Key Points: • The influence of the ultraenergetic relativistic electron precipitations on mode conversion in the terrestrial waveguide was analysed. • New statement of a mode conversion problem was used. • The effect of a normal wave conversion may be neglected in the problem of southern boundary determination, if the precipitations are not powerful. Abstract Previously the parameters of sporadic D s layer of electric conductivity caused by ultraenergetic relativistic electron (URE) precipitations were determined by us due to indirect electromagnetic method. Then we determined the southern boundaries of these precipitations in the frames of the following supposition: the effect of a normal wave reflection and its conversion into other normal waves on the boundary between disturbed and undisturbed parts of a radio path might have been ignored. Now we show by accurate simulation that it was true for strong and moderate URE precipitations. For the powerful disturbances of the same nature (16 events for 11 years) the effect is significant. In order to obtain these results, we had to change a traditional statement of problem about a normal wave conversion in the terrestrial waveguide and to solve numerically this new problem with an abrupt change of inhomogeneous properties on a transverse surface of the waveguide. We did not divide a near-Earth waveguide at two artificial altitude parts: with vacuum and with inhomogeneous conducting medium along the transverse coordinate. Formally the waveguide was considered by us as inhomogeneous from its top to its bottom.

The parameters of sporadic $D_s$ layer of electric conductivity caused by ultraenergetic relativistic electron (URE) precipitations are determined due to indirect electromagnetic method. Previously we determined the southern boundaries of these precipitations in the frames of the following supposition: the effect of a normal wave reflection and its conversion into other normal waves on the boundary between disturbed and undisturbed parts of a radio path might have been ignored. Now we show by accurate simulation that it was true for strong and moderate disturbances. For the powerful URE disturbances the effect is significant. In order to obtain this result we had to change a traditional problem statement about a normal wave conversion in the terrestrial waveguide and to solve numerically this new problem with a ${}^{\prime \prime}$volume${}^{\prime \prime}$ inhomogeneity.