A new method of computation of current distribution maps in bulk high-temperature superconductors: analysis and validation

We present a test and analysis of our method of computation of the distribution of currents in bulk superconducting samples, which is sensitive to current contribution in the deep layers of the sample. The procedure is based on measurements of the magnetic field with a Hall probe, inverted by linearization and orthogonal triangularization, known as QR decomposition, of the matrix in the resulting linear system. No assumptions on the number or geometry of domains are required. The only constraint on the method is that the critical current must be homogeneous along the c -axis. Our method is applied to real 3d samples with size in the cm range and different geometries of technological interest. The propagation of errors in the general case is analysed, and we also supply a method to estimate the error in every computation, which is applied to the computed J ( J x , J y ) in the above samples.