An asymptotic solution for the surface magnetic field within the paraxial region of a circular cylinder with an impedance boundary condition

It is well-known that the high-frequency asymptotic evaluation of surface fields by the conventional geometrical theory of diffraction (GTD) usually becomes less accurate within the paraxial (close to axial) region of a source excited electrically large circular cylinder. Uniform versions of the GTD based solution for the surface field on a source excited perfect electrically conducting (PEC) circular cylinder were published earlier to yield better accuracy within the paraxial region of the cylinder. However, efficient and sufficiently accurate solutions are needed for the surface field within the paraxial region of a source excited circular cylinder with an impedance boundary condition (IBC). In this work, an alternative approximate asymptotic closed form solution is proposed for the accurate representation of the tangential surface magnetic field within the paraxial region of a tangential magnetic current excited circular cylinder with an IBC. Similar to the treatment for the PEC case, Hankel functions are asymptotically approximated by a two-term Debye expansion within the spectral integral representation of the relevant Green's function pertaining to the IBC case. Although one of the two integrals within the spectral representation is evaluated in an exact fashion, the other integral for which an exact analytical evaluation does not appear to be possible is evaluated asymptotically, unlike the PEC case in which both integrals were evaluated analytically in an exact fashion. Validity of the proposed asymptotic solution is investigated by comparison with the exact eigenfunction solution for the surface magnetic field.