Spontaneous creation of magnetic flux in superconducting ring

We investigate the Kibble-Zurek mechanism of creation of topological defect s in a superconducting hollow cylinder ("ring") undergoing phase transition from the supercooled normal state. Solving numerically the set of the time -dependent Ginzburg-Landau (TDGL) equations, we show the evolution of the s pontaneously created topological vortices and antivortices inside the super conducting ring. It is shown that the Josephson weak links in the ring can significantly increase the spontaneous flux trapped in the ring's hole.