  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.
