Global Magnetohydrodynamic Simulation of the Two‐Dimensional Magnetosphere

The time-dependent magnetohydrodynamic interaction of the solar wind with a two-dimensional dipole magnetic field has been simulated using a novel Lagrangian particle type of MHD code that can treat local low density or vacuum regions without numerical instability. This enables one to simulate the time-dependent magnetic tail. When the solar wind field is southward, a magnetic field line topology consistent with Dungey's model emerges in steady state. The tail, however, is short, and the x-points are only slightly shifted from their vacuum locations, because of strong numerical resistivity. Different configurations resulting from different relative orientations of the solar wind magnetic field and dipole axis are also presented. While the magnetic field is relatively steady, the density and flow in the magnetosheath are turbulent, as are the bow shock and magnetopause; the Kelvin-Helmholtz instability may account for these phenomena. We also model a 'substorm' as the passage of a rotational discontinuity in the solar wind over the dipole. Both 90 and 180 deg shifts to a southward solar wind field cause a violent readjustment of the magnetic tail which eventually settles down to the Dungey configuration.