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

Published

October 1, 2004

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 epsilon_r(p,T)} of helium and argon. In a simple, crude approximation the cavity s shape is a triaxial ellipsoid with axes of length a}, 1.001a} and 1.005a}, 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 ε_r(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 ε_r(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

Pub Type

Journals

Keywords

argon, dielectric constant, helium, metrology, microwave resonator, permittivity, pressure, resonator, temperature

Citation

May, E. , Pitre, L. , Mehl, J. , Moldover, M. and Schmidt, J. (2004), Quasi-Spherical Cavity Resonators for Metrology Based on the Relative Dielectric Permittivity of Gases, Review of Scientific Instruments (Accessed October 11, 2025)