Plasma Relaxation and Topological Aspects in Electronmagnetohydrodynamics

TL;DR

This paper extends Parker’s plasma relaxation theory to electron MHD, revealing how magnetic energy bounds relate to topological invariants and showing parallels between EMHD Beltrami conditions and 2D hydrodynamic potential vorticity conservation.

Contribution

The study generalizes plasma relaxation to electron MHD, linking magnetic energy bounds to electron vorticity topology and establishing a novel analogy with 2D hydrodynamics.

Findings

Magnetic energy bounds depend on magnetic and electron vorticity topologies.

EMHD Beltrami condition is equivalent to 2D potential vorticity conservation.

Magnetic field line winding patterns evolve similarly to potential vorticity lines.

Abstract

Parker's formulation of isotopological plasma relaxation process toward minimum magnetics energy states in magnetohydrodynamics (MHD) is extended to electron MHD (EMHD). The lower bound on magnetic energy in EMHD is determined by both the magnetic field and the electron vorticity field topologies, and is shown to be reduced further in EMHD by an amount proportional to the sum of total electron-flow kinetic energy and total electron-flow enstrophy. The EMHD Beltrami condition becomes equivalent to the potential vorticity conservation equation in two-dimensional (2D) hydrodynamics, and the torsion coefficient and turns out to be proportional to potential vorticity. The winding pattern of the magnetic field lines appears to evolve therefore in the same way as "potential vorticity" lines in 2D hydrodynamics.