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Figure 9.10. Cluster 3 measurements during the inbound pass over the southern polar cap on February 13, 2001. The top two panels show the convection velocities measured by the electron drift instrument (EDI), after applying a 30 s-smoothing to the full-resolution data; V±xz is the component in the GSE (X, Z)-plane (with negative values implying anti-sunward convection), V^y the component along GSE-Y. The third and fourth panels show the ion density, N, and the parallel component of the bulk velocity, V|, measured by CIS/HIA, the fifth panel the magnetic field strength measured by FGM. The bottom panel shows the lagged IMF clock-angle, confirming the consistently southward direction of the IMF. (From Vaith et al., 2004).

feature under southward IMF. There is an almost identical case on February 20, 2001, and others are also evident in the first two years of the mission.

9.2.4 Statistical survey

While the case studies presented in the previous three sections can highlight important physics issues, a comprehensive analysis of a large number of crossings is required to really understand the cusp. An alternative approach is to carry out statistical surveys that discuss the cusp in terms of a number of key parameters to highlight general trends.

Lavraud et al. (2004a) carried out such a statistical survey of three years of high-altitude cusp encounters (2001 - 2003 inclusive). They discussed (1) the global

19:58 19:59 20:00 20:01 20:02 20:03 20:04 20:05 20:06 20:07 20:08 20:09 20:10

Figure 9.11. The magnetic field with a resolution of 22.4 vectors per second from 19:58 - 20:10 UT on February 13, 2001. The six panels show the magnetic field magnitude and components in GSE coordinates. (Figure provided by P. J. Cargill).

19:58 19:59 20:00 20:01 20:02 20:03 20:04 20:05 20:06 20:07 20:08 20:09 20:10

Figure 9.11. The magnetic field with a resolution of 22.4 vectors per second from 19:58 - 20:10 UT on February 13, 2001. The six panels show the magnetic field magnitude and components in GSE coordinates. (Figure provided by P. J. Cargill).

magnetic field and plasma properties of the high-altitude cusp diamagnetic cavity (the 'exterior cusp') and its surrounding regions, (2) the identification of the various boundaries surrounding the exterior cusp and (3) the dependence of cusp plasma flows on the IMF orientation. Motion of the cusp and magnetopause positions in response to solar wind conditions requires the use of appropriate transformations in order to ensure that averages are calculated from data that is spatially concordant. This can be achieved by the use of the Tsyganenko and Stern (1996): T96 magnetic field model to account for cusp angle deviations, and the magnetopause model of Shue et al. (1997) to include radial magnetopause variations. The technique is presented fully in Lavraud et al. (2004a).

Figures 9.12a and 9.12b show distributions of the average magnetic field vector and the ratio of measured magnetic pressure to the magnetic pressure estimated from the T96 model. Figures 9.12c and 9.12d show, respectively, the distribution of the average ion density normalised to that in the solar wind, and the ion temperature normalised to that predicted near the magnetopause at high latitudes, using the solar wind parameters as input in the Spreiter et al. (1966) magnetosheath model. Figures 9.13a and 9.13b show the distributions of the parallel plasma flows for southward and northward IMF orientations respectively, and Figures 9.13c and 9.13d the distributions of the perpendicular velocity components in the X direction of the normalised frame respectively for southward and northward IMF (Lavraud et al., 2005). In all plots, three distinct boundaries are shown as guides, and are discussed below.

Figure 9.12. The spatial distribution of (a) the magnetic field vectors, where the size of each vector is the field magnitude in logarithmic scale. The colour of the vectors corresponds to the deviation of the measured magnetic field to the T96 model field (Bmeas — Bj96). (b) The ratio of the measured magnetic pressure to that calculated from the T96 model. (c) The ratio of the measured density to that monitored in the solar wind and (d) the ratio of the measured temperature to the temperature predicted in the magnetosheath. In all panels, data are averaged over bins of 0.3 Re . In panels (b) - (d) the sizes of the squares are proportional to the number of samples but are saturated at the maximum (0.3 Re ) for more than 20 samples. The background field lines are calculated from the T96 model, and colour palettes are used to illustrate the amplitude of the parameters studied. In this figure all IMF conditions are taken into account. (Adapted from Lavraud et al., 2004a).

