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.
Categories: cond-mat.supr-con physics.acc-ph