Past exam of the condensed matter physics major option course of the University of Oxford / 2015 / 8 / b / Solution

Cool a thick superconducting ring through its transition in a controlled external flux, remove or change the applied field while keeping the ring superconducting, and measure the persistent trapped flux using a calibrated pickup coil and sensitive magnetometer. Repeating while varying the cooling flux selects successive winding sectors. The measured flux is close to steps separated by ${\Phi }_0$ when the kinetic-inductance correction is negligible. A SQUID-based flux readout can resolve that spacing; scanning local magnetic imaging offers another way to observe the trapped flux without identifying the ring current with an ordinary dissipative transport current.

The experiment tests the phase-winding/fluxoid relation in a. Self-inductance, London penetration depth and the size of the ring determine how nearly the measured geometric flux follows integer steps. A periodic response alone should not be used to infer an absolute trapped flux without calibration and the relevant inductive corrections.

TODO — source figure gap: the surviving ordinary-ring and two-junction-ring outlines and labels are readable, but page 9's figure form calls 52 absent raster objects, /R514 through /R565. The original archived parent has identical damage. An intact figure is needed to recover any missing image-specific details; those raster components have not been inferred or recreated. The observation method above answers the physical request without requiring the unavailable artwork; the TODO concerns verification of the input illustration rather than a missing part of the solution. The original circuit schematic used in c is an independent diagram of the stated model, not a claimed reconstruction of the unavailable artwork.