Minimum energy states of the plasma pinch in standard and Hall magnetohydrodynamics

TL;DR

This paper analytically derives minimum energy plasma states in standard and Hall MHD, revealing force-free configurations in Hall MHD and more complex states in standard MHD, with implications for reversed-field pinch devices.

Contribution

It provides the first analytical derivation of relaxed plasma states in both standard and Hall MHD, highlighting differences and potential applications.

Findings

Hall MHD relaxed state is force-free with uniform flow.

Standard MHD states are more complex due to velocity-magnetic coupling.

Application to reversed-field pinches discussed.

Abstract

Axisymmetric relaxed states of a cylindrical plasma column are found analytically in both standard and Hall magnetohydrodynamics (MHD) by complete minimization of energy with constraints imposed by invariants inherent in corresponding models. It is shown that the relaxed state in Hall MHD is the force-free magnetic field with uniform axial flow and/or rigid azimuthal rotation. The relaxed states in standard MHD are more complex due to the coupling between velocity and magnetic field. Application of these states for reversed-field pinches (RFP) is discussed.