Simple model for the RF field amplitude dependence of the trapped flux sensitivity in superconducting RF cavities

TL;DR

This paper introduces a simple nonlinear model based on modified Gittleman-Rosenblum equations to describe how trapped magnetic flux affects the surface resistance of superconducting RF cavities as a function of RF field amplitude.

Contribution

It presents a novel empirical model incorporating nonlinear pinning forces to explain the RF field dependence of trapped flux sensitivity in superconducting RF cavities.

Findings

The model accurately describes the linear dependence of additional surface resistance on RF field amplitude.

Proportionality between RF-dependent and independent resistance terms is explained.

Frequency dependence of RF-dependent resistance term is naturally derived from the model.

Abstract

The improvement of the performance of RF superconducting cavities has recently motivated a considerable research effort in order to elucidate the effect of trapped magnetic flux on the surface resistance $R_{s}$. In this paper we show that by introducing a non-linear pinning force in the Gittleman-Rosenblum equations for the RF power dissipation due to a trapped magnetic flux in a superconductor, we can empirically describe the linear dependence on the RF field amplitude $B_{rf0}$ of the additional surface resistance $R_{fl}$. We also show that the proportionality between the RF-field dependent and independent terms $R_{fl}^{1}$ and $R_{fl}^{0}$, and the frequency dependence of $R_{fl}^{1}$ follow naturally from this approach.