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

Magnetic flux trapped during the cooldown of superconducting radio-frequency cavities through the transition temperature due to incomplete Meissner state is known to be a significant source of radio-frequency losses. The sensitivity of flux trapping depends on the distribution and the type of defects and impurities which pin vortices, as well as the cooldown dynamics when the cavity transitions from a normal to superconducting state. Here we present the results of measurements of the flux trapping sensitivity on 1.3 GHz elliptical cavities made from large-grain niobium with different purity for different cooldown dynamics and surface treatments. The results show that lower purity material results in a higher fraction of trapped flux and that the trapped flux sensitivity parameter S is significantly affected by surface treatments but without much change in the mean free path 1. We discuss our results within an overview of published data on the dependencies of S(l, f) on 1 and frequency f using theoretical models of rf losses of elastic vortex lines driven by weak rf currents in the cases of sparse strong pinning defects and collective pinning by many weak defects. Our analysis shows how multiscale pinning mechanisms in cavities can result in a maximum in S(l) similar to that observed by the FNAL and Cornell groups and how pinning characteristics can be extracted from the experimental data. Here the main contribution to S come from weak pinning regions at the cavity surface, where dissipative oscillations along trapped vortices perpendicular to the surface propagate into the bulk well beyond the layer of rf screening current. However, the analysis of S as a function of only the mean free path is incomplete since cavity treatments change not only l but pinning characteristics as well. The effect of cavity treatments on pinning is primarily responsible for the change of S without much effect on l observed in this work. It also manifests itself in different magnitudes and peak positions in S(l), and scatter of the S-data coming from the measurements on different cavities which have undergone different treatments affecting both l and pinning. Optimizations of flux pinning to reduce flux sensitivity at low rf fields is discussed.