## 6 Discussions
### Collimator as Electron Screen
Figure 22: Evolution of the current use (top), propellant use (middle) and divergence angle (bottom) computed from current density distributions obtained with the collimator grounded and used as an electron screen. HT operates at 200 V and 250 V at 0.66 A.  
configuration a fraction of the ion current is collected by the collimator (electron screen) instead of the collector, see Figure 15 and 16. We observe in Figure 23 no ions are captured by the collimator. On the contrary the beam is better focused onto the cup for low energy ions. We also notice that an important part of the beam is collected by the side walls of the cup. In the second scenario we assumed ion beam trajectories with different incident angles, see Figure 24. At the top of the figure ions with low energy (10 eV) are flowing through the cup. The bottom figure shows results for 250 eV ions. The ion energy range was chosen based on the large ion energy distribution within the plume of a Hall thruster. For experimental purposes, the incident angles were chosen randomly, and the slope was accentuated to maximize the chance for an ion to be collected by the collimator. The goal here being to assess the probability of an incoming ion to reach the collimator placed behind the housing front. We observe that low energy ions are focused and directed towards the cup. However, highly energetic ones get closer to the collimator and a small fraction manage to touch it. Most of the ions are still collected by the side wall of the cup. Consequently, two additional simulations were run as shown in Figures 25 and 26. Here, we consider ion reflection or rebound from the original beam to the cup side and rear walls. The semi-half-angle of the possible reflected ions was maximized to 90\({}^{\circ}\). Figure 25 shows the results of 250 eV ion reflection from the cup side walls at different locations for 35 mm (black), 40 mm (red), 45 mm (green) and 50 mm (blue) the bottom of the cup. It is assumed that in the best case reflected ions lose more than 95% of their energy and in the worst case only 50%. Ions with 10 eV and 100 eV are flown with random horizontal velocity  
Figure 23: Ion simulations computed with the software SIMION. Each configuration displays the ion trajectory going through the FC. Potential is fixed at \(-\)50 V and \(-\)100 V for the collector and collimator, respectively. Ion energies are 5 eV (red), 10 eV (black), 100 eV (green) and 250 eV (blue). The probe aperture diameter is 5 mm. Figure 24: Ion simulations computed with the software SIMION. Each configuration displays the ion trajectory through the FC. The color code refers to different incident angles. Potential is fixed at \(-\)50 V and \(-\)100 V for the collector and collimator, respectively. Ion energies are 10 eV (**top**) and 250 eV (**bottom**). vectors. For each case, the Faraday cup has a collector at \(-50\,\mathrm{V}\) and the collimator is either grounded (top) or biased to \(-100\,\mathrm{V}\) (bottom). When the collimator is grounded, around 5% of the ions with high energy escape the cup while all low energy ones are completely redirected back to the collector. However, once the collimator is at \(-100\,\mathrm{V}\) close to 10% of low energy ions escape the cup or are collected by the collimator. Ions with \(100\,\mathrm{eV}\) are not affected by the change of equipotential field lines inside the cup. Figure 26 simulates ion rebounds from the bottom of the Faraday cup (\(50\,\mathrm{mm}\)) for energies of \(10\,\mathrm{eV}\) (black), \(50\,\mathrm{eV}\) (red), \(75\,\mathrm{eV}\) (green) and \(100\,\mathrm{eV}\) (blue). The collector is at \(-50\,\mathrm{V}\) while the collimator is either grounded (top) or \(-100\,\mathrm{V}\) (bottom). In the same manner than ion reflection from the side walls, applying a potential to the collimator does attract a small fraction of reflected ions from the cup bottom. Most of the ions collected by the collimator are low energy ones.