An integral E-field accuracy test for high frequency asymptotic solutions

Abstract

The increasing use of conformal slot arrays has generated considerable interest in the analysis of radiation on cylindrical structures. Since 1974, three different asymptotic solutions to the problem of radiation on an infinite circular cylinder have been published. These solutions, whose accuracy increases as some parameter (such as the wavenumber) increases, have the unfortunate property that it is difficult to estimate their accuracy when finite frequencies are used. Previous attempts to achieve an accuracy test for evaluating asymptotic solutions resulted in a test that was qualitative in nature and highly dependent on the source region accuracy of the proposed solution. Through the use of Green's identities, a new test based on satisfaction of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</tex> -field boundary condition is formulated. The proposed test is quantitative in nature, is straightforward in application, and displays a mixed local/global nature. Under some circumstances the test lends itself to application as an iterative equation for point-by-point improvement of a proposed solution.