Cluster observations of fast magnetosonic waves in the

Apr 23, 2001 - [9] Each Cluster spacecraft carries a payload of 11 instruments [Escoubet et al., 1997] including a Fluxgate. Magnetometer (FGM) [Balogh et al., ...
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GEOPHYSICAL RESEARCH LETTERS, VOL. 29, NO. 22, 2046, doi:10.1029/2002GL015582, 2002

Cluster observations of fast magnetosonic waves in the terrestrial foreshock J. P. Eastwood, A. Balogh, M. W. Dunlop, and T. S. Horbury Space and Atmospheric Physics, The Blackett Laboratory, Imperial College, London, UK

I. Dandouras CESR, Toulouse, France Received 31 May 2002; revised 25 September 2002; accepted 27 September 2002; published 19 November 2002.

[1] Cluster observations of ULF waves in the terrestrial foreshock are presented. Four spacecraft timing techniques on magnetic field measurements are used with plasma bulk velocity measurements to determine wave properties in the plasma rest frame. Based on the propagation speed and polarisation, the waves are found to be fast magnetosonic. The analysis is complemented by a direct examination of the correlation between plasma and field perturbations; consequently, an unambiguous and comprehensive identification of the wave is achieved. The advantages of the four spacecraft analysis are discussed and in particular, calculations of the propagation direction are compared to single spacecraft minimum variance techniques. The ratio of intermediate to minimum eigenvalues is used to characterise the degree to which the wave is circularly polarised. The results of a preliminary statistical survey indicate that if this ratio is greater than 10, minimum variance techniques agree INDEX TERMS: closely with the four spacecraft technique. 2154 Interplanetary Physics: Planetary bow shocks; 7871 Space Plasma Physics: Waves and instabilities; 7839 Space Plasma Physics: Nonlinear phenomena. Citation: Eastwood, J. P., A. Balogh, M. W. Dunlop, T. S. Horbury, and I. Dandouras, Cluster observations of fast magnetosonic waves in the terrestrial foreshock, Geophys. Res. Lett., 29(22), 2046, doi:10.1029/ 2002GL015582, 2002.

1. Introduction [2] The first observations of the bow shock revealed the existence of upstream wave activity [Greenstadt et al., 1968; Fairfield, 1969]. The region of space populated by such plasma waves is known as the foreshock, and several different wave types have been observed and identified [Greenstadt et al., 1995; Burgess, 1997]. Most commonly observed are large amplitude waves with periods close to 30 s (first observed by Greenstadt et al. [1968] and studied further by Fairfield [1969]) which are primarily transverse and left handed in the spacecraft frame of reference. [3] Paschmann et al. [1979] observed that these waves were associated with backstreaming ions and Hoppe et al. [1981] showed that different types of wave were associated with different beam distributions [Gosling et al., 1978]. This experimental data allowed models to be developed that were consistent with waves being generated by and subsequently

Copyright 2002 by the American Geophysical Union. 0094-8276/02/2002GL015582$05.00

