  Consistent with the predictions of Kibble and Zurek, scaling behaviour has
been seen in the production of fluxoids during temperature quenches of
superconducting rings. However, deviations from the canonical behaviour arise
because of finite-size effects and stray external fields.
  Technical developments, including laser heating and the use of long Josephson
tunnel junctions, have improved the quality of data that can be obtained. With
new experiments in mind we perform large-scale 3D simulations of quenches of
small, thin rings of various geometries with fully dynamical electromagnetic
fields, at nonzero externally applied magnetic flux. We find that the outcomes
are, in practice, indistinguishable from those of much simpler Gaussian
analytical approximations in which the rings are treated as one-dimensional
systems and the magnetic field fluctuation-free.
