The significance of solutions of the inverse Biot–Savart problem in thick superconductors

The evaluation of current distributions in thick superconductors from field profiles near the sample surface is investigated theoretically. A simple model of a cylindrical sample, in which only circular currents are flowing, reduces the inversion to a linear least squares problem, which is analysed by singular value decomposition. Without additional assumptions about the current distribution (e.g., constant current over the sample thickness), the condition of the problem is very bad, leading to unrealistic results. However, any additional assumption strongly influences the solution and thus renders the solutions again questionable. These difficulties are unfortunately inherent to the inverse Biot–Savart problem in thick superconductors and cannot be avoided by any models or algorithms.