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Impurity-doping is an exciting new technology in the field of SRF, producingcavities with record-high quality factor $Q_0$ and BCS surface resistance thatdecreases with increasing RF field. Recent theoretical work has offered apromising explanation for this anti-Q-slope, but the link between thedecreasing surface resistance and the short mean free path of doped cavitieshas remained elusive. In this work we investigate this link, finding that themagnitude of this decrease varies directly with the mean free path: shortermean free paths correspond with stronger anti-Q-slopes. We draw a theoreticalconnection between the mean free path and the overheating of thequasiparticles, which leads to the reduction of the anti-Q-slope towards thenormal Q-slope of long-mean-free-path cavities. We also investigate thesensitivity of the residual resistance to trapped magnetic flux, a propertywhich is greatly enhanced for doped cavities, and calculate an optimal dopingregime for a given amount of trapped flux.

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