  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.
