Enhanced model for characterizing the radiometer effect in space-borne gravitational wave detection

Gas molecules within the gravitational reference sensor (GRS) subjected to temperature fluctuations can give rise to a net disturbance force on the test mass (TM), known as the radiometer effect, which limits the low frequency sensitivity of space-borne gravitational wave (GW) detection. Prior research relied on the infinite-plate model to evaluate this effect, supplemented by a correction factor to account for the GRS geometric configuration, whose specific form remains unknown and is accessible solely through experiments or simulations. In this work, we rigorously derive an analytical expression for the radiometer disturbance force by analyzing the interaction between gas molecules and the TM within the GRS subjected to a linear temperature gradient. Our calculation transcends the conventional infinite-plate model by elucidating not only its dependence on sensor temperature and pressure but also explicitly revealing its correlation with the gap distances between the GRS and TM, effectively yielding a precise expression for the correction factor. To validate the established model, we conduct molecular Monte Carlo simulations, which exhibit favorable concordance with the theoretical predictions, reinforcing its reliability and efficacy. Consequently, this analytical approach offers a robust and efficient means of accurately assessing the radiometer disturbance force in space-borne GW detection. Furthermore, its insight into gap dependence provides theoretical guidance for optimizing sensor structural designs.