Ray trajectories in an absorbing ionosphere

Abstract

Abstract The present paper deals with the simulation of electromagnetic ray propagation in a cold collisional ionosphere in the presence of the Earth's magnetic field. This subject has been extensively studied in the past. The novel aspect here is our attempt to assess the effect of absorption on the ray trajectories, not merely the field intensity. In addition to the theoretical interest in this problem, practical questions, such as target location by means of Over The Horizon Radar (OTHR) systems, in the presence of high losses, provide the motivation. The analytical investigation of such problems is limited by the complexity of the wave propagation field problem and the physics of the ionosphere, which combine to yield a complex dispersion relation, and the restricted capability of available computers and mathematical software packages for handling the ray tracing model. The present model is based on the familiar Appelton-Hartree, sometimes called the Appelton-Lassen, dispersion equation for the cold, collisional, magnetized ionosphere. The way that the ray tracing is performed (ray tracing being an approximation) and the model chosen by the researcher predetermines the resultant ray trajectories. Thus, in the presence of losses, certain decisions regarding the use of the Hamiltonian ray tracing model have to be made. Unlike some studies which first compute the lossless trajectories, and then add on a posteriori the attenuation along these trajectories, as a perturbation of the lossless solution, here the Hamiltonian ray tracing formalism is extended in order to include the absorption effects in the formalism a priori. For small absorption all models yield more or less the same results; therefore, in the present study high losses are considered in order to emphasize the effects. However, the present study contributes to our understanding of the basic problem of ray propagation in the presence of arbitrary losses. The extended Hamiltonian ray tracing formalism used here assumes complex space, and an additional constraint that guarantees real space and time subspace for the ray trajectories, as well as for the group velocity, whereas the propagation vector and the frequency may be complex. Other formulations for the ray equations formalism exist too. At this time it remains an open problem whether ray trajectories computed by those models will agree with the results obtained here or not. Furthermore, in the absence of sufficient direct ray trajectories empirical data, where high absorption cases are compared to lossless cases, the question as to which model better describes the physical reality must remain open. The variation of the ray paths with frequency, launching angle, collision frequency, electron density profile and other variables, are examined for Chapman type E and F layers. By using typical F layer parameters, it is found that, in certain cases, a high collision frequency affects the ray path by as much as 500 km. This result is important for sub-ionospheric propagation and for target location tracking.