Ray tracing of spherical waves in magnetoplasma

In general, it is very difficult to find analytical solutions of the electromagnetic field in an inhomogeneous magnetoplasma such as the ionosphere and magnetosphere, even under the approximation of geometrical optics [Budden, 1988]. As a powerful technique, numerical ray tracing can give solutions in these cases, and it is widely used to reveal the physical property of wave propagation in magnetoplasma and to interpret observations. As it is well known, when the electromagnetic wave excited from a source is propagating in a magnetoplasma, in the classical ray-tracing, the wave is treated as one of two plane waves, either L mode or R mode, and the error introduced is generally believed to be negligibly small. The task of ray-tracing is to numerically solve the ray equation system including six partial differential equations for a given or an assumed three dimensional structure of the electron density and the imposed geomagnetic field [Haselgrove, 1955]. Because of the anisotropic property of the magnetoplasma, the group and phase velocity vectors for any mode plane wave are in general differing in both magnitude and direction. This results in a very complicated coupling situation for the three components of the refractive index vector in Haselgrove´s ray equation system, and numerical computations are time-consuming. It is time consuming in computation to find the numerical solutions, a disadvantage for real time applications in a time varying. We are proposing a spherical wave solution for which the directions of the phase and group vectors are equal.