Initial acquisition requirements for optical cavities in the space gravitational wave antennae DECIGO and B-DECIGO

Abstract: DECIGO (DECi-hertz Interferometer Gravitational Wave Observatory) is a space-based gravitational wave antenna concept targeting the 0.1-10 Hz band. It consists of three spacecraft arranged in an equilateral triangle with 1,000 km sides, forming Fabry-P\'erot cavities between them. A precursor mission, B-DECIGO, is also planned, featuring a smaller 100 km triangle. Operating these cavities requires ultra-precise formation flying, where inter-mirror distance and alignment must be precisely controlled. Achieving this necessitates a sequential improvement in precision using various sensors and actuators, from the deployment of the spacecraft to laser link acquisition and ultimately to the control of the Fabry-P\'erot cavities to maintain resonance. In this paper, we derive the precision requirements at each stage and discuss the feasibility of achieving them. We show that the relative speed between cavity mirrors must be controlled at the sub-micrometer-per-second level and that relative alignment must be maintained at the sub-microradian level to obtain control signals from the Fabry-P\'erot cavities of DECIGO and B-DECIGO.