Double-sphere model in the enclosed cavity perturbation technique

Abstract

Electrical conductivity can be conveniently measured by the enclosed microwave cavity perturbation technique. We have investigated the double-sphere model, in which the exact solutions of the full Maxwell’s equations can be calculated analytically. Focusing on the complex frequency shift Δω̂/ω0 as a function of the filling factor for conducting or the insulating sample, we argue that Waldron’s perturbation formula, which has been considered fundamental in the cavity perturbation technique, cannot be applied beyond the depolarization regime, even when |Δω̂/ω0|≪1. Based on the exact solutions for a spherical sample, we obtain approximating formulas that are sufficiently accurate for both the filling factor appearing in the actual measurements and the wide range of conductivity values. We found that the effects of the induced fields just outside the sample must be taken into consideration.