Computation of critical current in artificially structurated bulk samples from Hall measurements

Abstract

High-temperature superconducting artificially structured bulk samples, such as bulks with slanted drills or welds of different pieces along the c-axis with holes drilled in different asymmetric positions, pose a challenge for the computation of critical current maps able to spot the position of inhomogeneities, as they combine a current map in every ab-plane adapted to the drill/welding structure with the dependence of this structure on the position along the caxis. We improve and adapt our technique of Hall probe field measurement, discretization and QR inversion to this problem by measuring the magnetic field on top and bottom of the bulk sample to obtain some spatial resolution of the current. To test our technique we apply it to both simulations with asymmetrical geometry and a real artificially structured bulk samples.

Detection of Current Distribution in Bulk Samples With Artificial Defects From Inversion of Hall Magnetic Maps

“…This answer was pointed out by Eisterer [7], and is documented by simulation 1 from [5], in which a current density averaging is distributed in a cylinder so as to yield a maximum magnetic field of at distances of 0.2 mm or further.…”

“…It follows from previous work by Eisterer [7] and the authors [5] that these c-averages and vertical resolution are the maximal information that inversion of the Biot-Savart problem by any procedure may yield.…”

“…1 illustrates for the typical dimensions of HTS bulks, this weighting is not so top heavy that a fine superficial layer obscures the current circulation below it. Simulation 2 from [5] provides a typical check of this formula: it consists of a virtual c-stack of 12 1-mm thick cylinders, each of them with a regular current with constant density, but this density varies along the c-stack. The vertical magnetic field that such a stack generates at a height of 0.1 mm above and below the sample was computed, and our two-sided inverse Biot-Savart computation was performed, subdividing the sample into two c-stacked cylinders of thickness 6 mm, and each cylinder into a rectangular grid of elements.…”

“…As Table I shows, the result of the computation agrees with the (1/z)-average of the real density of formula (1), with a margin of error of 2%. (1/z)-weighted average of J (z) vs c-homogeneous J yielded by 2-sided inverse Biot-Savart computation in sample S1 from [5].…”

“…If it is measured on only one side, the shielding effect of simulation 1 in [5] becomes possible, and the existence of large c-inhomogeneous perturbations of affecting only slightly the magnetic field at the points of measure means that the inverse Biot-Savart problem is too ill-conditioned to solve. Even if we use all space components of the magnetic field, above the sample and on its sides, the inverse Biot-Savart problem is so ill-posed (condition numbers starting at ) that any noise in the measurement of B prevents the inversion.…”