To summarize the results, for all runs, at 50 mm, the maximum ion current density was seen at 10 to 20◦. At 100 mm and 150 mm, the maxima were seen at 10◦. The relative contributions of inward versus outward moving ions varied on a case to case basis, as described above. However, for all runs the peak corresponding to the inward moving ions was larger than that of the outward ions for angles from 10 to 30◦. Also, in all runs except the 650 W upstream run, the outward moving ions made a greater contribution at 60◦. This suggests that the simulated run produces a central jet which is made up primarily of inward moving ions.
When the upstream runs were compared to the downstream runs, the data showed that the beam was more collimated in the upstream runs. This is in line with the data shown in Section 6.2, since the averaged electric field plots suggest that more radial accel- eration occurs in the downstream runs, which would lead to a more divergent beam in the downstream runs.
W upstream run, from 45 to 65◦, the primary energy ion population is very small, and the distribution is dominated by a low energy peak centered at roughly 50 eV/q. This feature is sharpest at 50◦ off the channel centerline. Further increasing the angle from 70 to 80◦ (Figure 6.37) in the upstream run, continues to show a low energy peak, with negligible proportion of ions with energies above 150 eV/q. Charge exchange collisions could explain the presence of ions with low energies; however, as mentioned in Section 3.1.2, in the version of HPHall used here CEX collisions were not enabled. Therefore, the low energy peak seen at high angles is merely due to the acceleration of ions through the electric field.
The analysis of the potential and electric field plots in Section 6.2 suggested that there should be more ions with higher angle trajectories in the 650 W downstream run. This is indeed true, and can be seen in Figures 6.35 to 6.37. At angles from 45 to 55◦ off the thruster centerline, as shown in Figure 6.36, there is a broad population of ions centered roughly at the primary beam energy. The traces corresponding to angles greater that 55◦ show a broad structure extending from roughly 150 eV/q to 300 eV/q, rather than showing a sharper peak centered at about 50 eV/q, as was seen in the upstream run.
0 0.01 0.02
0.03 650 W
0 deg, up 0 deg, down
0 0.01 0.02 0.03
10 deg, up 10 deg, down
0 0.01 0.02 0.03
Proportion of Ion Current
20 deg, up 20 deg, down
0 0.01 0.02 0.03
30 deg, up 30 deg, down
0 50 100 150 200 250 300 350 400 450
0 0.01 0.02 0.03
Energy per Charge [eV/q]
40 deg, up 40 deg, down
Figure 6.35: RPA traces created from HPHall data, 650 W upstream and downstream runs, 0 to 40◦
0 0.01 0.02
0.03 650 W
45 deg, up 45 deg, down
0 0.01 0.02 0.03
50 deg, up 50 deg, down
0 0.01 0.02 0.03
Proportion of Ion Current
55 deg, up 55 deg, down
0 0.01 0.02 0.03
60 deg, up 60 deg, down
0 50 100 150 200 250 300 350 400 450
0 0.01 0.02 0.03
Energy per Charge [eV/q]
65 deg, up 65 deg, down
Figure 6.36: RPA traces created from HPHall data, 650 W upstream and downstream runs, 45 to 65◦
0 0.01 0.02
0.03 650 W
70 deg, up 70 deg, down
0 0.01 0.02 0.03
Proportion of Ion Current
75 deg, up 75 deg, down
0 50 100 150 200 250 300 350 400 450
0 0.01 0.02 0.03
Energy per Charge [eV/q]
80 deg, up 80 deg, down
Figure 6.37: RPA traces created from HPHall data, 650 W upstream and downstream runs, 70 to 80◦
6.4.2 200 W results
Figures 6.38 to 6.40 show the simulated RPA traces for the 200 W run. The 200 W upstream traces follow similar trends to the 650 W upstream run, i.e., a primary ion peak that decreases in magnitude with increasing angle, which is no longer seen at angles above 40◦, and a low energy peak that begins to form at 40◦ and dominates the distribution for angles above 40◦. In this run, the low energy peak is shorter and broader than in the 650 W run, although it is still centered at roughly 50 eV/q.
In the 200 W downstream run, one can see primary beam ions out at higher angles.
For example, there is still a substantial proportion of these ions at 50◦. As the angle is increased above 55◦, there is no clear peak in the data; instead, there is a broad population of ions with energies from 0 to about 250 eV/q. At 60◦ there is a peak within the data at approximately 130 eV/q, which corresponds roughly to the potential at z = 0.030 (as shown in Figure 6.16), so these ions could be the result of ions that are created just outside the exit plane of the thruster.
To summarize the simulated RPA results, in both of the upstream runs, primary energy, high angle ions are not seen at high angles off of the thruster centerline. In the downstream runs, ions with the primary energy are seen at high angles (up to 80◦), but as part of a broad distribution of ions with various energies, rather than being seen as a separate, narrow peak in the data centered at the primary beam energy.
0 0.01 0.02
0.03 200 W
0 deg, up 0 deg, down
0 0.01 0.02 0.03
10 deg, up 10 deg, down
0 0.01 0.02 0.03
Proportion of Ion Current
20 deg, up 20 deg, down
0 0.01 0.02 0.03
30 deg, up 30 deg, down
0 50 100 150 200 250 300 350 400 450
0 0.01 0.02 0.03
Energy per Charge [eV/q]
40 deg, up 40 deg, down
Figure 6.38: RPA traces created from HPHall data, 200 W upstream and downstream runs, 0 to 40◦
0 0.01 0.02
0.03 200 W
45 deg, up 45 deg, down
0 0.01 0.02 0.03
50 deg, up 50 deg, down
0 0.01 0.02 0.03
Proportion of Ion Current
55 deg, up 55 deg, down
0 0.01 0.02 0.03
60 deg, up 60 deg, down
0 50 100 150 200 250 300 350 400 450
0 0.01 0.02 0.03
Energy per Charge [eV/q]
65 deg, up 65 deg, down
Figure 6.39: RPA traces created from HPHall data, 200 W upstream and downstream runs, 45 to 65◦
0 0.01 0.02
0.03 200 W
70 deg, up 70 deg, down
0 0.01 0.02 0.03
Proportion of Ion Current
75 deg, up 75 deg, down
0 50 100 150 200 250 300 350 400 450
0 0.01 0.02 0.03
Energy per Charge [eV/q]
80 deg, up 80 deg, down
Figure 6.40: RPA traces created from HPHall data, 200 W upstream and downstream runs, 70 to 80◦
Table 6.4: Maximum error in the simulated Faraday probe data.
Distance [mm]
650 W upstream
[A/m2]
650 W downstream
[A/m2]
200 W upstream
[A/m2]
200 W downstream
[A/m2]
50 11.46 40.67 16.50 12.92
100 47.60 18.37 6.595 10.39
150 28.56 15.24 7.326 9.229