interacting with ions reflected from the bow shock [Barnes, 1970; Gary et al., 1981; Sentman et al., 1981]. [4] Dual spacecraft missions allowed the plasma rest frame properties of ULF waves to be estimated for the first time [Hoppe and Russell, 1983]. Minimum Variance Analysis (MVA) was used to estimate the direction of propagation of the phase front, a technique valid for circularly polarised waves [Song and Russell, 1999]. The phase velocity in the spacecraft frame, v(ph), was calculated according to v(ph) = S.n/t (S is the separation of the spacecraft, n is the propagation direction and t the time lag between the two time series). However, if S lies perpendicular to the propagation direction, t  0 and the phase speed cannot be determined. The plasma frame properties of the wave were then derived by Doppler shifting the spacecraft frame properties according to the solar wind velocity. It was concluded that the observed waves had rest frame frequencies 0.1  ci ( ci is the ion cyclotron frequency), wavelengths of 1 Re (1 Re = 6370 km) and, based on the polarisation, were magnetosonic in nature. It was not possible to complement the dual spacecraft analysis with a direct identification of the wave mode from the correlation of plasma and field perturbations. The ion beam accompanying these waves was described as ‘intermediate’, similar to a field aligned beam but with a larger spread in pitch angle. The scale size of the waves was further investigated by Le and Russell [1990]. [5] In this paper, we report on a study of ULF waves made using the four spacecraft Cluster mission. Cluster can be expected to contribute significantly to the general understanding of ULF foreshock waves for two reasons. Firstly, when calculating the speed and orientation of a particular phase front (in the spacecraft rest frame), it is assumed only that the phase speed is constant and that the wave front is planar on the scale of the spacecraft separation. The analysis is not restricted, for example, to circularly polarised waves. Secondly, the time resolution of the moment calculations, 4s in standard modes, ensures that the multi-spacecraft analysis is routinely complemented by plasma data capable of resolving the variations in typical ULF waves with observed periods of 20 –30 s in the spacecraft frame. [6] In this paper we investigate the properties of ULF waves as observed by Cluster. The technique used to analyse the Cluster data is summarised; this technique allows the properties of the waves in the plasma rest frame to be determined. The technique is illustrated by analysing an example interval of data; this analysis is complemented

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EASTWOOD ET AL.: CLUSTER FORESHOCK WAVE IDENTIFICATION

Differences between the four Cluster spacecraft are indistinguishable on this scale. [10] During this interval, Cluster was located in the solar wind. Initially, the magnetic field pointed southward, and did not connect Cluster to the bow shock. At 04:13 UT the magnetic field rotated into the ecliptic plane (qB  0), threading the bow shock. The magnetic field remained stable in this orientation until 07:30 UT, at which time the field direction changed, pointing southward again after 08:00 UT. While the magnetic field threaded the bow shock, there was a prolonged period of foreshock wave activity commencing just before 05:00 UT and continuing until the field rotated southward after 07:30 UT. The timing of the onset of the wave activity and its dependence on the orientation of the field, spacecraft and bow shock will be the subject of further investigations. In the next section, a short interval of wave activity is examined in detail, and a statistical survey of a longer interval is presented. Figure 1. Cluster Orbit on 23 April 2001 - Day 113. Spacecraft 1 trajectory is shown; the separations are magnified by 30. Note that the orbit is polar. by examining the field and plasma perturbations directly, allowing a uniquely comprehensive analysis of the wave to be made. The Cluster method is also compared directly to MVA, and the results of a preliminary statistical survey are presented. The limit beyond which MVA is not an appropriate tool for wave analysis is investigated; this is important for single spacecraft missions where the Cluster techniques are not available.

3. ULF Upstream Waves Observed by Cluster [11] In preparation for Cluster, a number of sophisticated analysis techniques were developed including ‘wave telescope’ techniques theoretically capable of distinguishing between waves of the same wavelength propagating in different directions at the same time. Glassmeier et al. [2001] discuss the techniques and present the first results of wave telescope analysis as applied to Cluster FGM data. The analysis assumes that the wave activity results from the interaction of a number of small amplitude sinusoidal perturbations, and a long time series of constant activity is required so that the Fourier transformation to (w, k) space is statistically significant. In the foreshock, the magnetic field

