A. S. Kryukovsky, D. S. Lukin, D. V. Rastyagaev

The modeling of electromagnetic wave propagation in non-uniform ionosphere in view of influence of a magnetic field of the Earth by the bi-characteristic method has been executed. The propagation singularities of ordinary and non-ordinary waves of electromagnetic fields both with the account, and without the account of radial symmetry of a problem on one-reflecting and multi-reflecting traces are considered. One-layer and double-layer models, and also model with a horizontal gradients leading to occurrence of the wave channel at working frequencies as higher, and below critical (plasma) frequency are considered. Caustic singularities of ray structures arising in the basic vertical section, in lateral sections and projection of ray trajectories to a horizontal plane are investigated. The important effect describing anisotropic media, is the ray exit from a propagation plane with formation caustic singularities, elementary of which are a smooth caustic and a cusp. Ray and caustic of structure in various cases are considered in detail. In particular, the propagation of an ordinary wave in an ionospheric plasma layer F (with various orientations of a magnetic field) is considered. As the plasma frequency of a layer is chosen a little bit below by worker, part of rays at angels of fall close to vertical, pass an ionospheric layer, and others come back to the Earth and form the cusp. The less initial angle of a deviation of a ray from a vertical, the grater it deviates concerning an initial plane of propagation, and then comes back. The rays which are propagating through an ionospheric layer, deviating on certain distance, do not come back more in an initial plane, as it is done by rays reflected from the ionosphere, and, the more initial angle between a ray and vertical, the deviation is more. For a non-ordinary wave the excess of working frequency above plasma up to some meaning does not result in infiltration through an ionospheric layer for any angles of falls.