Three-dimensional analytical magnetohydrostatic equilibria of rigidly rotating magnetospheres in cylindrical geometry

摘要

We present three-dimensional (3D) solutions of the magnetohydrostatic equations in the co-rotating frame of reference outside a magnetized rigidly rotating cylinder. We make no symmetry assumption for the magnetic field, but to be able to make analytical progress we neglect outflows and specify a particular form for the current density. The magnetohydrostatic equations can then be reduced to a single linear partial differential equation for a pseudo-potential U, from which the magnetic field can be calculated by differentiation. The equation for U can be solved by standard methods. The solutions can also be used to determine the plasma pressure, density and temperature as functions of all three spatial coordinates. Despite the obvious limitations of this approach, it can, for example, be used as a simple tool to create 3D models for the closed field line regions of rotating magnetospheres without rotational symmetry.