As discussed in Section 2.5, the RPA raw data represents the “integrated” ion current, i.e., the current corresponding to ions above a certain energy. To obtain the ion energy distribution, the derivative of the raw data must be taken. (The differentiation method is described in Section 2.5, as well as the uncertainty introduced to the data through this process.) In this chapter, just the differentiated data will be presented. The raw data can be found in Appendix B so that the reader can clearly compare the total ion current between scans if desired.
The individual RPA scans were taken at a fixed distance from the thruster center, at different angles off the thruster centerline (see Section 2.6). In the 200 W case, scans from 0 to 30◦ were taken at a radial distance of 600 mm, while scans from 40 to 90◦ were taken at a distance of 400 mm. The same was done for the 650 W case, except for the scan at 0◦, for which the radial distance was 1000 mm. The distance from the thruster was not the same for all scans due to facility constraints (at high angles the radius of the chamber limited the radius at which the RPA could be positioned), and due to device constraints (if the RPA was too close to the thruster, the high ion density inside the device led to electrical arcing between grids).
Energy distributions were calculated by taking the derivatives of the integrated cur-
rent plots. After the derivatives were taken, the energy distributions were normalized by the total ion current, so that the integral over all energies equals one for each plot. Therefore, the plots in Figures 5.16 to 5.21 show the proportion of ion current versus ion energy, rather than the value of the current itself. This normalization was done so that different scans could be compared on the same scale, even if the scans were taken at different distances from the thruster. The alternative was to adjust the data by using a certain scaling factor that corresponded to the distance at which the data was taken. For example, the total ion current could have been scaled by 1/R2. However, because of the uncertainty that this scaling would introduce, it was decided that the plots presented in this chapter would be normalized rather than scaled. For reference, the non-normalized plots can be found in Appendix B.
Figure 5.16 shows that, at the 200 W condition, as the angle increases the proportion of ion current due to primary beam ions decreases, and a greater proportion of ion current at lower energies is present. Note that at 200 W, the thruster acceleration potential was 250 V, and the measured extraction potential of the cathode was approximately 20 V, so one would expect to see primary beam ions at 230 eV/q, which is what is seen in Figures 5.16 to 5.18. At 20◦, ions with energies as low as 100 eV/q are seen, while at 40◦, ions with energies as low as 20 eV/q are observed. However, even at 40◦, there is still a substantial proportion of ion current at the primary beam energy. This suggests that at 200 W, the plume is not particularly well-collimated.
From 45 to 65◦, as shown in Figure 5.17, the peak corresponding to the high velocity ions continues to decrease in height, while a peak centered at roughly 30 to 40 eV emerges.
Previous research has suggested that this low energy peak can be explained by the effect of charge exchange (CEX) collisions in which a fast moving Xe+ ion trades momentum with a slow moving neutral Xe atom. Additionally, the mid-range energy ions (at roughly 50 to 200 eV) have been attributed to elastic scattering collisions [48]. For this angle range, there is a substantial proportion of mid-range energy ions, the proportion of which remains approximately constant as the angle is increased from 45 to 65◦. Looking at the 65◦ trace, one can see that the peak corresponding to the low energy CEX ions is larger than that due to the primary beam energy ions. From 70 to 90◦, as shown in Figure 5.18, the high velocity ion peak continues to decrease in height, while the low energy CEX peak increases in height, and the distribution of the elastically scattered ion energies shift toward lower
values. However, it should be noted that even at 80◦, a noticeable peak corresponding to the primary beam energy is still present, and even at 85◦, some high velocity ions can still be seen.
For the 650 W case, from 0 to 40◦ (Figure 5.19), a high velocity ion peak is seen, centered roughly at 270 eV/q. (Note that the acceleration potential for this case was 300 V, while the cathode extraction potential was roughly 25 V, so one would expect to see the primary beam peak at roughly 275 eV/q) From 0 to 10◦, the primary energy ion peak decreases in height as angle is increased, and the proportion of elastically scattered ions increases. At 0 and 10◦, one can also see a “tail” off the primary beam energy peak, extending to energies roughly 400 eV/q, which is substantially greater than the applied acceleration potential of 300 V. As discussed in Section 2.5, an explanation for ions with an energy per charge greater than the acceleration potential of the thruster is that these ions have gone from Xe2+ to Xe+ in a CEX collision.
