On the nature of visco-resistive MHD steady states

Static ideal MHD equilibria continue to provide the conceptual framework and vocabulary by which toroidal steady-state plasmas are described, despite the growing recognition that virtually all toroidal plasmas involve non-trivial flows. A more promising mathematical approach to realizable states would appear to be through the inclusion of finite transport coefficients (viscosity as well as resistivity) and non-ideal boundary conditions,where it has been known for some time that flows are a necessary consequence of the demands of axisymmetry and time independence. Heretofore [1,2], we have been able to describe toroidal resistive steady states in perturbation theory, expanding the solutions in powers of the Reynolds number or, more accurately, the Hartmann number. Using new numerical techniques that have become available, we are now able to lift this limitation and calculate voltage-driven toroidal steady states through a range of Hartmann numbers that runs from >1. The flow pattern ranges, as the Hartmann number is raised, from a previously identified pair of counter-rotating toroidal vortices (poloidal convection cells) to a pattern in which the flow is primarily in the toroidal direction. None of the flows identified is a simple rotation, poloidal or toroidal, sheared or otherwise. Detailed "weather maps" can now be drawn.