Distribution of the magnetic field and current density in superconducting films of finite thickness

An 1D equation describing the-distribution of the effective vector potential A(y) across a film width, which holds for thin (d < <lambda>) and thick (d > lambda) 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 lambda case, the distributions of the local magnetic field and current density are found both inside and outside superconductors. An approximation dependence A Oil, 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 him edge as a function of external magnetic field and geometrical parameters of the sample. (C) 2001 Elsevier Science B.V. All rights reserved.