Penetration of hydromagnetic waves of cylindrical symmetry through the high latitude ionosphere

The problem is formulated, and boundary conditions are developed, in order to solve numerically the equations for the penetration of hydromagnetic waves of horizontal cylindrical symmetry through a stratified high latitude ionosphere and atmosphere due to sources above the ionosphere. There are two orthogonal polarization modes. The numerical results are shown for various cases. It is found that near the ground the horizontal components of both the electric and magnetic fields along the circumference direction are much smaller than the radial components.