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 mea sured by means of pick-up or Hall probes and these data are used to reconst ruct the current distribution inside the cable. The efficiency and the accu racy 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 cur rent, the determination of the current distribution can be mathematically f ormulated as a linear inverse problem, in which the residual between the me asured and the computed field values at the probe locations is minimised. A linear least-squares problem results, which is solved by means of tile tru ncated singular value decomposition technique, applied to the matrix G whic h 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 th e 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.