The evaluation for plasma noise in arbitrary time-delay interferometry combinations

The Laser Interferometer Space Antenna (LISA) uses laser interferometry to measure gravitational wave-induced distance changes between freely falling test masses on separate spacecraft. In practice, the space-borne gravitational wave detector operates in a plasma medium, and subsequently, the variations in electron density affect the refractive index and add displacement noise to measurements. Geometric time-delay interferometry (TDI) is the TDI combinations searched by geometric method, which is employed to mitigate overwhelming laser phase noise. This study explores all forty-five second-generation geometric TDI combinations up to sixteen links, analyzing plasma noise effects via power spectral density (PSD) and cross-spectral density (CSD) calculations for different optical links. Our findings reveal that plasma noise can exceed the noise floor, which comprises optical metrology system (OMS) and test mass (TM) acceleration noise, in certain low-frequency regions due to different noise transfer behaviors. Further, we establish electron density requirements for various TDI combinations, showing that densities below $100~\text{cm}^{-3}/\sqrt{\text{Hz}}~@~10~\text{mHz}$ satisfy LISA's criteria across all forty-five combinations. This allows for optimized TDI selection based on specific plasma densities.