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

D. Yu. Vodolazov·I. L. Maksimov
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Abstract

A one-dimensional equation describing the distribution of the effective vector potential $\bar A(y)$ 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-Londons equation for superconducting films in a perpendicular magnetic field. The validity of this equation for a finite-thickness film is verified by a numerical analysis. An approximation dependence $\bar A(y)$, finite (with all of its derivatives) across the entire film width, is found for films, being 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 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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D. Yu. Vodolazov, I. L. Maksimov. 2000-01-04. Distribution of the magnetic field and current density in superconducting films of finite thickness. https://doi.org/10.1016/s0921-4534(00)01522-7

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