Field distributions around a rectangular crack in a metallic half-space excited by long current-carrying wires with arbitrary frequency

In this paper, we propose a semianalytical solution for evaluation of field distributions around a short rectangular crack in a metallic half-space excited by long current-carrying wires with arbitrary frequency. The governing Helmholtz equation is solved in three dimensions by separation of variables. The solution is obtained by developing 2-D Fourier series model and using exponential functions in the third dimension. To expand all possible field components in the metal, we first hypothesize a shielded dielectric rod waveguide where the shield enclosure lies at infinity, the surrounding dielectric (i.e., the metal) is a lossy material, and the rod dielectric is the crack opening. We then introduce hybrid modes each of which consists of two components, representing the TMy and TEy modes. The mode-matching technique is finally used to numerically solve the resultant boundary value problem. The unknown eigenvalues and field coefficients are found by searching for small singular values, using the singular value decomposition (SVD) in the resultant homogeneous linear system. The validity of our modeling technique is confirmed by comparison of our results with those obtained by measurement and finite integration code.