The present paper deals with the simulation of electromagnetic ray propagation in a cold collisional ionosphere in the presence of the earth magnetic field. The novel aspect here is our attempt to assess the effect of absorption on the ray trajectories. not merely the field intensity. Practical questions, such as target location by means of Over The Horizon Radar (OTHR) systems, in the presence of high losses, provide motivation. The analytical investigation of such problems is limited by the

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... mplexity of the wave propagation field problem, the physics of the ionosphere"and the restricted capability of available computers for handling the ray tracing model. 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 Chapman type F layer. Results for various conditions are displayed. By using typical F layer parameters, it was found that, in certain cases, high collision frequency affects the ray path by as much as 500 km. This result is important for low altitude propagation and for target location tracking. In general, the dispersion equation for