Inter-spacecraft offset frequency setting strategy in the Taiji program

For controlling the beat frequency of heterodyne interferometry so that the Taiji program can detect gravitational waves in space, an offset frequency setting strategy based on a linear programming algorithm is proposed. Considering factors such as Doppler frequency shift, phase-locking scheme, laser relative intensity noise, and phase detector bandwidth, inter-spacecraft offset frequency setting results suitable for the Taiji program are obtained. During the six years of running the detection process, the use of frequency bounds in the range of [5 MHz, 25 MHz] showed that offset frequencies will remain unchanged for a maximum of 1931 days. If the upper and lower bounds are adjusted, and the relative motion between spacecraft is further constrained, the offset frequencies do not need to change during the time of the mission. These results may provide insights into selecting the phase detector and designing operation parameters such as orbit and laser modulation frequency in the Taiji program.