3-DIMENSIONAL MAGNETOSPHERIC EQUILIBRIUM WITH ISOTROPIC PRESSURE

In the absence of the toroidal flux, two coupled quasi two-dimensional elliptic equilibrium equations have been derived to describe self-consistent three-dimensional quasi-static magnetospheric equilibria with isotropic pressure in an optimal (psi, alpha, chi) flux coordinate system, where psi is the magnetic flux function, chi is a generalized poloidal angle, alpha = phi - delta(psi, alpha, chi), phi is the toroidal angle, delta(psi, alpha, chi) is periodic in phi, and the magnetic field is represented as B = del psi x del alpha. A three-dimensional magnetospheric equilibrium code, the MAG-3D code, has been developed by employing an iterative metric method. The MAG-3D code is the first self-consistent three-dimensional magnetospheric equilibrium code. The main difference between the three-dimensional and the two-dimensional axisymmetric solutions is that the field-aligned current and the toroidal magnetic field are finite for the three-dimensional case, but vanish for the two-dimensional axisymmetric case. The toroidal magnetic field gives rise to a geodesic magnetic field curvature and thus a magnetic drift parallel to the pressure gradient direction, which gives rise to the field-aligned current.