Figure 9.12. The spatial distribution of (a) the magnetic field vectors, where the size of each vector is the field magnitude in logarithmic scale. The colour of the vectors corresponds to the deviation of the measured magnetic field to the T96 model field (Bmeas — Bj96). (b) The ratio of the measured magnetic pressure to that calculated from the T96 model. (c) The ratio of the measured density to that monitored in the solar wind and (d) the ratio of the measured temperature to the temperature predicted in the magnetosheath. In all panels, data are averaged over bins of 0.3 Re . In panels (b) - (d) the sizes of the squares are proportional to the number of samples but are saturated at the maximum (0.3 Re ) for more than 20 samples. The background field lines are calculated from the T96 model, and colour palettes are used to illustrate the amplitude of the parameters studied. In this figure all IMF conditions are taken into account. (Adapted from Lavraud et al., 2004a).

9.2.4.1 Global properties for all IMF conditions

The distribution of the magnetic field vector highlights the presence of an intermediate region between the magnetosheath and the magnetosphere which is the exterior cusp. In this region, both magnetic field direction and strength are variable (Figure 9.12a). The exterior cusp extends a few RE inside the nominal magnetopause location and is characterised by the presence of cold (Figure 9.12d) and dense (Figure 9.12c) plasma of solar wind origin. Comparison with the measured magnetic pressure (which shows a deficit) demonstrates that this region is diamag-netic.

The magnetic field and plasma distributions allow one to establish the unambiguous presence of three distinct boundaries surrounding the exterior cusp region: inner boundaries with the lobes at the poleward edge and the dayside magnetosphere at the equatorward edge, and an external boundary with the magnetosheath. These results also show that as one travels from the magnetosheath to the exterior cusp, the external boundary is characterised by a density decrease and temperature increase.

9.2.4.2 Dependence of large-scale plasma flows on IMF orientation

For southward IMF, solar wind plasma is statistically observed to be flowing Earthward (field-aligned) primarily at the equatorward side of the cusp (Figure 9.13a), and Figure 9.13c shows that these precipitating ions are characterised by large tailward convection. Overall, the convection in the cusp and plasma mantle is consistently directed tailward.

By contrast, under northward IMF conditions, no downward flows are seen at all at the equatorward edge of the cusp (Figure 9.13b). However, there is evidence for field-aligned downward flows at higher latitudes, near the boundary with the lobes. Consistent with this, no large-scale convection is observed in the cusp but a slight Sunward convection is present near the poleward boundary.

While convection is large and tailward in the exterior cusp for southward IMF, it is very small (and perhaps Sunward) for northward IMF conditions. This is compatible with the idea that convection is a consequence of reconnection and more specifically that the reconnected field lines need to travel opposite to the magne-tosheath flow in the case of high-latitude reconnection. All of the above statistical findings suggest that the whole high-altitude cusp region is structured, at large scales, by magnetic reconnection occurring near the lobes under northward IMF, but at the lower latitude magnetopause for southward IMF.

9.2.5 Waves and turbulence

The cusp is also now recognised as being the site of small-scale plasma processes, manifested in particular by electric and magnetic field fluctuations (e.g., Bahnsen et al., 1975; Gurnett and Frank, 1978; Pottelette et al., 1990; Pickett et al., 1999,

Figure 9.13. Spatial distributions of plasma flows in the high-altitude cusp region when IMF conditions are restricted to southward (IMF clock angle CA >120°) and northward (CA < 60°) orientations. (a) Field-aligned components of the plasma velocity for southward IMF. Its magnitude (in kms-1) is shown by the colour palette. (b) The parallel flow in the case of northward IMF. The lower panels show the spatial distribution of the X component of the perpendicular flow velocity for (c) southward IMF and (d) northward IMF. Other details are as in Figure 9.12. (Adapted from Lavraud et al., 2005).

Figure 9.13. Spatial distributions of plasma flows in the high-altitude cusp region when IMF conditions are restricted to southward (IMF clock angle CA >120°) and northward (CA < 60°) orientations. (a) Field-aligned components of the plasma velocity for southward IMF. Its magnitude (in kms-1) is shown by the colour palette. (b) The parallel flow in the case of northward IMF. The lower panels show the spatial distribution of the X component of the perpendicular flow velocity for (c) southward IMF and (d) northward IMF. Other details are as in Figure 9.12. (Adapted from Lavraud et al., 2005).

