Vortex dynamics and losses due to pinning: Dissipation from trapped magnetic flux in resonant superconducting radio-frequency cavities

TL;DR

This paper models vortex dynamics and pinning effects to understand and predict residual magnetic flux losses in superconducting RF cavities, providing formulas to optimize material performance.

Contribution

It introduces a combined analytical and numerical approach to describe vortex-induced dissipation and crossover regimes in superconducting cavities.

Findings

Hysteretic losses explain the linear dependence of residual resistance on trapped flux.

The model predicts a crossover from hysteretic to viscous dissipation regimes.

Formulas are provided to guide material tuning for better cavity performance.

Abstract

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 NbCu, doped-Nb and Nb$_3$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.