Electromagnetic penetration into a conducting circular cylinder through a narrow slot, TM case

A procedure is presented for calculating the electromagnetic field in the vicinity of an infinitesimally thin conducting circular cylindrical shell with an infinitely long shot illuminated by a TM plane wave. This field is the short-circuit field plus the field due to the slot. The field due to the slot stems from the axial electric field in the slot. Approximated by a linear combination of expansion functions that satisfy the edge conditions, the latter field is determined by testing the equation of continuity of the tangential magnetic field in the slot with non-negative powers of phi where phi is the angular distance from the center of the slot. Alternative expansion functions are introduced to preserve the accuracy of the solution in the vicinity of an internal resonance. Containing the resonant electric field, the first alternative expansion function is normalized so that its tangential magnetic field remains finite as the resonant frequency is approached. The rest of the alternative expansion functions are orthogonal to the resonant electric field.