Incompressible magnetohydrodynamic turbulence is considered for an axisymmetric plasma in cylindrical geometry. The equilibrium statistical states to which the plasma evolves are examined by imposing an external constraint of constant toroidal current on the equilibrium Gibbs ensemble. Only the state with maximal magnetic helicity to energy ratio has zero‐mean kinetic energy for intially quiescent systems. There is an upper bound on the toroidal current to toroidal flux ratio below which this unique stable force free state can exist and whose magnetic flux surfaces are basically concentric circles. Above this critical value, the plasma is unstable with islands present in the flux surfaces. This stability result is in sharp contrast with both the results of a linearized &dgr;Wanalysis as well as considering the stability of the linearized spectral coefficient evolution equations for nonforce‐free states.