## 3 Results and Discussion  
### Experimental Measurements  
#### 3.1.1 Plasma Potential  
The measurement of plasma potentials was performed at different axial and radial positions. An auxiliary tungsten filament (thermionic cathode) located in the vacuum chamber within the vicinity of the thruster could be used for partial compensation of the beam current by means of thermionic emission. Two cases were investigated:  
1. Filament is heated and kept floating \(\rightarrow\)**uncompensated** (UC) beam. 2. Filament is heated and allowed to source up to \(1\,\text{mA}\) of electrons, effectively reducing the total electric current emitted by the SSG \(\rightarrow\)**partially compensated** (PC) beam. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Name** & **Field BC** & **Particle BC** \\ \hline Inlet & \(\phi=\phi_{p}=18\,\text{V}\) & \(\text{Xe}^{+}\): \(n=1\times 10^{19}\,\text{m}^{-3}\), \(\text{u}=1600\,\text{m}\,\text{s}^{-1}\), \\  & & \(T_{\text{Xe}^{+}}=320\,\text{K}\) \\  & & \(\text{e}^{-}\): \(n=1\times 10^{19}\,\text{m}^{-3}\), \(T_{e}=3.5\,\text{eV}\) \\ Thruster & \(\phi=0\,\text{V}\) & All species are removed when crossing this BC. \\ Chamber & \(\phi=0\,\text{V}\) & All species are removed when crossing this BC. Ions \\ Floating probes (metal wire) & Floating BC (See [26] for implementation details.) & All species are removed when crossing this BC, and they leave their charge behind. \\ Dielectrics (probe mounts) & \(\partial\phi/\partial x=0\) & All species are removed when crossing this BC, and they leave their charge behind. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Numerical boundary conditions for plasma PIC-DSMC simulations. Uncompensated Beam  
Radial profiles of the plasma potential determined at three axial positions are shown in Figure 8 (left panel). Axial distances downstream of the thruster's exit plane ranged from 10 to 95 mm. The typical occurrence of a sudden increase in the plasma potential is observed when the probes enter the ion beam. Measured values outside of the beam are in the range of a few tens of volts, while a sudden jump of several hundred volts occurs when the probe is inside the beam. The voltage depends on the probe's distance to the thruster: the amplitude of the jump decreases further downstream. The broadening of the radial profiles with increasing distance corresponds to the visually observed ion beam divergence. To decide whether the measured profile represents the actual plasma potential or if this is just the result of beam disturbance, an additional measurement was carried out. In the case when the measured profile is the real one, the potential outside of the ion beam should be as low as 10 to 20 V as measured by the probe outside the beam and should not depend on the position of the movable probe. In the opposite case when the measured potential jump is the result of the disturbance, a certain spatial extent should be observable and should mitigate itself in other spatial positions outside of the ion beam. The additional fixed filament placed 5 cm away from the thrusters is used to monitor behavior of the plasma potential during movement of the probes through the beam. Measurement of the floating potentials of the two probes is performed simultaneously. Results of this procedure illustrating the potential of the fixed tungsten probe are shown in Figure 8 (right panel). It can be observed that as long as the emissive probe stays outside of the beam, the potential of the fixed probe is on the magnitude of 10 to 20 V, similar to the values measured at other positions outside of the ion beam. As soon as the movable probes enter the ion beam, the potential of the fixed probe shows a similar jump of several hundreds of volts (the measurement device used for the potential observation of the fixed probe has a limited upper voltage of 200 V). These results indicate that the high plasma potential values measured by both probes are not the real ones.