## 3 Results and Discussion
### Numerical Modeling  
In this section, results of the neutral gas DSMC and plasma PIC-DSMC simulations are presented. A contour and centerline plot of the neutral gas pressure predicted for the disturbed case is shown in Figure 14.  
As the neutral propellant exits the discharge chamber, it passes through the outlet channel of the thruster for about \(12\,\mathrm{mm}\). The fluid then freely flows into the vacuum chamber, and the pressure drops rapidly while the velocity increases due to gas expansion. At an axial distance of about \(100\,\mathrm{mm}\) from the thruster, the pressure is only slightly higher than the measured ambient vacuum chamber pressure of about \(1\times 10^{-4}\,\mathrm{Pa}\).  
Figure 13: Comparison of SSG currents in different situations. **Left**—the first probe is \(\Delta x=25\,\mathrm{mm}\) from the thruster and has an uncompensated vs. partially compensated beam. **Right**—the first probe is \(\Delta x=5\,\mathrm{mm}\) from the thruster and has a partially compensated beam with hot cathode vs. an uncompensated beam with cold cathode.  
The distribution of neutral gas within the domain varied only slightly within the vicinity of the probes. For the disturbed case, a stagnation zone in front of the probes builds up, leading to a small increase in pressure.  
In Figure 15, contours of plasma properties are outlined for both the disturbed and undisturbed cases. In general, it is observable that the beam divergence is larger in the disturbed case, which can be seen in the contours of the ion number density. The electron number density indicates more electrons being located between the thruster's exit region and the first probe. Furthermore, the (scaled to \(3.5\times 10^{4}\) to \(5\times 10^{4}\) m s\({}^{-1}\)) contours of ion velocity demonstrate that ions lose kinetic energy in front of the probes, hinting at an increase in the electric potential in this region. This premise is confirmed by the contours of potential, which illustrate a significantly higher potential of more than 350 V in the disturbed case compared to a few tens of volts in the undisturbed case.  
The axial centerline plot downstream shown in Figure 16 underlines this finding, proving the drastic growth of plasma potential in the disturbed case and also explaining the decrease in axial ion velocity. Further, this decrease leads to more CEX events and subsequent slow ions, since the collision cross-section increases with decreasing ion velocity (see Figure 7, green graph). These slow ions are accelerated outwards (i.e., radially in \(\pm y\)), which is visible in Figure 15 through the granular contours of ion velocity and number density outside the beam.  
Finally, in order to validate the PIC-DSMC simulations, the radial electron number density and electron energy distribution function (EEDF) at an axial distance of \(\Delta x=50\) mm is compared to the experimental measurements at different \(y-\)positions. The results are displayed in Figure 17 and reveal that the simulation is able to predict both the radial profile of the electron number density distribution as well as the absolute values of number density (left panel). Examining the right panel, it is evident that there is good agreement when determining the electron temperature from the EEDF predicted by PIC-DSMC at each measurement point.  
Figure 14: DSMC results of neutral gas with probes located inside beam. **Left**—contours of pressure, with centerline indicated by white dashed line. **Right**—centerline plot of pressure and velocity.  
Figure 15: Comparison of electron and ion number densities, axial ion velocity, and potential predicted from PIC-DSMC simulations for undisturbed and disturbed cases.