Dispersive Alfvén Waves Observed by Cluster at the Magnetopause

Transcription

1 Dispersive Alfvén Waves Observed by Cluster at the Magnetopause K. Stasiewicz 1,2, Y. Khotyaintsev 1, G. Gustafsson 1, A. Eriksson 1, and T. Carozzi 1 1 Swedish Institute of Space Physics, Uppsala, Sweden 2 Space Research Centre, Warsaw, Poland Camera-ready Copy for Annales Geophysicae Manuscript-No Offset requests to: K. Stasiewicz, ks@irfu.se

2 Annales Geophysicae (21) 25:1 6 Dispersive Alfvén Waves Observed by Cluster at the Magnetopause K. Stasiewicz 1,2, Y. Khotyaintsev 1, G. Gustafsson 1, A. Eriksson 1, and T. Carozzi 1 1 Swedish Institute of Space Physics, Uppsala, Sweden 2 Space Research Centre, Warsaw, Poland Received: March 21 Accepted:??? Abstract. We analyze ELF turbulence (.3 1 Hz) observed by Cluster at the magnetopause layer during multiple, 12 magnetopause crossings on a single event, December 31, 2, 9-16 UT. Waves below the proton gyrofrequency (f ci.3 Hz) are identified as kinetic Alfvén waves, while waves (.3-1 Hz) between the ion gyrofrequency and the lower hybrid frequency are consistent with drift-alfvén waves driven by strong density gradients. These waves exhibit an electrostatic character and from their dispersive properties we infer that they may have perpendicular scales less than ion gyroradius. Due to rapid convective flows at the magnetopause boundary the short wavelength structures are Doppler shifted and appear as broadband waves in satellite data. The Cluster observations show that the dispersive Alfvén waves at the magnetopause layer have electric field magnitudes of 5 mv/m and spectral peak power of 1 6 (V/m) 2 /Hz. These waves are expected to play an important role in the processes of energy/mass transport and diffusion across the magnetopause. 1 Introduction Low-frequency turbulence extending from well below the ion gyrofrequency f ci up to the lower hybrid frequency f lh is of considerable interest for space plasma research because it contains a large wave power, but its nature and origin is not well understood (e.g. Stasiewicz et al., 2a). The ELF turbulence is observed by satellites in all active regions of the magnetosphere, and in particular at the magnetopause layer, where it is expected to play an important role in the processes of reconnection, diffusion, mass and energy transport (see e.g. Sibeck et al., 1999). The relevant frequency range f ci f lh is.1 2 Hz for typical conditions at the magnetopause boundary layer (B 5 3 nt). The Cluster mission provides new exciting opportunities to study these processes at four spatial points simultaneously by four spacecraft re- Correspondence to: K. Stasiewicz, ks@irfu.se ferred to as C1, C2, C3, C4. In this paper we analyze measurements from the Electric Fields and Waves (EFW) instrument (Gustafsson et al., 1997, 21), which uses two pairs of spherical electrostatic probes deployed on wire booms in the spin plane to measure the electric field. The probe-to-probe separation is 88 m. For the event presented in this study, a sampling rate of 25 samples/s with an anti-aliasing filter at 1 Hz was used for the electric field components. We also use measurements (5 samples/s) of the potential of the spherical probes with respect to the spacecraft, which is a measure of the plasma density (Pedersen, 1995; Pedersen et al., 21). In our analysis of electromagnetic fluctuations we also use data from the fluxgate magnetometer (Balogh et al., 1997). 2 Magnetopause crossings of December 31, 2 In Fig. 1 we show spacecraft potential measured by C3 during 7 hours (9-16 UT) on December 31, 2. Spacecraft potential (here shown with a reversed sign) represents an approximately logarithmic measure of the plasma density. It also depends weakly on the plasma temperature (Pedersen, 1995; Escoubet et al., 1997). The reversed sign for potential is used in the plot because this representation looks like a logarithmic plot of the plasma density. The spacecraft potential of 5 V (25 V) on the magnetosheath (magnetospheric) side corresponds to the plasma density of 1 (.1) cm 3, respectively. In the analyzed case we registered over 12 boundary crossings. Because the satellites move at a speed of 3 km/s, which is much less than convective flows at the boundary ( 5-3 km/s), multiple magnetopause crossings are produced mainly by rapid boundary motions induced both by direct forcing of the interplanetary magnetic field (IMF) and solar wind pressure, and by surface waves on the boundary. Strictly speaking, the magnetopause is defined as a current layer separating the terrestrial and IMF regions. This current layer is clearly seen when there is a significant shear angle between IMF and the terrestrial fields. Because it separates dense magnetosheath plasma from tenuous magneto- 1

