Assessing the spatial and field dependence of the critical current density in YBCO bulksuperconductors by scanning Hall probes

Abstract

Although the flux density map of a bulk superconductor provides in principle sufficientinformation for calculating the magnitude and the direction of the supercurrent flow,the inversion of the Biot–Savart law is ill conditioned for thick samples, thusrendering this method unsuitable for state of the art bulk superconductors. If a thin(<1 mm) slab is cut from the bulk, the inversion is reasonably well conditioned and the variation of thecritical current density in the sample can be calculated with adequate spatial resolution.Therefore a novel procedure is employed, which exploits the symmetry of the problem andsolves the equations non-iteratively, assuming a planar thickness-independent currentdensity. The calculated current density at a certain position is found to depend on themagnetic induction. In this way the average field dependence of the critical current densityJc(B) is also obtained at low fields, which is not accessible to magnetization measurements due tothe self-field of the sample. It is further shown that an evaluation of magnetization loops,taking the self-field into account, results in a similar dependence in the field rangeaccessible to this experiment.