-sequence of the KHI growth and may contribute to plasmatransfer across the magnetopause: reconnection within or atthe edge of KH vortices [e.g., Otto and Fairfield, 2000;Nykyri and Otto, 2001; Nakamura et al., 2006, 2008], anddiffusive particle transport via turbulence induced withinfully developed KH vortices [Matsumoto and Hoshino,2004; Nakamura et al., 2004] or via kinetic Alfven waves(KAWs) excited through mode conversion from KH surfacewaves [e.g., Chaston et al., 2007]. From the observational

point of view, however, these microphysical processes in andaround the vortices are poorly understood. For example, keyquestions such as at what stage of the KHI development theybecome initiated and how remain to be answered. Theseissues are also coupled directly to the question of howMHD-scale structures in and around the vortices evolve to set thecondition for the onset of non-MHD processes.[5] Another issue concerns the wavelength of the mag-

netopause surface waves (a few 104 km) [e.g., Kivelson andChen, 1995; Hasegawa et al., 2004a] that appears to bemuch longer than predicted by the linear theory of the KHI[e.g., Walker, 1981; Miura and Pritchett, 1982] with thetypical thickness of the frontside magnetopause (<1000 km)[e.g., Berchem and Russell, 1982]. Belmont and Chanteur[1989] suggested that merging of KH vortices or an inversecascade can lead to such long wavelengths. This idea,however, poses another question, namely whether there issufficient time for such coalescence of vortices to beaccomplished while they propagate from the site of KHIexcitation (possibly on the dayside) to the observation site.It is thus crucial to determine on which part of themagnetopause the KHI is excited and how.[6] Here we revisit the case on 20 November 2001,

studied by Hasegawa et al. [2004a], Chaston et al.[2007], and Foullon et al. [2008], in which evidence forroll-up of KH vortices was identified from Cluster obser-vations on the dusk flank under extended northward IMFconditions, and simultaneous observations of the daysideLLBL upstream of Cluster were made by the Geotailspacecraft. Our aim is to address the excitation process ofthe KHI, MHD-scale and ion-inertia-length-scale aspects ofthe KH vortices concerning the KHI development, and theformation mechanism of the flank as well as dayside LLBLobserved in the event.[7] The paper is organized as follows. Section 2 presents

an overview of observations on 20 November 2001 to givea context for in-depth analyses in the following sections. Insection 3, Geotail data taken in and around the daysideLLBL are analyzed in terms of its structure and formationmechanism. In section 4, Cluster data taken in and aroundthe dusk-flank LLBL are analyzed in terms of MHD- andion-scale structures of the KH vortices. In section 5, wediscuss implications obtained from combined Geotail andCluster data analyses for the mechanism of KHI excitationand of the flank LLBL generation. Section 6 provides asummary of the results and our interpretations.

2. Overview of Observations

[8] An overview is presented of observations by theACE, Geotail, and Cluster spacecraft on 20 November2001 when rolled-up KH vortices were identified along

Figure 1. Trajectories in GSM coordinates of the Geotail,Cluster-1, and Cluster-3 spacecraft during the interval1900–2130 UT on 20 November 2001. The dashed linein Figure 1 (top) represents an average magnetopauseposition based on the Roelof and Sibeck [1993] model.

Figure 2. Time series of data in GSM taken by the ACE, Geotail, Cluster-1 (C1), and C3 spacecraft during the interval1900–2130 UT on 20 November 2001: (a) three components of the IMF, seen by ACE and time-shifted 62 min forward,(b–e) energy-versus-time spectrograms of omnidirectional ions and electrons detected by Geotail and C1, (f) iondensities from the LEP instrument [Mukai et al., 1994] on board Geotail and from CIS/HIA [Reme et al., 2001] on boardC1 and C3, (g) ion temperature, (h) ion beta (ion pressure divided by magnetic pressure), (i–k) three components of thebulk velocity at Geotail, C1, and C3, and (l–n) three components of the magnetic field from Geotail/MGF and fromCluster/FGM [Balogh et al., 2001]. Time resolutions are approximately 12 s for the Geotail/LEP data, 3 s for theGeotail/MGF data, and 4 s for the Cluster data. Until �1914 UT, the EA part of the LEP ion instrument was set to thesolar wind mode so that only higher-energy ions were sampled (Figure 2b).

A12207 HASEGAWA ET AL.: DEVELOPMENT OF MAGNETOPAUSE KH-WAVE

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the dusk-flank magnetopause with the aid of the Clustermultipoint measurements [Hasegawa et al., 2004a]. Figure 1shows trajectories in the GSM x-y and y-z planes of Geotail,Cluster-1 (C1), and C3 for a 2.5 h interval from 1900 UT to2130 UT. Geotail was moving from the dayside magneto-sheath into the equatorial magnetosphere at magnetic localtime (MLT) �1500, while Cluster was in the vicinity of thedusk-flank magnetopause �4 RE behind the terminator(MLT �1900). The innermost spacecraft C1 and the outer-most C3 were separated by �2000 km, mostly in the ydirection. The paths of these two sets of spacecraft made itpossible to observe the duskside LLBL simultaneously atvastly different local times.[9] Figure 2 shows time series of data in GSM taken

during the interval 1900–2130 UT by Geotail, Cluster, andACE which was embedded in the solar wind �210 RE

upstream of the bow shock nose. The ACE data are shifted62 min forward to take into account the transit time of thesolar wind from the ACE position to the magnetosphere.Figure 2a shows that although the IMF had nonzero x and ycomponents under a usual Parker spiral configuration, itwas persistently northward, the condition suitable for theKHI to grow along the low-latitude magnetopause [Miura,1995]. The IMF intensity was about 4 nT, slightly weakerthan its typical value.[10] During this extended northward IMF period, Geotail

traversed the magnetopause at 1500 MLT from the magneto-sheath into the dayside plasma sheet, as evident fromthe energy-versus-time spectrograms of ions and electrons(Figures 2b and 2c, respectively). A gap exists in the ion dataat energies less than 5 keV until �1914 UT. This is becausethe EA part of the LEP ion instrument [Mukai et al., 1994]was set to the solar wind mode during the correspondinginterval. An inbound magnetopause crossing occurred at�1919 UT, when the ion density decreased from �10 to�3 cm�3 (Figure 2f), ion temperature increased (Figure 2g),and the magnetic field intensity increased to an approximatelyconstant value 40 nT (Figure 2l). In a magnetosheath interval(1911–1919 UT) immediately before the boundary crossing,the field intensity increased and the density decreased gradu-ally. These are typical signatures of the plasma depletion layer,often formed outside the magnetopause for low magneticshears [Phan et al., 1994]. The magnetic shear, the anglebetween the fields on the magnetosheath and magnetosphericsides of the boundary, was indeed small (<40�).[11] A prominent LLBL (1920–1955 UT) was observed

by Geotail, where ions of magnetosheath origin weredetected in the energy range from one hundred eV to 1keV (Figure 2b), the density was >1 cm�3 (Figure 2f), andthe temperature was <1 keV (Figure 2g). Figure 2i showsthat in the outer part of this LLBL, ions were streamingtailward and duskward, generally along the magnetopause,whereas in the inner part they were mostly stagnant orwere streaming weakly toward the subsolar region (1944–1955 UT). For part of the LLBL interval (Figure 2b, 1943–1955 UT), magnetospheric ions of energy >1 keV coexistedwith the cool magnetosheath ions. On the other hand, theflux of magnetospheric electrons with energies �1 keV ormore was rather low for most of the entire LLBL interval(Figure 2c). All these features are consistent with earlierobservations in these regions under prolonged northwardIMF [Hasegawa et al., 2003, and references therein].

[12] Cluster, skimming the dusk-flank magnetopause,observed quasiperiodic perturbations of the plasma andmagnetic field parameters associated with large-amplitudeKH waves for more than 13 h [Hasegawa et al., 2004a;Foullon et al., 2008]. The dominant period of the KH waveswas 3–4 min, as inferred from Figures 2f, 2g, 2m, and 2nand demonstrated in section 4.1. The x component of themagnetic field was negative in less dense magnetosphericregions (Figures 2m and 2n), as expected from the fact thatCluster was �3 RE south of the x-y plane (Figure 1). In spiteof this and also the fact that the IMF had an antisunwardcomponent in both the upstream solar wind (Figure 2a) andthe dayside magnetosheath (Figure 2l), Bx was occasionallynearly zero or even positive in or around the dusk-flankboundary layer (Figures 2m and 2n). In concert with this Bx

variation, fluctuations of By and Bz were also observed. Thecause of these magnetic perturbations will be discussed insection 5.3.[13] Figure 2h shows that the ion beta (ion thermal to

magnetic pressure ratio) was moderate (�0.5), except fortransient enhancements to more than unity. These enhance-ments are consistent with dissipation of magnetic energyand hence its conversion to ion thermal (and perhaps bulk-flow) energy, possibly through reconnection at the edge ofrolled-up KH vortices, as discussed in section 4.3. Theycould also result from convective motion of localized higherbeta regions such as mirror-mode structures in the magneto-sheath [e.g., Constantinescu et al., 2003]. Velocity pertur-bations were less periodic than seen in the density,temperature, and magnetic field, and were present not onlyin the x and y but also in the z components (Figures 2j and2k). This could be due to three-dimensional (3D) develop-ment of the KHI, as discussed in section 5.3, or to couplingof the KH activity to the ionosphere. Figure 2d shows thatin the less dense boundary layer region, cool ions ofmagnetosheath origin and hot ions of magnetospheric origincoexisted with no strong mixing in energy space [Hasegawaet al., 2004a, 2004b]. On the other hand, low-energyelectrons of magnetosheath origin dominated the boundarylayer (Figure 2e) as on the dayside. Chaston et al. [2007]showed that these boundary layer electrons exhibitedenhanced fluxes at pitch angles �0� and �180�, behaviorconsistent with acceleration by field-aligned electric fieldassociated with KAWs mode converted from the KHsurface waves.

