Critical-state model for harmonic generation in a superconducting microwave resonator

A critical-state model is developed for the treatment of the nonlinear ac response of a superconducting coaxial-type transmission line. Analytical results are presented for the resistance and reactance as well as the response at overtone frequencies. Center conductors of both elliptical and rectangular thin-film cross section are considered. The dominant response, in the case of the elliptical geometry, is found to be independent of the aspect ratio of the ellipse. Significant differences are found between the elliptical and strip geometries. These differences are due to the difference in structure of the critical state in the two geometries. The model is applied to resonators with the assumption that end effects can be neglected. Qualitative agreement is found with experimental results.