Towards the dispersion relation for ionacoustic instabilities in weakly inhomogeneous ionospheric plasma at altitudes 80-200km and its low-frequency solution

In the paper within the approximation of the two-fluid magnetohydrodynamics and geometrooptical approximation the dispersion relation was found for ionacoustic instabilities of the ionospheric plasma at 80-200km altitudes in three-dimensional weakly irregular ionosphere. Low freqeuncy solution was found. The difference between obtained and standard solution becomes significant at altitudes above 140 km. As the analysis shown in this case the solution grows with time. The conditions for existence of such solution are the presence of co-directed electron density gradients and electron drifts and perpendicularity of line-of-sight to the magnetic field. The necessary conditions regularly exist at the magnetic equator. Detailed analysis has shown that this solution corresponds to well-known 150km equatorial echo and explains some of its statistical characteristics observed experimentally.