Resolution of 2D Currents in Superconductors from a 2D magnetic field measurement by the Method of Regularization
The problem of reconstructing a two-dimensional (2D) current distribution from a 2D magnetic field measurement is recognized as a first-kind integral equation and resolved using the method of Regularization. Regularization directly addresses the inherent instability of this inversion problem for non-exact (noisy) data, and performance of the technique is evaluated for data with varying amounts of added noise. Comparisons are made to other methods, and the advantage of the present method is demonstrated through its ability to achieve a better regularizing (noise filtering) effect while also employing the generalized-cross validation (GCV) method to choose the optimal regularization parameter from the data, without detailed knowledge of the true (and generally unknown) solution. Examples are given for both slab and thin film geometries, relevant for application to high temperature superconducting thin films and BiSrCaCuO (BSCCO) tapes respectively.