Approximate asymptotic solution of surface field due to a magnetic dipole on a cylinder

A simple approximate expression for the surface magnetic field due to a magnetic dipole on a conducting circular cylinder is obtained. This solution is asymptotic for a large cylinder radius, and may be used everywhere on the cylindrical surface including the penumbra and the deep shadow. In the limit that the cylinder radius is infinite, it becomes identical to the known exact solution of a dipole on a conducting plane. For a surface ray propagating in parallel to the axis of the cylinder, the transverse surface magnetic field is found to vary asymptotically as , where is the distance from the source. This behavior is distinctively different from the variation of the surface ray on a plane, and is explained in terms of the dependence of the surface curvature in the binormal direction of the ray. Our solution is basically derived from the classical work of V. A. Fock, but contains a conjecture that has been partially verified. We apply our solution to calculate the mutual admittance between two slots on a cylinder, and obtain results which are in excellent agreement with those calculated from the exact modal solution. For a cylinder with a radius of one wavelength or larger, this agreement is within several percent in magnitude and a few degrees in phase, even for zero separation between the two slots. A comparison of the present solution with two other asymptotic (GTD) solutions is also given.