The Importance of the Electron Mean Free Path for Superconducting RF Cavities

Impurity-doping is an exciting new technology in the field of SRF, producing cavities with record-high quality factor $Q_0$ and BCS surface resistance that decreases with increasing RF field. Recent theoretical work has offered a promising explanation for this anti-Q-slope, but the link between the decreasing surface resistance and the short mean free path of doped cavities has remained elusive. In this work we investigate this link, finding that the magnitude of this decrease varies directly with the mean free path: shorter mean free paths correspond with stronger anti-Q-slopes. We draw a theoretical connection between the mean free path and the overheating of the quasiparticles, which leads to the reduction of the anti-Q-slope towards the normal Q-slope of long-mean-free-path cavities. We also investigate the sensitivity of the residual resistance to trapped magnetic flux, a property which is greatly enhanced for doped cavities, and calculate an optimal doping regime for a given amount of trapped flux.