A detailed simulation of Advanced LIGO test mass optical cavities shows that parametric instabilities will excite acoustic modes in the test masses in the frequency range 28-35 kHz and 64-72 kHz. Using nominal Advanced LIGO optical cavity parameters with fused silica test masses, parametric instability excites 7 acoustic modes in each test mass, with parametric gain R up to 7. For the alternative sapphire test masses only 1 acoustic mode is excited in each test mass with R ~ 2. Fine tuning of the test mass radii of curvature cause the instabilities to sweep through various modes with R as high as ~2000. Sapphire test mass cavities can be tuned to completely eliminate instabilities using thermal g-factor tuning with negligible degradation of the noise performance. In the case of fused silica test mass, instabilities can be minimized but not eliminated.
@article{arxiv.gr-qc/0502079,
title = {Parametric instabilities and their control in advanced interferometer GW detectors},
author = {C. Zhao and L. Ju and J. Degallaix and S. Gras and D. G. Blair},
journal= {arXiv preprint arXiv:gr-qc/0502079},
year = {2009}
}