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

In the present paper, a sensitivity analysis scheme for designing the shape of cylindrical probe coils is presented. These coils are used for the indu ction 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 funct ion, which is related to the desired and the estimated values of the magnet ic vector potential, is minimized by applying the Newton's gradient based o ptimization method. The estimated values of the magnetic potential are comp uted by an integral formulation, which is derived from the diffusion equati on. During each iteration of the minimization process, the gradient and the second order partial derivatives of the error function, with respect to th e design variables, are evaluated analytically. In numerical results, the m ethod is applied to the induction of a uniform eddy current distribution pa rallel to the axis of a conducting cylinder.