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

Abstract

The improvement of the performance of superconducting rf 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 nonlinear 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.