Electromagnetic Penetration into a Conducting Circular Cylinder through a Narrow Slot, TE 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 slot illuminated by a TE plane wave. This field is the short-circuit field plus the field due to the slot. The short-circuit field is the field that would exist if there were no slot. The field due to the slot stems from the Φ -component of the electric field in the slot. Approximated by a linear combination of expansion functions that satisfy the edge conditions, this field component is determined by testing the equation of continuity of the axial magnetic field in the slot with non-negative powers of Φ where |Φ| 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 axial magnetic field remains finite as the resonant frequency is approached. The resonant electric field is that interior electric field whose Φ -component approaches zero on the closed surface consisting of the cylindrical shell and the slot as the frequency approaches the resonant frequency. The rest of the alternative expansion functions are orthogonal to the resonant electric field.