3 2 Stasiewicz et al.: Cluster observations of dispersive Alfvén waves [V] 1 2 C [V] Time [min] from 9 Fig. 1. Spacecraft potential (reversed sign) measured by C3 spacecraft on December 31, 2 during 9-16 UT. Low values correspond to.1 cm 3 on the magnetospheric side and high values to 1 cm 3 in the magnetosheath side. During this case we registered over 12 crossings of the median value of 15 V (n.5 cm 3 ). spheric plasma, it is usually accompanied by density gradients. In this paper we do not analyze the magnetometer data and all magnetopause crossings are meant here as crossings of steep density gradients as those shown in Fig. 1. The data in Fig. 1 represent over 12 crossings of a median value of 15 V for spacecraft potential, which corresponds to the plasma density of.5 cm 3. A similar case of multiple magnetopause crossings by Cluster on the dusk flank has been recently analyzed by Bale et al. (21) who found that the magnetopause speeds range from 2 to 2 km and thicknesses from 2 to 12 km. The satellite orbit for the present case is shown in Fig. 2, superimposed on the magnetopause model by Shue et al. (1998). The orbit interval is shown in GSE coordinates with markers every 1 hour from 9 to 16 UT. At the time 9 UT the position of spacecraft C3 was (3, 11, 9) R E GSE and it advanced to (6, 15, 7) at time 16 UT. The separations of four spacecraft were between 4 1 km. Two magnetopause models are shown for two solar wind pressure parameters 1 and.3 npa. The Wind spacecraft, which monitors solar wind parameters was at a large distance from the Earth (Y GSM 25 R E ) and recorded a steady solar wind pressure of 1 npa. The IMF measured on Wind was also quite steady with total B 5 nt and B z close to zero, with some northward excursions. The particle instruments on Cluster were not operating on this particular day, so we cannot verify the local plasma pressure conditions. The positions of first magnetopause crossings at time 93 UT are consistent with the model, but the crossings at the end of the time interval would require much smaller dynamic pressure (.3 npa) to be consistent with the model. If the crossings are produced by surface waves, it would require large amplitude excursions of ±1.5 R E from the average model position. sqrt(y 2 + Z 2 ) [R E ] X [R E ] Fig. 2. Cluster-3 trajectory during , 9-16 UT with tick marks every 1 hour. Superimposed is also a magnetopause model according to Shue et al. (1998), for two solar wind pressure conditions 1 and.3 npa (see text). 3 ELF turbulence as drift-kaw We shall now focus on some details of the many magnetopause crossings from the case in Fig. 1. Let us examine the electric field data shown in Fig. 3. The curve (scp) with the potential shows that the spacecraft was in a region with high density plasma (magnetosheath) when an outward boundary motion moved the satellite into the magnetosphere and then back toward the magnetosheath at 129 UT. The structure at 126 UT corresponds to a partial inward/outward boundary motion. Using data from the four spacecraft we can estimate the boundary speed to 17 km/s and thickness of the density ramp to 1 km for the first crossing. The front normal was directed about 115 o from the GSM Ox axis. The traces of the satellite potential for all spacecraft, which were used to determine the boundary motion and thickness are shown in Fig. 4. It is interesting to see that the first satellite (C4) that

