## 2 Theoretical Models
### Geometric Models  
To simulate the interaction between the spacecraft and plasma, the numerical model must consider the electrical properties of the surface materials. When evaluating the interplay between the surface and numerical grid density, each spacecraft surface is defined by its outer coating material, represented as a macroscopic electrical node in the model. These surface nodes are connected to the spacecraft ground or other nodes via an equivalent RC circuit. Our calculations prioritize potential differential charges between the dielectric surface and the spacecraft structure, considering factors like dielectric thickness and surface and bulk conductivities.  
The spacecraft features a complex structure, consisting of the spacecraft main body, a large curved composite material antenna, a sizable solar panel, and Hall thrusters. The spacecraft's main body is a cube with a side length of 2.5 m. The large curved composite material antennas are composed of various materials, with an exterior consisting of two layers--one layer of carbon fiber and another layer of aluminum film. The interior includes a large glass panel. The dimensions of the solar panels are 7.0 \(\times\) 2.5 m, with a thickness of 15 cm. The Hall thruster is a cubic structure with a length of 14 cm and a circular outlet surface. It is positioned 5 m away from the spacecraft main body at Position 1 and to the left of the spacecraft main body at Position 2. In the simulations below, unless otherwise emphasized, the thruster is located at Position 1. Figure 2 shows the geometric model of the spacecraft. Due to the glass portion on the antenna, the illumination on the front and back faces varies, prompting the division of the antenna into two nodes. The remaining spacecraft is partitioned into nodes based on functionality and material differences, with each node connected to the satellite's structural ground via specific circuits. The materials on various surfaces of the spacecraft model, along with the node assignments and the equivalent RC circuit settings, are outlined in Table 1. In the plasma environment, the spacecraft is considered a capacitor, possessing a floating potential relative to the space plasma. The capacitance of a spacecraft typically depends on its materials and volume. In this study, the capacitance value was determined after setting parameters such as spacecraft materials, resistances, and environmental conditions, with the global parameter \"exactCSat\" set to 1 for computation. The capacitance of the spacecraft was set to 2.0 \(\times\) 10\({}^{-4}\) F. During the simulation, sunlight is incident from the -Z direction, with the satellite's -Z face consistently oriented towards the sun. The boundary conditions mainly refer to the plasma boundary within the computational domain. The properties of the plasma within the domain often depend on the numerical settings of the plasma model boundaries and initial conditions, with two types of boundary conditions: plasma boundary conditions and electric field boundary conditions. In this study, the plasma boundary conditions are set to an open boundary, where particles can be injected from or absorbed by the surface. The electric field boundary conditions are set to Fourier boundary conditions.