Abstract
The gyroscopic effect in compact toroidal plasmas is investigated using a minimum energy principle in which the angular momentum is added as a constraint. If attention is limited to incompressible plasmas, the flow and field vectors can be expanded in eigenfunctions of the curl (Beltrami functions). Then the flow and field appear, in general, as a spectrum of Beltrami vectors. Adding the angular momentum as a constraint has a strong effect on the energy ordering of the system. Without this constraint, the state with lowest “ordered” energy has a fine structure element that would, in practice, decay, leading to a force-free state. However, if a nonzero angular momentum is specified, then the lowest-energy state has finite pressure and significant flow. For angular momentum of sufficient magnitude, this is a “smooth” state that should have good magnetic confinement. These effects may be an indicator that the gyroscopic effect improves the stability. However, this is by no means certain since a rigorous link between minimum energy and stability in a flowing plasma has not yet been established.
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