4 Stasiewicz et al.: Cluster observations of dispersive Alfvén waves 3 ScP: V Ey: mv/m Ey ScP C3: time [min] from 1 UT Fig. 3. Electric field component and spacecraft potential at a sequence of magnetopause crossing. Strong electric field turbulence is co-located with the boundary crossings (density gradients). crosses the boundary observes a density wave with a period of 1 s, which is not seen by the second satellite (C2) which is 2 km apart in the radial direction. The electric field in Fig. 3 is quite regular on both the magnetospheric and magnetosheath sides but exhibits strong turbulence during the boundary crossings. Turbulent fields of 5 mv/m are larger than the dc field of 2 mv/m, and are clearly co-located within the density gradients. The electric field is shown in this paper in the despun satellite coordinates with the z-axis along the satellite spin axis (roughly Oz GSE), the x axis in the spin plane toward the Sun (roughly Ox GSE), and the y axis completes the right hand system (roughly Oy GSE). The power spectrum of the electric field measured around 126 UT is shown in Fig. 5. There is a large wave power between the proton cyclotron frequency f ci =.25 Hz and the lower hybrid frequency f lh =11Hz, whose origin is a subject of controversy. The power spectrum of Fig. 5 extends to higher frequencies, which are covered by STAFF (Cornilleau et al., 1997) WHISPER (Decreau et al., 1997) and WBD (Gurnett et al., 1997) instruments, but generally with falling power at higher frequencies. We would like to emphasize that, generally, waves mea V C4 V=17 km/s D=1 km C1 C2 C seconds from 12 Fig. 4. Spacecraft potential for all satellites at the magnetopause crossing at 122 in Fig. 3. The thickness of the magnetopause (the density ramp) is estimated to 1 km and speed to 17 km/s. sured by a satellite are observed not at the true frequency ω but at an apparent frequency ω ω = ω k v (1) where v is the velocity of the medium (plasma) with respect to the satellite. At the topside ionosphere the convective plasma flows (v E = E B/B 2 ) are generally smaller than the satellite speed v s and therefore v v s 7 km/s. On the other hand, at the magnetospheric boundary layers, the convective plasma flow speeds are much larger than the satellite speed and therefore v v E 15 km/s. At the boundary layer, typical characteristic spatial scales are: ion gyroradius ρ i 1 km, ion inertial length λ i = c/ω pi 1 km, and inertial electron length λ e = c/ω pe 2 km. The ion acoustic gyroradius (ρ s =(T e /m i ) 1/2 /ω ci, at the electron temperature) is 2-3 times smaller than ρ i = (T i /m i ) 1/2 /ω ci because T i T e. Observed by a moving satellite, plasma wave structures at, say, ω /2π <f ci.3 Hz, and with perpendicular scales λ on the order of ρ i λ i, or λ e, immersed in the convective flows v 1 km/s would be seen as wave structures at an apparent frequency of 1, or 5 Hz, respectively. Thus, broadband waves ω can be produced by time domain waves ω as well as by Doppler shifted spatial structures k v. By spatial we do not mean purely static structures (ω =), but waves that fulfill the condition ω < k v, i.e. dominated by Doppler shift. We shall now examine the hypothesis that the broadband spectrum in the frequency range.1 1 Hz, i.e. between the ion gyrofrequency and the lower hybrid frequency, may be produced by Doppler shift of short length waves at frequency below f ci. Recent analyzes of electromagnetic measurements at ionospheric altitudes on Freja (Stasiewicz et al., 2b; Stasiewicz and Khotyaintsev, 21) and at high latitude boundary layer on Polar (Stasiewicz et al., 21) indicate that broadband turbulence could be attributed to short perpendicular scale dispersive Alfvén waves which are Doppler shifted to higher frequencies either by the satellite, or the plasma medium motion. Because the ordering ρ i > ρ s λ e the dispersive properties of waves will be determined by kinetic effects related to finite ion Larmor radius and not by the inertial electron effects. Distinction between true time-domain waves ω and Doppler shifted spatial waves k can be done directly with multiple probe measurements, or indirectly with the help of the dispersion relation. Specifically, kinetic Alfvén waves (KAW) which are expected at the magnetospheric boundary have the polarization dispersion (Stasiewicz et al., 2a) δe y δb x = v A (1 + k 2 ρ2 i ) [1 + k 2 (ρ2 s + ρ 2 v i )]1/2 A 1+k 2 ρ2 i, (2) where ρ i is the ion gyroradius ( 1 km) and k the perpendicular to B wave vector. In the above approximation we have used a typical experimental condition T i /T e 1 which implies ρ i >ρ s. Note that in the derivation of (2) a Padé approximation has been used for the Bessel function

