Ray trajectories in an absorptive ionosphere

Simulates EM ray propagation in a cold collisional ionosphere in the presence of the geomagnetic field. A novel aspect is our attempt to assess the effect of absorption on the ray trajectories, not merely the field intensity. The present model is based on the familiar Appelton-Hartree dispersion equation for the cold, collisional, magnetized ionosphere, where slow variation (on the scale of a wavelength) of the terrestrial magnetic field is assumed. 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. High losses are considered in order to emphasize the effects. The present study contributes to our understanding of the basic problem of ray propagation in the presence of arbitrary losses. The variation of the ray paths with frequency, launching angle, collision frequency, electron density profile and other variables, are examined for the Chapman type F layer. Results for various conditions are displayed. By using typical F layer parameters, it is found that, in certain cases, high collision frequency affects the ray path by as much as 500 km. The paper is motivated by over-the-horizon radar