Revised electrostatic model of the LISA Pathfinder inertial sensor

Abstract

A comprehensive electrostatic finite-element (FE) analysis of the LISA Pathfinder Inertial Sensor (IS) has been carried out at Astrium GmbH. Starting with a detailed geometrical model of the IS housing and test mass (TM) flight units, FE results were derived from multiple analyses runs applying the Maxwell 3D field simulation software. The electrostatic forces and torques on the TM in 6DoF, as well as all non-negligible capacitances between the TM, the 18 electrodes, and the housing, have been extracted for different TM translations and rotations. The results of the FE analyses were expected to confirm the existing IS electrostatic model predictions used for performance analysis, simulations, and on-board algorithms. Major discrepancies were found, however, between the results and the model used so far. In general, FE results give considerably larger capacitance values than the equivalent infinite non-parallel plate estimates. In contrast, the FE derived forces and torques are in general significantly lower compared to the analytic IS electrostatic model predictions. In this paper, these results are discussed in detail and the reasons for the deviations are elaborated. Based on these results, an adapted analytic IS electrostatic model is proposed that reflects the electrostatic forces, torques, and stiffness values in the LISA Pathfinder IS significantly more accurate.