Reconstruction of Interfaces between Electrically Conducting Fluids from Electrical PotentialMeasurements

A possibility for the determination of the interface between two electrically conducting fluids in cylindrical geometry is presented. The fluids with different conductivities are situated in an infinite cylinder. Along the axis of the cylinder a homogeneous electrical current is applied. The perturbation of the interface leads to an inhomogeneous electrical current and, therefore, results in an electrical potential change in the fluids and a magnetic field modification outside the fluids. The dependence of the electrical potential on the interface shape is obtained analytically. The interface profile is then recovered from data of the electrical potential measurements which have been generated numerically. This inverse problem is solved for the cases of an axisymmetric and non-axisymmetric interface using the singular value decomposition method and Fourier transform. The number of modes which have to be reconstructed is obtained using L-curve criterion.