Poloidal flows in resistive MHD equilibria

We argue that poloidal velocity fields are a necessary part of any resistive toroidal MHD steady state. They are a consequence of force balance in toroidal geometry, and need involve no instabilities of any kind. If a current density j results from an axisymmetric toroidal electric field that is curl-free inside the toroid, it leads to a magnetic field B such that the curl of j x B is non-vanishing; j x B cannot be balanced, therefore, by the gradient of any scalar pressure. In a steady state, velocity fields are required, associated with toroidal vorticity. The effect is purely geometrical, and disappears in the ''straight periodic cylinder'' approximation. In the limit of low Reynolds numbers, the velocity field may be straightforwardly calculated for stress-free boundary conditions. A recent generalization to no-slip boundary conditions in toroidal coordinates has likewise proved possible. Zero-flow steady states are possible if the conductivity is allowed to be spatially non-uniform; but the non-uniformity is such that the conductivity varies over a flux surface, and is likely unphysical. Our picture of confined steady states in toroidal MHD should necessarily include flows, from the outset. (orig.)