3. Analysis of Geotail Data

3.1. Perturbations at 1500 MLT

[14] Here we inspect if significant fluctuations associatedwith KH waves were seen by Geotail and, if not, whetherseed perturbations existed that may have given rise to theKH waves detected by Cluster. Figure 3 shows Geotail 3 sresolution data for the interval 1915–2015 UT which fullycovers the LLBL period (1920–1955 UT). Figure 3b showsthree velocity components in the LMN boundary normalcoordinate system [Russell and Elphic, 1978], where themagnetopause normal N is determined by the model devel-oped by Roelof and Sibeck [1993], with the input parame-ters IMF Bz = 3 nT and solar wind dynamic pressure of1.7 nPa. The velocity variations were mostly in the Mdirection. Except for a few spikes, VN fluctuations in the


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LLBLwere relatively weak, indicating that at 1500MLT therewas no surface or KHwave activity or, if present, its amplitudewas still small, which is further confirmed in section 3.2.Consistently, the condition for the linear KHI growth,

V1 � V2ð Þ � kh i2

>r1 þ r2m0r1r2

B1 � k� B2 � k� �h i2

; ð1Þ

often used in literature [e.g., Ogilvie and Fitzenreiter, 1989;Gratton et al., 2004], is only marginally satisfied for themagnetopause traversed by Geotail, even when the wavevector is optimally chosen to have an angle 17–32� withrespect to the GSM x-y plane so that the waves propagateantisunward but somewhat southward. Here, ‘‘1’’ and ‘‘2’’

refer to either side of the velocity shear layer, and r, V, B,and k are mass density, flow velocity, magnetic field, and aunit vector along the wave vector, respectively.[15] In the LLBL, appreciable magnetic fluctuations were

seen mainly in directions transverse to the mean field(Figure 2l). Figure 3c shows two field components perpen-dicular to the mean field orientation computed from runningaverage over ±2 min, Bt,M and Bt,N being the componentsapproximately tangential and normal to the boundary,respectively. The fluctuations were stronger in the tangentialthan in the normal direction, i.e., approximately linearlypolarized, and no significant increases in the field magnitudewere observed (Figure 2l), indicating that these magneticsignatures are not of flux transfer events (FTEs) [Russell andElphic, 1979]. Figure 3d shows a power spectrum (scalo-gram) of the tangential field component, Bt,M, from a wavelettransformation with Morlet wavelet function [Torrence andCompo, 1998]. The LLBL fluctuations had significant powerat periods from 100 to 300 s, together with some intermittentfeatures at shorter periods (higher frequencies).[16] Figure 3e shows time variation of the total (magnetic

plus ion) pressure, which was not fully constant across andaround the magnetopause, contrary to what is expected in anequilibrium. For an interval from 1925 UT to 1937 UT,corresponding to the outer LLBL, the pressure perturbationhad significant power at a period of �200 s (Figure 3f).Comparison with Figure 3a shows that for the aboveinterval, the pressure was somewhat anticorrelated withthe density. It might thus be that because of degradationof the ion detector (LEP-EAi) with time since the beginningof its operation in 1993, the density is underestimated in thedense magnetosheath-like regions, leading to poor satisfac-tion of the pressure balance; the level of pressure fluctuationmay be overestimated. However, density and VM variationsin the outer LLBL are somewhat anticorrelated and corre-lated, respectively, with the pressure, which suggests that aweak surface wave activity existed with a period of �200 s(part of the pressure perturbation should be real). Theseweak surface waves could have been excited in relation tothe transverse magnetic waves with a similar period(Figure 3d), and may well have provided seed perturbationsfor the growth of KH surface waves detected by Cluster,which also had a similar period of 3–4 min (Figure 2 andsection 4.1). The origin of these LLBL fluctuations isdiscussed in section 3.3 and the excitation mechanism ofthe surface waves in section 5.1.

3.2. Structure of the Dayside LLBL

[17] The structure of the dayside LLBL traversed byGeotail is analyzed using a method for reconstruction ofthe velocity field from single-spacecraft measurements, asdeveloped by Sonnerup et al. [2006] and first applied byHasegawa et al. [2007a]. The technique generates two-dimensional (2D) maps of streamlines and other plasmaparameters in a rectangular domain surrounding the path ofan observing spacecraft, by solving a Grad-Shafranov-like(GS-like) equation for the compressible stream functionusing measured data as spatial initial values. The basicassumptions underlying the method are that the structuresmoving past the spacecraft are 2D and time independentwhen seen in their proper moving frame of reference. Theseassumptions are never precisely satisfied in any real appli-

Figure 3. Geotail data for the interval 1915–2015 UT.(a) Ion density, (b) three components of the ion velocity inLMN boundary coordinates, (c) magnetic field componentstransverse to the mean field direction, one Bt,M approxi-mately along the M direction (green) and the other Bt,N

along the N direction (red), (d) wavelet power spectrum ofBt,M, (e) total (magnetic plus ion) pressure, and (f) waveletspectrum of the total pressure. Data of 3 s resolution areused here. In the wavelet spectra, results above the obliquelines may be dubious. The red and blue bars mark theintervals for the Walen analysis (Figure 5) and for Grad-Shafranov-like (GS-like) reconstruction of streamlines(Figure 4), respectively.


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cations, but experiments using synthetic data from time-dependent 2D or 3D numerical simulations indicate thatthis type of reconstruction nevertheless can producequalitatively correct streamline or field line patterns[Hasegawa et al., 2007a, 2007b].[18] Figure 4 shows the map of streamlines in the

reconstruction x-y plane recovered from Geotail data forthe interval 1930:51–1932:35 UT. The invariant (z) axis isparallel to the mean magnetic field orientation for theinterval; z = (�0.0741, 0.2236, 0.9719) in GSM. Thevelocity of the comoving frame in which the reconstructionis performed was chosen to be 90% of the center-of-massvelocity Vcom = (�71, 105, �15) km/s, computed from theplasma parameters measured on both sides of the magneto-pause. This choice generated a better organized map and isbased on MHD simulations of the KHI in a finite-thicknessvelocity shear layer, which suggest that KH waves propa-gate at a phase velocity between the average and center-of-mass velocities, (V1 + V2)/2 and (r1V1 + r1V2)/(r1 + r2),whereas the linear theory shows that the phase velocity on azero-thickness surface is equal to the center-of-mass veloc-ity [Chandrasekhar, 1961]. The x axis is the projection ofthe spacecraft path onto the plane perpendicular to the zaxis, and hence is parallel to the x-y projection of �Vcom;the reconstruction x axis has an angle of 13� with respect tothe GSM x-y plane.[19] The map shows that the velocity shear layer on the

dayside had a full width of about 1000 km or less, which iscomparable to the typical thickness (600–800 km) of themagnetopause current layer [Berchem and Russell, 1982;Phan and Paschmann, 1996], but is much smaller than thatof the LLBL as reported [Øieroset et al., 2008]. This smallwidth is consistent with abrupt VM changes in the LLBLdespite that VN, a proxy of the normal motion of theboundary, was rather small (Figure 3b). A small vortex ofwidth less than 1000 km was embedded in the shear layer,as seen at x = 8000–10000 km in the map. Becauseof instrument degradation over time and possible timeevolution of the structure [Hasegawa et al., 2007a], thereconstructed density may not be reliable.