5 4 Stasiewicz et al.: Cluster observations of dispersive Alfvén waves (V/m) 2 /Hz Ey power spectrum at 126 ut Scp: V Frequency [Hz] Fig. 5. Electric field power at time 126 in Fig. 3 (with argument k 2 ρ2 i ) in the ion dispersion relation (see discussion in Stasiewicz et al. (2a, page 435). Consequently, equation (2) is valid also for large ion gyroradius (high β- plasma), and not only in small argument limit (k ρ i 1), as in the original derivation of Hasegawa (1976) with 3/4 in front of k 2 ρ2 i. For waves with λ smaller than ρ i this ratio may be much larger than the Alfvén velocity v A and such waves would be identified as electrostatic, non-alfvénic type. The separation of the Cluster spacecraft is generally larger than the ion gyroradius in the dayside magnetosphere and therefore the spacecraft configuration cannot be directly used to resolve structures smaller than ρ i. However, if there are waves with broad k spectra, they should be Doppler shifted and observed as broadband waves. Thus, KAW spectrum k described by equation (2) should be observed on a spacecraft as a frequency spectrum δe y δb x v A πρi f v cos θ 2, (3) where f = k v/2π is an apparent Doppler frequency in the satellite frame, θ is the angle between the k -vector and the velocity v, and brackets represent a spatial average. Strictly speaking, the above equation (Stasiewicz et al., 2b, 21) should be complemented by an additional term resulting from the Galilean electric field transformation E = E + v B, where v is speed of the medium with respect of the satellite. If B is predominantly in the z direction, then E y = E y v x B z. Equation (3) should be thus complemented with an additional term δ(v x B z ) δb x 1. This additional term should be negligible in case when the velocity v x is much smaller than the Alfvén speed v A, or when the magnetic field variations are mainly transverse (δb z /δb x 1) as for example in shear Alfvén waves. To verify this relation, we use data from Fig. 6, which show the spacecraft potential and perpendicular components of the electric field. Again a clear correlation can be seen between the density gradient and the electric field turbulence. A clear correlation between the electric and magnetic components (not shown here) on a macroscopic scale is observed in the boundary layer at UT. A general observation is that the magnetic field is less structured at higher fre- Ey mv/m C3: minutes from 1 UT Fig. 6. Spacecraft potential and electric field component. quencies (smaller scales) than the electric field, which is consistent with dispersions (2) and (3). Also, high time resolution magnetometer measurements on Equator-S (Lucek et al., 21) do not show much structures at higher frequency, except at the lower hybrid frequency. In order to test equation (3) we compute the δe y /δb x ratio as a function of frequency in the indicated interval and show the result in Fig. 7. The ratio of the power spectra can be well fitted by equation (3) with v A 35 km/s, ρ i 8 km, v 15 km/s, and cos θ 1. The obtained value for v A would correspond to B 18 nt and n 1 cm 3, which is consistent with local measurements. The convection speed v E fluctuates between 7 2 km/s within the magnetopause boundary at 155:3 156:1 and drops to v E =5 km/s at 156:3 in Fig. 6. The result of this analysis corroborates earlier findings (Stasiewicz et al., 2b, 21) that broadband ELF turbulence observed in different regions of the magnetosphere represents most likely the Doppler shifted spatial turbulence of dispersive Alfvén waves. Dispersions (2)-(3) and Fig. 7 show that the δe y /δb x ratio increases by a factor of 1 from km/s C3: δ E/δ B for UT Frequency [Hz] 35*sqrt(1+12*f 2 ) Fig. 7. Ratio δe y/δb x for the time interval in Fig. 6.

