Plasma relaxation and topological aspects in Hall magnetohydrodynamics

Abstract

Parker’s formulation of isotopological plasma relaxation process in magnetohydrodynamics (MHD) is extended to Hall MHD. The torsion coefficient α in the Hall MHD Beltrami condition turns out now to be proportional to the potential vorticity. The Hall MHD Beltrami condition becomes equivalent to the potential vorticity conservation equation in two-dimensional (2D) hydrodynamics if the Hall MHD Lagrange multiplier β is taken to be proportional to the potential vorticity as well. The winding pattern of the magnetic field lines in Hall MHD then appears to evolve in the same way as potential vorticity lines in 2D hydrodynamics.