Relaxed plasma-vacuum systems

Taylor's theory of relaxed toroidal plasmas (states of lowest energy with f ixed total magnetic helicity) is extended to include a vacuum between the p lasma and the wall. In the extended variational problem, one prescribes, in addition to the helicity and the magnetic fluxes whose conservation follow s from the perfect conductivity of the wall, the fluxes whose conservation follows from the assumption that the plasma-vacuum interface is also perfec tly conducting (if the wall is a magnetic surface, then one has the toroida l and the poloidal flux in the vacuum). Vanishing of the first energy varia tion implies a pressureless free-boundary magnetohydrostatic equilibrium wi th a Beltrami magnetic field in the plasma, and in general with a surface c urrent in the interface. Positivity of the second variation implies that th e equilibrium is stable according to ideal magnetohydrodynamics, that it is a relaxed state according to Taylor's theory if the interface is replaced by a wall, and that the surface current is nonzero (at least if there are n o closed magnetic field lines in the interface). The plane slab, with suita ble boundary conditions to simulate a genuine torus, is investigated in det ail. The relaxed state has the same double symmetry as the vessel if, and o nly if, the prescribed helicity is in an interval that depends on the presc ribed fluxes. This interval is determined in the limit of a thin slab. (C) 2001 American Institute of Physics.