Flux Conservation in Multiply Connected Type-I Superconductors in Fields Generated in the Voids

The behavior of multiply connected type-I superconductors in magnetic fields generated in the voids can be accounted for quantitatively by assuming flux conservation within the total system rather than in the void alone. The properties are similar to the "anomalous" properties observed when hollow cylinders are cooled in static fields and do not appear to involve intermediate-state formation. The results and analysis of the results show that in these configurations the transition from the pure superconducting state to the normal state occurs through a single sharp $S-N$ boundary which begins at the inside wall and moves to the outside wall with increasing solenoid current (or internal field). This interface moves reversibly, both with increasing and decreasing field and with increasing and decreasing temperature. Such an interface is not associated with hysteresis in the bulk material and does not lead to field retention in the void when the solenoid current is reduced to zero. Field retention in the void and in the bulk, when the solenoid current is removed, occurs only after sufficient current is initially applied to drive the wall into the intermediate state. The effects also occur in hollow cylinders of unfavorable geometries (short thick walls) and provide a means of making unambiguous measurements of the velocity of the superconducting-normal interface.