3.3. Formation Mechanism of the Dayside LLBL

[20] The Walen relation, satisfied for Alfven waves or arotational discontinuity (RD) [Sonnerup et al., 1987], was

tested for a 53 s interval 1919:56–1920:49 UT when atransverse variation or rotation of the magnetic fieldoccurred at the magnetopause (Figure 3). The deHoffmann-Teller (HT) velocity was determined to be VHT = (�15, �5,�385) km/s in GSM, with the correlation coefficient be-tween three components of �V � B and �VHT � B for theanalyzed interval of ccHT = 0.916; the HT frame is not verywell determined. The Walen plot shown in Figure 5 exhibitsan appreciable correlation, especially for the x and y compo-nents. This indicates that the magnetopause was locally open(RD). The positive slope and the dominance of the south-ward (z) component of the HT velocity both indicate that theRD or Alfven wave was emitted from a reconnection sitenorthward of Geotail. The absence of FTE signatures sug-gests that the associated reconnection site was not near toGeotail. While it is possible that Geotail may have missedsmall FTEs generated locally, it seems unlikely that suchsmall-scale local reconnection created the prominent LLBLas observed. Our observations are thus consistent with theoccurrence of remote reconnection, most likely at the high-latitude magnetopause near the northern cusp, under thenorthward and tailward IMF conditions (Figure 2a). Theslope less than unity (0.71) and large scatter of the datapoints may indicate that the Walen plot is contaminated bynorthward propagating Alfven waves from possible high-latitude reconnection in the southern hemisphere.[21] Transverse magnetic fluctuations similar to that in

the Walen-test interval were seen throughout the LLBLinterval (Figure 3c), although they did not satisfy the Walenrelation. We infer that they are of KAWs or that Alfvenwaves were propagating in highly inhomogeneous regions,as surmised from Figures 3a and 3b, thus violating theassumptions underlying the Walen test that Alfven wavesare planar and of ideal MHD. KAWs can be excited throughreconnection [Chaston et al., 2005], and could have prop-agated from a possible high-latitude reconnection sitetoward the equator to cause the observed perturbations.No preferred direction of wave polarization is seen nearthe reconnection site [Chaston et al., 2005, Figure 1]. Thedominance of the BM over BN component (Figure 3c) maythus have resulted from preferential damping or conversionto BM of BN in the stratified LLBL, possibly by such amechanism as studied by Mann and Wright [1995], and/or

Figure 4. Streamlines in the dayside low-latitude boundary layer (LLBL) recovered from GS-likereconstruction using Geotail 3 s resolution data taken during 1930:51–1932:35 UT, with themagnetosheath on the top and the subsolar point to the right. Black curves are the reconstructedstreamlines. Colors show the reconstructed density, and white arrows show the projection onto the x-yplane of actually measured velocity vectors, transformed into the comoving frame. The frame velocityalong the x axis is 115 km/s and is equal to the projection onto the x-y plane of 0.9 times the center-of-mass velocity based on the measurements on the magnetosheath and LLBL sides (see text for details).GSM components for the reconstruction axis orientations are as follows: x = (0.5517, �0.8026, 0.2267),y = (0.8307, 0.5530, �0.0639), and z = (�0.0741, 0.2236, 0.9719). The z axis is the orientation of themean magnetic field for the analyzed interval.


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from preferential excitation of BM through interaction of thereconnection jets with nonuniform regions in/around thecusp. In this scenario, the wave quasiperiodicity (Figure 3d)could be due to intermittency of high-latitude reconnectionor temporal variation of the reconnection rate. Such quasi-periodic behavior of reconnection may be caused byinteraction with the magnetopause of compressional mag-netosheath fluctuations, as discussed next.[22] Another, perhaps more likely, explanation is that the

transverse fluctuations are of KAWs mode converted fromcompressional or magnetosonic waves in the magnetosheathand are associated with toroidal-mode field line resonance[Johnson and Cheng, 1997; Johnson et al., 2001]. Themagnetic field in the ambient magnetosheath did exhibitcompressional fluctuations (1900–1915 UT in Figure 2l),but at a period (300–400 s) longer than �200 s in theLLBL. Considering that the difference in period can beexplained by Doppler effects, the compressional as well astransverse fluctuations in the LLBL may have been excitedby such magnetosheath waves. The mode conversion pro-cess naturally explains why BM � BN, because modeconversion leads to transverse waves with small-scalestructure normal to the magnetopause (kN � kM) with theconsequence that BM� BN. The compressional fluctuationswere seen only in more magnetosheath-like portion of theLLBL (Figure 3f) while the transverse waves were observedin the inner LLBL as well (Figure 3d). This also seemsconsistent with conversion of compressional magnetosheathwaves into Alfven waves in the magnetosphere [Johnsonand Cheng, 1997; Belmont and Rezeau, 2001, and refer-ences therein].[23] We cannot conclude with certainty what mechanism

generated the dayside LLBL as observed, because neither3D velocity distributions nor pitch angle information of ionsas well as electrons, necessary for identifying, e.g., field-aligned beams of ions and/or electrons generated throughreconnection [e.g., Fuselier, 1995; Onsager et al., 2001] orions heated perpendicular to the field via KAWs [Johnson

and Cheng, 2001], were available for the interval underdiscussion. However, the most likely mechanism to explainthe LLBL densities is high-latitude or poleward-of-the-cuspreconnection, possibly in both hemispheres [Song andRussell, 1992]. The absence of hot magnetospheric elec-trons in the LLBL (Figure 2c) suggests that the LLBL fieldlines were open or had previously been open, allowing fortheir field-aligned escape into the magnetosheath, or that thefield lines were originally of IMF type, as expected by thedual poleward-of-the-cusp reconnection model [Song andRussell, 1992]. The positive Walen slope and southward HTvelocity component (Figure 5) are also consistent withexpectation from the antisunward polarity of the IMF(Figure 2a) that reconnection would have occurred first inthe northern hemisphere.[24] As shown in previous sections 3.1 and 3.2, no

significant surface waves existed at the Geotail local time.Therefore, plasma entry through nonlinear growth of theKHI [e.g., Fairfield et al., 2000; Hasegawa et al., 2004a]and diffusive transport via KAWs mode converted fromsurface waves [Chaston et al., 2007] can be excluded.Furthermore, abrupt jumps in velocity as well as density(Figures 3a and 3b) suggest that diffusive transport, such asinduced via mode conversion from magnetosheath com-pressional waves [Johnson and Cheng, 1997], was notstrong in the LLBL. This is consistent with the fact thatthe observed modes had long wave periods or wavelengthsalong the magnetopause for which the estimated diffusioncoefficient, which is due mostly to the normal magneticfield fluctuations [Hasegawa and Mima, 1978; Johnson andCheng, 1997], is low. However, even in a region wherecross-field diffusion is not strong, electron heating can stillbe significant for normal magnetic field fluctuations as lowas a few percent [Hasegawa and Mima, 1978]. Ion heatingin KAWs also does not depend significantly on the directionof the perpendicular wave vector [Johnson and Cheng,2001]. Therefore, KAWs are a reasonable candidate toexplain the gradual increase in electron and ion temper-atures from the magnetosheath to the magnetosphere asseen in Geotail measurements (Figures 2c and 2g).

4. Analysis of Cluster Data

4.1. MHD-Scale Structure of the Vortices

[25] Here we investigate MHD-scale aspects of the rolled-up KH vortices detected by Cluster at 1900 MLT. Within ahighly rolled-up KH vortex, centrifugal forces acting onrotating plasmas should approximately balance the forcesfrom the total pressure gradient, provided that effects oftemporal variations and magnetic tension are negligible; thisforce balance relation forms the basis for the GS-likereconstruction of streamlines [Sonnerup et al., 2006;Hasegawa et al., 2007a]. Accordingly, rolled-up vorticesare expected to involve substantial pressure perturbations(minimum at their center and maximum at their edge) [e.g.,Miura, 1997]. Figure 6 indeed shows significant fluctua-tions of the total pressure whose amplitude was about 15%or more of its average value when the rolled-up vorticeswere identified. The dominant mode had a period of�200 s;it can be translated into the wavelength 4.2 � 104 km or6.6 Re, with a rough estimate of the phase speed 211 km/sof the KH vortices [Hasegawa et al., 2004a]. This velocity

Figure 5. Walen relation using Geotail 3 s resolution datain GSM taken from 1919:56 UT to 1920:49 UT, when asharp velocity jump occurred in the density gradient layer ator in the proximity of the magnetopause (Figure 3).


