On the possibility of using an electromagnetic ionosphere in global MHD simulations

Global magnetohydrodynamic (MHD) simulations of the Earth's magnetosphere must be coupled with a dynamical ionospheric module in order to give realistic results. The usual approach is to compute the ®eld-aligned current (FAC) from the magnetospheric MHD variables at the ionospheric boundary. The ionospheric potential is solved from an elliptic equation using the FAC as a source term. The plasma velocity at the boundary is the E B velocity associated with the ionospheric potential. Contemporary global MHD simulations which include a serious ionospheric model use this method, which we call the electrostatic approach in this paper. We study the possibility of reversing the ̄ow of information through the ionosphere: the magnetosphere gives the electric ®eld to the ionosphere. The ®eld is not necessarily electrostatic, thus we will call this scheme electromagnetic. The electric ®eld determines the horizontal ionospheric current. The divergence of the horizontal current gives the FAC, which is used as a boundary condition for MHD equations. We derive the necessary formulas and discuss the validity of the approximations necessarily involved. It is concluded that the electromagnetic ionosphere-magnetosphere coupling scheme is a serious candidate for future global MHD simulators, although a few problem areas still remain. At minimum, it should be investigated further to discover whether there are any di€erences in the simulation using the electrostatic or the electromagnetic ionospheric coupling.