Application of chaos theory to ray tracing in ducts

To predict the radar cross section of large ducts and cavities it is common to employ ray tracing methods of one kind or another. Electromagnetic engineers traditionally employ a first-order ray theory based on the Deschamps (1972) formulation. This is not the only formulation and it is shown that the semi-classical tangent-plane methods employed in quantum physics offer some advantages. The special case of straight ducts of arbitrary cross section in considered where the existing theory of billiard dynamics shows that such ray tracing is in general a chaotic process. In a duct or cavity the average rate of increase of ray divergence or change in ray intensity is thus proportional to the Lyapunov exponent. A relationship is provided between the accuracy of the geometry and/or mesh size, the angle of incidence, the duct length and the Lyapunov exponent for a straight duct. This establishes a computational limit on the ability to make numerically deterministic predictions using shooting-and-bouncing or related ray-tracing methods. For a sufficiently long duct of general cross section, away from normal incidence, it is not possible to achieve convergence using these methods