Influence of Young’s modulus temperature dependence on parametric instability in Advanced LIGO interferometer

Abstract

We discuss the influence of Young’s modulus temperature dependence on the number of parametrically unstable modes in a Fabry-Perot cavity of Advanced LIGO interferometer. Some unstable modes may be suppressed by changing the mirror’s temperature due to temperature dependence of Young’s modulus. Varying the temperature of the mirrors we can change their frequencies of the elastic modes; it, in turn, can change the number of unstable modes, leading to nonlinear effect of parametric oscillatory instability. Preliminary estimations of the optimal values of the temperature variations for some elastic modes are made to reduce the number of unstable modes. The applications of this method in cryogenic detectors like LIGO Voyager or Einstein Telescope are proposed.