States of equilibrium of a superconducting thin film carrying an alternating current

The states of thermal equilibrium of a thin superconducting film carrying an alternating current are considered. The temperature field of the film is modelled within a ranges of frequency and temperature where density of normal current is comparable with that of superconducting electrons. The equation for heat conduction in a superconducting state, deduced with allowance for energy dissipation by normal electrons within the framework of a double-fluid model, features a nonlinear function of heat sources. The analysis of homogeneous states of equilibrium and their dependence on control parameters is carried out. Its results, presented in the form of isotherms of the equilibrium states in a phase-plane, reveal dependence of singular points on control parameters. This allows retrieving of the structure of phase-space dissection and states of equilibrium for various values of control parameters. The stability of these states, considered within the boundary value problem with periodic boundary conditions, is proved. The range of a bistability of the film is defined and the numerical modelling of waves of switching between stationary states is accomplished.