Nonlinear axisymmetric resistive magnetohydrodynamic equilibria with toroidal flow

Abstract

The equilibrium of a resistive axisymmetric plasma with purely toroidal flow surrounded by a conductor is investigated within the framework of nonlinear magnetohydrodynamic theory. It is proved that (a) the poloidal current-density vanishes and (b) apart from an idealized case, the pressure profile should vanish on the plasma boundary. For the cases of isothermal magnetic surfaces, isentropic magnetic surfaces and magnetic surfaces with constant density, the equilibrium states obey an elliptic partial differential equation for the poloidal magnetic flux function, which is identical in form to the corresponding equation governing ideal equilibria. The conductivity, which can be neither uniform nor a surface quantity, results, however, in a restriction of the possible classes of equilibrium solutions; for example for the cases considered, the only possible equilibria with Spitzer conductivity are of cylindrical shape.