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First consider all thirteen XY-planes (all sample count plots which are not explicitly dis- cussed in this section can be seen in AppendixA. The northern hemisphere (+Z planes) contains more data than the southern hemisphere (-Z planes) with 591207 counts to 468134 counts and therefore has the greatest data coverage. Due to the orbital incli- nation of the Cluster spacecraft and the southerly progression of the orbit throughout the mission, it would be expected that there would in fact be more data in the southern

Figure 4.23: Sample count plots displaying tailward (left) and earthward (right)

plasma flow in the XY plane where Z = -3±1.5 RE.

hemisphere. However, much of the most southerly data was removed due to contamina- tion with data collected in the magnetosheath.

In addition, the spatial distribution of the data collected is more comprehensive in the northern than the southern hemisphere. For example, at lower latitudes there are a good deal more bins occupied in the northern hemisphere than the southern. For the plane covering z = 3± 1.5 RE (Figure4.22), 46 bins (tailward) contain data, whereas for the plane covering z = -3±1.5 RE (Figure4.23), just 31 bins (tailward) are filled. The same trend is evident at higher latitudes, where the plane covering z = 6 ± 1.5 RE (Figure 4.24), 34 tailward bins contain data, whereas the plane covering z = -6±1.5 RE (Figure 4.25) only has 19 tailward bins filled. This distribution is likely to have occurred due to the elliptical orbit and its inclination. This means the perigee of Cluster’s orbit occurs most frequently in the region about the equatorial plane, so the spacecraft spend more time at closer distances to the Earth in this region. The apogee of Cluster’s orbit occurs most frequently in the region below the Earth’s equatorial plane, hence the spacecraft spends more time at larger distances in this region.

In the northern hemisphere there is an asymmetrical data distribution with a greater coverage in the dawn side (negative Y region) than in the dusk (positive Y region) across all the northern planes. The distribution across each plane in the southern hemisphere is generally more sparse than the northern region with the majority of data concentrated

Figure 4.24: Sample count plots displaying tailward (left) and earthward (right)

plasma flow in the XY plane where Z = 6±1.5 RE.

Figure 4.25: Sample count plots displaying tailward (left) and earthward (right)

plasma flow in the XY plane where Z = -6±1.5 RE.

to greater X positions at larger distances from the equatorial plane (Figure 4.26). The distribution is more symmetric about midnight in the southern hemisphere than the northern region, although in general there is more data in the dusk sector, and the data becomes distributed progressively more earthward and duskward with greater distance from the equatorial plane.

Figure 4.26: Sample count plots displaying tailward (left) and earthward (right) plasma flow in the XY plane where Z = -12±1.5 RE.

For the plane centred about Z = 0 RE, the inner edge of the data distribution is the more sparsely populated, with the most densely occupied bins lying at radial distances greater than about 10 RE, with a couple of lower density bins at midnight and at the periphery of the dataset. These spatial distribution patterns and the count gradient are both artefacts of the Cluster spacecraft trajectories, with the spacecraft generally visiting the regions centred about a radial distance of 10 RE more frequently. There is also a dawn-dusk asymmetric spatial data-distribution with greater coverage on the dawn side with 19 bins occupied as opposed to 16 bins in the dusk side.

Looking across all thirteen XY planes in the z-direction (all sample count plots which are not explicitly discussed in this section can be seen in Appendix A, it is clear that overall there is more earthward directed plasma flow than tailward flow, except in the regions of -16.5 RE <Z<-7.5 RE and 4.5 RE <Z<13.5 RE where tailward flow dom- inates, table 4.1. This is unsurprising when considering previous studies. Zhang et al.

