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Applying this technique to the interval 05:00-05:06 UT, the waves were found to have a speed of -220 kms-1 in the direction n = (0.67, -0.73, -0.13), which makes an angle of 25° against the magnetic field. The phase velocity in the solar wind rest frame was 65 kms-1, compared to an Alfven speed of 75 kms-1 and a sound speed of 30kms-1. The waves propagate sunwards in the solar wind rest frame and are intrinsically right handed, which identifies them as being on the fast magnetosonic branch of the kinetic dispersion relation (Krauss-Varban et al., 1994). The wavelength was found to be ^6000 km and the frequency 0.014 Hz, an order of magnitide below the local ion cyclotron frequency of 0.13 Hz. Hence this analysis is consistent with and confirms previous dual spacecraft analysis, and other multi-spacecraft analyses.

The multi-spacecraft capabilities of the Cluster mission are complemented by the existence of 3D plasma data at a resolution that allows the variations within a wave cycle to be resolved. This is demonstrated by Figure2.13, which shows the correlation between the magnetic field strength (shown in black at 5 Hz resolution) and the density computed at 4 s resolution from the full 3D particle distribution on board the spacecraft (shown in red). The density and field perturbations are clearly correlated as already shown by ISEE observations (Paschmann et al., 1979). It is immediately apparent that these waves are fast magnetosonic, since the perturbations in the field strength are correlated with the density perturbations.

Figure 2.14 shows the results of a case study of MVA performance, reported by Eastwood et al. (2002). The interval 05:00-06:00 UT was filtered to remove high frequency noise and split into 30 2-min sections. Of these, 6 intervals were rejected on the basis of insufficient wave activity. For the other intervals, the minimum variance direction, averaged over the four spacecraft was calculated, as was the 4 spacecraft direction of propagation. The angle between the propagation direction and the average minimum variance direction (forced to point upstream) was then calculated. This angular difference is plotted as a function of intermediate/ minimum eigenvalue (X2/X3) in Figure 2.14. In the case of linearly polarised signals, the variation is confined to one direction, identified as the maximum variance direction. The intermediate and minimum variance directions are degenerate, and consequently X2/X3 = 1. For circularly or elliptically polarised waves, X2/X3 > 1. If the ratio of eigenvalues is >10, it is clear that the two techniques are in agreement. If the ratio is <5, the estimates from the two techniques diverge. This is presumably due to the failure of MVA in the limit that the waves become more and more linearly polarised.

2.3.1.2 Kinetic Alfven waves

Under typical foreshock conditions, the ion-beam instability generates kinetic fast magnetosonic waves (cf., e.g., Gary, 1993), which appear left handed in the spacecraft time series. However, if the beam is hot, or if the core distribution is anisotropic, the growth rate of the right-hand mode may be exceeded by the left-hand mode

05:00:00 05:05:00 05:10:00 05:15:00 05:20:00 05:25:00

Figure 2.12. Magnetic field observed by the Cluster spacecraft between 05:00 and 05:30 UT on April 23 , 2001. The time series are coloured black, red, green and magenta corresponding to spacecraft 1, 2, 3 and 4. Spacecraft 4 is plotted last: hence the magenta dominates because the time series are well correlated. The data are at 22 Hz resolution. (Figure provided by J. P. Eastwood).

05:00:00 05:05:00 05:10:00 05:15:00 05:20:00 05:25:00

Figure 2.12. Magnetic field observed by the Cluster spacecraft between 05:00 and 05:30 UT on April 23 , 2001. The time series are coloured black, red, green and magenta corresponding to spacecraft 1, 2, 3 and 4. Spacecraft 4 is plotted last: hence the magenta dominates because the time series are well correlated. The data are at 22 Hz resolution. (Figure provided by J. P. Eastwood).

growth rate, in which case the dominant unstable wave mode is the left-handed Alfvén/Ion cyclotron or 'kinetic Alfven' wave.

Two possibilities arise for observation of left-hand polarised waves in the spacecraft time series. The first is that they are intrinsically right handed, and are propagating anti-sunwards, in the opposite direction to the beam that generated them. The solar wind Doppler shift would not cause a reversal in polarisation. The second is that they are intrinsically left handed, and propagate sunwards with the beam. The solar wind Doppler shift here causes the observed polarisation to be reversed.

In the first case, the ion beam excites such waves through the non-resonant firehose instability (Sentman et al., 1981). In the second case the left-hand resonant ion beam instability dominates (Gary, 1985). The firehose instability requires the beam to be fast and dense, whereas the left-hand resonant instability requires the beam to be hot. Before the launch of Cluster the exact nature of waves observed to be right-handed in the spacecraft frame was not clear. Single spacecraft studies comparing experimental wave transport ratios with those expected using kinetic theory suggested the existence of Alfven waves (Blanco-Cano and Schwartz, 1997). Dual spacecraft studies were limited by geometry; reviews of foreshock physics before

Magnetic Field Strength and Plasma Density observed by Cluster 1

Magnetic Field Strength and Plasma Density observed by Cluster 1

Figure 2.13. Correlation between magnetic field strength (black) and ion density as measured by HIA (red). Note that the cadence of the ion measurements is 4 s, whereas the magnetic field is shown at 5Hz resolution. The correlation between the two parameters indicates the existence of a fast mode wave according to MHD models. (After Eastwood et al., 2002).

Figure 2.13. Correlation between magnetic field strength (black) and ion density as measured by HIA (red). Note that the cadence of the ion measurements is 4 s, whereas the magnetic field is shown at 5Hz resolution. The correlation between the two parameters indicates the existence of a fast mode wave according to MHD models. (After Eastwood et al., 2002).

the launch of Cluster noted that observations of right handed waves were not well understood (e.g., Le and Russell, 1994).

Figure 2.15 provides an overview of the data recorded by Cluster 1 FGM, as reported by Eastwood et al. (2003). The left three panels show the magnetic field recorded by the Flux Gate Magnetometer on Cluster 1 from 00:00-14:00 UT, at 4 s resolution. Initially, Cluster was in the solar wind, crossing extended bow shock structure just after 05:00 UT and entering the magnetosphere at approximately 09:15 UT. The four left panels show an interval of foreshock wave activity, between 04:00 UT and 04:10 UT. The top panel is the magnetic field strength, and the lower three panels are the components of the field in GSE coordinates. The data are shown at 22Hz resolution. The waves are exceptionally well defined, with very low turbulent noise, and have periods of approximately 10 s in the spacecraft frame.

Minimum variance analysis was applied to the interval 04:04:00-04:04:30 UT. The results are shown in Figure 2.16. The upper four panels show hodograms for each of the four spacecraft. In each case, the waves are right handed with respect to the magnetic field. The data are shown at 22 Hz resolution, and have not been smoothed or filtered. The waves are almost circularly polarised.

Figure 2.14■ Performance of MVA: in the limit of linear wave polarisation, the MVA and 4 spacecraft estimates of wave propagation direction diverge. (From Eastwood et al., 2002).
Figure 2.15. Overview of Cluster magnetic field observations on February 3, 2002. (From Eastwood et al., 2003).
-10 0 10 B(maximum), nT C1
-10 0 10 B(maximum), nT C3
-10 0 10 B(maximum), nT C2
0 0

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