Looking at Figure 5.19, between 10◦ to 20◦ the high energy peak actually increases in height. This may be due to the CEX phenomena mentioned in the previous paragraph;
Xe2+ ions that would have contributed to the peak height have been converted to Xe+ and their energies have spread out in the high energy tail portion of the distribution. As the angle is increased further from 20 to 40◦, the primary beam energy peak decreases in height, and the proportion of elastically scattered and CEX ions increases. At 40◦, the energies corresponding to elastic scattering dominate the distribution.
As in the 200 W case, as the angle is increased from 45 to 65◦ (Figure 5.20), the low energy CEX peak increases in height while the primary beam energy peak decreases in height. At 65◦, there is no ion current due to the ions with the primary beam energy. As the angle is further increased from 70 to 90◦, the proportion of ions corresponding to elastic scattering decreases, while the low energy CEX peak increases slightly in height. No high velocity ions are present at these angles either.
Comparing the 200 W case to the 650 W case suggests that the 200 W case is significantly less collimated than the 650 W case, since a larger proportion of ions with the primary energy are seen at higher angles off of the thruster centerline in the 200 W case. This can be seen clearly by comparing Figure 5.16 to 5.19, Figure 5.17 to 5.20, and Figure 5.18 to 5.21. For example, by comparing the two cases at 45◦, it is clear that in the 200 W case, the high velocity ions make up a major proportion of the ion current, whereas
0 0.02 0.04 0.06
0 deg
0 0.02 0.04 0.06
10 deg
0 0.02 0.04 0.06
Proportion of Ion Current
20 deg
0 0.02 0.04 0.06
30 deg
0 50 100 150 200 250 300 350 400 450
0 0.02 0.04 0.06
Energy per Charge [eV/q]
40 deg
Figure 5.16: Differentiated RPA data at 200 W, 0 to 40◦ from centerline.
0 0.01
0.02 45 deg
0 0.01
0.02 50 deg
0 0.01 0.02
Proportion of Ion Current
55 deg
0 0.01
0.02 60 deg
0 50 100 150 200 250 300 350 400 450
0 0.01 0.02
Energy per Charge [eV/q]
65 deg
Figure 5.17: Differentiated RPA data at 200 W, 45 to 65◦ from centerline.
0 0.01
0.02 70 deg
0 0.01
0.02 75 deg
0 0.01 0.02
Proportion of Ion Current
80 deg
0 0.01
0.02 85 deg
0 50 100 150 200 250 300 350 400 450
0 0.01 0.02
Energy per Charge [eV/q]
90 deg
Figure 5.18: Differentiated RPA data at 200 W, 70 to 90◦ from centerline.
0 0.01
0.02 0 deg
0 0.01
0.02 10 deg
0 0.01 0.02
Proportion of Ion Current
20 deg
0 0.01
0.02 30 deg
0 50 100 150 200 250 300 350 400 450
0 0.01 0.02
Energy per Charge [eV/q]
40 deg
Figure 5.19: Differentiated RPA data at 650 W, 0 to 40◦ from centerline.
0 0.01
0.02 45 deg
0 0.01
0.02 50 deg
0 0.01 0.02
Proportion of Ion Current
55 deg
0 0.01
0.02 60 deg
0 50 100 150 200 250 300 350 400 450
0 0.01 0.02
Energy per Charge [eV/q]
65 deg
Figure 5.20: Differentiated RPA data at 650 W, 45 to 65◦ from centerline.
0 0.01 0.02 0.03 0.04
70 deg
0 0.01 0.02 0.03 0.04
75 deg
0 0.01 0.02 0.03 0.04
Proportion of Ion Current
80 deg
0 0.01 0.02 0.03 0.04
85 deg
0 50 100 150 200 250 300 350 400 450
0 0.01 0.02 0.03 0.04
Energy per Charge [eV/q]
90 deg
Figure 5.21: Differentiated RPA data at 650 W, 70 to 90◦ from centerline.
in the 650 W case, the mid-range elastic scattering energies dominate the distribution.
In terms of high angle ions with the primary beam energy, in the 200 W case, these ions can be seen out to 85◦, while in the 650 W case these ions can be seen out to 60◦ from centerline. This begs the question: if the thruster is designed such that the electric field is primarily axial, then how are initially axial ions being accelerated out to high angles off the centerline? The answer to this question will be addressed in Chapter 6, and is an important issue to arise from the experimental investigation, primarily because it has repercussions for thruster integration onto spacecraft.