A different approach to the MHD equilibrium

TL;DR

This paper derives plasma equilibrium equations from energy principles, revealing that MHD equilibrium can exist even with zero magnetic field regions, and links confinement stability to electromagnetic tension and current configurations.

Contribution

It introduces a novel derivation of MHD equilibrium from energy considerations and clarifies the destabilizing effects of certain magnetic field configurations.

Findings

MHD equilibrium can occur with locally vanishing magnetic fields.

Confinement is related to electromagnetic tension via helicity conservation.

Axisymmetric currents circling the axis can destabilize the plasma.

Abstract

Equations describing plasma equilibria are derived from the total energy of the system. The MHD equilibrium is shown to hold even for systems where the magnetic field may locally vanish. Through conservation of helicity, confinement is shown to be intimately related to electromagnetic tension. For an axisymmetric device, the presence of a magnetic field or current circling the axis is shown to be destabilising. This provides a simple explanation for the poor performance of some devices for which MHD predicts stability.