In the context of superconductivity, in type II superconductors fluxons (also known as Abrikosov vortices) can form when the applied field lies between
The magnetic field through such a whisker and its neighborhood, which has size of the order of London penetration depth
In the context of long Superconductor-Insulator-Superconductor Josephson tunnel junctions, a fluxon (aka Josephson vortex) is made of circulating supercurrents and has no normal core in the tunneling barrier.
Supercurrents circulate just around the mathematical center of a fluxon, which is situated with the (insulating) Josephson barrier.
In the context of numerical MHD modeling, a fluxon is a discretized magnetic field line, representing a finite amount of magnetic flux in a localized bundle in the model.