Quasi-spherical cavity resonators for metrology based on the relative dielectric permittivity of gases

We evaluate a quasi-spherical, copper, microwave cavity resonator for accurately measuring the relative dielectric permittivity εr(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 each of the triply degenerate microwave resonance frequencies of a sphere (f11TM,f12TM,…,f11TE,f12TE,…) into three nonoverlapping, easily measured, frequencies. The frequency splittings are consistent with the cavity’s shape, as determined from dimensional measurements. We deduced εr(p,T) of helium and of argon at 289 K and up to 7 MPa from the resonance frequencies flnσ, the resonance half-widths glnσ, and the compressibility of copper. Simultaneous measurements of εr(p,T) with the quasi-spherical resonator and a cross capacitor agreed within 1×10−6 for helium, and for argon they differed by an average of only 1.4×10−6. This small difference is within the stated uncertainty of the capacitance measurements. For helium, the resonator results for εr(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 εr(p,T) determinations. Ultimately, a quasi-spherical resonator may improve dielectric constant gas thermometry and realize a proposed pressure standard based on εr(p,T).