# High-Speed Tomography--A New Approach to Plasma Bulk Velocity Measurement
## 3 Results
### Plasma Bulk Velocities  
The velocity of the plasma bulk was determined according to the procedure described in Section 2.3. The parameters used in the measurements are listed in Table 1.  
All measurements were performed at about 20 mbar. The time delay between two exposures of the image intensifier was kept constant at 10 \(\upmu\)s. After a measurement, the data were divided into six different bins, where one bin corresponded to one centimeter, and the mean and standard deviation of all bins were calculated. This provided a spatial resolution of the velocity along the axis of the plasma generator.  
The graph in Figure 16 shows the calculated plasma bulk velocities along the axis of the generator at a distance of 1 cm to 7 cm downstream of the nozzle outlet. The blue-shaded area around the line in Figure 16 marks the standard deviations of the velocity results, which were about 20%. According to the graph, the plasma bulk accelerates to about three centimeters from the nozzle outlet, where an average velocity of 1061 m/s is reached. Further downstream, the velocity decreases slightly and reaches a mean value of 919 m/s at seven centimeters, with a small dip in the curve at four centimeters.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Current [A]** & **Gas Flow [slpm]** & **Exposure Time [ns]** & **Delay [\(\upmu\)s]** \\ \hline
40 & 35 & 200 & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters used for the performed measurements.  
Figure 15: Validation of the reconstruction algorithm based on a comparison of the 3D models: (a) original simulated model; (b) reconstructed model based on the six directions of view.  
The reconstructed cross-sectional images used to calculate the velocity were also used to generate a rough 3D visualization of the plasma plume, allowing for a spatial study of the plasma plume.  
Figure 17 presents a computed 3D reconstruction of the plasma plume at six different points in time (a-f). For a better visualization, a simplified 3D model of the plasma generator is added to each plume reconstruction. The corresponding image used for the calculations is also marked in the figure with colored boxes in each picture (compare Figure 10). Furthermore, distinct features of the plasma plume observed in each image are marked with an arrow. The movement of the marked feature, combined with the known time delay of 10 us between each exposure of the image intensifier, allows for the calculation of the plasma bulk velocity. Besides the velocity measurement, the 3D models calculated by the proposed method show that the reconstruction based on six viewing directions is sufficient to visualize the elementary shape of the plume with its characteristic features.  
Figure 16: Locally resolved plasma bulk velocity along the axis of a DC plasma torch operated with a current of 40 A and an argon flow of 35 slpm at about 20 mbar. The shaded area marks the standard deviation.  
Figure 17: Calculated 3D models of the plasma plume at six different points in time: (**a**) first exposure; (**b**) second exposure; (**c**) third exposure; (**d**) fourth exposure; (**e**) fifth exposure; (**f**) sixth exposure.