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Magnetic flux trapped during the cooldown of superconducting radio-frequencycavities through the transition temperature due to incomplete Meissner state isknown to be a significant source of radio-frequency losses. The sensitivity offlux trapping depends on the distribution and the type of defects andimpurities which pin vortices, as well as the cooldown dynamics when the cavitytransitions from a normal to superconducting state. Here we present the resultsof measurements of the flux trapping sensitivity on 1.3 GHz elliptical cavitiesmade from large-grain niobium with different purity for different cooldowndynamics and surface treatments. The results show that lower purity materialresults in a higher fraction of trapped flux and that the trapped fluxsensitivity parameter $S$ is significantly affected by surface treatments butwithout much change in the mean free path $l$. We discuss our results within anoverview of published data on the dependencies of $S(l,f)$ on $l$ and frequency$f$ using theoretical models of rf losses of elastic vortex lines driven byweak rf currents in the cases of sparse strong pinning defects and collectivepinning by many weak defects. Our analysis shows how multiscale pinningmechanisms in cavities can result in a maximum in $S(l)$ similar to thatobserved by the FNAL and Cornell groups and how pinning characteristics can beextracted from the experimental data. Here the main contribution to $S$ comefrom weak pinning regions at the cavity surface, where dissipative oscillationsalong trapped vortices perpendicular to the surface propagate into the bulkwell beyond the layer of rf screening current.

Flux expulsion in niobium superconducting radio-frequency cavities of different purity and essential contributions to the flux sensitivity