A contribution to the analysis of the current-density distribution in elongated hard type-II superconductors with rectangular cross-section

Abstract

Analytical expressions are given for the spatial distribution of the magnetic flux density B ( r ) of a sample with rectangular cross-section ( xy-plane) elongated in the z direction in which a given electric current density j z ( x, y) = Σ n = 0,1,… a n ( x − 0) n exists. Application of these formulae to magneto-optical Faraday effect measurements of the B y field obtained at the surface of a type-II superconductor in the mixed state allows one to calculate the current-density distribution in the samples. The analysis of the magneto-optical measurements performed on thick Nb bars and thin stripe-structured YBa 2Cu 3O 7− x films show that after full flux penetration the current density is spatially constant in the sample. The characteristic features of the magnetic flux-density distribution of a homogeneous current ( n = 0), e.g., the spatial field-line distribution, inverse flux zones and the influence of external magnetic fields, are described as functions of the sample thickness. The analysis of the Faraday measurements of the thin stripes show that for partly penetrated flux an additional current distribution in the flux-free region has to be taken into account. Analytical expressions are given to calculate the critical current density of a sample with width W and thickness D from measurements of the B y field in the center or at the sample edge. Furthermore simple expressions are given for the external applied field necessary for full flux penetration.