Mathematical theory of the ionospheric dynamo

A mathematical theory of the three-dimensional ionospheric dynamo is described, which is exact within the context of the assumption that the magnetic field lines are perfectly conducting.Explicit formulae are obtained for the electric fields, and hence for the current systems, which are excited by the dynamo e.m.f. associated with an arbitrary given wind field.They can also be applied to determine the fields arising from an external source of e.m.f., originating for example in the magnetosphere.The convergence properties of the solution are investigated for a simple symmetric wind field; it is found that inclusion of spherical harmonics up to degree 80 is sufficient to yield the features of the electrojet region, now fully coupled to the global current system.