## 5 Impact of the Collimator Characteristics
### Collimator Diameter  
Here, the collection solid angle of the FC is modified using five grounded graphite collimators with different aperture diameters (\(d\)): 10 mm (G.10.E), 7 mm (G.07.E), 5 mm (G.05.E), 3 mm (G.03.E) and 1 mm (G.01.E). The length of the cup is 50 mm. On-axis I-V characteristics are displayed in Figure 11. At \(U_{d}=200\) V, the current density measured by G.01.E is constant until 100 V then it starts to rise. This behavior remains so far unexplained. At higher discharge voltage I-V curve measured with G.01.E is more unstable than the other curves. With a diameter of 1 mm the probe alignment with the thruster axis is difficult. A slight deviation of the probe pointing vector can lead to a large decrease in the measured ion current. Misalignment could then explain the different behavior observed between 200 V and 250 V. Figure 11 indicates the current density decreases when the collimator diameter is reduced. Figure 11: On-axis I-0V curves obtained at 200 V and 250 V and with different collimator diameters (I\({}_{d}=0.66\) A). FC are equipped with a grounded graphite collimator. Configurations used are G.01.E, G.03.E, G.05.E, G.07.E and G.10.E. Figure 10: Current and propellant use obtained from \(j_{i}\) profile with designs G.10.E and Mo.10.E. Narrowing down the inlet aperture of the probe can prevent some thermal ions from being collected; however, the ion thermal current is small in the ISCT200 plasma plume [70]. Additionally, the drop in current does not vary linearly with the reduction of the collimator diameter. Figure 12 shows the rate of change of the current density for different collimator diameters factor of reduction. It refers to the aperture diameter diminution compared to a 10 mm diameter (_G_.10._E_). The Hall thruster fires at 250 V and 0.66 A. We observe a linear increase of the current density until a factor 6. After, the rate of change slows down and reaches a maximum when the diameter of the collimator is reduced by a factor 10. Figure 12(a),b show the beam profile of the HT for 200 V and 250 V at constant \(I_{d}\). The double peak shape visible on the thruster axis is due to the annular geometry of HTs. It is better seen at high voltages. Note when operated at 200 V and 0.66 A the thruster plume has instead a rounded shape. At this power level the thruster operates with a low efficiency. As can be seen in Figure 13, we observe four distinct zones, unrelated to the probe design and characteristic of the Hall thruster plume. For a given zone the differences observed between each profile is due to the probe configuration. The zone width depends on the thruster discharge voltage. Each zone is defined by a sharp change in current density slope. Zone 1 depends the most on the thruster operation. Indeed, we note that at 200 V zone 1 lies between \(-15^{\circ}\) and \(24^{\circ}\) while at 250 V the zone width does not exceed \(12^{\circ}\). This is due to the thruster performance. Indeed, at 200 V the thruster ionization process is not optimal which implies that ions travelling on the thruster axis have broader energy distributions and their velocity vector deviates more easily from the thruster firing axis. Therefore, when the aperture diameter of the FC is reduced it diminishes the probability for an ion to reach the collector. In contrast, at 250 V the ionization is better which creates a more focus beam with narrower ion energy distributions. Therefore, zone 1 is narrower. Please note that within zone 1, a major current density drop is observed with FC G.03.E. Moreover, in this zone the current density rate of change between each FC configuration is constant between 200 V and 250 V. Eventually, zone 2, 3 and 4 are larger at higher discharge voltage. Zones 3 and 4 are usually referred to the Hall thruster wings. They contain most of the slow ions with random velocity vectors induced by CEX and scattering collisions [71]. Please note that other thruster design parameters such as electric field distribution and zone of the ionization contribute to Hall thruster wings [70,72].