Flows in toroidal steady states of visco-resistive magnetohydrodynamics

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Abstract

Ideal magnetohydrodynamics (MHD) still provides the mathematical framework and the textbook vocabulary in which the possible states of a toroidal plasma are discussed, generally regarded as static equilibria. This is so, despite the increasing realization that virtually all toroidal magnetofluids have non-trivial fluid flows (finite velocity fields) in them. A very different perspective results from non-ideal MHD, including both resistivity and viscosity and invoking non-ideal boundary conditions. There, it is shown that if Ohm's law and Faraday's law are given equal importance with force balance, flows are an inevitable consequence of the assumptions of time independence and axisymmetry. Emphasis is on the character of these necessary velocity fields (mass flows) that toroidal geometry demands.Using perturbation theory and recently newly available numerical programs, the allowed steady states of an axisymmetric, current-carrying, toroidal magnetofluid are solved for nonlinearly. The flow patterns range from a predominantly poloidal pair of counter-rotating "convection cells" revealed by the perturbation theory to a pattern in which the toroidal kinetic energy of flow considerably exceeds the poloidal kinetic energy. In no case is the flow discovered a simple rotation. One of the most interesting results to emerge is the sensitive dependence of the flow pattern on the shape of the toroidal cross section boundary: the dipolar poloidal flow that appears for cross sections that are symmetric about a midplane is seen to deform continuously into a monopolar pattern for an asymmetric and more realistic "D-shaped" cross section as the viscous Lundquist number is increased.
Original languageEnglish
Title of host publicationProceedings of the Joint Varenna – Lausanne International Workshop on Theory of Fusion Plasmas, 30 August-3 September 2004, Varenna, Italy
Place of PublicationItaly, Varenna
Pages249-256
Publication statusPublished - 2004

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