Flux penetration into flat superconductors of arbitrary shape: Patterns of magnetic and electric fields and current

Abstract

The penetration of magnetic flux into flat type-II superconductors of various shapes in a perpendicular magnetic field is investigated in detail. The magnetic field distribution at the sample surface is observed by the magneto-optical Faraday effect and calculated from first principles. The investigations are performed on DyBa2Cu3O7−δ and YBa2Cu3O7−δ samples which were shaped into a cross or an indented rectangle by a laser-cutting technique. Magnetic and electric field and current distributions are calculated from Maxwell’s equations treating the superconductor as a conductor with a highly nonlinear current-voltage law and zero reversible magnetization. A large concentration of magnetic flux and electric field and a high flux-line velocity occur at concave sample corners. This results from the fact that the flux lines can penetrate into regions of the sample which are bounded by the extensions of the sample edges only at these points. This large electric field and related energy dissipation are particularly relevant for superconducting tapes, in which ‘‘sausaging’’ effects (variations of the filament cross section) reduce their performance as an ideal conductor. Huge jumps of the electric field occur where the current flow changes from a straight to a circular path. This jump diverges as one over the distance to the corner at sharp indents or concave corners. © 1996 The American Physical Society.

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