Analytic axisymmetric magnetohydrodynamic equilibria of a plasma torus with toroidal mass flow

Several classes of analytic equilibria of a toroidal axisymmetric plasma with toroidal mass flow are obtained for isothermal as well as isentropic magnetic surfaces under various pressure and toroidal current density profiles. The effects of flow on certain global equilibrium and stability characteristics are examined. It is shown that for a wide family of equilibria the average beta 〈 β〉 does not depend explicitly on flow and falls within the limits of static equilibria. In particular, for the case of field-reversed configurations 〈 β〉 is totally independent of plasma flow. Calculations based on a specific equilibrium solution for a tokamak with fixed average toroidal magnetic energy show that plasma elongation is an increasing function of the Mach number whereas the safety factor is a decreasing function of it.