The Optimization of Frequency Distribution Based on Genetic Algorithm for Space Gravitational Wave Observatories

The three spacecraft of the space gravitational wave antenna employ heterodyne interferometry to mitigate the effects of Doppler shift. Constrained by laser relative intensity noise (RIN) and the sampling frequency constraints of phase readout circuits, the widespread adoption of fixed offset frequencies effectively regulates the frequency of heterodyne interferometric beat notes within a reasonable frequency domain of [5 MHz, 25 MHz]. In this work, a high-precision fitness genetic algorithm for heterodyne interferometry is utilized to generate the initial offset frequency distribution scheme. To address issues with unreasonable switching times and offset frequency settings in the initial scheme for partial frequency domains, optimization strategies are proposed from three aspects: frequency domain selection extension, switch times control, and numerical low frequency. Results demonstrate that the optimization of frequency domain selection extension narrows the reasonable frequency domain to [5 MHz, 15 MHz] and [7 MHz, 17 MHz]. Optimization of switch times control ensures that switching times of offset frequency distribution scheme generated under the settings of [6 MHz, 17 MHz] and wider frequency domains can be controlled within a reasonable range of 6 to 13 times. Fixed offset frequency settings are generally reduced by 24.3% after low-frequency optimization. This methodology and result can provide a reliable reference for Program Taiji and even related space gravitational wave antenna projects.