Modelling Parametric Instabilities at Advanced LIGO and ET

Abstract

Parametric instabilities in Fabry-Perot cavities were first introduced in 2001 as a potential pitfall and serious problem for laser interferometer gravitational-wave detectors [1, 2]. Parametric instabilities emerge from the optomechanical interaction between the high power optical field resonating in the cavity and the cavity mirrors which act as test masses. In Advanced LIGO each test mass is a $\sim$40 kg fused silica cylinder, and at design levels they are subject to $\sim$800 kW of optical power. Under some conditions the optical field will yield energy to the test mass in a way that excites a particular mechanical resonance. If the amplitude of such excitation grows exponentially in time, it is referred to as an oscillatory parametric instability (PI). These perturbations are of purely dynamical nonlinear origin. If not addressed, they can saturate the interferometer control systems and displace the instrument away from a suitable operating point.