# Plasma Expansion Characterization of a Vacuum Arc Thruster with Stereo Imaging
## 3 Results  
First, the results of the calculation of the are shown, followed by the reconstructed 3D models. Figure 11 shows two diagrams with the results from the calculation of the area of the plume expansion. For all points in time, the mean value of the recordings was calculated and is displayed with the standard deviation as an error bar. The partly large deviations and discrepancies originate from the highly non-uniform discharge of the thruster. This fluctuation in the formation of the plasma jet was also found in studies by project participants [17]. Graph (a) shows the calculated values at the mentioned points in time from Table 1 without a nozzle, and (b) shows the values when using a magnetic nozzle. It can be seen that when increasing the time distance between the ignition of the thruster and recording of the images, the calculated areas increase in both cases as well. This seems plausible based on the PJP discharge duration of 25 \(\upmu\)s. The calculated areas for the setup without a magnetic nozzle show higher values within a delay of 750 ns between ignition and image acquisition. For a delay higher than 750 ns, the setup with a magnetic nozzle shows higher values. Essentially, the values indicate a more uniform shape formation when using a magnetic nozzle, because of the lower percentage deviation between both directions of observation. Only for the 10 \(\upmu\)s point in time, a higher deviation between the calculated areas of both directions of observation can be recognized. The reason for this is physical-based, because a qualitative difference in the plume expansion is already recognizable in the recordings of Figure 12b for instance, which is confirmed by the different area values for the setup without a magnetic nozzle. Furthermore, a more homogenous qualitative expansion of the plume as in Figure 13b demonstrates a small deviation in the area values of both directions of view for the setup with a magnetic nozzle. These observations are confirmed by the other recordings in Figures 14 and 15b,e,h. Figure 11: Calculated areas (blue: left direction of observation; green: right direction of observation) from the sliced contours of both perspectives: (**a**) thruster without magnetic nozzle; (**b**) thruster with magnetic nozzle. Figure 12: Calculated 3D models of the plasma plume at 1 \(\upmu\)s without magnetic nozzle and with the PJP model: (**a**) reconstructed plume left direction of observation; (**b**) recorded image with both directions of observation; (**c**) reconstructed plume right direction of observation; (**d**) isometric view of left direction of observation with PJP; (**e**) front view with PJP; (**f**) isometric view of right direction of observation with PJP. Figure 13: Calculated 3D models of the plasma plume at 1 \(\upmu\)s with magnetic nozzle and with the PJP model: (**a**) reconstructed plume left direction of observation; (**b**) recorded image with both directions of observation; (**c**) reconstructed plume right direction of observation; (**d**) isometric view of left direction of observation with PJP; (**e**) front view with PJP; (**f**) isometric view of right direction of observation with PJP. By comparison to the discharge current, a correlation between the discharge current and the plume area can be recognized [17]. The correlation is valid tendentially for both cases, with and without a magnetic nozzle, whereas the use of the magnetic nozzle shows a stronger increase in area. These conclusions from the above figures were investigated additionally by computing a 3D model from both perspectives. Figure 12 shows the calculated 3D model of the plasma plume for the setup of ignition without a magnetic nozzle. This model was computed from recording 1 \(\upmu\)s after ignition, seen in (b). While (a) represents the left perspective, (c) shows the right direction of view. To obtain a better spatial idea of the reconstructed model, the 3D model of the PJP was included and an isometric view of the reconstruction is shown.