  Interferometric gravitational wave detectors operate with high optical power
in their arms in order to achieve high shot-noise limited strain sensitivity. A
significant limitation to increasing the optical power is the phenomenon of
three-mode parametric instabilities, in which the laser field in the arm
cavities is scattered into higher order optical modes by acoustic modes of the
cavity mirrors. The optical modes can further drive the acoustic modes via
radiation pressure, potentially producing an exponential buildup. One proposed
technique to stabilize parametric instability is active damping of acoustic
modes. We report here the first demonstration of damping a parametrically
unstable mode using active feedback forces on the cavity mirror. A 15,538 Hz
mode that grew exponentially with a time constant of 182 sec was damped using
electro-static actuation, with a resulting decay time constant of 23 sec. An
average control force of 0.03 nNrms was required to maintain the acoustic mode
at its minimum amplitude.
