The microwave response of thin superconducting films with trapped magnetic flux

A theoretical model of the microwave response of superconducting thin films with trapped magnetic flux is proposed. The model developed allows us to calculate the energy losses and other measurable quantities for films with arbitrary distributions of the trapped flux (Abrikosov vortices) and ac current. It is shown that the response of the film for rather low frequencies is a nonmonotonic function of both the trapped flux and the temperature. The nonmonotonic dependence of the losses obtained is discussed and compared with available experimental data.