Penetration of electric field from the surface layer to the ionosphere

A mathematical model has been proposed for describing quasi-stationary atmospheric electric fields with approximate, but fairly accurate account for the ionosphere conductivity. It is shown that some well-known models of electric field penetration from the Earth into the ionosphere have to be taken as being inadequate, though they work well in the atmosphere below 50 km. In these models, the arbitrary specified boundary condition in the upper boundary of the atmosphere omits the existing good conductor or adds insignificant one. The maximum possible field in our model is far less than in the models where the ionosphere conductivity is not taken into account, but vastly larger than in the models based on the approximation with infinite Pedersen conductivity in the upper ionosphere.