Smallscale, localized electromagnetic waves ... - Wiley Online Library

GEOPHYSICAL RESEARCH LETTERS, VOL. 35, L22107, doi:10.1029/2008GL035956, 2008

Small-scale, localized electromagnetic waves observed by Cluster: Result of magnetosphere-ionosphere interactions A. V. Streltsov1 and T. Karlsson2 Received 9 September 2008; revised 7 October 2008; accepted 13 October 2008; published 26 November 2008.

[1] We present results from a numerical study of smallscale, localized electromagnetic structures measured by the Cluster satellites on May 19, 2002, in the nightside magnetosphere. A comprehensive analysis of these structures by Karlsson et al. (2004), Johansson et al. (2004) and Marklund et al. (2004) demonstrates that they can be interpreted as two relatively stationary magnetic field-aligned currents and higher frequency shear Alfveń waves, populating the region in between, but no explanation was given of what physical mechanism may cause such particular combination of waves and currents in the plasma sheet boundary layer. Our simulations demonstrate that these structures can be interpreted as a characteristic signature of the active ionospheric feedback, which appears when large-scale magnetic field-aligned currents interact with the ionosphere. Citation: Streltsov, A. V., and T. Karlsson (2008), Small-scale, localized electromagnetic waves observed by Cluster: Result of magnetosphere-ionosphere interactions, Geophys. Res. Lett., 35, L22107, doi:10.1029/ 2008GL035956.

1. Introduction [2] One of the main questions in modern auroral physics is what physical mechanism is responsible for the generation of small-scale, localized ultra-low-frequency electromagnetic waves commonly observed on auroral magnetic field lines. The interest in these waves has been steadily increasing with observations showing that they frequently associate with fluxes of accelerated electrons, heavy ions outflow, and plasma density cavities. Numerous theoretical and numerical studies of these waves at high latitudes have been reviewed by Borovsky [1993], Stasiewicz et al. [2000], and Paschmann et al. [2003]. [3] The intrinsic complexity and interconnection of the coupled magnetosphere-ionosphere system, where different geophysical processes with different spatial and temporal scales can occur simultaneously, make it difficult to identify a single physical mechanism which causes the observed phenomena. To date, one of the best space platforms for studying small-scale waves is a constellation of four Cluster satellites [Karlsson et al., 2004; Johansson et al., 2004; Wright et al., 2008]. Figure 1 (adapted from Karlsson et al. [2004]) shows one example of these small-scale waves recorded by Cluster in the nightside plasma sheet boundary 1 Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire, USA. 2 Division of Plasma Physics, Alfveń Laboratory, KTH, Royal Institute of Technology, Stockholm, Sweden.

Copyright 2008 by the American Geophysical Union. 0094-8276/08/2008GL035956

layer at a geocentric distance of 5 RE on May 19, 2002. It shows two perpendicular (to the ambient magnetic field) components of the high-frequency (frequency > 0.033 Hz) magnetic field, measured by four Cluster satellites from 05:26 to 05:36 UT. In Figure 1, the y-direction corresponds approximately to geomagnetic west, and the z-direction corresponds approximately to geomagnetic north. During this time interval, the invariant magnetic latitude of the Cluster satellite positions changes from 69.76° to 68.36°, and the magnetic local time was around 19:50 hours. A comprehensive analysis of three magnetic field components and two electric field components measured by the four Cluster satellites during this event has been performed by Karlsson et al. [2004], Johansson et al. [2004], and Marklund et al. [2004]. These authors conclude that the event consists of two relatively stationary magnetic fieldaligned currents (FACs) centered near 05:30 and 05:33 UT and higher frequency shear Alfveń waves, populating the region between these two currents. The similarities between electromagnetic structures observed near 05:30 and 05:33 UT lead these authors to a conclusion that Cluster satellites cross a single folded current sheet extended along the ambient magnetic field and traveling westward with a constant velocity [Marklund et al., 2004]. This is a quite reasonable explanation for the stationary currents because folds and spirals are common features of dynamics of discrete auroral arcs, but it does not explain what physical mechanism may cause such a particular combination of higher-frequency waves (10 – 20 mHz) and currents as observed in this event. [4] The goal of this study is to answer this question. In particular, we will investigate a hypothesis that this particular combination of waves and currents is a characteristic signature of the active ionospheric feedback on the structure and amplitude of the large-scale FACs and associated electric fields interacting with the ionosphere. The basic idea of the ionospheric feedback is that when FACs interact with the ionosphere, they change the ionospheric density and conductivity by precipitating/removing electrons into/ from the ionosphere, and these variations in the conductivity feed back on the structure and amplitude of FACs by changing their reflection from the ionosphere. The ionospheric feedback mechanism may explain small-scale, intense electromagnetic fields frequently measured above the auroral ionosphere in a vicinity of large-scale FACs [Golovchanskaya et al., 2006]. If, during these interactions, a large-scale electric field with a magnitude 20 mV/m exists in the ionosphere and there is a resonant cavity in the magnetosphere, then the feedback may lead to an instability [Atkinson, 1970], causing a significant amplification of the resonant waves and density disturbances. Intense electromagnetic structures generated by the ionospheric feedback

