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Although the flux density map of a bulk superconductor provides in principlesufficient information for calculating the magnitude and the direction of thesupercurrent flow, the inversion of the Biot-Savart law is ill conditioned forthick samples, thus rendering this method unsuitable for state of the art bulksuperconductors. If a thin (< 1 mm) slab is cut from the bulk, the inversion isreasonably well conditioned and the variation of the critical current densityin the sample can be calculated with adequate spatial resolution. Therefore anovel procedure is employed, which exploits the symmetry of the problem andsolves the equations non-iteratively, assuming a planar z-independent currentdensity. The calculated current density at a certain position is found todepend on the magnetic induction. In this way the average field dependence ofthe critical current density Jc(B) is obtained also at low fields, which is notaccessible to magnetisation measurements due to the self-field of the sample.It is further shown that an evaluation of magnetisation loops, taking theself-field into account, results in a similar dependence in the field rangeaccessible to this experiment.

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