Charging of a Fused Silica Optic by an Electrostatic Drive

Gravitational-wave interferometers with suspended optics may use an electrostatic drive (ESD) as a position fine adjust. An ESD is an electrode pattern printed onto a reaction mass with alternating positive and negative voltages. According to measurements at Moscow State University (MSU), the ESD contributes displacement noise by redistributing charge on the optic. We sought to verify the MSU result by measuring the induced charge distribution from an ESD with a Kelvin capacitive probe. A fused silica optic was exposed to an ESD and then moved via a motorized translation stage to the probe for measurement at high vacuum (10$^{-5}$ torr). Calibration with a known voltage source determined a sensitivity 1V = 6$\times $10$^{-12}$ C/cm$^{2}$. A voltage of $\pm $ 600V was applied to the electrodes for a period of one week, then shut off for one week, and reversed for another week. The charging rate was found to be 7$\times $10$^{-15}$ C/cm$^{2}$/hr, fourteen times slower than the MSU result. The decay time constant found was 3700 $\pm $ 900 hours, about 3 times faster than the MSU result.