2001; Le et al., 2001; Savin et al., 2004). Such fluctuations are important because they can lead to particle energisation and/or scattering. Electric field fluctuations

X Normal, Re

Figure 9.14■ The spatial distribution of the magnetic wave power between 1 and 10 Hz measured by the STAFF experiment between 2001 and 2003. All IMF orientations are included. Other details may be found in Figure 9.12 caption. (Figure provided by N. Cornilleau-Wehrlin).

X Normal, Re

Figure 9.14■ The spatial distribution of the magnetic wave power between 1 and 10 Hz measured by the STAFF experiment between 2001 and 2003. All IMF orientations are included. Other details may be found in Figure 9.12 caption. (Figure provided by N. Cornilleau-Wehrlin).

can also provide the localised diffusion needed to, for example, initiate and sustain the magnetic reconnection process.

A good summary of the extent of cusp magnetic field turbulence can be obtained from a statistical survey using the method discussed in Section 9.2.4. Figure 9.14 shows the magnetic wave power in the high-altitude cusp measured in the frequency range between 1 and 10 Hz by the Cluster STAFF experiment. High intensities are seen in both the magnetosheath and in the outer regions of the exterior cusp. A decreasing level of wave power is seen as one moves further into the cusp. The funnel-shape of wave power above 10~2'5 nT2 resembles the distribution of both the density and magnetic field cavity shown in Figure 9.12. These distributions could either reflect the transport of waves into the cusp, or their in-situ generation, but to resolve this issue requires detailed case-study analysis of the waves.

A good example of the nature of cusp magnetic field turbulence can be found during the March 17, 2001 encounter discussed above. This shows bursty turbulence, an association of wave power with sheared plasma flows (see Figure 9.3), and the evidence of major power enhancement at the ion cyclotron frequency and its harmonics. Figure 9.15 shows the power in the magnetic field fluctuations in the

lime (LFT}

Figure 9.15. The power in perpendicular magnetic field fluctuations between 05:00 and 07:00 UT on March 17, 2001. The power is integrated over the frequency range 0.5 - 7 Hz. (Figure provided by K. Nykyri).

lime (LFT}

Figure 9.15. The power in perpendicular magnetic field fluctuations between 05:00 and 07:00 UT on March 17, 2001. The power is integrated over the frequency range 0.5 - 7 Hz. (Figure provided by K. Nykyri).

interval 05:00 - 07:00 UT as determined from the four FGM instruments (Nykyri et al., 2003,2004). The level of wave power changes considerably as Cluster moves through the cusp, and varies by up to an order of magnitude between the spacecraft at some locations. At cusp entry the onset of the waves is extremely rapid, and can be directly linked to the sudden appearance of reconnection flows (Holland et al., 2004): Section 9.2.1). Indeed CIS data indicates that the power level is in general closely associated with the presence of field-aligned plasma flows. This is especially striking at 05:30 UT where the rapid drop-out and subsequent enhancement in wave power corresponds to a vanishing and subsequent enhancement of the bulk flows, despite the continued presence of magnetosheath plasma.

The detailed wave properties such as polarisation, propagation direction and correlation between spacecraft have also been analysed (Nykyri et al., 2004). An example of the power spectrum at four different times is shown in Figure 9.16. Particularly important points to note are the large differences in power between the spacecraft, the differences in the peak power at different times and the peaks in the spectrum at the first and second harmonics of the ion cyclotron frequency. Indeed, examination of STAFF data in the interval around 05:27 UT reveals up to five cyclotron harmonics between 1 and 10 Hz (Figure 9.17). A correlation analysis between the four spacecraft (which are separated by approximately 600 km) reveals no correlation between the various signals. A similar analysis has been carried out for two cusp crossings in 2002 (March 2 and March 9) and show broadly similar results, including sometimes a lack of correlation when the separation is only 100 km.

Whether these waves are generated remotely and convected to the spacecraft, or are generated in situ is unclear at present. Clearly the sheared bulk flows are a possible energy source for the waves, and there exists an extensive literature on the generation of ion cyclotron waves and harmonics in such a situation. However, the

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