found in the JPL study that the code underpredicted the experimentally measured electron temperature by about 10 eV, while in Fife’s study one of the cases overpredicted SPT-70 measured values by about 10 eV. This suggests that it is difficult to assess the accuracy of the electron temperature predicted by HPHall. Therefore, a discrepancy of about 10eV between the current study and the previous studies is not necessarily cause for alarm.
run.
The 200 W runs also show a similar trend (Figure 6.26). In the 200 W upstream run, the height of the peak increases from about 700 A/m2 at 50 mm, to 950 A/m2 at 100 mm, and then decreases slightly to 850 A/m2 at 150 mm. In the 200 W downstream run, the peak height decreases from about 1000 A/m2 at 50 mm to 800 A/m2 at 100 mm, and then to 600 A/m2 at 150 mm. As in the 650 W runs, the maximum ion current density occurs at a shorter axial distance in the downstream run.
Just by examining the data in Figures 6.25 to 6.26, it isn’t possible to see the transition from ring to jet, since all of the plots simply show a sharp peak at the center of the distribution. However, if the Faraday probe data at 25 mm is also plotted, one can see this transition in some of the runs. Figure 6.27 shows a comparison between the Faraday probe traces at 25 mm for the four different runs. The top plot shows the 650 W runs, while the bottom plots show the 200 W runs. It is clear from these plots that for both upstream runs, the central peak is much shorter, and there are short secondary peaks corresponding to the two sides of the channel. This suggests that the transition from ring to jet is definitely occurring at a farther axial distance in the downstream runs than in the upstream runs.
0 1000 2000 3000
650 W 150 mm, up
150 mm, down
0 1000 2000 3000
Ion Current Density [A/m2 ]
100 mm, up 100 mm, down
−1000 −50 0 50 100
1000 2000 3000
Transverse Location [mm]
50 mm, up 50 mm, down
Figure 6.25: Faraday probe traces created from HPHall data, 650 W upstream and down- stream runs.
0 200 400 600 800 1000
200 W 150 mm, up
150 mm, down
0 200 400 600 800 1000
Ion Current Density [A/m2 ]
100 mm, up 100 mm, down
−1000 −50 0 50 100
200 400 600 800 1000
Transverse Location [mm]
50 mm, up 50 mm, down
Figure 6.26: Faraday probe traces created from HPHall data, 200 W upstream and down- stream runs.
0 500 1000 1500 2000 2500 3000
Ion Current Density [A/m2 ]
650 W upstream 650 W downstream
−1000 −50 0 50 100
200 400 600 800 1000
Transverse Location [mm]
200 W upstream 200 W downstream
Figure 6.27: Faraday probe traces created from HPHall data, all runs at an axial distance of 25 mm.
6.3.2 ExB Probe Results
Figures 6.28 to 6.31 show the simulated ExB data for the 650 W runs, at the three axial distances of 50, 100, and 150 mm. Each of the plots represents ions at a different angle, and the plots have been constructed so that they can be directly compared to the experimental scans (see Chapter 5). Figure 6.28 shows that at 50 mm, in the upstream run the current density is largest at 10 to 20◦ (the maxima of these two traces are both about 25 A/m2). In the downstream run, the largest ion current density is due to ions traveling at 20◦ relative to the centerline, and the total ion current density at 20◦ is much larger in the downstream case than in the upstream run.
At angles of 20◦ and above, the current density in the downstream run is much larger than in the upstream run, whereas at 0◦ the current density in the upstream run is significantly greater. At 10◦ the two runs show approximately equal values. This shows that the ion beam is significantly less collimated in the downstream case than in the upstream case. It is also worth noting that, for both the upstream and downstream runs, as the angle is increased above zero degrees, the peak corresponding to inward moving ions (the right peak) is considerably larger than that corresponding to the outward moving ions (the left peak). This is seen at angles from 10 to 20◦ in the upstream run and 10 to 60◦ in the downstream run.
