Assessing the spatial and field dependence of the critical current   density in YBCO bulk superconductors by scanning Hall probes
  Although the flux density map of a bulk superconductor provides in principle sufficient information for calculating the magnitude and the direction of the supercurrent flow, the inversion of the Biot-Savart law is ill conditioned for thick samples, thus rendering 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 the critical 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 and solves the equations non-iteratively, assuming a planar z-independent current density. The calculated current density at a certain position is found to depend on the magnetic induction. In this way the average field dependence of the critical current density Jc(B) is obtained also at low fields, which is not accessible to magnetisation measurements due to the self-field of the sample. It is further shown that an evaluation of magnetisation loops, taking the self-field into account, results in a similar dependence in the field range accessible to this experiment. 
F. Hengstberger, M. Eisterer, M. Zehetmayer and H. W. Weber