Astronomy and Astrophysics – Astrophysics – Earth and Planetary Astrophysics
Scientific paper
2009-06-04
Astronomy and Astrophysics
Astrophysics
Earth and Planetary Astrophysics
13 pages, 2 figures, accepted for publication by Geophysical and Astrophysical Fluid Dynamics
Scientific paper
10.1080/03091920903103862
We present three-dimensional 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 three-dimensional models for the closed field line regions of rotating magnetospheres without rotational symmetry.
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