An upper bound to the frequency dependence of the cryogenic vacuum-gap capacitor

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; the crucial difficulty has been: How do we measure frequency dependence down to 0.01 Hz? In this paper, we succeed in putting an upper bound on the frequency dependence, from 0.01 Hz to 1 kHz, of about 2 x 10(-7). We do this by considering a model for the dispersion in 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.