Designing quasi-spherical resonators for acoustic thermometry

We describe a quasi-spherical, noble-gas-filled cavity designed to determine the thermodynamic temperature of the gas from measurements of the frequencies and the half-widths of microwave and acoustic resonances in the cavity. The quasi-spherical shape retains the advantages of spherical acoustic resonators (non-degenerate, radially symmetric acoustic modes, negligible viscous damping at the boundary) while simplifying the determination of the cavity's thermal expansion using microwave resonances. As a specific example, we consider a cavity bounded by four quadrants of a perfect sphere of radius a connected to each other by narrow cylindrical sections of thickness 21a and 22a, where 1 and 2 are of the order of 10−3. The cylindrical sections split the degenerate microwave triplets (TM11, TE11, TM12, etc) into three easily resolved components with predictable orientations. Preliminary measurements show that two judiciously located microwave probes excite and detect all three components of each microwave triplet with approximately equal amplitudes. We discuss the placement of acoustic transducers and the dimensions of ducts that admit gas from a manifold into the cavity. Corrections were made to this article on 14 June 2004. The corrected electronic version is identical to the print version. The corrections are in the first two paragraphs of section 5.2 and in table 6.