# Plume Divergence and Discharge Oscillations of an Accessible Low-Power Hall Effect Thruster
## 3 Results and Discussion
### Thruster Performance  
As previously mentioned, this study was performed during two vacuum facility evacuations separated by removal and reinstallation of the WHT44. Hall thruster performance and testing is typically completed below \(1\times 10^{-4}\) Torr background pressure to minimize the impact on performance [15]. Trends in the results impacted by elevated pressure are highlighted by the authors when discussing the relevant performances. Faraday probe data measured during the first evacuation were recorded at ten radial probe distances ranging from 3.2 to 9 thruster diameters downstream (TDD) and in increments of 0.58 TDD. An example of the FP data collected from the thruster plume at the standard 200-V, 215-W operating point is shown in Figure 4.  
Figure 4: Sample Faraday probe current density measurements at 10 different thruster diameters downstream (TDD) distances plotted together for the nominal 200-V, 215-W operating condition. Figure 3: Photograph of the (**a**) WHT44 post-test and (**b**) the WHT44 operating at the nominal operating point. Faraday probe data recorded during the second evacuation were measured at four radial probe distances ranging from 4 TDD to 7.45 TDD in increments of 1.16 TDD. While data collection at less than 4 TDD using a hemispherical coordinate system is not recommended, the authors wished to observe trends in the beam properties of the transitionary area between the near and far-field regions of the plume. As a result, data measured at all TDD were analyzed in accordance with the the polar coordinate system methods outlined in reference [12]. Uncertainty in the divergence angle and utilization efficiencies are estimated to have an accuracy of \(\pm\)5% based upon estimates calculated by [PERSON] [12]. Total ion current as a function of TDD is plotted in Figure 5. Between 4.5 TDD and 9 TDD, where error analysis is valid, total ion beam current decreases by only 0.0175 A, which is within measurement error margins. This shows total ion current as a function of TDD is conserved, further validating the results from Faraday probe measurements. While the analysis methods used for Faraday probe data lose efficacy in the near plume below 4 TDD the trends can still be useful. Thruster divergence results are shown in Figure 6. Firstly, divergence angle as a function of discharge voltage (Figure 6a) and as a function of magnet current (Figure 6b at a downstream distance of 4.5 TDD are shown. Next, the divergence angle at the nominal 200-V, 215-W operating condition as a function of probe distance downstream in TDD lengths is shown in Figure 6c. As seen in other thrusters, the plume divergence half-angle increases as collisions between the plume and background neutrals results in a diffusion of the beam into the chamber [12]. Lastly, the divergence angle as a function of CFF at a probe distance downstream of 4 TDD is shown in Figure 6d. As expected with an HET, the divergence angle decreased with increasing discharge voltage. No significant change in plume divergence angle was detected within the measurement error previously indicated over the full range of discharge voltage, anode flow rate, and magnet current tested. An increase in plume divergence angle of about 9\({}^{\circ}\) was measured over the full range of downstream distances at the nominal 215-W operating condition. These results show divergence angles that are large when compared to other similarly powered HETs [16; 17]. Both of these trends are likely exacerbated by the high operational pressures. Figure 5: Total ion beam current as a function of TDD at the nominal 200-V, 215-W operating condition. Utilization efficiencies as a function of discharge voltage and magnet current are shown in Figure 7,b, respectively. Figure 7 shows utilization efficiencies as a function of CFF at the 200-V, 215-W nominal operating condition.