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

Research output: Research - peer-reviewArticle



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.


Original languageEnglish
Pages (from-to)74-95
Number of pages21
JournalGeophysical and Astrophysical Fluid Dynamics
Issue number1
Early online date30 Nov 2017
StatePublished - 2018

    Research areas

  • Magnetohydrodynamics, Analytical solutions, Rotating magnetospheres, Three-dimensional equilibria

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