Distributed current source modeling method for 3D eddy current problem in magnetic conductor with discrete state-space J-φ formulation

This paper presents a distributed-current-source (DCS) modeling method to analyze the eddy-current (EC) induced in an electrically conductive material with a weak magnetic permeability. Formulated in state space to solve for an unknown EC density J and electric potential φ, the method decomposes the conductor into elemental volume/surface current sources to model the eddy-current and magnetization effects. The closed-form solutions to a three-dimension (3D) EC problem with geometrical boundary effects are derived and verified by comparing with finite-element methods and published data, both numerically and experimentally. An element-refinement method, which accounts for the skin-depth effects and non-uniform boundary EC, is proposed and validated. The DCS modeling method has been applied to a field-reconstruction application for parametric analysis demonstrating its effectiveness and efficiency.