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STRELTSOV AND KARLSSON: SMALL-SCALE WAVES

Figure 1. Small-scale part of the perpendicular components of the magnetic field measured by four Cluster satellites on 05/19/2002. Data from different Cluster satellites are shown with different colors. Adapted from Karlsson et al. [2004]. instability have been observed and studied inside the cavity formed by the entire magnetic flux tube standing between two magnetically conjugate locations in the ionosphere [Sato, 1978; Watanabe et al., 1993; Pokhotelov et al., 2002], and inside the cavity formed by the bottom of the ionosphere and a strong gradient in the Alfveń velocity at the altitude about 1 RE [Trakhtengertz and Feldstein, 1984, 1991; Lysak, 1991; Lysak and Song, 2002; Rother et al., 2007]. This latter cavity is called the ionospheric Alfveń resonator (IAR), which was introduced by Polyakov and Rapoport [1981]. [5] In this paper, the idea that small-scale fields and currents observed by Cluster can be produced by the interaction between the large-scale FACs and the ionosphere [Glassmeier, 1983; Streltsov and Lotko, 2003b, 2004] will be verified by numerical simulations of the interaction between two-dimensional magnetic field-aligned current sheets and the ionosphere. Because the numerical model has only two spatial directions (one is along the ambient magnetic field and another is normal to the dipole magnetic shell), we will model the structure of only one of the perpendicular components of the magnetic field measured by the Cluster 1 satellite. In particular, to avoid any artificial effects related to the data conversions between different coordinate systems we will model the z component of the disturbed magnetic field recorded by the Cluster 1 satellite in the original GSE coordinate system, which is different from the coordinate system used by Karlsson et al. [2004]. We limit our analysis to the data from only one satellite because during the event there was very little spatial/ temporal separation between the satellites, and the data from all four of them look similar. (For details, see Karlsson et al. [2004] and Johansson et al. [2004]). The little spatiotemporal separation between the satellites makes it hard to use this event to study the temporal dynamics of small-scale structures, and we will consider the event as a ‘‘snapshot’’ of small-scale structures produced by interactions between the large-scale FACs and the ionosphere. [6] The original Bz data measured by the Cluster 1 satellite during the event is shown in Figure 2a with the solid line. The dashed line in Figure 2a shows the largescale background magnetic field (trend), which should be

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removed from the data before the spectral analysis of the data can be made. Figure 2b shows the amplitude of the spectral density of the data with the trend removed. During 600 s of the event, Cluster 1 measures 149 data points with a temporal descritization of 4.018 s; therefore, the maximum frequency of this spectrum is 0.1244 Hz. We apply to this data a low-pass filter with a cut-off frequency of 6.8 mHz, and divide the signal into the low-frequency part (frequency < 6.8 mHz), shown in Figure 2c with the blue dashed line, and the high-frequency part (frequency > 6.8 mHz), shown in Figure 2c with the red, solid line. [7] The idea investigated in this paper is that the highfrequency (or small-scale) part of the disturbed Bz is the result of the interaction between the low-frequency (or largescale) currents and the ionosphere. This hypothesis will be verified by numerical simulations of the physical model described in the next section. It is worth mentioning here that the data shown in Figure 1 and analyzed by Karlsson et al. [2004], Johansson et al. [2004] and Marklund et al.