2. Overview of Cluster Data [7] Cluster consists of four identical spacecraft in eccentric polar orbits around the Earth; the orbital apogee and perigee occur in the ecliptic plane at 19.6 Re and 4 Re. The individual orbits are arranged so that the four spacecraft maintain an approximately constant separation, the scale of which can be altered during different mission phases from 10 s of km to 1 Re (Earth radius) depending on the different science objectives. [8] Figure 1 shows the orbit of Cluster on the 23 April 2001 in the x-y GSE (Geocentric Solar Ecliptic) and x-z GSE planes. The trajectory shown is that of spacecraft 1 and the relative positions of the other three spacecraft, magnified by 30, are shown. The spacecraft separation was of the order of 600 km. At the start of the day, the spacecraft were located in the solar wind, on the dawn flank of the bow shock in the ecliptic plane. During the day, the spacecraft descended south under the ecliptic plane, entering the magnetosphere via the southern cusp. The first bow shock crossing occurred at 08:12 UT. [9] Each Cluster spacecraft carries a payload of 11 instruments [Escoubet et al., 1997] including a Fluxgate Magnetometer (FGM) [Balogh et al., 1997] and an Ion Spectrometer (CIS) [Reme et al., 1997]. Figure 2 shows the magnetic field measured by the FGM instrument on spacecraft 1 between 04:00 UT and 08:00 UT on the 23 April 2001. Spin averaged data (4 second resolution) has been used. jB is the angle relative to the x GSE axis in the x-y ecliptic plane, and qB is the angle out of the ecliptic.

Figure 2. Magnetic Field measured by Cluster 1 04:00 UT – 08:00 UT, 23 April 2001. Spin averaged data has been used. Differences between the individual Cluster spacecraft are indistinguishable on this scale.

EASTWOOD ET AL.: CLUSTER FORESHOCK WAVE IDENTIFICATION

Figure 3. Magnetic Field (FGM) and Plasma Density (CIS) measured by Cluster 1, 05:00 UT – 05:10 23 April 2001. The plasma data has 4 s resolution, the field data 0.2 s resolution.

and the counter-streaming generation mechanism introduce a strong anisotropy, and given theoretical predictions we expect waves to be (approximately) aligned to the field. Given the expected simplicity of the wave geometries and the fact that the waves are large amplitude and tend to be intermittent, a simpler method was developed with the ‘wave telescope’ to be implemented, if needed, to enhance the results in a secondary analysis. It is also noted that the spacecraft array is moving at super-magnetosonic speeds with respect to the plasma. [12] It is assumed that the phase front is travelling at constant speed, and that the waves are planar and uniform on the scale of the spacecraft separation. In this case the spacecraft separation is 600 km, an order of magnitude less than the scale size of similar waves observed using ISEE [Le and Russell, 1990]. [13] If spacecraft a located at Ra observes the phase front at time ta, then given a plane wave with a frame invariant direction of propagation n and spacecraft frame phase speed v(ph), the following equations can be constructed,   Rb  R1  n ¼ vðphÞ  t b  t1 vðphÞ ¼ vðphÞ  n

ðb ¼ 2; 3; 4Þ

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propagation direction of n = [0.67 0.73 0.13], at an angle of 25 to the magnetic field. The error in the propagation direction is of the order of a few degrees. This corresponded to a phase velocity of 65 kms1 sunwards in the plasma rest frame. The alfve´n speed for this interval was calculated to be 75 kms1 and the sound speed 30 kms1. MVA reveals the wave to be left handed with respect to the magnetic field in the spacecraft rest frame. However due to the Doppler shift, the wave is right handed in the plasma rest frame. It can therefore be identified as fast magnetosonic, attempting to propagate upstream but being convected downstream by the solar wind flow. The plasma frame frequency and wavelength were estimated to be 0.014 Hz and 6030 km. The ion cyclotron frequency in this interval was estimated to be 0.13 Hz. Hence these waves have similar properties to those analysed using different methods by Hoppe and Russell [1983] where  0.1  ci and l  1Re. [15] The Cluster analysis is complemented by the existence of high resolution plasma data. Figure 3 shows the magnetic field strength (at 0.2 s resolution) and the density (at 4 s resolution) for the interval 05:00 UT to 05:10 UT. The density was calculated from measurements taken on the low sensitivity side of the Hot Ion Analyser (HIA) CIS instrument operating in solar wind mode [Reme et al., 1997]. It is immediately apparent that these waves are fast magnetosonic, since the perturbations in the field strength are correlated with the perturbations in the density. Thus, in this case, we are able to comprehensively identify the nature of the waves. Of interest is the propagation direction of the waves. In particular they are not field aligned, as has previously been reported (e.g., Le and Russell [1994]), although this is consistent with the fact that they are compressive. This issue will be discussed in a following paper together with the use of the wave telescope. [16] MVA has been used here to determine the polarisation of the waves with respect to the magnetic field.

