Electromagnetic Response of Superconducting RF Cavities

TL;DR

This paper models the electromagnetic response of superconducting niobium RF cavities, explaining frequency shift anomalies near the critical temperature and their dependence on surface disorder, with results aligning with experimental data.

Contribution

It introduces a theoretical framework combining nonequilibrium superconductivity and Maxwell's equations to analyze surface current response and frequency shifts in Nb SRF cavities.

Findings

Anomalies are sensitive to impurity disorder.

Frequency shift anomalies match experimental data for anisotropic gaps.

Quality factor peaks at intermediate disorder levels.

Abstract

Recently reported anomalies in frequency shift of order $\delta f\sim 0.1 -10\,\mbox{kHz}$ for Niobium SRF cavities in a narrow temperature region near $T_c\simeq 9\,\mbox{K}$ are sensitive to the surface preparation and Nitrogen doping. We developed methods for calculating the surface current response of Nb SRF cavities, as well as the resonant frequency shift and quality factor, as functions of temperature, frequency and disorder based on the Keldysh formulation of the theory for nonequilibrium superconductivity coupled with Maxwell's theory and boundary conditions for the response functions and electromagnetic field. We show that the anomaly is sensitive to impurity disorder. Our results for the anomaly in the frequency shift are in good agreement with experimental results for Nb with an anisotropic gap on the Fermi surface and inhomogeneous non-magnetic disorder. We also show that the quality factor as a function of the impurity scattering rate is maximum for in SRF cavities with intermediate disorder, $\hbar/\tau\Delta\sim{\cal O}(1)$ with the maximum $Q$ decreasing with increasing frequency.