The aim of this work is to validate the China Seismo-Electromagnetic Satellite 01 (CSES-01) Electric Field Detector (EFD) measurements through the analysis of the instrument response to various inputs: (a) geomagnetic field variations, (b) plasma density depletions, and (c) electromagnetic signals from natural and artificial sources such as Schumann resonance and VLF (Very Low Frequency) antennas. The knowledge of the geomagnetic induced electric field $v_s\times B$ (where $v_s$ is the satellite speed and B and the local magnetic field), and the plasma variations effect, described by the Orbit Motion Limited (OML) theory, are key parameters to determine the expected theoretical values of the EFD sensors potentials data. Based on the CSES on-board measurements of plasma parameters and geomagnetic field, a direct quantitative validation is presented. In addition, the electromagnetic signals detection capability is checked but only qualitatively confirmed, since the ionospheric complexity does not allow an accurate theoretical computation of waves modulation. The quantitative comparison highlights the very good agreement between observed and theoretical potentials values during average condition. Conversely, in case of strong electric fields, the OML theory shows partial inability in reproducing the actual space plasma conditions resulting in a reduced theoretical values reliability. Finally, both natural and artificial electromagnetic signals are satisfactorily identified showing a reliable sensitivity in different frequency bands.

High-precision inertial sensors or accelerometers can provide references for free-falling motion in gravitational fields in space. They serve as the key payloads for gravity recovery missions such as CHAMP, the GRACE-type missions, and the planned Next-Generation Gravity Missions. In this work, a systematic method for electrostatic inertial sensor calibration of gravity recovery satellites is suggested, which is applied to and verified with the Taiji-1 mission. With this method, the complete operating parameters including the scale factors, the center of mass offset vector, and the intrinsic biased acceleration can be precisely calibrated with only two sets of short-term in-orbit experiments. This could reduce the gaps in data that are caused by necessary in-orbit calibrations during the lifetime of related missions. Taiji-1 is the first technology-demonstration satellite of the “Taiji Program in Space”, which, in its final extended phase in 2022, could be viewed as operating in the mode of a high–low satellite-to-satellite tracking gravity mission. Based on the principles of calibration, swing maneuvers with time spans of approximately 200 s and rolling maneuvers for 19 days were conducted by Taiji-1 in 2022. Given the data of the actuation voltages of the inertial sensor, satellite attitude variations, precision orbit determinations, the inertial sensor’s operating parameters are precisely re-calibrated with Kalman filters and are relayed to the Taiji-1 science team. The relative errors of the calibrations are <1% for the linear scale factors, <3% for center of mass, and <0.1% for biased accelerations. Data from one of the sensitive axes are re-processed with the updated operating parameters, and the resulting performance is found to be slightly improved over the former results. This approach could be of high reference value for the accelerometer or inertial sensor calibrations of the GFO, the Chinese GRACE-type mission, and the Next-Generation Gravity Missions. This could also create some insight into the in-orbit calibrations of the ultra-precision inertial sensors for future GW space antennas because of the technological inheritance between these two generations of inertial sensors.

The precise movement of the test mass along a geodesic is crucial for gravitational wave detection in space. To maintain this motion, the core payload-inertial sensor incorporates multiple functional units designed to mitigate various sources of stray force noise affecting the test mass. Understanding the limits of these noise sources is essential for enhancing the inertial sensor system design. Additionally, thorough ground-based verification of these functional units is necessary to ensure their reliability for space missions. To address these challenges, we developed a low-frequency torsion pendulum apparatus that utilizes a commercial autocollimator as the optical readout element for testing this type of space inertial sensor. This paper provides a comprehensive overview of the apparatus’s operating principle, structural characteristics, and the results of laboratory tests of its background noise. Experimental data demonstrate that the torsion pendulum achieves a sensitivity of 1 × 10⁻¹¹ Nm/Hz^1/2 within the measurement band from 1 mHz to 0.1 Hz, confirming its suitability for various inertial sensor tests. Furthermore, the insights gained from constructing the torsion pendulum will inform future system upgrades.

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.

High-precision inertial sensors or accelerometers can provide us references of free-falling motions in gravitational field in space, and serve as the key payloads for gravity recovery missions. In this work, a systematic method of electrostatic inertial sensor calibrations for gravity recovery satellites is introduced, which is applied to and verified with the Taiji-1 mission. Taiji-1 is the first technology demonstration satellite of the ``Taiji Program in Space'', which, in its final extended phase in 2022, could be viewed as a gravity recovery satellite operating in the high-low satellite-to-satellite tracking mode. Based on the calibration principles, swing maneuvers with time span about 200 s and rolling maneuvers for 19 days were conducted by Taiji-1 in 2022. The inertial sensor's operating parameters including the scale factors, the center of mass offset vector and the intrinsic biased acceleration are precisely re-calibrated and are updated to the Taiji-1 science team. Data from one of the sensitive axis is re-processed with the updated operating parameters, and the performance is found to be slightly improved compared with former results. This approach could be of high reference value for the accelerometer or inertial sensor calibrations of the GFO, the Chinese GRACE-type mission, and the planned Next Generation Gravity Missions. This could also shed some light on the in-orbit calibrations of the ultra-precision inertial sensors for future GW space antennas because of the technological inheritance between these two generations of inertial sensors.