Plane (Z=nRE) Nearthward Ntailward Ntotal % Earthward % Tailward 18 0 0 0 - - 15 0 0 0 - - 12 229 411 640 35.8 64.2 9 12777 34778 47555 26.9 73.1 6 100633 161905 262538 38.3 61.7 3 177796 102678 280474 63.4 36.6 0 323830 147191 471021 68.8 31.2 -3 130189 64067 194256 67.0 33.0 -6 62460 56005 118465 52.7 47.3 -9 41254 88105 129359 31.9 68.1 -12 7855 16955 24810 31.7 68.3 -15 509 735 1244 40.9 59.1 -18 0 0 0 0 0 Totals 857532 672830 1530362 56.0 44.0 Table 4.1: Sample count distribution for the XY plane across 13 cuts in the z-direction.

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

(2015a,b) use spatial parameters to only select data from the plasma sheet, encompass- ing -4 RE <Z <4 RE. In these studies, as previously mentioned, Zhang presents that Earthward flow is dominant in the region, so the results presented here are consistent with Zhang’s results. Extrapolating out the reasoning for Zhang’s spatial parameters suggests that he believes that the plasma sheet does not extend out beyond |Z| = 4 RE, and as such this must be close to the plasma sheet boundary layer, the region in which the magnetospheric lobes meet the plasma sheet. The results presented in this chapter are again consistent with this since the outer regions beyond Z = 4.5 RE and Z = -7.5 RE are dominated by tailward plasma flow. They are also in agreement with Ohtani et al.(2009) who showed that in the region -8 RE >X≥-15 RE and|Y|<5 RE (although it is unclear how wide the data sample is in the z-direction), 37% of plasma flow was tailward. In comparison, looking at Table 4.1, it can be seen that if just the central equatorial plane is considered with a thickness of 3 RE in the z-direction, 31.2% of the plasma flow is tailward. If considering the central three planes with a thickness of 9 RE in the z-direction spanning|Z|< 4.5 RE, the plasma flow is tailward 33.6% of the time. From this, it is clear that this study presents a strong correlation with Ohtani’s results.

Following the classic convection model ofDungey(1961) (as discussed in section4.1), it is expected that over large time-scales, the rate of magnetic reconnection at the dayside and nightside should be equal. If the dayside rate is higher, then it adds more open flux to the nightside and erodes flux on the dayside, making this side of the magnetosphere thinner. If the nightside rate is higher then it closes all the open flux eventually leaving a closed magnetosphere. As presented in this section, it is shown that on average between 2001

and 2006, 55.8% of the time tailward flow is dominant. However, the rate of reconnection on both the dayside and the nightside is not inherently connected with the direction of plasma flow. Following nightside reconnection, the Dungey cycle continues transporting plasma contained on newly closed field lines, however, tailward of the reconnection x-line, the fully disconnected field lines which have been returned to the solar wind, still possess negative Vx and are still documented by the Cluster spacecraft. As this additional tailward data follows the nightside reconnection event, it is outside of the balanced- reconnection rate parameters and as such, leads to the imbalance of plasma flow rates. Another possible explanation for tailward flows being recorded more than half of the time could be due to the bursty nature of magnetospheric reconnection. For example, if dayside reconnection is occurring at a slow and steady rate, but tail reconnection occurs impulsively in bursts, you could expect to see more periods of tailward flow. This is because even though the reconnection rates balance out on average, it is the amount of time plasma is seen flowing earthward/tailward being measured rather than the amount of flux seen convecting earthward/tailward. A third contributing factor to the imbalance of flow rates could be due to the sampling position of the spacecraft at any given time in comparison to the NENL during substorm events (which are included in this section of the research). During the steady flow of the normal Dungey cycle, the magnetospheric reconnection line is usually situated at a great distance tailward of the Earth, thus the spacecraft are always Earthward of this boundary, where Earthward flow almost certainly dominate. However, when a NENL is triggered during substorm activity (which does occur many times a day), this new reconnection line may well now sit Earthward of the spacecraft and as such, tailward flows would certainly dominate during this period. So from this it is clear that while broadly speaking the flow rates should be balance, spacecraft sampling position could play a role in displacing this.