A Ray-Tracing Technique for Determining Ray Tubes in Anisotropic Media

Ray-tracing techniques are commonly used for calculating the paths taken by electromagnetic waves in a medium that has an associated refractive index, such as the earth´s ionospheric plasma. Ray equations derived from Hamilton´s equation are usually used to determine ray paths and ray tubes defined by tracing adjacent rays separately. There are advantages in describing ray tubes in terms of a main ray and variational rays. In this paper, equations for variational rays are derived for anisotropic inhomogeneous media such as the earth´s ionosphere. The ray-tracing technique is ideal for simulating ionospheric propagation experiments, and examples are given of ground illumination as a function of ground range and frequency.