  The magnetic inverse source problem of reconstructing the positions and
currents of very long parallel conductors is considered in a two-dimensional
situation, with applications to power line measurements. The input data is the
magnetic field on a contour surrounding the conductors to be reconstructed.
Using a scalar-vector Green identity, an explicit reconstruction algorithm is
derived. The numerical implementation of the algorithm is described and
simulation results are presented, demonstrating the influences from numerical
errors and uncertainties in measurement data. The algorithm can handle an
arbitrary number of conductors, but stability problems associated with the
illposedness accelerate with increasing number of conductors. Mathematically,
the Green identity approach removes the influence of external disturbances and
thus have potential usefulness in current reconstruction for determining
optimal sensor positions and how to process measurement data.