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211 km/s is indeed between the average and center-of-massvelocities based on the Cluster measurements on both sidesof the magnetopause.[26] A striking feature is that for an earlier interval until

2025 UT, the pressure perturbation had appreciable poweralso at a period of �400 s (Figure 6b), twice the dominant-mode period. The power of this fluctuation is comparable toor slightly lower than seen at the dominant-mode period.Note that in the dayside LLBL, no pronounced waveactivity was found at this longer period (Figure 3; note thatthe spectra above the oblique lines may not be reliable).This indicates that the KH mode with �400 s period shouldnot have involved strong driving on the dayside, while the�200 s mode was probably driven. Provided that the waveperiod can be transformed into the wavelength, it is inferredthat two dominant-mode vortices just began to coalesce toform a larger vortex, or an inverse cascade of energy to thesubharmonic mode set in [Belmont and Chanteur, 1989;Miura, 1999; Takagi et al., 2006]; the KHI was in the verystage where nonlinear dynamics are important. Such a fea-ture was not seen in the C3 power spectrum (Figure 6d).Since at C3 even the dominant-mode period had less intensepower than at C1, it is likely that C3 was not passingthrough the vicinity of the vortex center so that the effect ofvortex merging was not sensed. We also point out that nopower at�400 s for the later interval (2025–2130 UT) shouldnot be taken as a signature of cascade from 400 s periodmode to 200 s mode or breakup of longer-wavelength vor-tices. This is because the vortices are propagating tailward

and hence spacecraft nearly at a fixed point in space overtens of minute (Figure 1) cannot track temporal evolution ofthe same vortices, and because the KHI linear growth timeis too long for the longer-period mode to have such poweras observed by Cluster (the growth rate for the 400 s modeis about half that for the 200 s mode) [e.g., Miura andPritchett, 1982]. The temporal change as seen in Figure 6would thus be associated with time evolution of the KHIexcitation process, such as temporal variation of the seedperturbation amplitude.[27] Figure 7 shows the GS-like maps of streamlines

derived from C1 data for a 241 s interval from 2044:39 to2248:41 UT and from C3 data for a 245 s interval from2044:40 to 2048:45 UT, both of which fully cover onedominant-mode period. The upper maps show reconstructeddensity in color, along with ion velocity vectors measuredby C1, C3, and C4 and transformed into the comovingframe. The lower maps show reconstructed ion temperature,along with measured components of the magnetic fieldprojected onto the reconstruction plane; ideally these com-ponents should not exist under the model assumptions[Sonnerup et al., 2006]. No maps were generated from C4data, since ion data from CIS/CODIF were less reliable thanthose from CIS/HIA. The speed of the comoving frame ischosen as 90% of the center-of-mass velocity Vcom =(�213, 98, �17) km/s, as in the application to the daysideLLBL (section 3.2). Initial reconstruction x and y axes arealong �Vcom and the cross product of the mean fieldorientation and �Vcom, respectively. The invariant z axis,

Figure 6. Total (magnetic plus ion) pressures and their wavelet spectra, based on the C1 and C3 data forthe interval 2000–2130 UT. The intervals enclosed by the blue boxes were used in the GS-likereconstruction of streamlines shown in Figure 7.


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common to the C1 and C3 maps, completes the orthogonalright-handed system with the initial x and y axes such thatthe mean field direction is embedded in the x-z plane. Thefinal x and y axes are obtained by rotating the initial onesabout the z axis by �2� for C1 and �1.5� for C3; suchrotations yielded better organized streamline maps. Theorientation of the final x axis (see caption for Figure 7)indicates that the KH waves were propagating tailward andduskward with only a minor k vector component in theGSM z direction. Foullon et al. [2008] reached a similarconclusion on the wave propagation direction.[28] For magnetohydrostatic GS reconstruction of the

magnetic field [Hau and Sonnerup, 1999], the choice ofreconstruction axes can be optimized by a method used byHasegawa et al. [2004c]; they maximized the correlationcoefficient between in-plane (x, y) components of theactually measured magnetic or velocity field and thosepredicted from the map at points along the paths of otherspacecraft that were not used for the reconstruction butprovided measurements. However, such optimization wasnot possible for the present case. This may be due to(1) unreliable reconstruction of density [Hasegawa et al.,2007a], which would lead to poor prediction of the velocitycomponents because the compressible stream functionmust be divided by the reconstructed density to get them,(2) temporal and 3D effects that would have existed, as

inferred from modest structural differences between themaps from C1 and C3 that were separated by 615 km inthe z direction and as discussed by Hasegawa et al. [2004a],and/or (3) less good quality of the velocity measurementsthan of the magnetic field. Indeed, producing a streamlinemap that looks reasonable was possible only for a fewintervals including the one shown, which suggests theimportance of temporal and 3D effects in the present event.However, the overall structure of the streamlines from theC1 and C3 data is similar in terms of their topology and thewidth and length of the vortices embedded in the boundarylayer, suggesting the robustness of the recovered structures.We also confirmed that for an earlier part of the recon-structed interval, a vortex can be recovered from the MHDreconstruction, developed by Sonnerup and Teh [2008] andfirst applied by Teh and Sonnerup [2008] (not shown).[29] The most remarkable feature revealed by the GS-like

reconstruction is the existence of two vortices of compara-ble size (�2 RE by 1 RE) within one dominant-mode period.Vortices of similar size are seen also in the maps generatedfor other intervals. We also note that the pressure fluctua-tions occasionally had some power at a period �100 s, halfthe dominant-mode period (Figure 6). At first sight, thesefeatures seem consistent with breakup of a dominant-modevortex or cascade of energy toward shorter-wavelength

Figure 7. Streamlines (black curves) in Kelvin-Helmholtz (KH) vortices recovered from the GS-likereconstruction using (a) C1 data taken during 2044:33–2048:41 UT and (b) C3 data during 2044:40–2048:45 UT, with the magnetosheath on the top and the subsolar region to the right. Colors show thereconstructed density (Figures 7a and 7b, top) and temperature (Figures 7a and 7b, bottom), and whitearrows show the projection onto the x-y plane of actually measured velocity vectors as viewed in thecomoving frame (Figures 7a and 7b, top) and of the magnetic field (Figures 7a and 7b, bottom). The framevelocity along the x axis is �211.5 km/s. In the C1 map, x = (0.8907, �0.4475, 0.0805), y = (0.4543,0.8687,�0.1974), and z = (0.0184, 0.2124, 0.9770) in GSM, and C3 is separated with respect to C1 in the x,y, and z reconstruction-axis directions by �106 km, 1824 km, and �615 km, respectively. In the C3map, x = (0.8946, �0.4399, 0.0788), y = (0.4465, 0.8726, �0.1981), and z = (0.0184, 0.2124, 0.9770).


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modes. The generation mechanisms of those smaller vorti-ces will be discussed in section 5.2.

4.2. Ion-Scale Current Sheet at the Vortex Edge

[30] The structure of current sheets detected at the trailingor sunward facing edge of the KH vortices is examined.

Figures 8a and 8b show electron density (0.2 s resolution),estimated from the spacecraft potential measurements[Pedersen et al., 2001, 2008], and L component of themagnetic field (22 Hz resolution) at C3 for the interval2026–2051 UT. Here the maximum variance direction L isdetermined from variance analysis using magnetic field data(MVAB) [Sonnerup and Scheible, 1998], but slightly rotatedto be optimal for a boundary crossing at 2035 UT fullyanalyzed later (the exact axis orientation is presented inthe next paragraph). During this interval, precipitous andnegative-to-positive changes in BL, namely, current sheetcrossings occurred when C3 traversed density boundaries atthe magnetopause from its magnetospheric to magnetosheathside. From our previous study [Hasegawa et al., 2004a], itis known that C1 was passing through the proximity ofthe vortex center and that the KH wavelength was about4 � 104 km or more (see also section 4.1), namely, muchlarger than the interspacecraft distance �2000 km. We notethat the outbound (magnetospheric to magnetosheath)traversals occur on the trailing side of the tailward propagatingKH waves (Figure 9a). Since the density boundaries at thetrailing edge can be regarded as planar on the scale of thespacecraft separation (Figure 9a), so-called four-spacecrafttiming analysis [Schwartz, 1998] can be used to estimate theorientation andmotion of the boundary. Using results from thetiming analysis applied to electron density data (Figure 8a andTable 1), the full width of three conspicuous current sheets at

Figure 8. Cluster data for a focused interval. (a) Electrondensity estimated from the spacecraft potential measure-ment and (b) L component of the magnetic field at C3 forthe interval 2026–2051 UT. The juxtaposition of thincurrent sheets and sharp density gradients (magnetopause)is indicated by the vertical red bars. (c) Electron density, (dand e) energy-time spectrograms of omnidirectional elec-trons and protons detected by PEACE [Johnstone et al.,1997] and CIS/CODIF, respectively, on board C3, (f) Ncomponent of the ion velocity in the boundary-rest frame,(g) ion beta, where the ion data are interpolated to have timeresolution equal to the field data, and (h) magnitude and(i and j) L and N components of the magnetic field during2034:35–2035:35 UT. Red triangles show times whenelectron velocity distributions in Figure 11 were recorded.

Figure 9. (a) Two-dimensional two-fluid simulation of theKH instability [Nakamura et al., 2008], showing plasmadensity (red, dense; blue, tenuous) in a nonlinear stage, within-plane magnetic field lines overlaid. The hyperbolic pointis a stagnation point in the KH-wave rest frame aroundwhich flow lines form hyperbolae. (b) Schematic ofreconnection signatures seen by C3 at the trailing edge ofa rolled-up vortex: (1) nonzero BN consistent withinterconnection of the magnetosheath and plasma sheetfield lines, (2) outflow jet, and (3) field-aligned electronbeam.


