Effective height‐integrated conductivity of the ionosphere

The validity of the standard formulas for the height-integrated ionospheric conductivity for problems involving current flow between the magnetosphere and the ionosphere is examined. The problem of the horizontally stratified ionosphere with an oblique magnetic field is studied by use of both an analytic and more realistic numerical model. An electric field harmonically varying in the horizontal direction is assumed at the top of the ionosphere, and an equation for the electrostatic potential within the ionosphere is solved. The height-integrated currents are then calculated from the electric field within the ionosphere. It is found that, down to wavelengths of the order of 10 km, the approximate formulas for the height-integrated conductivity agree very well with the values calculated in this paper. The principal conclusion is that the formulas originally derived for the atmospheric dynamo are useful approximations for magnetospheric problems.