Sample Count

This section presents the spatial distribution of the data in the XZ-planes. Looking across all thirteen XZ planes in the y-direction (all sample count plots which are not explicitly discussed in this section can be seen in Appendix B, the dawn hemisphere (-Y planes) contains more data than the dusk hemisphere (741544 counts to 547511 counts) and therefore has the greatest data coverage. The spatial distribution of the data collected is more comprehensive in the inner dusk hemisphere (between y = 1.5 RE and y = 7.5 RE, for example Figure4.37) than the inner dawn sector (for example Figure 4.38), however at greater distances from Earth there are more bins occupied in the dawn hemisphere than the dusk hemisphere. For example, the plane covering y = 3

±1.5 RE has 30 tailward bins with data in, whereas for plane covering y = -3±1.5 RE, 23 bins are filled. At higher latitudes the plane covering y = 15 ± 1.5 RE, only has 5 tailward bins of data, whereas for the plane covering y = -15 ±1.5 RE has 18 tailward bins filled. This distribution provides evidence for the orbital shape and positioning of the Cluster spacecraft. It suggests that in the dusk hemisphere, the spacecraft follows a wider trajectory in the z-direction and a shallower trajectory in the y-direction. In the dawn hemisphere, the spacecraft appears to follow a shallower trajectory in the z- direction and a deeper trajectory in the y-direction. This idea is supported by the fact there was no data collected beyond y = 16.5 RE whereas there were several thousand data points collected in the plane centred on y = -18±1.5 RE. This orbital trajectory also goes some way in explaining why there is more data collected in the dusk hemisphere. Looking across all y-planes, there is an asymmetrical data distribution in both the dawn and dusk hemispheres. In the dawn (-y planes), there tends to be more bins occupied in the northern hemisphere than the southern hemisphere with no data collected beyond z = -13.5 RE (an example of this can be seen in Figure 4.38). This trend is reversed on the dusk side (+y planes) with no data beyond z = 10.5 RE (an example of this can be seen in Figure 4.37). This difference in distribution can be explained by Cluster’s orbital inclination in the YZ plane, whereby when the orbit is predominantly in the dawn hemisphere, the orbit is tilted in the positive z direction and when the orbit is mostly in the dusk sector, the orbit is tilted in the negative z direction. While the orbital plane is fixed in inertial space, because the GSM coordinate system is being used, the frme of reference is being rotated in inertial space. As such a seasonal effect occurs in the form of this orbital tilt, as shown in Figure 4.7.

Figure 4.37: Sample count plot for XZ plane Y = 6± 1.5 Redisplaying tailward (left)

and earthward (right) plasma flow.

Figure 4.38: Sample count plot for XZ plane Y = -6± 1.5 Re displaying tailward

(left) and earthward (right) plasma flow.

As discussed in the previous section, there is more earthward flow than tailward flow across all of the data collected (Table 4.3). However, when observing the data distribu- tion in XZ planes, the central three planes all have more tailward than earthward flow

Figure 4.39: Sample count plot for XZ plane Y = -12± 1.5 Re displaying tailward

(left) and earthward (right) plasma flow.

occurrences. When using theZhang et al. (2015a) plasma sheet spatial parameters as a rough guide, this result becomes more obvious. Zhang suggests that the plasma sheet spans 8 RE in the z-direction and 20 RE in the y-direction and therefore it is now clear that there is likely to be less plasma sheet data contained within the XZ plane and po- tentially proportionally more contaminant magnetosheath and tail-lobe data contained within each plane. The data distribution further out away from Earth is somewhat more perplexing as earthward flows become dominant beyond z =±4.5 RE. Looking at this distribution more closely in Figure 4.39, it can be seen that in the row centred on z = 0 (red boxes), the number of earthward flows double the tailward flow occurrence rate (51,273 earthward counts equalling over two thirds that of all tailward flow for the plane). The large earthward flow occurrence rate found at greater y-positions along the equatorial plane in this study suggests that the plasma sheet does extend out beyond Zhang’s conservative spatial parameter of -10 RE <y<10 RE. These results provide strong evidence that at times the plasma sheet can extend out as far as 19.5 RE in y-direction and extrapolating this, it could be said that during these periods, the mag- netosphere could stretch as wide as 39 RE. Of course it is a dynamic such the plasma sheet boundaries are not static, expanding and contracting with varying magnetospheric conditions.

Plane (Y = nRE) Nearthward Ntailward Ntotal % Earthward % Tailward 18 - - - - - 15 10588 8417 19005 55.7 44.3 12 58090 31961 90051 64.5 35.5 9 99999 41687 141686 70.6 29.4 6 74296 41800 116096 64.0 36.0 3 80362 100311 180673 44.5 55.5 0 77424 163883 241307 32.0 68.0 -3 52658 64077 116735 45.1 54.9 -6 65676 50452 116128 56.6 43.4 -9 89739 49391 139130 64.5 35.5 -12 148327 73542 221869 66.9 33.1 -15 97904 45656 143560 68.2 31.8 -18 2469 1653 4122 59.9 40.1 Totals 857532 672830 1530362 56.0 44.0 Table 4.3: Sample count distribution for the XZ plane across 13 cuts in the y-direction.

The Y value given is the position on which the plane is centred on.