Cylindrical ideal magnetohydrodynamic equilibria with incompressible flows

It is proved that (a) the solutions of the ideal magnetohydrodynamic equation, which describes the equilibrium states of a cylindrical plasma with purely poloidal flow and arbitrary cross-sectional shape [G. N. Throumoulopoulos and G. Pantis, Plasma Phys. Controlled Fusion 38, 1817 (1996)], are also valid for incompressible equilibrium flows with the axial velocity component being a free surface quantity and that (b) for the case of isothermal incompressible equilibria the magnetic surfaces necessarily have a circular cross-section.