Time evolution of parametric instability in large-scale gravitational-wave interferometers

TL;DR

This paper investigates the non-linear dynamics of parametric instability in large-scale gravitational-wave detectors, revealing a saturation phase that could enable stable operation despite instabilities.

Contribution

It provides the first non-linear analysis of three-mode parametric instability, showing the transition from exponential growth to a stable equilibrium.

Findings

Initial exponential growth of modes is followed by saturation.

Stable equilibrium states are achievable despite instabilities.

Implications for simplifying interferometer suppression strategies.

Abstract

We present a study of three-mode parametric instability in large-scale gravitational-wave detectors. Previous work used a linearised model to study the onset of instability. This paper presents a non-linear study of this phenomenon, which shows that the initial stage of exponential rise of the amplitudes of a higher order optical mode and the mechanical internal mode of the mirror is followed by a saturation phase, in which all three participating modes reach a new equilibrium state with constant oscillation amplitudes. Results suggest that stable operation of interferometers may be possible in the presence of such instabilities, thereby simplifying the task of suppression.