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The information about the current-carrying ability of a type-IIsuperconductor can be obtained by studying the flux relaxation and vortexpenetration phenomena in the superconductor. In early studies, the infiniteseries models of the flux relaxation and vortex penetration phenomena wereconstructed at a vanishing current density and vanishing internal field,respectively. However, this is not the only possibility. Here it is shown thatone can reconstruct the theoretical models at the critical points. The newpolynomial model of the flux relaxation (vortex penetration) phenomenon wasconstructed by expanding the vortex activation energy as an infinite series ofthe current density (internal field) about the critical current density(equilibrium internal field). The unification of the polynomial models wasproposed. The inverse model of the flux relaxation (vortex penetration)phenomenon was also constructed by expanding the vortex activation energy as aninfinite series of the inverse current density (inverse internal field) aboutthe critical current density (equilibrium internal field).

Infinite series models of flux relaxation and vortex penetration constructed at critical points and their unification