Optimal TDI2.0 of sensitive curve for main space GW detector

Abstract: Time-delay interferometry (TDI) is a crucial technology for space-based gravitational wave detectors. Previous studies have identified the optimal TDI configuration for the first-generation. In this research, we used an Algebraic approach theory to describe the TDI space and employed a method to maximize the signal-to-noise ratio (SNR) to derive the optimal TDI combination for the second-generation. When this combination is used in the sensitivity curve, we observed enhancements of up to 1.91 times in the low-frequency domain and 2 to 3.5 times in the high-frequency domain compared to the Michelson combination. Furthermore, changes in the detector index significantly affect the optimization effect. We also present detection scenarios for several low-frequency gravitational wave sources. Compared to the first-generation TDI optimization, the SNR value for verification double white dwarfs (DWD) and the detection rate for DWD increase by 16.5%.