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In the context of superconductivity, especially related to type II superconductor, a fluxon (aka Abrikosov vortex) is a small whisker of normal phase surrounded by superconducting phase. Supercurrents circulate around its center. The magnetic field through such a whisker and its neighborhood, which has size of the order of London penetration depth (~100 nm), is quantized because of the phase properties of the magnetic vector potential in quantum electrodynamics, see magnetic flux quantum for details.
In the context of long Josephson junctions, a fluxon (aka Josephson vortex) is made of circulating supercurrents and has no normal core. Supercurrents circulate just around the mathematical center of a fluxon, which is situated with the (insulating) Josephson barrier. Again, the magnetic flux created by circulating supercurrents is equal to a magnetic flux quantum (or a bit less if the superconducting electrodes of the Josephson junction are thinner than ).
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. Fluxon models are explicitly designed to preserve the topology of the magnetic field, overcoming numerical resistivity effects in Eulerian models.
- FLUX, a fluxon-based MHD simulator