We use a model of vortex dynamics and collective weak-pinning theory to study the residual dissipation due to trapped magnetic flux in a dirty superconductor. Using simple estimates, approximate analytical calculations, and numerical simulations, we make predictions and comparisons with experiments performed in CERN and Cornell on resonant superconducting radio-frequency $\mathrm{Nb}\mathrm{Cu}$, doped-$\mathrm{Nb}$ and ${\mathrm{Nb}}_3\mathrm{Sn}$ cavities. We invoke hysteretic losses originating in a rugged pinning potential landscape to explain the linear behavior of the sensitivity of the residual resistance to trapped magnetic flux as a function of the amplitude of the radio-frequency field. Our calculations also predict and describe the crossover from hysteretic-dominated to viscous-dominated regimes of dissipation. We propose simple formulas describing power losses and crossover behavior, which can be used to guide the tuning of material parameters to optimize cavity performance.

• Received 4 August 2018
• Revised 22 October 2018

DOI:https://doi.org/10.1103/PhysRevApplied.10.054057

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society