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about 2031, 2035, and 2038 UTwas found to be�770,�240,and �390 km, respectively. These values are somewhatsmaller than the average width of the magnetopause currentlayer on the dayside (600–800 km) [Berchem and Russell,1982; Phan and Paschmann, 1996].[31] We now focus on one such current sheet encoun-

tered at 2035 UT that was found to be the thinnest amongthose traversed during the above interval. The timinganalysis led to the direction normal to the boundary N =(0.779, 0.627, �0.027) in GSM, and the boundary normalvelocity V0 = �79 km/s (Table 1). The negative sign of V0

indicates an earthward motion of the boundary, consistentwith the outbound traversal. The normal orientation iscompatible with the axes used in the GS-like reconstruc-tion (see caption for Figure 7); N had an angle of only �7�with respect to the reconstruction x-y plane. The normaldirection is also similar to the one obtained by Foullon etal. [2008] (see their Table 4) using electron temperatureand magnetic field data for another outbound crossing at2021 UT. Local LMN coordinates for this particularboundary are determined as follows: given the maximumvariance direction L1 from MVAB, M is defined as thecross product of N (from the timing method) and L1, and Lcompletes the right-handed orthogonal system. The result-ing L and M directions are: L = (0.542, �0.650, 0.533),and M = (0.316, �0.430, �0.846) in GSM. The full widthof the current sheet �240 km, estimated from the duration�3 s of the crossings by C1 and C3 (Figure 8i), is afew times ion inertia length on the magnetosheath side(�100 km).[32] We note that the magnetic shear across the current

sheet (�60�) was larger than seen by Geotail on the dayside(<40�), and claim in section 5.3 that the larger magneticshear resulted from the 3D development of the KHI asdiscussed by Hasegawa et al. [2004a] and Takagi et al.[2006]. Figure 8f shows the ion velocity Vi,N along thenormal in the boundary-rest frame (Vi,N = Vsc,i�N � V0,where Vsc,i is ion velocity in the spacecraft frame).Although fluctuating, Vi,N tends to be positive (negative)on more plasma sheet (magnetosheath) side; ions weregenerally flowing toward the current sheet. The thinness ofthe current sheet is probably due to these converging flowsgenerated around the hyperbolic point in the vortex(Figure 9), where streamlines form hyperbolae whenviewed in the vortex-rest frame [Nakamura et al., 2004,2008]. The fact that Vi,N was on average negative in andnear the current sheet is consistent with entry of solar windions into the magnetosphere, which may or may not have

resulted from reconnection in this ion-scale current sheetdiscussed next.

4.3. Signatures of Vortex-Induced Reconnection

[33] Here we present signatures consistent with recon-nection occurring at the trailing edge of the vortex, byshowing C3 observations in and around the ion-scalecurrent sheet analyzed in section 4.2. The M componentof the current jM (Figure 10f) is estimated from jM = DBL/(m0jV0jDt), assuming a planar current sheet. The currentsheet was bifurcated, as represented by the two verticaldashed lines, and was similar to the Petschek-type recon-nection layer except for the strong guide field BM involvedin this event (Figure 10d). Each of the two current sheetsconstituting the bifurcated layer had a total thickness of�40 km (Figures 10e and 10f), smaller than the ion inertialength, so that they were likely supported by electron flows.

Table 1. Orientation and Motion of the Boundary at Three

Outbound Crossings During the Interval Shown in Figures 8a and

8b, From the Timing Analysis Applied to the Electron Density

Measurementsa

Time ofCrossing (UT)

Normal Orientationin GSM

Speed(km/s)

Thickness(km)

�2031 (�0.682, �0.723, �0.109) 85.6 �770�2035 (�0.779, �0.627, �0.027) 79.1 �240�2038 (�0.854, �0.458, 0.246) 38.5 �390

aThe total thickness of the current layer is estimated by the normal speedof the boundary multiplied by an approximate duration of the current layertraversal.

Figure 10. Reconnection signatures seen by C3.(a) Electron density, (b) electric wave energy density inthe 2–80 kHz range, (c–e) N, M, and L components of themagnetic field, (f) current density in the M direction, and(g and h) L components of the ion and E0 � B driftvelocities. The thick line at the bottom denotes the intervalwhen the electron distribution in Figure 11 (left half and redlines) was obtained.


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Bifurcated current sheets are often seen in association withreconnection in the solar wind [Gosling and Szabo, 2008].Note that pronounced current bifurcation may result fromreconnection in current sheets across which substantialdensity jump and velocity shear exist [La Belle-Hamer etal., 1995], as in the present case (Figures 10a and 10g).[34] The most remarkable signature of reconnection is an

increase in the absolute value of the L component of thevelocity VL within the bifurcated current sheet, evident fromboth the ion (Figure 10g) and E0 � B drift measurements(Figure 10h), although the time resolution of the ion data isnot enough to resolve the current sheet structure. Theelectric field in the boundary-rest frame E0, used inFigure 10h, is calculated from E0 = E + V0N � B. Here V0

V0 is the boundary normal velocity (�79 km/s) from thetiming method (section 4.2) and E is the electric field in thespacecraft-rest frame measured by the EFW instrument[Gustafsson et al., 2001], the component along the spin

axis being computed on the assumption that E�B = 0. Thevelocity jump across the magnetosheath-side edge of thecurrent sheet �60 km/s (Figure 10h) is comparable to theAlfven speed 90 km/s, computed from the field componentin the L direction outside the current sheet BL = 10 nT andmagnetosheath density n = 6 cm�3, suggesting that C3 sawa reconnection jet. The current sheet coincides with aminimum in the magnetic field intensity and maximum inion beta (Figures 8g and 8h), consistent with magnetic toion energy conversion through reconnection. Moreover,Figure 10c shows penetration of the magnetic field intothe plasma sheet (BN < 0), although BN varied possibly dueto the propagation of magnetic bulges/islands created bytime-dependent and/or multiple X line reconnection[Eriksson et al., 2009]. The reconnection rate roughlyestimated from the average BN � �1.0 nT and the recon-necting field component BL is R = BN/BL = 0.1, similar toprevious estimates in the case of negligible guide field [e.g.,Vaivads et al., 2004]. This value may seem surprisinglyhigh, considering the presence of a strong guide field. Wehowever emphasize that vortex-induced reconnection has adriven rather than spontaneous nature [e.g., Nakamura etal., 2008], so that fast reconnection may be achieved. Theelectron density within the bifurcated current sheet wasnearly equal to the magnetosheath value (Figure 10a),consistent with entry of magnetosheath electrons alongreconnected field lines. The transfer of solar wind plasmainto the plasma sheet is evident also from somewhat heatedmagnetosheath ions of energy �1 keV present on theplasma sheet side (Figure 8e, 2034:35–2034:55 UT),although it is not clear if the entry of these ions was trulydue to reconnection in this ion-scale current sheet.[35] While microphysical signatures of reconnection such

as the Hall effects have been searched for in the weak guide-field cases [Mozer et al., 2002; Vaivads et al., 2004; Retinoet al., 2007], such attempt does not seem possible becausethere is currently no theoretical prediction that can becompared with the present observation where not only theintense guide field BM = �20 nT (Figure 10d) but alsosignificant density and velocity jumps across the currentsheet were involved. Instead, we found another featureconsistent with ongoing reconnection: magnetic field-aligned stream of accelerated electrons within the bifurcatedcurrent sheet (Figure 11). The phase space density (PSD) ofelectrons in the parallel direction is higher in the currentsheet (solid red line in Figure 11b) than in the magneto-sheath (black line) at velocities >3000 km/s. Withinthe current sheet, the magnetic field was dominated by thenegative M component (Figures 10c–10e) so that theparallel PSD represents that in the �M direction. Thefield-aligned electrons had a PSD peak at �3000 km/s(�50 eV), comparable to the electron Alfven speed(3900 km/s) on the magnetosheath side. We interpret thesefield-aligned electrons as those transferred from the mag-netosheath and accelerated within and/or in the vicinity ofthe diffusion region by tangential electric field (positive EM)expected in an active reconnection layer (Figure 9b).Figure 10b shows that the electric wave energy densityfrom the WHISPER instrument [Decreau et al., 2001],integrated over the frequency range 2–80 kHz, was highin and immediately earthward of the current sheet. Theintense power of these high-frequency waves could be due

Figure 11. Electron velocity distributions seen by C3 inthe bifurcated current sheet (CS: left half in Figure 11a andred lines in Figure 11b) and in the magnetosheath (SH: righthalf and black lines).


