Time-delay interferometry combinations to suppress two of six test-mass disturbances in space-borne gravitational wave detectors

Significant disturbances in the test masses, arising from unforeseen instrument anomalies during scientific measurements, have a considerable impact on space-borne gravitational wave detection. Therefore, exploring effective data processing methods to mitigate these effects is of crucial importance. In a pioneering effort, previous literature proposed the use of time-delay interferometry for this purpose and developed a first-generation combination to mitigate disturbances from two test masses on the same spacecraft. However, due to its inherent limitations in suppressing laser phase noise, it is not suitable for actual data processing in space-borne gravitational wave detection. This paper aims to devise a comprehensive approach to derive more practical second-generation time-delay interferometry combinations. The technique was initially developed for laser phase noise suppression. Specifically, laser interference data streams between and within satellites are preprocessed to form six synthetic data streams, which contain three laser phase noises. Then, time-delay interferometry combinations are applied to these six data streams to construct virtual equal-arm interference, thereby suppressing the three laser phase noises. This process leaves two degrees of freedom, which can be strategically used to reduce one or two major disturbances in the test masses. Therefore, we used an algebraic approach to construct the necessary constraint equations. From these, we derived more practical second-generation time-delay interferometry combinations capable of simultaneously suppressing laser phase noise and disturbances from two test masses, either within one spacecraft or across two spacecraft. In addition, for acquiring second-generation time-delay interferometry combinations, both the geometric approach and the combinatorial algebraic approach have been proven effective. The former utilizes the synthesis of virtual optical paths, which have intuitive physical interpretations, while the latter employs algebraic methods to solve equations with some constraints. However, it is found that the combinatorial algebraic approach, as well as second-generation geometric combinations of length not exceeding 16 links, cannot address all scenarios of the test mass anomalies. This work provides a strategy for addressing large disturbances from partial test masses in space-borne gravitational wave detection from a data processing perspective, thereby contributing to the implementation of the detection task.