Figure 2.20. Spatial distribution of wave phase velocities in the plasma rest frame plotted together with the location of wave observations, projected into the xr plane in GSE (r = \Jy2 + z2). The phase velocities are normalised to the local Alfven velocity. The dashed, curved line is a nominal bow shock. (From Narita et al., 2004).

velocities are found the order of the Alfven speed. Some of the waves, however, propagate downstream in the plasma rest frame. Such waves tend to have phase velocities smaller than the Alfven velocity, but a few cases near the shock show larger phase velocities.

Figure 2.21 shows distributions of frequencies, wave numbers, propagation angles, and ellipticities. The left panel in Figure 2.21 gives the distribution of normalised frequencies, a>rest/Q.cp, as function of the magnitudes of normalised wave numbers kVA/Qcp, i.e., the average dispersion relation. A magnification of the region near rn/Q.cp ~ 0 and kVA/Q.cp ~ 0.1 has been embedded into the panel.

The dotted line represents Alfven waves propagating along B with dispersion relation rn/k = VA. Most of the waves are found at rn/Q.cp ~ 0.1 and kVA/Q.cp ~ 0.1. The major wave population thus propagates at speeds below and up to the Alfven velocity. Some waves are found up to rn/Q.cp ~ 5 and kVA/Q.cp ~ 1.2. These waves are scattered in dispersion, few of them following the Alfven branch.

The middle panel in Figure 2.21 shows the distribution of frequencies as a function of dkB. Waves which propagate within 30° of the magnetic field line tend to be

Figure 2.21. Distribution of rest frame frequencies, wave numbers, propagation angles, and el-lipticity in the plasma rest frame including error bar estimates. The small plot embedded in the left panel magnifies the frequencies and the wave numbers near the origin. The dotted, straight line in the left panel is the dispersion relation for the extended linear Alfven waves. (From Narita et al., 2004).

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