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to Langmuir/upper-hybrid waves presumably excited by thefield-aligned electron beam, as reported by Vaivads et al.[2004] and Retino et al. [2006].[36] The reconnection electric field EM is roughly esti-

mated to be 0.1 mV/m, from the reconnection rate of 0.1.Note that estimation of EM directly from the electric fielddata was not possible because there is no reliable method fordetermining a proper frame in which the relevant X line isseen stationary (the method developed by Sonnerup andHasegawa [2005] did not work probably because of tem-poral and/or 3D effects). Assuming that the generation ofthe field-aligned electrons at �50 eV is purely due to EM inthe reconnecting current sheet, the electrons should havetraveled �500 km along the �M direction, which must beshorter than the length of the relevant X line. Bipolarperturbations in the normal magnetic field component BN

seen by C4 at 2035:15 UT (Figure 8j) may have beencaused by the motion of magnetic islands produced bymultiple X line reconnection in the vortex, as predicted bysimulations (Figure 9a) [e.g., Nakamura et al., 2008] (herewe referred to the result from 2D simulation because thereare presently no 3D simulations of the KHI that haveaddressed both reconnection and 3D geometry of the flankmagnetosphere, the latter having been modeled by Takagi etal. [2006], and to date global MHD simulations are suc-cessful in reproducing large-amplitude KH vortices forsouthward IMF only [Claudepierre et al., 2008]). Sincethe other three spacecraft did not clearly see thecorresponding magnetic perturbations, the size of the pos-sibly formed magnetic islands must have been smaller thanthe Cluster tetrahedron (�2000 km). Likewise, no outflowjet as seen by C3 was found in the current sheets traversedby the other spacecraft. All these findings suggest thatreconnection induced at the edge of the vortex was highlylocalized, with a spatial scale smaller than the spacecraftseparation �2000 km in both M and L directions.[37] Observations in other adjacent current sheets do not

seem to provide convincing evidence of reconnection. Thismay be due to the fact that those current sheets were thicker

than the one studied above and thus were not yet at the stageof reconnection. It is thus inferred that reconnection iden-tified at the thinnest current sheet was still incipient, i.e., itbegan rather recently near the Cluster observation site as aconsequence of the roll-up of KH vortex. In a postnoonmagnetopause crossing event reported recently by Erikssonet al. [2009], signatures of reconnection in the form of FTEswere detected at the trailing edge of KH waves despite theirearly (probably linear) growth phase. The earlier occurrenceof reconnection in their event may be due to magnetosheathbeta (�0.1) being much lower than in the present event(�0.5) so that reconnection was more easily initiated[Paschmann et al., 1986].

5. Discussion

5.1. Excitation of the KH Waves

[38] In the present event, compressional and/or transversemagnetic fluctuations with a period of �200 s seen in thedayside LLBL most likely served as seed perturbations forthe excitation of the KH waves (section 3.1). We also notethat their excitation may have been aided by the presence ofa rather dense LLBL on the dayside, that presumablyresulted from high-latitude or double poleward-of-the-cuspreconnection [Song and Russell, 1992] (section 3.3); thelinear KHI condition expressed by inequality (1) becomessatisfied more readily when the magnetospheric density ishigher. For example, Bouhram et al. [2005] showed that theexistence of heavy ions such as O+ in the magnetopauseboundary layer can have a significant influence on the KHIexcitation.[39] In Figure 12, a possible scenario of the KHI excita-

tion under northward IMF is illustrated based on ourobservations. We infer that the KH waves may be excitedby combined effects of the formation of a dense and thickLLBL through reconnection at the high-latitude magneto-pause [Øieroset et al., 2008] and of compressional fluctua-tions in the magnetosheath. Magnetosheath ULF wavescould be of those downstream of quasi-parallel bow shocksor be excited by the mirror instability [e.g., Hasegawa,1969; Constantinescu et al., 2003]. In this scenario, morefrequent occurrence of KH waves/vortices during northwardthan southward IMF periods [Chen et al., 1993; Kivelsonand Chen, 1995; Fairfield et al., 2000; Fujimoto et al.,2003; Hasegawa et al., 2006] can reasonably be explained.Further, the wavelength/period of the KH waves is deter-mined by the nature of magnetosheath ULF fluctuationsthat, by interacting with the magnetopause, can be modeconverted to compressional surface waves and/or Alfvenwaves in the dayside LLBL to serve as seed perturbationsfor the KHI.

5.2. Development of the KH Waves

[40] Here we discuss the growth time of the KHI and howit has developed along the magnetopause to generate thevortices as observed by Cluster. First, it must be stressedthat the dominant KH mode, which had a period �200 s(Figure 6) and the wavelength >4 � 104 km (Figure 7) at theCluster location (�1900 MLT), is unlikely to be the fastestgrowing mode expected from the estimated full width�1000 km of the dayside velocity shear layer (Figure 4).According to the linear theory of the MHD KHI [e.g.,

Figure 12. Schematic of the equatorial magnetosphereshowing how KH waves with wavelengths longer thanpredicted by the linear theory can be excited undernorthward IMF (see text for details).


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Walker, 1981; Miura and Pritchett, 1982], the wavelengthfor the most unstable mode is about eight times the initialtotal thickness of the shear layer, i.e., �8000 km. The waveperiod corresponding to this wavelength is �70 s (8000 km/115 km/s, see caption for Figure 4). Therefore, the domi-nant-mode period �200 s (wavelength >4 � 104 km)contradicts the fastest growing mode, even if its wavelengthwas somewhat elongated as a consequence of spatialdevelopment of the KHI [Manuel and Samson, 1993;Claudepierre et al., 2008] and/or as the flow speed on themagnetosheath side increased with downtail distance fromthe wave excitation site. The dominance of �200 s periodmode rather than the fastest growing mode would thus bedue to strong excitation by the fluctuations in the daysideLLBL, presumably mode converted from compressionalmagnetosheath fluctuations (Figure 12 and section 3.3).[41] As for the formation mechanism of the smaller

vortices of length �2 RE embedded within one dominant-mode wavelength (Figure 7), there are at least three possi-bilities. One is a cascade process by which a parent vortexmay break up into smaller vortices. Such breakup mayoccur through secondary instabilities induced within anMHD-scale rolled-up KH vortex [Nakamura et al., 2004;Matsumoto and Hoshino, 2004], although magnetic fieldcomponents in the wave vector direction may well suppressthose instabilities. Smaller vortices may also result from 3Dcoupling of the KHI to KH-stable regions when the wave-length of parent vortices is comparable to, or shorter than,the latitudinal width of the KH-unstable region [see Takagiet al., 2006, Figure 3]. The fact that pressure perturbationscorresponding to the smaller vortices (with period �100 s)were not clearly seen for the intervals used in the recon-structions (Figure 6) may indicate that the force balance inthe vortices was affected by 3D effects, such as magnetictension arising in the nonlinear phase [Takagi et al., 2006].Another possibility is that those smaller vortices are infact of the fastest growing mode, possibly excited nearthe Geotail longitude, provided that the wavelength(�8000 km) for that mode was roughly doubled or tripledduring the course of spatial development along the flankmagnetopause. If this is the case, one may argue that thedominant KH mode could have resulted from coalescenceof the fastest growing mode vortices. However, it is unlikelythat such vortex coalescence occurs regularly such that thedominant-mode period �200 s is maintained over tens ofminute as observed (Figure 6), because there would be nopreference for the adjacent (leading or trailing) vortex withwhich a vortex is about to merge.[42] According to KHI simulations with periodic bound-

aries in the wave vector direction [e.g., Takagi et al., 2006],it takes about 5 min for the fastest growing KH wave to rollup, with the velocity jump across and initial total thicknessof the shear layer of 200 km/s and 1000 km, respectively.Given the full width of the dayside shear layer �1000 km(Figure 4) and that the initial (dayside) wavelength for thedominant KH mode was a few times the fastest growingmode wavelength (�8000 km), the dominant mode wouldtake about 10 min to form a rolled-up vortex, with itsgrowth rate roughly half that for the fastest growing mode[e.g., Miura and Pritchett, 1982]. This growth time iscomparable to the time taken for KH waves to propagatefrom 1500 MLT to 1900 MLT along the magnetopause, with

the separation between Geotail and Cluster of �15 RE

(Figure 1) and the KH-wave phase speed �150 km/s(remember that the estimated phase speed is �115 km/s atGeotail and �211 km/s at Cluster). It thus seems reasonableto conclude that the KH vortices detected by Cluster gotexcited and began to grow around 1500 MLT. The conclu-sion is also consistent with our findings that the KHIcondition (inequality (1)) is only marginally satisfied forthe postnoon magnetopause, and that only a weak surfacewave activity was seen in the dayside LLBL (section 3).

