Plasma relaxation and topological aspects in Hall magnetohydrodynamics

Parker's formulation of isotopological plasma relaxation process in magnetohydrodynamics (MHD) is extended to Hall MHD (Shivamoggi [1]). The torsion coefficient $al$ in the Hall MHD Beltrami condition turns out now to be proportional to the {\it potential vorticity}. The Hall MHD Beltrami condition becomes equivalent to the {\it potential vorticity} conservation equation in two-dimensional (2D) hydrodynamics if the Hall MHD Lagrange multiplier $\beta$ is taken to be proportional to the {\it potential vorticity} as well. The winding pattern of the magnetic field lines in Hall MHD then appears to evolve in the same way as {\it potential vorticity} lines in 2D hydrodynamics.\\[4pt] [1] Shivamoggi, B. K.: {\it Phys. Plasmas} {\bf 19}, 072124, (2012).