As discussed earlier, one of the reasons for the large peaks in the ion current density near the thruster centerline is because the simulated ion current must be divided by the area, which is smaller near the centerline. Looking at the ion current data itself in Figure D.1, one can see that for angles from 10 to 20◦ the contribution due to inward moving ions is larger in both runs. At 30◦ the contribution from outward moving ions is larger in the upstream run, although inward ions still dominate the 30◦ traces in the downstream run. This shows that, from 10 to 20◦ in the upstream run, and 10 to 30◦ in the downstream run, inward moving ions account for a significantly larger amount of the ion current.
Since the ion current is largest from 0 to 30◦in both runs, and falls off significantly as the angle is increased beyond 30◦, this shows clearly that inward moving ions are responsible for a much greater proportion of the total ion current in both the 650 W upstream and downstream runs. Similar trends are seen at the other distances (100 and 150 mm), and in the 200 W runs. This is strong evidence that within the ion beam, there is a greater
number of inward moving versus outward moving ions, and that the greater ion current density seen in both the experimental and simulated data is not merely due to geometry (i.e., ions moving into a smaller area).
Rather than present both the ion current density dataand the ion current data for all of the runs in this chapter (which would result in a very large number of graphs), the ion current data for the rest of the runs has been put in Appendix D for reference. Ion current density data is used as the standard in this chapter because it can be directly compared to the experimental data in Chapter 5, while the ion current data cannot.
At 100 mm (Figure 6.30), the largest current density contribution is made by ions traveling at 10◦ in both the 650 W upstream and downstream run. At this distance, for both runs, the inward moving ions make a larger contribution to the current density at 10 to 30◦. As the angle is further increased, the inward and outward moving ion contributions are about the same in the upstream run, while the inward moving ion peak is larger at 40 and 50◦ in the downstream run.
At 150 mm (Figure 6.31), the largest current density contribution is made by ions traveling at 10◦ in both 650 W runs. At this distance, for both runs, the inward moving ions make a larger contribution to the current density at 10 to 30◦. As the angle is further increased, the inward and outward moving ion contributions are about the same in the upstream run, while the inward moving ion peak is larger at 40◦ in the downstream run.
0 0.01 0.02
Axial Distance = 50 mm, 650 W 60 deg, up
60 deg, down
0 0.05
0.1 50 deg, up 50 deg, down
0
0.5 40 deg, up 40 deg, down
0 5
Collimated High Velocity Xe+ Current Density [A/m2 ]
30 deg, up 30 deg, down
0 100
200 20 deg, up
20 deg, down
0
20 10 deg, up
10 deg, down
−400 −350 −300 −250 −200 −150 −100 −500 0 50 5
10
Transverse Location [mm]
0 deg, up 0 deg, down
Figure 6.28: ExB probe traces created from HPHall data at 50 mm, 650 W upstream and downstream runs.
0
5x 10−5 Axial Distance = 50 mm, 650 W 60 deg, up
60 deg, down
0 1
x 10−4
50 deg, up 50 deg, down
0 2 4
x 10−4
40 deg, up 40 deg, down
0 1
x 10−3
Collimated High Velocity Xe+ Current [A]
30 deg, up 30 deg, down
0 2 4x 10−3
20 deg, up 20 deg, down
0 5
x 10−3
10 deg, up 10 deg, down
−400 −350 −300 −250 −200 −150 −100 −500 0 50 5x 10−3
Transverse Location [mm]
0 deg, up 0 deg, down
Figure 6.29: ExB probe traces created from HPHall data at 50 mm, 650 W upstream and downstream runs. Ion current, not ion current density (i.e., not divided by area).
0 5
x 10−3 Axial Distance = 100 mm, 650 W
60 deg, up 60 deg, down
0 0.02
0.04 50 deg, up 50 deg, down
0 0.1
0.2 40 deg, up 40 deg, down
0 0.5 1
Collimated High Velocity Xe+ Current Density [A/m2 ]
30 deg, up 30 deg, down
0
5 20 deg, up
20 deg, down
0
100 10 deg, up
10 deg, down
−400 −350 −300 −250 −200 −150 −100 −500 0 50 5
10
Transverse Location [mm]
0 deg, up 0 deg, down
Figure 6.30: ExB probe traces created from HPHall data at 100 mm, 650 W upstream and downstream runs.
