MIDIT OFD CATS Modelling, Nonlinear Dynamics Optics and Fluid Dynamics Chaos and Turbulence Studies and Irreversible Thermodynamics Risø National Laboratory Niels Bohr Institute and Technical University of Denmark Building 128 Department of Chemistry Building 321 P.O. Box 49 University of Copenhagen DK-2800 Lyngby DK-4000 Roskilde DK-2100 Copenhagen Ø Denmark Denmark Denmark

by **By David Montgomery**,

Dartmouth (U.S.A.) and,

Eindhoven University of Technology,

Netherlands

**Thursday, May 31, 2001, 14.00 h
at OFD Meeting Room, Building 130, Risø National Laboratory**

**Abstract**:
Treatments of toroidal magnetohydrodynamic (MHD) confinement have almost
always started from ideal MHD equilibria, via the "Grad-Shafranov Equation".
If, by analogy with fluid mechanics, one insists on small but finite
transport coefficients from the beginning, Ohm's law and Faraday's law are
promoted to equal importance with the MHD equation of motion in determining
possible steady states. The situation in a current-carrying toroid changes
drastically, for largely geometrical reasons: vortical flows are required
for the existence of steady states. The changes for the toroid are much
greater than those for the periodic straight cylinder. However, in both
geometries, values of the Hartmann number and the viscosity assume a
significance that is new.