Surface impedance boundary conditions near corners and edges: rigorous consideration

The two-dimensional problem of the magnetic field distribution inside and outside an imperfectly conducting, 90-degree edge is solved using the perturbation technique. The well-known solution of the problem for a perfectly conducting edge is used as an initial approximation. The surface impedance near the edge is represented in the form of asymptotic expansions in the small parameter proportional to the ratio of the skin depth and characteristic size of the conductor surface. An analytical solution for the electric field in the conductor near the edge is obtained. The solution behavior is investigated and the approximate boundary conditions relating the tangential components of the electric and magnetic fields on the conductor surface near the edge are proposed in a form suitable for numerical implementation.