Finite Element Analysis of Electrostatic Coupling in LISA Pathfinder Inertial Sensors

In the LISA Pathfinder (LPF) mission, electrostatic noise can reach the femto-Newtonian level despite the fact that the LPF's sensors are equipped with potential shielding. Most of the existing simulation studies focus on the electrostatic edge effect and related fields, while the simulation study of the patch effect is neglected. For that reason, this paper analyzes the basic principle of electrostatic noise and constructs a simulation model for studying the coupling effects of a TM's residual charge and stray bias voltage. The patch effect and other perturbation factors are simulated by the simulation model with finite element operation, focusing on the suppression effect of the protective ring on the edge effect, the realization of the patch effect in the simulation model, and the possible influence. The results show that electrode area and the spacing between the electrode and the TM together limit the suppression effect of the protective ring on the edge effect. The spatial and temporal variations of the patch effect significantly affect the distributed electric field between the electrodes and the TM, as well as the charge distribution density of the TM. In the worst-case scenario of LPF electrostatic input parameters, the electrostatic noise is about 1.03 × 10^-15 m/s²/√Hz at 1 mHz, which is about 6% different from the expected performance estimate. Finally, considering the limitations of multiple environmental factors on the inertial sensors, the present model will be useful to explore the interactive effects of multi-field coupling and to further investigate the impact of low-energy electron charging on the performance of the inertial sensors.