Simple analytical examples of boundary driven evolution of a two-dimensional magnetohydrostatic equilibrium

AIM – Unité Mixte de Recherche CEA – CNRS – Université Paris VII – UMR No 7158, Centre d'Études de Saclay, 91191 Gif-sur-Yvette Cedex, France e-mail: jean-jacques.aly@cea.fr

Received: 20 July 2009
Accepted: 1 September 2009

Abstract

Aims. We construct families of time-sequences of x-invariant magnetostatic equilibria which describe ideal quasi-static evolutions driven by stationary shearing motions imposed on a boundary. The change in the thermal pressure of the plasma is determined by imposing either an adiabatic, or an isothermal, or an isobaric, prescription.

Methods. We start from a well known family of linear force-free fields, on which we effect simple transforms.

Results. In either case, the magnetic field and the pressure are expressed analytically as functions of space and time. The field is found to suffer an indefinite expansion, with a decrease to zero of the pressure in the adiabatic and isothermal cases, and to eventually open. Moreover, the configurations forming any sequence are shown to be linearly stable with respect to x-invariant perturbations.