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Figure 2.2. Probability distributions for the electric field amplitudes observed by the Cluster 3 WBD plasma wave receiver with fits to the Gaussian function predicted by stochastic growth theory (solid lines). (a) Probability distribution for all values of Df (see text for description). (b) Probability distributions for selected ranges of Df. From Sigsbee et al. (2004b).

2.2.2 Internal boundaries in the ion foreshock: Particle observations

Through the analysis of single and dual spacecraft foreshock observations, the basic morphology of the ion foreshock is reasonably well understood. Figure 2.3 shows a schematic picture of the ion foreshock for an IMF cone angle of 45°, here corresponding to a sunward pointing Parker spiral. The solar wind flows vertically from the top of the figure with velocity vsw. The tangent field line marks the point at which the solar wind becomes magnetically connected to the bow shock; behind this tangent point, ions can escape from the shock back into the upstream region. They are ejected with velocity vFAB, which here is shown to be field aligned. However, the backstreaming ions are also subject to E x B drift in the solar wind convection electric field, and therefore the upstream boundary of the ion foreshock is not aligned to the magnetic field. Note also that the upstream boundary of the ion foreshock does not intersect the tangent field line surface.

Field aligned distributions, which are not observed in conjunction with ULF waves, are typically observed at and near the leading edge of the ion foreshock, whereas intermediate and diffuse distributions, observed in the presence of ULF waves are observed deeper in the foreshock, upstream of the quasi-parallel shock (e.g., Russell and Hoppe, 1983). Consequently, there exists a second boundary within the ion foreshock confining the region of ULF wave activity. This boundary

! Selected Bins of Df : -1.0<Df<-0.50 N=20849 ■ -0.50<Df<0.0 N=52135 r 0.0<D,<0.50 N=5071 ! 0.50<Df<1.0 N=12898

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