Integral equation method for modeling the linear electromagnetic response of superconducting films in the mixed state

A mathematical model describing the linear rf response of thin superconducting films in the mixed state with arbitrary spatial distribution of the vortices and the exciting rf field is developed. The model is formulated in terms of an integro-differential equation, algorithm of numerical solution to which is proposed. The stability of the solution, its dependence on the model parameters and profiles of the magnetic field for symmetric and antisymmetric excitation of rf current inside the film is discussed.