Accuracy test for high-frequency asymptotic solutions

Asymptotic solutions, or solutions whose accuracy increases as some parameters increase, have seen increasing use in recent years. For example, the problem of a magnetic dipole radiating on an infinite circular cylinder has had three different asymptotic solutions proposed. Unfortunately, it is difficult to assess the accuracy of these asymptotic solutions, or even to determine theft relative accuracy. An accuracy test based on the satisfaction of the
E
-field boundary condition on the cylinder surface is proposed. The test is performed by relating the spectral domain representation of the surface
H
-field (given by the asymptotic solution) to that of the
E
-field and then inverse transforming to obtain the surface
E
-field. In some cases analytic and numerical techniques axe combined to aid in evaluation of the spectral content of the surface
H
-field. The proposed test is applied to two of the published solutions and to a third solution generated to bridge the differences between them. Three-dimensional plots of the resulting surface
E
-field axe presented. It was found that the proposed test is most sensitive to the source-region behavior of the solution and relatively insensitive to the large path length behavior.