Test mass ring dampers with minimum thermal noise

Advanced laser interferometers gravitational wave detectors may need to substantially reduce the Q-factor of test mass normal modes to eliminate parametric instability. In this Letter we investigate various ring damper configurations for two different laser beam geometries. We show that there is a well-defined location near the mid point of a test mass where the thermal noise degradation from the ring damper is minimised. A Q-factor reduction by a factor of 5 can be obtained for at least 30% of the investigated normal modes at the cost of a 1% increase in thermal noise as seen by a 5 cm diameter incident laser beam. Ring dampers can be up to about 10 mm wide while maintaining minimum thermal noise effect contribution. Of the remaining modes, 30% are very weakly damped