Three-dimensional analytical magnetohydrostatic equilibria of rigidly rotating magnetospheres in cylindrical geometry

TL;DR

This paper derives three-dimensional analytical solutions for magnetohydrostatic equilibria around a rotating cylinder, enabling modeling of complex magnetospheres without symmetry assumptions, by simplifying the equations to a solvable linear PDE.

Contribution

It introduces a method to obtain 3D analytical solutions for rotating magnetospheres without symmetry assumptions, using a linear PDE for a pseudo-potential.

Findings

Solutions allow calculation of magnetic fields, plasma pressure, density, and temperature in 3D.

Method provides a simple tool for modeling closed field line regions in rotating magnetospheres.

Analytical approach facilitates understanding of magnetospheric structures in cylindrical geometry.

Abstract

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.