An Upper Bound to the Frequency Dependence of the Cryogenic Vacuum-Gap Capacitor
Neil M. Zimmerman, Brian J. Simonds, Yicheng Wang
In attempting to develop a capacitance standard based on the charge of the electron, one question which has been open for many years is the frequency dependence of the vacuum-gap cryogenic capacitor. In this paper, we succeed in putting an upper bound on that frequency dependence from 0.01 Hz to 1 kHz of about 2x10-7. We do this by considering a model for the dispersionin the surface insulating films on the surface of the Cu electrodes; the crucial prediction of this model is that the dispersion falls to very low values at low temperatures. By measuring the frequency dependence over a restricted range of frequencies, we have verified this prediction, and thus provide adequate support to conclude that the model is correct. We also point out that, independent of the capacitance standard, this cryogenic capacitor provides a frequency-independent standard for measurements in fields such as the low-temperature dynamics of amorphous materials.