Analysis of the optimal location of magnetic field probes for the determination of the current distribution inside S/C cables

During the tests on superconducting cables, the magnetic field is often measured by means of pick-up or Hall probes and these data are used to reconstruct the current distribution inside the cable. The efficiency and the accuracy of the reconstruction procedure depend on the algorithm adapted and on the location of the field probes. For a given geometry of the lines of current, the determination of the current distribution can be mathematically formulated as a linear inverse problem, in which the residual between the measured and the computed field values at the probe locations is minimised. A linear least-squares problem results, which is solved by means of the truncated singular value decomposition technique, applied to the matrix G which relates the unknown currents to the computed magnetic field values. The condition number of G is proposed here as an index of the quality of the location of the probes: a good location corresponds to a well conditioned G, while a bad location gives a worse conditioned matrix. In this paper a reconstruction procedure is presented and a criterion for the optimal probe positioning is shown.