Time-domain analytical solutions to pulsed eddy current field excited by a probe coil outside a conducting ferromagnetic pipe

Using the second-order vector potential formalism and block matrix, the non-axisymmetric eddy current field induced by a probe coil positioned perpendicularly outside a conducting ferromagnetic pipe is solved analytically. Then, the time-domain expressions of induced voltage and eddy current density in the pipe are obtained through the Laplace inverse transformation, which is carried out by calculating the residues of poles. Furthermore, the diffusion process of pulsed eddy current in the pipe is examined. Finally, the analytical solutions are verified through the experiment results of two steel pipes with different wall thickness.