Cylindrical ideal magnetohydrodynamic equilibria with incompressible flows

Abstract

It is proved that (a) the solutions of the ideal magnetohydrodynamic equation, which describe the equlibrium states of a cylindrical plasma with purely poloidal flow and arbitrary cross sectional shape [G. N. Throumoulopoulos and G. Pantis, Plasma Phys. and Contr. Fusion 38, 1817 (1996)] are also valid for incompressible equlibrium flows with the axial velocity component being a free surface quantity and (b) for the case of isothermal incompressible equilibria the magnetic surfaces In a recent paper [1] it is proved that, if the ideal MHD stationary flows of a cylindrical plasma with arbitrary cross sectional shape are purely poloidal, they must be incompressible. This property simplifies considerably the equilibrium problem, i.e. it turns out that the equlibrium is governed by an elliptic partial