0 2 4
x 10−3 Axial Distance = 150 mm, 650 W
60 deg, up 60 deg, down
0 0.01
0.02 50 deg, up
50 deg, down
0
0.05 40 deg, up 40 deg, down
0 0.5
Collimated High Velocity Xe+ Current Density [A/m2 ]
30 deg, up 30 deg, down
0
2 20 deg, up
20 deg, down
0
50 10 deg, up
10 deg, down
−400 −350 −300 −250 −200 −150 −100 −500 0 50 5
Transverse Location [mm]
0 deg, up 0 deg, down
Figure 6.31: ExB probe traces created from HPHall data at 150 mm, 650 W upstream and downstream runs.
Figures 6.32 to 6.34 show the simulated ExB data for the 200 W upstream and downstream runs, at the three axial distances. In the 200 W upstream run, the total ion density is roughly constant from 0 to 20◦ (if you add up the two peaks, the total is roughly 10 A/m2). In the 200 W downstream run, the maximum in total ion density is at 20◦. Additionally, it can be seen in both runs that from 10 to 30◦ the contribution to the current density due to the inward moving ions is greater than the outward moving ions. In the downstream case, the peak corresponding to the inward moving ions also is larger in the 40◦ trace.
One also sees that, as in the 650 W runs, at 0◦, the current density in the 200 W downstream run is about half of the 200 W upstream run. At 10◦ they are about even, but at angles higher than 20◦ the current density is about an order of magnitude higher in the downstream run. This suggests a less-collimated beam for the downstream run. At 100 mm away from the thruster exit plane (Figure 6.33) one can see that in both runs, the maximum current density is seen at 10◦, and that the inward moving ions make a greater contribution at angles from 10 to 30◦. At 150 mm (Figure 6.34), the same trends are seen.
0 1
2x 10−3 Axial Distance = 50 mm, 200 W 60 deg, up
60 deg, down
0 0.005
0.01 50 deg, up 50 deg, down
0 0.1
0.2 40 deg, up 40 deg, down
0 1
Collimated High Velocity Xe+ Current Density [A/m2 ]
30 deg, up 30 deg, down
0
50 20 deg, up
20 deg, down
0 5
10 10 deg, up
10 deg, down
−400 −350 −300 −250 −200 −150 −100 −500 0 50 5
Transverse Location [mm]
0 deg, up 0 deg, down
Figure 6.32: ExB probe traces created from HPHall data at 50 mm, 200 W upstream and downstream run.
0 5
x 10−4 Axial Distance = 100 mm, 200 W
60 deg, up 60 deg, down
0 2 4
x 10−3
50 deg, up 50 deg, down
0
0.05 40 deg, up 40 deg, down
0 0.2
Collimated High Velocity Xe+ Current Density [A/m2 ]
30 deg, up 30 deg, down
0
2 20 deg, up
20 deg, down
0
50 10 deg, up
10 deg, down
−400 −350 −300 −250 −200 −150 −100 −500 0 50 2
4
Transverse Location [mm]
0 deg, up 0 deg, down
Figure 6.33: ExB probe traces created from HPHall data at 100 mm, 200 W runs.
0 2
4x 10−4 Axial Distance = 150 mm, 200 W
60 deg, up 60 deg, down
0 1 2
x 10−3
50 deg, up 50 deg, down
0
0.02 40 deg, up 40 deg, down
0 0.1
Collimated High Velocity Xe+ Current Density [A/m2 ]
30 deg, up 30 deg, down
0 0.5
1 20 deg, up
20 deg, down
0
20 10 deg, up
10 deg, down
−400 −350 −300 −250 −200 −150 −100 −500 0 50 2
Transverse Location [mm]
0 deg, up 0 deg, down
Figure 6.34: ExB probe traces created from HPHall data at 150 mm, 200 W upstream and downstream runs.
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.