Optimum theory for the energy dissipation in a turbulent pinch

Lower bounds are computed for the total energy dissipation in a steady, driven reversed-field pinch. A variational principle is given in which energy and helicity balance, conservation of toroidal magnetic flux, and the ensemble-averaged Ohm's law are imposed as constraints. The lowest bounds are found with the natural boundary condition derived from the variational principle. The effect of the space variation of the resistivity is also included. It is shown that the theoretical results are consistent with observations from the Los Alamos ZT-40M experiment [Phys. Fluids 27, 1671 (1984)].