Microwave-Dimensional Measurements of Cylindrical Resonators for Primary Acoustic Thermometry

Abstract

Acoustic gas thermometry relies on the fundamental relationship between the speed of sound in a monatomic gas and its thermodynamic temperature. The speed of sound is calculated from the resonance frequencies of a cavity whose dimensions or thermal expansivity must be measured with high accuracy. For quasi-spherical cavities, the use of microwave resonances is a successful and proven dimensional measurement technique. The simplicity and economy of cylindrical resonators makes them an attractive alternative to quasi-spherical resonators, particularly for high-temperature thermometry. This article summarizes the basic theory of cylindrical microwave resonators, and describes methods for obtaining cavity dimensions from the mode frequencies. The perturbing effects of cavity shape deformations, the wall to end-plate junction, coupling probes and non-conducting surface layers are discussed. The results of an experiment with a simple aluminum cavity are presented, which demonstrate the superior performance of the TE0$pq$ modes over the more commonly used TM0$pq$ modes.