Thermal analysis of the inertial sensor during the preliminary stage of the TianQin project

Space-based gravitational wave detection projects require stringent temperature stability of core payloads in the frequency domain. To facilitate thermal design iterations in the preliminary stage, it is essential to establish thermal disturbance requirements for different thermal disturbance sources surrounding the core payloads at the outset of the mission. A significant challenge in this process is determining the impact of noise sources on the core payloads when their characteristics are not fully known. In this paper, we investigate the influence of different potential noise sources on the inertial sensors within the core area of the TianQin project. Our process involves transforming the mechanical construction model into a thermal mathematical model and deriving the system's transfer function matrix by a linear control methods. This matrix enables an analysis of the effects of thermal disturbance sources on the inertial sensor's temperature stability within a bandwidth from $0.01\phantom{\rule{0.2em}{0ex}}\mathrm{mHz}$ to $0.1\phantom{\rule{0.2em}{0ex}}\mathrm{Hz}$. Additionally, thermal stability requirements for these noise sources at $0.1$ and $1\phantom{\rule{0.2em}{0ex}}\mathrm{mHz}$ are listed through the inertial sensor's requirement, providing meaningful guidance for the subsequent thermal design of TianQin. The analytical process, demonstrated for TianQin, can be applied to other space missions requiring stringent temperature stability in their core payload during preliminary stages.