5.3. Formation Mechanism of the Ion-ScaleCurrent Sheet

[43] Here we discuss how the current sheets of magneticshear �60�, detected at the trailing edges of the vortices(section 4.2), were generated. In 2D situations studiedextensively by simulations, there exist a couple of mecha-nisms whereby thin current sheets that may facilitate recon-nection can be created in the course of KHI development.When no antiparallel magnetic field components along theKH wave vector exist across the velocity shear layer, roll-upof the vortices and resulting stretching of field lines generatecurrent sheets that are fully embedded in either a magneto-sheath or magnetospheric plasma [e.g., Otto and Fairfield,2000; Nykyri and Otto, 2001]. Reconnection induced in thistype of current sheet is termed Type-II by Nakamura et al.[2008] and involves magnetospheric or magnetosheath fieldlines only. This mechanism cannot be responsible for thecurrent sheets in our event, because they were detected atthe interface between magnetospheric and magnetosheathplasmas, namely at the magnetopause (Figures 8a and 8b).[44] Another type of thin current sheet formation and

resultant reconnection was studied, e.g., by Liu and Hu[1988], Pu et al. [1990], Chen et al. [1997], and Nakamuraet al. [2006, 2008], and occur when antiparallel fieldcomponents exist across the shear layer, i.e., when a currentsheet is collocated with the velocity jump. This type ofreconnection is termed Type-I [Nakamura et al., 2008], andoccurs often near the hyperbolic point in an MHD-scalevortex where vortical flows squeeze and thin the currentsheet (Figure 9a). If reconnection occurs at multiple sites onthe interface or in the neighboring vortices as well, magneticislands are formed wherein plasmas can be mixed. Loca-tionwise, this mechanism may seem consistent with ourobservations, but we argue that the polarity of the magneticfield component in the wave vector direction was the sameacross the shear layer when the KHI just got excited.[45] Figure 13 shows three LMN components of the

magnetic field for the interval 1900–2130 UT as a functionof ion density, where LMN coordinates are based on themodel magnetopause [Roelof and Sibeck, 1993] and thus aredifferent from those used in section 4 for a particularboundary crossing (Figures 8 and 10). The normal compo-nent BN is on average zero as expected, but the data pointsare widely scattered, reflecting a corrugated magnetopausesurface in the nonlinear phase of the KHI. Note that BM wasnegative in both low-density magnetospheric and high-density magnetosheath regions, while it was occasionallypositive in the transition region characterized by the densityn = 2–6 cm�3. Considering that the KH waves propagatedapproximately in the �M direction, it is inferred that thefield components on the two sides of the boundary initially


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had the same polarity in the wave vector direction. Thepositive excursions of BM in the transition region, respon-sible for the current sheets at the vortex edges, are exactlywhat can result from the mechanism as discussed byHasegawa et al. [2004a] and Takagi et al. [2006]; bendingor deformation of magnetosheath field lines immediatelyoutside the magnetopause is caused by 3D growth of theKHI in the magnetospheric configuration where a KH-unstable region (the plasma sheet) is sandwiched by twoKH-stable regions (north and south lobes). The L componentwas positive throughout the analyzed interval, consistentwith the extended period of northward IMF. Note that BL

was generally larger on the magnetosheath than on theplasma sheet side, but had amaximum in the transition regionwhere n � 3 cm�3. This maximum in BL seems consistentwith draping of the IMF over the undulating magnetopause[Chen et al., 1993; Kivelson and Chen, 1995], or may be dueto compression of the field by vortical flows.[46] In conclusion, the magnetic perturbations, leading to

the current sheet formation, were most likely caused by the

3D development of the KHI in the magnetospheric geom-etry [Hasegawa et al., 2004a; Takagi et al., 2006]. Wenote that with this mechanism, magnetic shear can begenerated exactly at the magnetopause, even though theboundary has no magnetic shear initially; the magneticshear �60� at Cluster, which is higher than seen byGeotail on the dayside, would be due to this 3D mecha-nism. Significant magnetic shears are usually produced inregions away from the most KH-unstable latitude, but at acertain latitude both finite magnetic shear and filamentarydensity structures as evidence for overturning of KH wavescan be found, as seen in a 3D MHD simulation byHasegawa et al. [2004a].

5.4. Formation Mechanism of the Flank LLBL

[47] It is noted that the density (�2 cm�3) in the dusk-flank LLBL encountered by Cluster was comparable to that(�3 cm�3) in the dayside LLBL which appeared to haveformed via high-latitude reconnection (section 3.3). Basedon this, we argue that the magnetosheath-like plasmas seenin the flank LLBL may not simply be due to tailwardconvection along the LLBL of those injected on the dayside.First, suppose that flux tubes in the dayside LLBL wereclosed and already dipole-like, i.e., close to an equilibriumafter relaxation of field line kinks at the high-latitudereconnection sites. Then, the volume of a magnetosphericflux tube at Cluster would be roughly three times that atGeotail, because the field magnitude at Cluster (�20 nT)was about half of that at Geotail (�40 nT) and thegeocentric distance of Cluster was about 1.5 times that ofGeotail. Accordingly, simple expansion and advectionof the dayside flux tube would have resulted in the densityof only �1 cm�3 at Cluster.[48] Suppose, then, that the dayside flux tubes were those

recently closed by dual high-latitude reconnection near thecusps. In this case, a significant fraction of magnetosheathplasmas that were originally on an IMF-type flux tubewould flow into magnetosphere-side portions of the closedflux tube which were previously of lobes or of plasma sheet[Onsager et al., 2001] and hence were much less dense thanin the magnetosheath, although some minor fractions,reflected at the RD magnetopause or mirrored at lowaltitudes, may flow equatorward from both hemispheres.Therefore, if an approximate equilibrium is reached at aboutthe same longitude (�1500 MLT), the resulting equatorialdensity would be at most the original value (�3 cm�3). Theobservation thus implies that additional entry of solar windplasmas occurred across the dusk-flank magnetopausebetween 1500 and 1900 MLT. A similar conclusion wasreached from investigation of energy space distributions ofboundary layer electrons in another event under northwardIMF [Taylor et al., 2008].[49] There exist at least two mechanisms that can become

efficient as consequence of the KHI growth and wherebysolar wind plasmas can be transported into the magneto-sphere: reconnection within or in the vicinity of KHvortices, as discussed by Otto and Fairfield [2000], Takagiet al. [2006], and Nakamura et al. [2006, 2008], anddiffusive transport through KAWs [Hasegawa and Mima,1978; Johnson and Cheng, 1997]. However, the formerdoes not seem to be the dominant entry mechanism in thepresent event. This is because reconnection identified at the

Figure 13. Three components in LMN coordinates of themagnetic field recorded by C1 and C3 for the interval1900–2130 UT on 20 November 2001. The axes used are asfollows: L = (0.0, 0.1469, 0.9891), M = (0.8823, �0.4656,0.0692), and N = (0.4707, 0.8727, �0.1297) in GSM,taking into account that Cluster was on the southward sideof equator (z � �3 RE). This coordinate system is differentfrom the local one used in Figures 8 and 10, determined forparticular boundary traversals.


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edge of the vortices had an incipient nature (section 4.3) andthus would not have caused large-scale transport. Moreover,as shown in Figure 14, ion velocity distributions taken inthe flank LLBL do not have features characteristic ofreconnection, such as D-shaped distributions [e.g., Fuselier,1995] and field-aligned beams [Nishino et al., 2007] (notehowever that D-shaped distributions are not alwaysobserved even in clear reconnection jets [Phan et al.,2004]). In fact, magnetosheath-like ions heated morestrongly in the perpendicular than parallel direction, evidentfrom comparison between Figures 14a and 14b at velocities<400 km, are rather consistent with the latter KAW mech-anism [Johnson and Cheng, 2001]. KAWs can be excitedvia mode conversion from KH surface waves (internaldriving) [e.g., Chaston et al., 2007] or from magnetosheathcompressional waves (external driving) [Johnson andCheng, 1997]. It must be stressed that even though exter-nally driven KAWs initially have the transverse wavelengthmuch longer than the normal wavelength (kt� kn) as on thedayside (section 3.3), strong gradients in density and/ormagnetic field in the developed vortices can refract KAWssuch that the normal and transverse scales can becomecomparable (kt � kn). In this case, the KAW diffusioncoefficient could be large (109–1010 m2 s�1) even for

fluctuation levels as seen in the dayside LLBL, consistentwith estimates by Chaston et al. [2008].[50] In summary, the simultaneous Geotail and Cluster

observations of the LLBL suggest that additive entry ofsolar wind plasmas across the flank magnetopause occurred,presumably via KAW-associated diffusion [Hasegawa andMima, 1978; Johnson and Cheng, 1997] which can beenhanced by the KHI growth [e.g., Chaston et al., 2007],or via reconnection at a remote location unidentified byCluster [e.g., Fuselier et al., 2002]. In the latter scenario, theadditional entry would have occurred along field lines whilethey remained open, namely, during part or all of the timethey convected from the Geotail to Cluster location. Notealso that we cannot exclude the possibility that full-blownreconnection expected further downstream of Cluster mayplay a role in plasma transfer across more distant tailmagnetopause.

