  The spontaneous self-organization of two-dimensional magnetized plasma is
investigated within the framework of magnetohydrodynamics with a particular
emphasis on the symmetry-breaking induced by the shape of the confining
boundaries. This symmetry-breaking is quantified by the angular momentum, which
is shown to be generated rapidly and spontaneously from initial conditions free
from angular momentum as soon as the geometry lacks axisymmetry. This effect is
illustrated by considering circular, square, and elliptical boundaries. It is
shown that the generation of angular momentum in nonaxisymmetric geometries can
be enhanced by increasing the magnetic pressure. The effect becomes stronger at
higher Reynolds numbers. The generation of magnetic angular momentum (or
angular field), previously observed at low Reynolds numbers, becomes weaker at
larger Reynolds numbers.
