A CONTRIBUTION TO THE ANALYSIS OF THE CURRENT-DENSITY DISTRIBUTION INELONGATED HARD TYPE-II SUPERCONDUCTORS WITH RECTANGULAR CROSS-SECTION

Analytical expressions are given for the spatial distribution of the m agnetic flux density B(r) of a sample with rectangular cross-section ( xy-plane) elongated in the z direction in which a given electric curre nt density j(z)(x, y) = SIGMA(n=0.1),...a(n)(x-x0)n exists. Applicatio n 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 distributi on in the samples. The analysis of the magneto-optical measurements pe rformed on thick Nb bars and thin stripe-structured YBa2Cu3O7-x films show that after full flux penetration the current density is spatially constant in the sample. The characteristic features of the magnetic f lux-density distribution of a homogeneous current (n = 0), e.g., the s patial field-line distribution, inverse flux zones and the influence o f external magnetic fields, are described as functions of the sample t hickness. The analysis of the Faraday measurements of the thin stripes show that for partly penetrated flux an additional current distributi on in the flux-free region has to be taken into account. Analytical ex pressions are given to calculate the critical current density of a sam ple with width W and thickness D from measurements of the B(y) field i n the center or at the sample edge. Furthermore simple expressions are given for the external applied field necessary for full flux penetrat ion.