ð1Þ ð2Þ

v(ph) and n are then determined by solving these equations. The phase velocity in the plasma rest frame is then calculated by subtracting vsw  n (the projection of the solar wind bulk velocity onto the direction of propagation) from v(ph). [14] As an example, this technique was applied to the interval 05:00 UT – 05:06 UT. The data was filtered to remove high frequency noise (of physical origin) and the spacecraft time series were cross correlated to determine the lags between the spacecraft. Using this method, the waves were found to have a phase velocity of 220 kms1, with a

Figure 4. Angle between MVA and the 4 spacecraft estimate of the propagation direction as a function of the ratio of intermediate - minimum eigenvalues (a proxy for the degree to which the wave is circularly polarised). Each point corresponds to a 2 minute section of the given interval.

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However in the case of circularly polarised waves, the minimum variance direction is identified (with a 180 ambiguity) as the direction of wave propagation. It is instructive to compare the results of MVA with the multispacecraft analysis. [17] Figure 4 shows the result of a preliminary statistical survey on these waves. The interval 05:00 UT – 06:00 UT was filtered to remove high frequency noise as before, and then split into 30 2 minute sections. Each interval was examined by eye for the existence of waves; on this basis 6 intervals were discarded due to the lack of wave activity. For each of the remaining 24 intervals, the MVA and 4 spacecraft propagation directions were calculated and the angle between them determined. In Figure 4 this angle is plotted as a function of the average ratio (taken over the four spacecraft) between intermediate and minimum eigenvalues. If a wave is circularly polarised, this ratio is large; if the wave is linearly polarised this ratio approaches unity, there is an indeterminacy between the two directions and the direction of propagation is ill-defined. MVA is not expected to be accurate when applied to linearly polarised waves, whereas the four spacecraft method is unaffected. It is clear that if the ratio of intermediate/minimum eigenvalues is greater than 10, the two methods agree; in this regime the assumptions behind each method are correct. For values less than 10, the two methods do not agree. This can be attributed to the linear polarisation of the waves. With four spacecraft, the properties of the majority of observed waves can be determined, not just those that are strongly circularly polarised.

4. Discussion and Future Work [18] In this paper, we have presented high time resolution plasma and magnetic field measurements of ULF waves in the terrestrial foreshock. We have comprehensively identified the existence of fast magnetosonic waves. In particular, the conclusions of the four spacecraft analysis are complemented by direct comparison of the field and plasma perturbations. In dual spacecraft analysis the spacecraft separation must not be perpendicular to the propagation direction, and the waves must be circularly polarised. The four spacecraft technique presented here is not theoretically limited in this manner. The differences between MVA and the four spacecraft technique have been characterised and preliminary results indicate that MVA does not accurately estimate the direction of propagation if the ratio of intermediate/minimum eigenvalues is less than 10. A more complete survey using a larger dataset will be completed to corroborate this result, and to characterise the multispacecraft technique in more detail. Further work on this topic, in particular studying the association of ion distributions with the observed waves, studying more closely the

variations within single wave cycles, and determining the existence of multiple wave modes is also planned. [19] Acknowledgments. This work is supported by PPARC.

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J. P. Eastwood, A. Balogh, M. W. Dunlop, and T. S. Horbury, Space and Atmospheric Physics Group, The Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 2BW, UK. I. Dandouras, CESR, 9 Avenue du Colonel Roche, 31028 Toulouse Cedex 4, France.