Study of parametric instability in gravitational wave detectors with silicon test masses

Parametric instability is an intrinsic risk in high power laser interferometer gravitational wave detectors, in which the optical cavity modes interact with the acoustic modes of the mirrors, leading to exponential growth of the acoustic vibration. In this paper, we investigate the potential parametric instability for a proposed next generation gravitational wave detector, the LIGO Voyager blue design, with cooled silicon test masses of size 45 cm in diameter and 55 cm in thickness. It is shown that there would be about two unstable modes per test mass at an arm cavity power of 3 MW, with the highest parametric gain of ∼76. While this is less than the predicted number of unstable modes for Advanced LIGO (∼40 modes with max gain of ∼32 at the designed operating power of 830 kW), the importance of developing suitable instability suppression schemes is emphasized.