Phys. Rev. B Vol. 50, p. 571 (1994) (PDF)
A heuristic model of flux flow and vortex cutting that does not imply a build up of longitudinal flux is given for type-II superconducting cylinders carrying a current in the presence of an axial magnetic field.
Flux Flow and Flux Cutting in Type-II Superconductors Carrying a Longitudinal Current