Three-Dimensional Solutions of the Magnetohydrostatic Equations For Rigidly Rotating Magnetospheres in Cylindrical Coordinates

TL;DR

This paper introduces new analytical three-dimensional magnetohydrostatic solutions in cylindrical coordinates for rotating magnetospheres, expanding modeling capabilities for planetary and stellar magnetic environments.

Contribution

It presents novel solutions to the magnetohydrostatic equations applicable to rotating cylindrical bodies, extending previous models to fractional multipole configurations.

Findings

Solutions applicable to planetary magnetospheres and stellar coronae

Extension to fractional multipole magnetic field configurations

Potential for more flexible and comprehensive magnetic modeling

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.