Abstract
An 1D equation describing the distribution of the effective vector potential A(y) across a film width, which holds for thin ( d< λ) and thick ( d> λ) films alike, is derived based on the analysis of a 2D Maxwell–London equation for superconducting films in a perpendicular magnetic field. For a finite λ case, the distributions of the local magnetic field and current density are found both inside and outside superconductors. An approximation dependence A(y) , finite (with all of its derivatives) across the entire film width, is found for films in the Meissner state. The flux-entry field is evaluated for a film of arbitrary thickness. An approximation expression is obtained for the distribution of the sheet current density in the mixed state of a pin-free superconducting film with an edge barrier. The latter approximation allows one to estimate magnetic field concentration factor at the film edge as a function of external magnetic field and geometrical parameters of the sample.
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