## 3 Results
### Impact of Thrusters at Various Locations on Spacecraft Charging and Discharging Effect  
In order to meet the diverse demands and tasks of spaceflight, Hall thrusters are typically installed at various positions on spacecraft. The plume effect of Hall thrusters in different positions is simulated and analyzed to understand the distinct charging effects on the spacecraft. Results for thrusters located at Position 1 are presented in Figures 3 and 4, while simulation outcomes for thrusters at Position 2 and the temporal variation of the average surface potential at each node are depicted in Figures 9 and 10. Figure 8: Density distribution of photoelectrons under two operating conditions: (**a**) thruster is turned on; (**b**) thruster is turned off. Figure 9: Surface potential distribution when the thruster is at Position 2. Figures 9 and 10 reveal that when the thruster is located at Position 2 and all node potentials are in equilibrium, the majority of node potentials converge around \(-1.1\) V. This is approximately \(1.3\) V higher than the potential at Position 1. The surface potential on the glass front (Node 4) is negative, peaking at \(-21.4\) V. In contrast to the charging phenomenon at Position 1, the potentials on the glass back (Node 9) and other regions are similar. Analyzing these discrepancies requires considering the changes in surface charging currents of various particles on the spacecraft and the temporal variations in surface currents at the two nodes when the thruster operates at these distinct positions. The comparison of Figure 11 with Figure 7a shows that there are differences in the CEX ion, photoelectron, secondary electron, Xe+, and Xe++ currents with respect to the total surface currents of the spacecraft particles. When the thruster is in Position 2, the incident photoelectron current is \(-1.75\times 10^{-4}\) A, the incident secondary electron current is \(-6\times 10^{-5}\) A, the incident CEX_Xe+ current is \(5\times 10^{-3}\) A, and the incident Xe+ and Xe++ currents are \(8\times 10^{-6}\) A and \(3.25\times 10^{-5}\) A. Compared with that of the thrusters at Position 1, there is a reduction in incident photoelectron and secondary electron currents, while the incident CEX_Xe+ current significantly increases, rising by an order of magnitude (approximately tenfold). Additionally, the currents of incident Xe+ and Xe++ also show an increase. This indicates that the plume generated by thrusters positioned closer to the main body of the spacecraft disperses around the spacecraft, resulting in an elevated ion density  
Figure 11: Variation of total surface particle currents on the spacecraft when the thruster is at Position 2. Figure 10: The charging process of the average surface potential at various nodes when the thruster is at Position 2.  
in the vicinity. Consequently, this increased density more efficiently attracts photoelectrons and secondary electrons, exerting a notable influence on the spacecraft surface potential. Furthermore, the increase in the CEX_Xe+ current incident on the spacecraft surface causes a rise in the number of CEX ions returning to the surface. This, in turn, intensifies the depositional contamination on the spacecraft surface and contributes to a reduction in its negative potential. Although Xe+ and Xe++ in the plume experience less influence from the electric field due to their high velocity and density, a portion of these ions still return to the spacecraft surface because of the close proximity between Position 2 and the main body, causing a decrease in the surface negative potential. It is noteworthy that our current observations pertain to the overall spacecraft surface particle currents. Due to differences in materials and light exposure across various sections of the spacecraft, there are variations in surface currents at different nodes. It is not possible to ascertain the predominant particle type at a specific node solely through the comprehensive spacecraft surface particle current.