Mechanics of cosmic rings

In a flat background, simple non-conducting string loops have no strictly stationary equilibrium states, but for cosmic string loops of superconducting kind such ``vorton'' states will exist, with rotating circular configurations appropriately describable as ``cosmic rings'' (which may conceivably be a significant contributor to the material content of the universe) whose equilibrium is obtained for zero angular velocity of retrograde characteristics. Such a ``cosmic ring'' is characterised by its mass M and angular momentum J say, corresponding at a microscopic level to two independent quantum numbers, namely charge number C and a topological phase number N whose product determines the angular momentum, J=CN, while their ratio determines the local intrinsic state of the string, which may be qualitatively classified as being of ``electric'' or ``magnetic'' type depending on whether C/N is greater or less than a critical value dependent on the underlying theoretical model.