6 Stasiewicz et al.: Cluster observations of dispersive Alfvén waves 5 a: Ey Bx correlation Freq. [Hz] rd b: Ey Bx phase Freq. [Hz] Fig. 8. Cross-correlation spectrum (a) and phase (b) of signals E y-b x for the same time interval as in Fig. 7. Waves below the proton gyrofrequency (.3 Hz) are clearly KAW..3 to 3 Hz. Considering that the electric field power (Fig. 5) decreases also by a factor of 9 (amplitude by a factor of 3) then the expected magnetic field amplitude at an (apparent) frequency 3 Hz should be ca 3 times smaller than the magnetic field amplitude at.3 Hz, which could explain the diminishing amplitude of magnetic perturbations at higher frequencies. An additional confirmation of the Alfvénic character of the electro-magnetic fluctuations can be obtained from the crosscorrelation spectrum between the electric and magnetic field components, which is shown in Fig. 8. High correlation, and zero phase shift is seen in the perpendicular components E y - B x at frequencies below the proton gyrofrequency (f ci.3 Hz). Thus, the measurements are consistent with kinetic Alfvén waves at frequencies below f ci. The diminishing amplitude of magnetic fluctuations and probably a random distribution of Doppler shifts could account for lack of E y -B x correlation at higher frequencies in Fig. 8. We should mention here that the frequency range.25 1 Hz is unreliable for scientific analysis, as it suffers from parasite frequencies related to the spin frequency of.25 Hz and its harmonics.5 and 1 Hz. For example, a large peak at 1 Hz in Fig. 7 is related to instrumental quarter of the spin period, which affects the electric field measurement. 4 Discussion There is clearly a lot of free energy to generate KAW at the magnetopause layer. One possibility is large scale surface waves (which in fact produced 12 magnetopause crossings in the analyzed case) that can couple to KAW (Hasegawa, 1976; Lee et al., 1994; Johnson and Cheng, 1997). Another free energy source is related to strong density gradients. Laboratory observations that have a direct bearing on the observation by spacecraft of Alfvénic fluctuations associated with density gradients were made on the Large Plasma Device (LAPD) at UCLA (Maggs and Morales, 1997; Gekelman et al., 1997). Alfvénic fluctuations generated spontaneously on a density gradient are explained in terms of a coupling between the dispersive Alfvén wave and the electrostatic drift wave producing a mode known as the drift-alfvén wave. In the presence of the density gradient, both the electrons and ions (charge q j, temperature T j ) acquire a diamagnetic drift velocity v dj = T j B n, (4) q j nb2 which results in the perpendicular current j = B p/b 2. Here, we have the possibility of coupling between KAW described by ω = k z v A 1+k y(ρ 2 2 s + ρ 2 i ), (5) with the drift waves ω dj = k y v dj (Shukla et al., 1984). Alternative explanation has been provided by Rezeau and Belmont (21); DeKeyser et al. (1999); Belmont and Rezeau (21) who argued that ULF fluctuations already exist in the magnetosheath (coming from the bow shock) and are only resonantly amplified at the magnetopause layer. Sheared flows observed at the magnetopause could also produce Alfvén-ion cyclotron waves. A review of sheardriven processes in the ionosphere and in laboratory plasmas has been published recently by Amatucci (1999). Experiments performed in the Naval Research Laboratory demonstrate that broadband waves in the ion-cyclotron frequency range can be driven solely by a transverse localized electric field. Electrostatic fluctuations that can be supported by inhomogeneous parallel flows were investigated by (Gavrishchaka et al., 1999), and by the inhomogeneous energydensity driven (IEDD) instability by Koepke et al. (1999). Interesting theoretical results have been obtained by Penano and Ganguli (2) who argue that the velocity shear associated with the background electric field can destabilize Alfvén waves when the magnitude of the velocity shear frequency exceeds the ion cyclotron frequency. The mechanism that may produce structures less than ion gyroradius at the magnetopause could be related to sub-alfvénic solar wind expansion toward the magnetosphere. Structuring of the expansion plasma front has been observed in laboratory experiments (Ripin et al., 1987) and with barium releases in the magnetosphere (Bernhardt et al., 1987; Hassam and Huba, 1987; Huba et al., 1992). The instability is driven by the deceleration of the plasma expansion front which produces a force equivalent to gravity in the reference system moving with the plasma g = du/dt. The mechanism for the instability is related to the charge separation at the plasma front due to the differential electron and ion drifts, and has been referred to as a large Larmor radius Reyleigh-Taylor instability (Ripin et al., 1987). For a review of finite Larmor radius effects in the magnetosphere see e.g. Stasiewicz (1994). A detailed comparison of observations with various theoretical models for drift-kinetic Alfvén waves and mechanisms for producing structures smaller than the ion gyroradius at the magnetopause will be addressed in a forthcoming publication.

