Stationary toroidal equilibria at finite beta

We investigate the effects of plasma flow on axisymmetric, self-consistent equilibria in toroidal geometry. The investigation is of considerable interest in relation to hot plasmas confined in toroidal systems with longitudinal current. On the basis of the one-fluid MHD plasma model, we use a concise formulation to elucidate important features of the equilibrium. In contrast to previous flow calculations which were treated almost exclusively in the low-beta approximation, we retain, together with flow, all beta effects.As in the treatment of the full flow problem at low beta, we find conditions for equilibrium. The form of our description allows a quite general discussion of its nature and existence for finite beta. This shows that there is a close relationship between the solvability conditions for equations arising from integrals of the system, and the nature of the characteristics of the partial differential equation describing the radial force balance. In the case of large aspect-ratio, these considerations lead to a generalized Bennett relation and to an expression for plasma displacement exhibiting beta and flow effects.