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

An 1D equation describing the-distribution of the effective vector potentia l 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-L ondon equation for superconducting films in a perpendicular magnetic field. For a finite lambda case, the distributions of the local magnetic field an d current density are found both inside and outside superconductors. An app roximation dependence A Oil, finite (with all of its derivatives) across th e entire film width, is found for films in the Meissner state. The flux-ent ry field is evaluated for a film of arbitrary thickness. An approximation e xpression is obtained for the distribution of the sheet current density in the mixed state of a pin-free superconducting film with an edge barrier. Th e latter approximation allows one to estimate magnetic field concentration factor at the him edge as a function of external magnetic field and geometr ical parameters of the sample. (C) 2001 Elsevier Science B.V. All rights re served.