Interpretation of experimental Critical Current Density and Levitation of Superconductors, and a second Temperature Limit to protect Superconductors against Quench

Abstract

A recently introduced numerical model to calculate relaxation rates and relaxation time of superconductors is revisited. Relaxation time is needed to reorganise, after a disturbance, the electron system of the superconductor to new dynamic equilibrium. The idea is to extend this model to evaluation of experimental results reported in the literature for critical current density, JCrit, for levitation height and force, for stability functions, persistent currents, and, in principle, for a check of all observables that depend on JCrit. It is only after completion of the relaxation process that experimental, JCrit-dependent results can be verified uniquely. In its second part, using the same numerical model, this paper, as a corollary, investigates correlation between densities of critical current and concentration of electron pairs. As a highlight, it suggests existence of a second "critical" temperature, TQuench, expected at temperature below standard critical temperature in a High Temperature Superconductor. If under a disturbance sample temperature increases to T > TQuench, relaxation of the electron system of the superconductor to a new dynamic equilibrium might not be completed within given process time. Critical current density then cannot develop to its potentially possible, full value, JCrit(T), to provide zero-loss current transport. After decay of electron pairs under disturbances, why should the decay products at all be motivated to re-combine (relax) to electron pairs? To answer this question, the paper finally calculates entropy differences as the driving force for relaxation, and it investigates a probably existing correlation between entropy production and relaxation process.