A 3-DIMENSIONAL ITERATIVE MAPPING PROCEDURE FOR THE IMPLEMENTATION OFAN IONOSPHERE MAGNETOSPHERE ANISOTROPIC OHM LAW BOUNDARY-CONDITION INGLOBAL MAGNETOHYDRODYNAMIC SIMULATIONS

The mathematical formulation of an iterative procedure for the numeric al implementation of an ionosphere-magnetosphere (IM) anisotropic Ohm' s law boundary condition is presented. The procedure may be used in gl obal magnetohydrodynamic (MHD) simulations of the magnetosphere. The b asic form of the boundary condition is well known, but a well-defined, simple, explicit method for implementing it in an MHD code has not be en presented previously. The boundary condition relates the ionospheri c electric field to the magnetic field-aligned current density driven through the ionosphere by the magnetospheric convection electric field , which is orthogonal to the magnetic field B, and maps down into the ionosphere along equipotential magnetic field lines. The source of thi s electric field is the flow of the solar wind orthogonal to B. The el ectric field and current density in the ionosphere are connected throu gh an anisotropic conductivity tensor which involves the Hall, Pederse n, and parallel conductivities. Only the height-integrated Hall and Pe dersen conductivities (conductances) appear in the final form of the b oundary condition, and are assumed to be known functions of position o n the spherical surface R = R(1) representing the boundary between the ionosphere and magnetosphere. The implementation presented consists o f an iterative mapping of the electrostatic potential psi, the gradien t of which gives the electric field, and the field-aligned current den sity between the IM boundary at R = R(1) and the inner boundary of an MHD code which is taken to be at R(2) > R(1). Given the field-aligned current density on R = R(2), as computed by the MHD simulation, it is mapped down to R = R(1) where it is used to compute psi by solving the equation that is the IM Ohm's law boundary condition. Then psi is map ped out to R = R(2), where it is used to update the electric field and the component of velocity perpendicular to B. The updated electric fi eld and perpendicular velocity serve as new boundary conditions for th e MHD simulation which is then used to compute a new field-aligned cur rent density. This process is iterated at each time step. The required Hall and Pedersen conductances may be determined by any method of cho ice, and may be specified anew at each time step. In this sense the co upling between the ionosphere and magnetosphere may be taken into acco unt in a self-consistent manner.