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

We discuss the influence of Youngu0027s 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 mirroru0027s temperature due to temperature dependence of Youngu0027s 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. The determination of the optimal values of the temperature variations for some elastic modes to reduce the number of unstable modes is fulfilled. Both new fine tuning supression method of parametric instability and radius of curvature(ROC) change method in the next generation of gravitational wave detectors are discussed. The applications of this method in cryogenic detectors like LIGO Voyager or Einstein Telescope are proposed.