Figure 2. (a) Bz measured by the Cluster 1 satellite (solid curve); (b) Spectral density of Bz with trend removed; (c) Lower-frequency (blue, dashed curve) and higherfrequency (red, solid curve) components of Bz.

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[2004] represent the high-frequency part (frequency > 33.3 mHz) of the original signal, which is included in the part of the signal that we will model in this study.

2. Model [8] Active interactions between the two-dimensional FAC system and the ionosphere will be modeled by using a numerical algorithm based on a reduced, two-fluid MHD equations described in detail in several papers, e.g., Streltsov and Lotko [2003b, 2004]. The background plasma in the model is considered to be warm, quasineutral, and consisting of protons and electrons only. The model includes the parallel electron momentum equation, the density continuity equation, and the current continuity equation: @vke e 1 Ek þ rk ðnTe Þ ¼ n e vke ; þ vke rk vke þ @t me me n0

ð1Þ

two spatial dimensions); nE is the height-averaged plasma density inside the E-region; MP = 104 m2/sV is the ion Pedersen mobility; e is the elementary charge; h = 20 km is the effective thickness of the E-layer; q 11° is the angle between the dipole computational boundary and the ionosphere at 120 km altitude; a = 3 107 cm3/s is the recombination coefficient; and nE0 = 3 104 cm3 is the equilibrium plasma density. These values provide a background value of SP0 = 1 mho. The ambient magnetic field in the model is directed away from the ionosphere (which corresponds to the southern hemisphere, where the Cluster observations shown in Figure 1 were made), so the upward current (which flows away from the ionosphere) has a positive sign, and the downward current has a negative sign. [11] The simulations start by launching the large-scale magnetic field-aligned current toward the ionosphere from the magnetospheric boundary of the domain. There the wave magnetic field is specified as

@n ^ ¼ 0; þ r nvke b @t

^þ r jk b

1 1 1 @E? r 2þ 2 ¼ 0: m0 c vA @t

B? ðt; LÞ ¼

ð2Þ

ð3Þ

Here the subscripts k and ? denote vector components in ^ = B0/B0; vke is the directions parallel and perpendicular to b the parallel component of the electron velocity; Te is the pffiffiffiffiffiffiffiffiffiffiffiffiffiffi background electron temperature, vA = B0/ m0 n0 mi is the Alfveń speed; and n e is the electron collision frequency. [9] They are implemented numerically in the computational domain formed by a dipolar flux tube, extending from the ionosphere to the equatorial plane and limited in latitude by the L = 7.35 and the L = 8.36 magnetic shells (which correspond to the invariant latitudes 68.35° and 69.76°.) At the equatorial plane, the dipole flux tube is spliced onto a cylindrical magnetic flux tube [see Streltsov and Lotko, 2003a, Figure 2]. The dipole part of the domain accurately represents the magnetic field geometry at low altitudes, whereas the cylindrical extension is used to provide a ‘‘buffer zone’’ where the wave can propagate after the reflection from the ionosphere. [10] The ionospheric boundary of the computational domain is set at the altitude 120 km where the E-layer density is maximum. Here the boundary conditions describing active ionospheric interactions between the magnetospheric FAC and the ionosphere are implemented via relations connecting the parallel current density with the plasma density and the perpendicular electric field in the ionosphere: r ðSP E? Þ ¼ jk

ð4Þ

jk @nE ¼ þ a n2E0 n2E @t eh

ð5Þ

Here SP = nE MP h e/cos q is the height-integrated Pedersen ionospheric conductivity (the Hall conductivity is not included in equation (1) because the model is limited to

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BðtÞ sinð2pð L LC Þ=lÞ if jL LC j l=2 ð6Þ 0 if jL LC j > l=2

Here B(t) = B*t/tr when t < tr, and B(t) = B* when t tr . The parameter tr = 19 s is a ‘ramp time’ used to smooth out the front of the propagating wave. Its value has been estimated empirically from several test runs. Values of B* = 3 nT, LC = 7.77 and l = 2.67 are chosen to match parameters of the large-scale magnetic field observed by the Cluster 1 satellite (shown with blue, dashed line in Figure 2c).

