Suppression of parametric instabilities in future gravitational wave detectors using damping rings

The next generation of laser interferometer gravitational wave detectors requires optical cavities with stored power approaching 1 MW. However, such proposed cavities are subject to parametric instability where carrier power resonantly downconverts to drive a large number of test mass acoustic resonances. Damping rings on the test mass circumference have been proposed as a means of suppressing such instabilities, and in previous work, the affect of such a ring on test mass acoustic modes and thermal noise was analysed. The purpose of this paper is to investigate the general issue of parametric instability suppression with damping rings. We determine the optimal position and geometry of damping rings, so as to obtain sufficient instability suppression with the least thermal noise penalty. It is shown that unilateral stability can be attained with a ring damper alone at the expense of a 20% increase in thermal noise, while if just one optical mode is suppressed, there is only a 5% noise penalty.