Three-dimensional solutions of the magnetohydrostatic equations for rigidly rotating magnetospheres in cylindrical coordinates

Abstract

We present new analytical three-dimensional solutions of the magnetohydrostatic equations, which are applicable to the co-rotating frame of reference outside a rigidly rotating cylindrical body, and have potential applications to planetary magnetospheres and stellar coronae. We consider the case with centrifugal force only, and use a transformation method in which the governing equation for the “pseudo-potential” (from which the magnetic field can be calculated) becomes the Laplace partial differential equation. The new solutions extend the set of previously found solutions to those of a “fractional multipole” nature, and offer wider possibilities for modelling than before. We consider some special cases, and present example solutions.

Keywords:

• Magnetohydrodynamics
• analytical solutions
• rotating magnetospheres
• three-dimensional equilibria

Acknowledgements

The authors would like to thank the anonymous referees, whose comments have helped to improve this manuscript.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Science and Technology Facilities Council [grant number ST/K000950/1], [grant number ST/N000609/1].