Equilibrium of a Current-Carrying Toroidal Plasma

A current-carrying plasma confined in a smooth toroidal magnetic field tends to expand due to the nonuniformity of the field and the self-interaction of the current. This expansion can be nullified, in the absence of externally imposed rotational transform, by means of a vertical magnetic field (perpendicular to the plane of the toroid). Macroscopically considered, such a vertical magnetic field interacts with the Ohmic heating current to supply an inward ponderomotive force. This paper derives the magnitude of the plasma expansion tendency and of the vertical field required to achieve steady state conditions. It is also demonstrated that if the plasma configuration is determined by an aperture limiter, helical fields are equivalent to an applied vertical field, insofar as the plasma equilibrium is concerned.