Magnetic bubbles and magnetic towers - I. General properties and simple analytical models

Abstract

We consider magnetostatic equilibria in which a bounded region D containing a magnetized plasma is either fully confined by a field-free external medium – magnetic bubble equilibria (MBEqs) – or is confined by both such a medium and line-tying in a dense plasma region – magnetic tower equilibria (MTEqs). We first establish some of their general properties. In particular, we derive a series of useful integral equalities relating the magnetic field and the thermal pressures inside and outside D, respectively. We use them to prove the non-existence of an axisymmetric MBEq with a purely poloidal field, and to discuss some recent results of Braithwaite on MBEq formation by relaxation from an initial non-equilibrium state. We next present two families of exact analytical axisymmetric MBEqs with, respectively, spherical and toroidal shapes. The first family is extracted from Prendergast’s model of a self-gravitating magnetized body, while the second one is constructed by using Palumbo’s theory of isodynamic equilibria, for which both magnetic and thermal pressures take constant values on any flux surface. MTEqs with a large variety of structures are thus obtained in a simple way: we start from an arbitrary MBEq and just consider the part of it above a given plane cutting the bubble D. For MBEqs and MTEqs in either family, we compute in closed form most of the interesting physical quantities (such as energy, magnetic helicity and twist). Our results are expected to be useful for building up simple models of several astrophysical objects (such as X-ray cavities in the intracluster medium, jets emitted by disc accreting compact objects, eruptive events in stellar coronae and their ejecta).