3. Results and Discussion [12] Figure 3 shows three consecutive snapshots of B? and jk taken from the simulation at time t = 163 s, t = 196 s, and t = 229 s. At time t = 163 s, the large-scale FACs just reached the ionosphere, and the ionospheric conductivity has not been significantly modified yet. The amplitude and the perpendicular size of the magnetospheric driver provides FACs with an amplitude of 10 mA/m2 in the ionosphere. If the active ionospheric boundary conditions given by equations (4) and (5) would be ‘‘turned off,’’ then the structure of B? and jk, shown at time t = 163 s, would remain the same during the rest of the simulation. [13] Snapshots of B? and jk shown in Figure 3 at t = 196 s and t = 229 s demonstrate that the ionospheric feedback causes small-scale, intense electromagnetic structures, which are ‘‘more visible’’ in jk than in B?. The important feature of the wave dynamics shown in these snapshots is that the most intense small-scale structures are formed on the boundary between upward and downward current channels. This effect was investigated by Streltsov and Lotko [2004], who explained it by the interaction between the upward-downward current (UDC) pair and the ionosphere. The reason for that is that the upward current increases the plasma density in the ionosphere and the downward current decreases it. As a result a strong gradient in the ionospheric plasma density (and conductivity) is formed at that location. According to equation (4), this gradient, together with the strong electric field produced by the current closure through the ionosphere, cause magnetic field-aligned current. This current can escape from the ionospheric Alfveń resonator if its frequency is lower than the characteristic frequency of

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Figure 3. Snapshots of simulated B? and jk.

IAR (normally 0.1 – 1.0 Hz [Polyakov and Rapoport, 1981; Trakhtengertz and Feldstein, 1984]), and it can propagate into the magnetosphere to 5 – 6 RE geocentric distance. [14] Streltsov and Lotko [2004] demonstrate that when the UDC pair interacts with the ionosphere, the primary, most intense, small-scale waves are generated on the boundary between these currents, and secondary small-scale waves are generated inside the downward current channel. The frequency, scale-size, and amplitude of these waves depend on the amplitude of the perpendicular electric field and plasma density in the ionosphere, and these parameters change dynamically, so typically, the frequency of secondary waves is higher than the frequency of the primary FACs. Hence, the numerical study by Streltsov and Lotko [2004] predicts that for the geometry of FACs shown in the first snapshots in Figure 3, the ionospheric feedback mechanism will ‘‘populate’’ the downward current channel with smallscale electromagnetic waves. And this prediction is confirmed by the simulation illustrated in Figure 3 at times t = 196 s and t = 229 s. [15] To make a more detailed comparison between the numerical results and the data measured by the Cluster 1 satellite, Figure 4 shows the experimental data and the

profile of B? taken from the simulations at time t = 225 s at Cluster altitude (near the geocentric distance of 5 RE). The same low-pass filter has been applied to the numerical and experimental data. The low-frequency part of the fields are shown with blue, dashed lines, and the high-frequency parts are shown with red, solid lines. The comparison between Figures 4a and 4b demonstrates a relatively good, quantitative agreement between the amplitudes and spatial structures of experimental and numerical results. This agreement, which is particularly good in the region between L = 7.86 and L = 7.35 magnetic shells, supports the main hypothesis investigated in this paper, namely that the localized, intense, small-scale electromagnetic waves and currents detected in the magnetosphere at a geocentric distance up to 5 RE can be generated by the interaction between large-scale FACs and the ionosphere. At the same time, our simulations does not reproduce in detail smallscale structures observed by the Cluster between L = 8.36 and L = 7.86 magnetic shells. One possible explanation for this disagreement is that the model does not include effect of the transverse motion of the large-scale current sheet on the generation of small-scale structures in the ionosphere. The presence of this motion in the Cluster data has been

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Figure 4. (a) Bz measured by the Cluster 1 satellite and (b) the simulated B? at geocentric distance of 5 RE. emphasized by Marklund et al. [2004], and it certainly can change structure, dynamic, and location of the small-scale waves. We leave this effect for future studies with more advanced numerical algorithm. [16] Acknowledgments. The research has been supported by the International Space Science Institute (ISSI), Switzerland and by the NASA grants NNX08AI36G and NNX08AM14G.

