Quasi-static MHD processes in Earth's magnetosphere

The purpose of this paper is to demonstrate how the MHD equilibrium theory can be used to describe the global magnetic field configuration of Earth's magnetosphere and its time evolution under the influence of magnetospheric convection. The MHD equilibrium theory represents magneto-hydrodynamics in the slow-flow approximation. The MHD equilibrium theory is not a static theory, though, because time derivatives and flow velocities remain first order quantities in the continuity equation, in the thermodynamic equation of state, and in the induction equation. Therefore one can compute slowly time-dependent processes, such as magnetospheric convection, in terms of series of static equilibrium states. MHD equilibria discussed in this paper result from linear and non-linear solutions to the two-dimensional Grad-Shafranov equation for isotropic thermal plasma pressure.