I r 1 2 k VQcp 0kB24

Figure 2.19. Dispersion relations in the rest frame derived from different sources: dispersion from the wave telescope and polarisation from the minimum variance analysis for (a) and computation using a multi-fluid plasma model for (b). Wave number k is projected to a mean propagation direction Oks = 24°. Angular frequency CO and wave number k are normalised. (From Narita et al., 2003).

frame. Based on Cluster 3 CIS/HIA velocity moments this frequency was Doppler transformed into the plasma frame. Moreover, using quasi-monochromatic optical technique to determine the spectral density matrix (Bendat and Piersol, 1980; Born and Wolf, 1980) for the magnetic fluctuation field B( f, T) as function of frequency f and time record length T, the polarisation angle P was computed.

The results of this investigation are displayed in Figure 2.20 which shows the spatial distribution of phase velocities in the plasma rest frame projected into the xr plane in GSE (r = \Jy2 + z2). Small black filled circles give the locations, while the arrows indicate phase velocities normalised to the local Alfven velocity VA. The dashed curve is a nominal bow shock under quiet solar wind conditions.

Most of the waves propagate upstream and are more or less aligned with shock normal directions at various positions, near the x-axis to near shock flanks. Phase

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