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Johansson, T., S. Figueiredo, T. Karlsson, G. Marklund, A. Fazakerley, S. Buchert, P.-A. Lindqvist, and H. Nilsson (2004), Intense high-altitude electric fields—Temporal and spatial characteristics, Ann. Geophys., 22, 2485. Karlsson, T., G. T. Marklund, S. Figueiredo, T. Johansson, and S. Buchert (2004), Separating spatial and temporal variations in auroral electric and magnetic fields by Cluster multipoint measurements, Ann. Geophys., 22, 2464. Lysak, R. L. (1991), Feedback instability of the ionospheric resonant cavity, J. Geophys. Res., 96, 1553. Lysak, R. L., and Y. Song (2002), Energetics of the ionospheric feedback interaction, J. Geophys. Res., 107(A8), 1160, doi:10.1029/2001JA000308. Marklund, G., T. Karlsson, S. Figueiredo, T. Johansson, P.-A. Lindquist, M. Andre´, S. Buchert, L. Kistler, and A. Fazakerley (2004), Characteristics of quasi-static potential structures observed in the auroral return current region by Cluster, Nonlinear Processes Geophys., 11, 709. Paschmann, G., S. Haaland, and R. A. Treumann (Eds.) (2003), Auroral Plasma Physics, Space Sci. Ser., vol. 15, Kluwer Acad., Dordrecht, Netherlands. Pokhotelov, D., W. Lotko, and A. V. Streltsov (2002), Harmonic structure of field line eigenmodes generated by ionospheric feedback instability, J. Geophys. Res., 107(A11), 1363, doi:10.1029/2001JA000134. Polyakov, S., and V. Rapoport (1981), The ionospheric Alfveń resonator, Geomagn. Aeron., 21, 816. Rother, M., K. Schlegel, and H. Lo¨hr (2007), CHAMP observation of intense kilometer-scale field-aligned currents, evidence for an ionospheric Alfveń resonator, Ann. Geophys., 25, 1603. Sato, T. (1978), A theory of quiet auroral arcs, J. Geophys. Res., 83, 1042. Stasiewicz, K., et al. (2000), Small scale Alfveńic structure in the aurora, Space Sci. Rev., 92, 423. Streltsov, A. V., and W. Lotko (2003a), Reflection and absorption of Alfveńic power in the low-altitude magnetosphere, J. Geophys. Res., 108(A4), 8016, doi:10.1029/2002JA009425. Streltsov, A. V., and W. Lotko (2003b), Small-scale electric fields in downward auroral current channels, J. Geophys. Res., 108(A7), 1289, doi:10.1029/2002JA009806. Streltsov, A. V., and W. Lotko (2004), Multiscale electrodynamics of the ionosphere-magnetosphere system, J. Geophys. Res., 109, A09214, doi:10.1029/2004JA010457. Trakhtengertz, V., and A. Y. Feldstein (1984), Quiet auroral arcs: Ionospheric effect of magnetospheric convection stratification, Planet. Space Sci., 32, 127. Trakhtengertz, V., and A. Y. Feldstein (1991), Turbulent Alfveń boundary layer in the polar ionosphere: 1. Excitation conditions and energetics, J. Geophys. Res., 96, 19,363. Watanabe, T., H. Oya, K. Watanabe, and T. Sato (1993), Comprehensive simulation study on local and global development of auroral arcs and field-aligned potentials, J. Geophys. Res., 98, 21. Wright, A. N., C. J. Owen, C. C. Chaston, and M. W. Dunlop (2008), Downward current electron beam observed by Cluster and FAST, J. Geophys. Res., 113, A06202, doi:10.1029/2007JA012643.

T. Karlsson, Division of Plasma Physics, Alfveń Laboratory, KTH, Royal Institute of Technology, SE-10044 Stockholm, Sweden. (tomas.karlsson@ ee.kth.se) A. V. Streltsov, School of Engineering, Dartmouth College, 8000 Cummings Hall, Hanover, NH 03755, USA. ([email protected])

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