We study stationary free boundary configurations of an ideal incompressible
magnetohydrodynamic fluid possessing nested flux surfaces. In 2D simply
connected domains, we prove that if the magnetic field and velocity field are
never commensurate, the only possible domain for any such equilibria is a disk,
and the velocity and magnetic field are circular. We give examples of
non-symmetric equilibria occupying a domain of any shape by imposing an
external magnetic field generated by a singular current sheet charge
distribution (external coils). Some results carry over to 3D axisymmetric
solutions. These results highlight the importance of external magnetic fields
for the existence of asymmetric equilibria.Comment: revised version. 18 pages, 3 figure