7 6 Stasiewicz et al.: Cluster observations of dispersive Alfvén waves 5 Conclusions Analysis of electromagnetic fluctuations observed by Cluster at the magnetopause layer shows that waves in the frequency range.3.3 Hz, ie. below the proton gyrofrequency (f ci.3 Hz in the analyzed case) could be identified as kinetic Alfvén waves, which appear to have a wide spectrum of spatial scales: from large scale wavelengths which can be resolved by four Cluster spacecraft to structures smaller than an ion gyroradius. The existence of small wavelengths is inferred from a theoretical polarization relation which is found to agree with Cluster measurements. Small-scale structures are Doppler shifted by fast convective flows and observed as higher frequency waves in satellite data (in our case between the ion gyrofrequency and the lower hybrid frequency;.3-1 Hz). The results corroborate earlier findings made with Freja at ionospheric altitudes (Stasiewicz et al., 2b) and Polar at the high latitude boundary layer (Stasiewicz et al., 21) that ELF turbulence observed in different regions of the magnetosphere can be interpreted as Doppler shifted dispersive Alfvén waves at small perpendicular wavelengths. Further studies are needed to assess the mechanism of generation these waves and structures and their role in the process of energy/mass transport, and diffusion across the magnetosphere. Acknowledgements. The authors would like to thank Laurence Rezeau for useful comments on the manuscript and the FGM team for providing data used to compute spectra in Figures 7 and 8. References Amatucci, W., Inhomogeneous plasma flows: A review of in situ observations and laboratory experiments, J. Geophys. Res., 14, , Bale, S. D. et al., The normal, thickness, and speed of the dusk magnetopause current layer from Cluster EFW measurements of spacecraft potential, Geophys. Res. Lett., p. submitted, 21. Balogh, A. et al., The Cluster magnetic field investigation, Space Sci. Rev., 79, 65 91, Belmont, G. and Rezeau, L., Magnetic reconnection induced by magnetosheath Hall-MHD fluctuations, J. Geophys. Res., in press, 21. Bernhardt, P. A. et al., Observations and theory of the AMPTE barium release, J. Geophys. Res., 92, 5777, Cornilleau, N. et al., The Cluster spatio-temporal analysis of field fluctuations STAFF, Space Sci. Rev., 79, , Decreau, P. et al., WHISPER, a resonance sounder and wave analyser, Space Sci. Rev., 79, , DeKeyser, J., Roth, M., Reberac, F., Rezeau, L., and Belmont, G., Resonant amplification of MHD waves in realistic subsolar magnetopause configurations, J. Geophys. Res., 14, 2399, Escoubet, C. P., Pedersen, A., Schmidt, R., and Lindqvist, P. A., Density in the magnetosphere inferred from ISEE 1 spacecraft potential, J. Geophys. Res., 12, 17,595, Gavrishchaka, V., Ganguli, S., and Ganguli, G., Electrostatic oscillations due to filamentary structures in the magnetic-field-aligned flow: The ionacoustic branch, J. Geophys. Res., 14, , Gekelman, W., Vincena, S., Leneman, D., and Maggs, J., Laboratory experiments on shear Alfvén waves and their relationship to space plasmas, J. Geophys. Res., 12, 7225, Gurnett, D. A., Huff, R. I., and Kirchner, D. I., The wide-band plasma wave