Using finite element simulation to evaluate charge measurement precision for space inertial sensors

Abstract Non-contact measurement and control are essential for accumulated charges on the test mass (TM) of space inertial sensors, as these charges can worsen the sensitivity of space-based gravitational wave detection. However, it is a challenge to evaluate measurement precision due to the limitations of experimental methods. In this study, the charge measurement process is described using an electrostatic force model, and five influence factors in terms of measurement precision are quantitatively evaluated through finite element simulation. The results indicate that the main contributors to mean relative errors (MREs) are the geometric structure of inertial sensors and the charge distribution on the TM. By correcting the capacitance gradient coefficient in the measurement model, the MRE caused by geometric structure can be reduced from 48% to 2%. Furthermore, the rotational modulation scheme demonstrates lower MREs and relative standard deviations, making it a preferred scheme for charge measurement. This study provides a feasible approach to designing and evaluating the charge measurement scheme for space-based gravitational wave detection.