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Quasi-Spherical Cavity Resonators for Metrology Based on the Relative Dielectric Permittivity of Gases

Published

Author(s)

E May, Laurent Pitre, J B. Mehl, Michael R. Moldover, James W. Schmidt

Abstract

We evaluate a quasi-spherical, copper, microwave cavity resonator for accurately measuring the relative dielectric permittivity {epsilonr(p,T)} of helium and argon. In a simple, crude approximation the cavity s shape is a triaxial ellipsoid with axes of length {a}, 1.001{a} and 1.005{a}, with {a} = 5 cm. The unequal axes of the quasi-sphere separated the triply-degenerate microwave resonance frequencies of a sphere {fTM11, fTM12,... fTM11, fTM12,...}into three non-overlapping, easily measured, frequencies. The frequency splittings are consistent with the cavity s shape, as determined from dimensional measurements. We deduced epsilon of εr(p,T) of helium and of argon at 289 K and up to 7 MPa from the resonance frequencies {fsigma,en,} the resonance half-widths {gen,sigma} , and the compressibility of copper. Simultaneous measurements of epsilon of εr(p,T) with the quasi-spherical resonator and a cross capacitor agreed within 1x10-6 for helium, and for argon they differed by an average of only 1.4(multiplied by}10-6. This small difference is within the stated uncertainty of the capacitance measurements. For helium, the resonator results for {epsilon r(p,T)} were reproducible over intervals of days with a standard uncertainty of 0.2×10^-6^, consistent with a temperature irreproducibility of 5 mK. We demonstrate that several properties of quasi-spherical cavity resonators make them well suited to {epsilon r(p,T)} determinations. Ultimately, a quasi-spherical resonator may improve dielectric constant gas thermometry and realize a proposed pressure standard based on {epsilon r(p,T)}.
Citation
Review of Scientific Instruments
Volume
75
Issue
No. 10

Keywords

argon, dielectric constant, helium, metrology, microwave resonator, permittivity, pressure, resonator, temperature
Created October 1, 2004, Updated February 17, 2017