Impeded growth of magnetic flux bubbles in the intermediate state pattern of type I superconductors

Normal state bubble patterns in type I superconducting indium and lead slabs are studied by the high resolution magneto-optical imaging technique. The size of bubbles is found to be independent of the long-range interaction between the normal state domains. Under bubble diameter and slab thickness proper scaling, the results gather onto a single master curve. We calculate the equilibrium diameter of an isolated bubble resulting from the competition between the Biot-and-Savart interaction of the Meissner current encircling the bubble and the superconductor-normal interface energy. A good quantitative agreement with the master curve is found over two decades of the magnetic Bond number. The isolation of each bubble in the superconductor and the interface energy are shown to preclude any continuous size variation of the bubbles after their formation, contrary to the prediction of mean-field models.