  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 analyzed 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.
