Equilibrium and Stability of Helical Hydromagnetic Systems

This is the authors' abstract. We don't add key points for this paper.

A formalism for representing helically invariant hydromagnetic systems is introduced. Such systems are the most general two-dimensional configurations in three-dimensional space, since they include translation-invariant and rotation-invariant configurations as special cases. Expressions for the magnetic field and, when the system is in equilibrium, the current are given in terms of an appropriate nonorthogonal coordinate system. An energy integral is given which forms the basis of a numerical relaxation procedure for obtaining equilibria. The relationship between this formalism and that in which the equilibrium problem is reduced to solving a partial differential equation for the stream function is established. The necessary and sufficient condition for the stability of helically invariant systems with respect to localized displacements is obtained.