Three-Dimensional Solutions of the Magnetohydrostatic Equations For Rigidly Rotating Magnetospheres in Cylindrical Coordinates
arXiv:1711.03755 · doi:10.1080/03091929.2017.1404594
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.
arXiv comment21 pages, 17 figures
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