Shape design of cylindrical probe coils for the induction of specified eddy current distributions

A sensitivity analysis scheme for designing the shape of cylindrical probe coils is presented. These coils are used for the induction of specified eddy current distributions inside cylindrical conducting specimens. This requirement is satisfied by designing the outer surface of the coil, while the excitation current density is assumed to be known and constant all over the cross-section of the coil. An appropriate error function, which is related to the desired and the estimated values of the magnetic vector potential, is minimized by applying Newton´s gradient based optimization method. The estimated values of the magnetic potential are computed by an integral formulation, which is derived from the diffusion equation. During each iteration of the minimization process, the gradient and the second order partial derivatives of the error function, with respect to the design variables, are evaluated analytically. In numerical results, the method is applied to the induction of a uniform eddy current distribution parallel to the axis of a conducting cylinder