investigation, Space Sci. Rev., 79, , Gustafsson, G. et al., The electric field and wave experiment for the Cluster mission, Space Sci. Rev., 79, , Gustafsson, G. et al., First results of the electric field and density observations by Cluster EFW, Ann. Geophys., this issue, 21. Hasegawa, A., Particle acceleration by MHD surface wave and formation of aurora, J. Geophys. Res., 81, , Hassam, A. B. and Huba, J. D., Structuring of the AMPTE magnetotail barium releases, Geophys. Res. Lett., 14, 6, Huba, J. D., Bernhardt, P. A., and Lyon, J. G., Preliminary study of the crres magnetospheric barium releases, J. Geophys. Res., 97, 11 24, Johnson, J. R. and Cheng, C. Z., Kinetic Alfvén waves and plasma transport at the magnetopause, Geophys. Res. Lett., 24, 1423, Koepke, M., Carroll, J., and Zintl, M., Laboratory simulation of broadband elf waves in the auroral ionosphere, J. Geophys. Res., 14, , Lee, L. C., Johnson, J. R., and Ma, Z. W., Kinetic Alfvén waves as a source of plasma transport at the dayside magnetopause, J. Geophys. Res., 99, 17,45 17,411, Lucek, E. A. et al., The magnetopause at high time resolution: structure and lower hybrid waves, Geophys. Res. Lett., 28, , 21. Maggs, J. E. and Morales, G. J., Fluctuations associated with filamentary density depresions, Phys. Plasmas, 4, 29, Pedersen, A., Solar wind and magnetosphere plasma diagnostics by spacecraft electrostatic potential measurements, Ann. Geophys., 13, , Pedersen, A. et al., Four-point high time resolution information on electron densities on cluster, Ann. Geophys,, this issue, 21. Penano, J. and Ganguli, G., Generation of ELF electromagnetic waves in the ionosphere by localized transverse dc electric fields: Subcyclotron frequency regime, J. Geophys. Res., 15, , 2. Rezeau, L. and Belmont, G., Magnetic turbulence at the magnetopause, a key problem for understanding the solar wind/magnetosphere exchanges, Space Sci. Reviews, 95, 427, 21. Ripin, B. H. et al., Large-larmor radius interchange instability, Phys. Rev. Lett., 59, 2299, Shue, J.-H. et al., Magnetopause location under extreme solar wind conditions, J. Geophys. Res., 13, 17,691 17,7, Shukla, P. K., Yu, M. Y., Rahman, H. U., and Spatschek, K. H., Nonlinear convective motion in plasma, Phys. Rep., 15, , Sibeck, D. et al., Plasma transfer processes at the magnetopause, Space Sci. Rev., 1-2, 27, Stasiewicz, K., Finite larmor radius effects in the magnetosphere, Space Sci. Rev., 65, 221, Stasiewicz, K., Bellan, P., Chaston, C., Kletzing, C., Lysak, R., Maggs, J., Pokhotelov, O., Seyler, C., Shukla, P., Stenflo, L., Streltsov, A., and Wahlund, J.-E., Small scale Alfvénic structure in the aurora, Space Sci. Rev., 92, , 2a. Stasiewicz, K., Khotyaintsev, Y., Berthomier, M., and Wahlund, J.-E., Identification of widespread turbulence of dispersive Alfven waves, Geophys. Res. Lett., 27, , 2b. Stasiewicz, K. and Khotyaintsev, Y., Reply to comment on identification of widespread turbulence of dispersive Alfven waves, Geophys. Res. Lett., 28, 145, 21. Stasiewicz, K., Seyler, C., Mozer, F., Gustafsson, G., Pickett, J., and Popielawska, B., Magnetic bubbles and kinetic Alfven waves in the high-latitude magnetopause boundary, J. Geophys. Res., in press, 21.