## 3 Results  
### Impact of Thrusters on Surface Charging and Discharging Effects in Spacecraft  
In order to assess the influence of thruster plumes on spacecraft surface charging, an analysis was conducted on the surface charging conditions when the thruster was operational and when it was in a deactivated state. When the thruster is in operation, Figures 3 and 4 depict the potential distribution of the spacecraft surface and the temporal evolution of the average surface potential at different nodes within the harsh plasma environment of the GEO. In contrast, with the thruster turned off, Figures 5 and 6 portray the potential distribution of the spacecraft surface and the temporal evolution of the average surface potential at various nodes in the harsh plasma environment at the GEO. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Density/(cm\({}^{-3}\))** & **Temperature/(keV)** \\ \hline elec1 & 0.2 & 0.4 \\ elec2 & 1.2 & 27.5 \\ ion1 & 0.6 & 0.2 \\ ion2 & 1.3 & 28 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: GEO extreme plasma environment parameters. Figure 3: The surface potential distribution of the spacecraft when the thruster is turned on. Observations indicate that when the thruster is in operation, all node potentials reach an equilibrium state within 30 s, with the surface potential concentrated around \(-2.4\) V. The highest surface potential is on the thruster itself, reaching 24.4 V. The sunlit side of the solar panel (Node 5) maintains a surface potential close to 0 V. On the glass backside (Node 9), the surface potential is negative, peaking at \(-21.6\) V. When the thruster is turned off, after a charging time of 2000 s, except for the sunlit side of the solar panel, the potentials of the other nodes have not reached an equilibrium state. The surface potential continues to gradually rise to higher negative values, with most nodes reaching \(-140\) V. The average  
Figure 4: The charging process of the average surface potential at various nodes when the thruster is turned on. Figure 5: The spacecraft surface potential distribution when the thruster is turned off. Figure 6: The charging process of the average surface potential at various nodes when the thruster is turned off. surface potential on the sunlit side of the panel is 3.45 V. Node 9 exhibits the highest surface potential, reaching up to \(-3900\) V, with a significant potential difference of 3760 V compared to neighboring areas, making it prone to electrostatic discharge. To analyze these distinctions, we must consider variations in spacecraft surface charging current and compare the total surface currents of each particle over time under different thruster operating conditions. It can be seen from Figure 7 that in the two working conditions, there are differences in the total surface currents of various particles on the spacecraft under two operating conditions, including CEX_Xe+ current, photoelectron current, and secondary electron current. When the thruster is off, the incident photoelectron current on the surface of the spacecraft is \(-4.3\times 10^{-4}\) A, and the incident secondary electron current is \(-1.64\times 10^{-4}\) A; when the thruster is open, the incident photoelectron current on the surface of the spacecraft is \(-2.27\times 10^{-4}\) A, and the incident secondary electron current is \(-7.75\times 10^{-5}\) A, and the CEX_Xe+ current is \(4\times 10^{-4}\) A. Given that the photoelectron and secondary electron currents emitted from the spacecraft surface material remain constant under both operating conditions, the unchanged secondary electron emission coefficient indicates that the interaction of the plume with the spacecraft does not affect the material properties [16]; photoelectrons and secondary electrons typically possess lower energies (\(\sim\)1 eV\(\sim\)100 eV), slower velocities, and lighter masses. Due to Coulombic interactions among charged particles, low-energy photoelectrons and secondary electrons may be captured by nearby ions.