NEWTONIAN AND NON-NEWTONIAN MAGNETIC-FIELD RELAXATIONS IN SOLAR-CORONAL MHD

Abstract

This paper treats the relaxation of a magnetic field into a minimum-energy force-free state in a cold (pressure-less) viscous fluid, under the frozen-in condition of perfect electrical conductivity and letting the viscosity-dissipated energy be completely lost. A non-Newtonian fluid in popular use is studied in relation to the Newtonian viscous fluid, as two alternative numerical means to (1) construct force-free fields representing solar coronal structures in realistic geometry and (2) investigate the Parker theory of spontaneous formation of electric current sheets as a basic MHD process. Faraday's induction equation imposes an independent condition on the fluid velocity at rigid, perfectly conducting boundaries. This boundary condition is quite compatible with Newtonian mechanics but not with the non-Newtonian fluid model where velocity is equated to the Lorentz force with a free, positive multiplicative-factor. This defining property gives rise to unphysical or artificial singularities not previously known that are completely distinct from the physically admissible singularities representing the current sheets of the Parker theory. In particular, the non-Newtonian fluid takes a magnetic field with neutral points from any one of a continuum of initial states into an unphysical state instead of the proper force-free end-state accessible by Newtonian relaxation. The validity of previously published MHD results based on this non-Newtonian fluid, including some counterclaims against the Parker theory, is dubious. Investigating the Parker theory requires numerical relaxation models capable of anticipating and accurately describing inevitable current-sheet singularities. By including a weak resistivity to dissipate the inevitable current sheets as they form, the field can change topology intermittently to seek a terminal force-free state free of singularities. The minimum-energy state of this more complete model corresponds to the long-lived relaxed structures in the corona.