Vortex Dynamics and Losses Due to Pinning: Dissipation from Trapped Magnetic Flux in Resonant Superconducting Radio-Frequency Cavities

The dynamics of superconducting vortices is important in accelerator physics, for its influence on the quality of resonant superconducting rf accelerating cavities, yet a theoretical description of the regime of non-Ohmic power dissipation observed in recent experiments has remained elusive. This study uses ideas from collective weak pinning to solve for the dynamics of a vortex line subject to a disordered potential landscape, and an ac magnetic field parallel to a superconductor's surface. The solutions describe hysteretic power losses and crossover behavior, and can be used to guide the tuning of material parameters to optimize cavity performance.