Transport current and magnetization problems for thin type-II superconducting films

Thin film magnetization problems in type-II superconductivity are usually formulated in terms of the magnetization function alone, which allows one to compute the sheet current density and the magnetic field but often inhibits computing the electric field in the film. Accounting for the current leads presents an additional difficulty encountered in thin film transport current problems. We generalize, to the presence of a transport current, the two-variable variational formulation proposed recently for thin film magnetization problems. The formulation, written in terms of the magnetization function and the electric field, is used as a basis for a new numerical approximation enabling us to solve the magnetization and transport current problems for flat films of arbitrary shapes, including multiply connected films. The advantage of this approach is in its ability to compute accurately all variables of interest, including the electric field, for any value of the power in the power law current-voltage relation characterizing the superconducting material. In the high power limit the critical state model solution is obtained.