Tokamak-like equilibria at beta close to unity

This paper describes a computer study of tokamak equilibria, which resulted in configurations at β-values close to one. The cross-section that was studied most intensely was a vertical racetrack with an elongation of two to one. A circular cross-section and a D-shaped vessel did not allow equilibria at as high a β as the racetrack. The safety factor q was kept greater than one everywhere, and the q-profile was kept flat. The corresponding broad current profile has been observed in pinches, where it has very favourable influence on equilibrium and stability. This favourable influence also displays itself in the equilibria computed; even at a peak β of 82%, the magnetic axis shifts over only 37% of the half-width of the cross-section. The outer boundary of the cross-section was assumed to be a flux surface (e.g. a metal shell). Stability of localized modes was studied by means of the Mercier criterion; it was possible to satisfy this criterion, except in the vicinity of the magnetic axis. Calculations with narrow pressure profiles showed that the plasma did not contract to a round shape; the broad current profile apparently helps to maintain the elongated shape of the plasma. The very high β-values reported here are of interest for extrapolations of fast pulsed tokamaks. It is also important to note that even a modest broadening of the current profile in a conventional tokamak would improve the stability and reduce the shift at moderate β. (author)