6. Summary

[51] We have examined the magnetopause and its bound-ary layer encountered at low latitudes by Geotail at 1500MLT and by Cluster at 1900 MLT on 20 November 2001,when the IMF remained northward and antisunward for an

Figure 14. Ion velocity distributions (a) in the boundary layer and (b) in the magnetosheath, taken byC3/HIA during the interval shown in Figure 8. Figures 8a (bottom) and 8b (bottom) show cuts of thedistribution function in the directions parallel (black) and perpendicular (green) to the magnetic field,transformed into the frame of bulk flow.


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extended period of time. The event was studied with a viewto revealing the excitation process and MHD- and ion-scaleaspects of the KHI that turned out to grow nonlinearly toform rolled-up vortices at the Cluster location (x = �4 RE)[Hasegawa et al., 2004a]. Additionally, the formationmechanism was discussed of the LLBL present at both1500 and 1900 MLT. Our conclusions and interpretationsare summarized as follows:[52] 1. No significant activity of magnetopause surface

waves was detected at 1500 MLT, consistent with thecondition for the linear KHI growth (inequality (1)) beingonly marginally satisfied across the postnoon magneto-pause. However, fluctuations in the dayside LLBL of thetotal pressure and of the transverse magnetic field compo-nent both had appreciable power at a period of �200 s.Since this period is nearly equal to that of the KH wavesdetected at 1900 MLT, it is inferred that these daysidefluctuations played a role as seed perturbations in theexcitation of the KHI. The KHI condition most likelybecame satisfied as a consequence of the LLBL formationvia high-latitude reconnection.[53] 2. The KH wavelength (>4 � 104 km) for the

dominant mode at 1900 MLT is much longer than that(�8000 km) for the fastest growing mode predicted by thelinear theory [e.g., Miura and Pritchett, 1982] from the totalthickness (�1000 km) of the dayside velocity shear layer. Itis thus suggested that the KH waves in the present eventwere not the fastest growing mode, but driven by thefluctuations as observed in the dayside LLBL. The largevortex length at the flank may also be due to elongation ofthe wavelength as the KHI developed spatially along theflank LLBL [Manuel and Samson, 1993; Claudepierre etal., 2008], and/or as the magnetosheath flow speed andhence the KH-wave phase speed increased with downtaildistance from the KHI onset site.[54] 3. The streamline structure from the Grad-Shafranov-

like reconstruction and wavelet spectra of the total pressurein the flank LLBL are consistent with the beginning at�1900 MLT of forward and/or inverse cascade of energy(breakup and/or coalescence of KH vortices). It indicatesthat the KHI seen by Cluster was fully in the nonlinear stagewhere neighboring vortices may interact with each other.The smaller vortices of length �15000 km embedded withinone dominant-mode wavelength (Figure 7) might in fact beof the fastest growing mode, rather than those broken up.This is because the wavelength of the smaller vortices canbe explained by elongation of the fastest growing modewavelength when the KHI grows spatially and the magneto-sheath flow speed increases with downtail distance.[55] 4. Current sheets whose full width was a few times

ion inertia length (�100 km) and whose magnetic shear was�60� were detected at the sunward facing edge of therolled-up KH vortices. Since magnetic shear across thedayside magnetopause at 1500 MLT was smaller (<40�),we infer that the magnetic shear at 1900 MLT arose from theKHI development presumably through the 3D mechanismproposed by Hasegawa et al. [2004a] and Takagi et al.[2006]. The thinness of the ion-scale current sheet is mostlikely due to local compression by vortical flows directedtoward the hyperbolic point in the vortex [Nakamura et al.,2004, 2008].

[56] 5. Signatures consistent with the occurrence ofmagnetic reconnection in the ion-scale current sheet werefound in the form of (1) Alfvenic outflow jet within abifurcated current sheet, (2) nonzero magnetic field com-ponent normal to the current sheet, whose fluctuations arealso suggestive of the formation and propagation of meso-scale magnetic flux ropes (of size �1000 km), (3) enhance-ment of field-aligned electrons at energies comparable toand more than 50 eV, consistent with acceleration by thereconnection electric field, and (4) density in the currentsheet nearly equal to that on the magnetosheath side,consistent with local entry of magnetosheath plasmasthrough reconnected field lines.[57] 6. A prominent LLBL characterized by the coexis-

tence of magnetosheath and magnetospheric ions existed at1500 MLT. Since no strong KH-wave activity was found,the formation of this LLBL cannot be due to plasmatransport through the nonlinear KHI. The most likelyformation mechanism of this dayside LLBL is high-latitudereconnection either poleward or equatorward of the cusp,possibly in both hemispheres [Song and Russell, 1992;Øieroset et al., 2008]. The Walen relation being fairly wellsatisfied across the postnoon magnetopause, the nearlycomplete absence of magnetospheric hot electrons, abrupt(rather than gradual) changes in the velocity as well asdensity in the LLBL (Figures 3a and 3b), all support thisreconnection scenario, rather than diffusive entry scenarios.[58] 7. The density (�2 cm�3) in the flank LLBL at

1900 MLTwas comparable to that (�3 cm�3) in the daysideLLBL at 1500 MLT, despite that the flux tube volumeat 1900 MLT would be considerably larger than that at1500 MLT with a dipole-like configuration. This fact sug-gests that additional entry of solar wind plasmas occurred viathe dusk-flank magnetopause between 1500 and 1900 MLT.Since local reconnection at the edge of a rolled-up KHvortex, identified from the Cluster observations, wasincipient and hence would not have led to the LLBL at1900 MLT, the additive entry across the flank magnetopausecould have been due to diffusive transport associated withkinetic Alfven waves mode converted from the KH waves[Chaston et al., 2007] or to remote reconnection unidentifiedby Cluster which may or may not be associated with the KHI[e.g., Fuselier et al., 2002].[59] Finally we emphasize that an MHD-scale rolled-up

vortex in a collisionless plasma is an intriguing systemwherein cross-scale coupling may play a crucial role: roll-upof the vortex leads to the generation of magnetic shear andthinning of current sheet, followed by reconnection in thethinned current sheet, eventually leading to outflow jets andelectron acceleration. The jets may in turn alter flowpatterns in and around the parent vortex [Nakamura andFujimoto, 2008], possibly creating the path along whichplasmas transferred across the magnetopause can be carriedover a distance comparable to the vortex width by convec-tive and/or field-aligned flows. Vortex-induced reconnectionis also akin to reconnection in a turbulent plasma, demon-strated recently by Retino et al. [2007], in that thin currentsheets subject to reconnection form as a consequence oflarger-scale dynamics.

[60] Acknowledgments. The authors thank Alban Rochel for provid-ing the Cluster/WHISPER data, T.-D. Phan for producing plots of ion


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velocity distribution, and T. Nagai for allowing our use of the magneticfield data from the Geotail/MGF instrument. H.H. thanks C. C. Chaston forhelpful discussion on diffusion processes and Alfven waves. The high-resolution FGM data were provided via the Cluster Active Archive http://caa.estec.esa.int/. The software for wavelet analysis was downloaded fromhttp://paos.colorado.edu/research/wavelets/ [Torrence and Compo, 1998].Work by B.U.O.S. and W.-L.T. was supported by NASA grant NNG-05GG26G to Dartmouth College. The CIS activity at CESR was supportedby a CNES grant. The WHISPER support at CETP was provided by CNESunder contract 60015.[61] Zuyin Pu thanks Jay Johnson, Stefan Eriksson, and another

reviewer for their assistance in evaluating this paper.

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��M. Andre, Y. Khotyaintsev, and A. Vaivads, Swedish Institute of Space

Physics, Uppsala, SE-75121, Sweden.P. Canu, Centre d’Etude des Environnements Terrestre et Planetaires,

IPSL, CNRS, 38-40 rue du General Leclerc, F-92131 Velizy, France.

M. Fujimoto, H. Hasegawa, T. K. M. Nakamura, Y. Saito, and Y. Seki,Institute of Space and Astronautical Science, JAXA, 3-1-1 Yoshinodai,Sagamihara, Kanagawa 229-8510, Japan. ([email protected])H. Reme, Centre d’Etude Spatiale des Rayonnements, 9 Avenue du

Colonel Roche, B.P. 4346, F-31028 Toulouse, France.A. Retino, Space Research Institute, Austrian Academy of Science,

Schmiedlstr. 6, A-8042, Graz, Austria.S. J. Schwartz, Blackett Laboratory, Imperial College, Prince Consort

Rd., London SW7 2BZ, UK.B. U. O. Sonnerup, Thayer School of Engineering, Dartmouth College,

Hanover, NH 03755, USA.W.-L. Teh, Laboratory for Atmospheric and Space Physics, University of

Colorado at Boulder, 1234 Innovation Dr., Boulder, CO 80303-7814, USA.


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