Analytical solution for interaction of an arbitrary frequency curved rectangular inducer with a transverse ring shaped groove surrounding a long conductive cylinder

Field distributions around a transverse flaw surrounding a conductive cylinder which is excited by a three-dimensional inducer at arbitrary frequency are presented analytically. The solution is obtained by developing a two-dimensional Fourier series model and using Bessel functions in the third dimension. The metal is assumed as a lossy material and all possible field components in the conductor are expanded. After applying the mode-matching technique, a linear system of AX=B is solved to obtain the unknown coefficients. The accuracy of the proposed modeling technique is confirmed by comparing our results with those obtained by CST finite integration code.