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

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 Rs. 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 Brf0 of the additional surface resistance Rfl. We also show that the proportionality between the rf-field-dependent and -independent terms Rfl1 and Rfl0 and the frequency dependence of Rfl1 follow naturally from this approach.