Search

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., Comment: A very recently completed paper (A second temperature limit to protect superconductors against quench) upon request by the arXiv Content Management & Support Team should be integrated into the original (Interpretation of experimental Critical Current Density..., arXiv 2212.09333). Total length now extends to 148 pages, 23 Figures, but results are the same, no errors to be corrected

A superconductor is stable if it does not quench. Quench is a short-time physics problem. For its deeper understanding of, and how to avoid quench, the physics behind stability has to be analysed. A previously suggested dynamic relaxation model is re-considered and applied to YBaCuO 123 and BSCCO 2223 high-temperature, thin film superconductors. Parallel to this investigation, an unconventional approach using an electrical resistance network (a cell model) is applied to introduce a method how to estimate the extent by which, in resistance measurements, exact determination of critical temperature of superconductors is possible. This resistive cell model, when considering its numerical convergence behaviour, in a side result may provide an alternative explanation of (at least a contribution to) bending of resistivity vs. temperature curves, and perhaps also an alternative to standard explanations of the thermal fluctuations impact on these curves. The dynamic relaxation and the resistance models provide a parenthesis that correlates, in terms of the Ginzburg-Landau order parameter, (i) solution of superconductor stability problem (the main objective of this paper), with tentative explanation of (ii) bending of the resistivity curves near critical temperature and (iii) with predictions from thermal fluctuations., Comment: Updated; correcting typing errors (solely within manuscript) like dimension of Fermi energy; same results as before; reduced length of the abstract; more comments added to correlations between stability, order parameter and impact of thermal fluctuations problem on resistivity vs temperature curves; Summary focused on main objective of the paper (correlation between stability and relaxation). arXiv admin note: text overlap with arXiv:2205.09582

How exactly can critical temperature be determined from results obtained in resistivity measurements? An unconventional approach using an electrical resistance network is presented in this paper to find an answer to this question. In a first step, a recently suggested, dynamic relaxation model is refined and extended beyond its proper applicability and competence range (superconductor stability against quench). This step addresses bending of the resistivity vs. temperature curves near critical temperature. In a second step, an alternative solution of the thermal fluctuations problem is presented. From both results, existence of a non-local, transition boundary layer can be postulated, a temperature uncertainty around critical temperature. Finally, severe limitations to calculate total current through superconductor/normal conductor thin film junctions become obvious from this approach if any non-Ohmic contributions (like Andreev reflection or Josephson currents) have to be taken into account. This problem is a parallel to multi-component heat transfer., Comment: No errors to be corrected. The paper only for formal reasons shall be withdrawn because it has been integrated into arXiv 2208.0190

Superconductors like other solids cannot relax instantaneously from thermally excited (disturbed) states to thermodynamic equilibrium. In this paper, relaxation of a multi-filamentary and of a thin film superconductor from thermal excitations is simulated. Absorption of radiation or, under conductor movement, release and transformation of mechanical tension to thermal energy are examples. The paper applies numerical simulations of superconductor energy states, as many-particle systems, under basic thermodynamic and standard, multi-component heat transfer principles (solid conduction plus radiation in thin films). A recently described microscopic stability model and application of a traditional, continuum cell model allows to explain curvature of the resistance vs. temperature excursion below critical temperature, TCrit, and suggests an alternative to standard explanation of increased electrical conductivity at temperature exceeding TCrit. A non-local, resistivity boundary layer (a temperature uncertainty) is observed near critical temperature within which the resistivity curve smoothly approaches, from the superconducting state, the normal conduction resistivity. Keywords Superconductor; phase transition; relaxation; critical current density; critical temperature; thermal fluctuations; boundary layers, Comment: No errors to be corrected. The paper only for formal reasons shall be withdrawn because it has been integrated into arXiv 2208.0190

Superconductors like other solids cannot relax instantaneously from excited states to thermodynamic equilibrium. In this paper, relaxation from thermal excitations is investigated, like after absorption of radiation or, under conductor movement, release and transformation of mechanical tension to thermal energy. Relaxation proceeds within finite periods of time the length of which increases the more strongly the closer the superconductor temperature has already approached its critical value. Properties of many-particle systems (as explained, by an analogy to nuclear physics), basic thermodynamic considerations (temperature uniquely defined under solely equilibrium condition) and standard, multi-component heat transfer principles (solid conduction plus radiation in thin films) are applied as tools to prove this expectation. Energy gap, superconductor critical current density and critical temperature, as a result, are tightly related to relaxation rates and relaxation times of the superconductor electron system. By numerical simulations, an attempt is made to find a quantitative correlation of these properties in a thin film superconductor., Comment: This paper was originally submitted, by September 2021, to one of the World's leading Journals. We could not find referees willing to review the subject. All Figures in the Appendix are provided solely for convenience of the readers to relieve them from running through a series of 11 previous papers, all on more or less the same subject, all peer-reviewed and published in JOSC

Under disturbances, superconductors may experience sudden, most undesirable phase transitions (quench) from superconducting to normal conducting state. Quench may lead to damage or even to catastrophic conductor failure. A superconductor is stable if it does not quench. Exact determination of superconductor transient, resistive states (flux flow, Ohmic) thus is mandatory to safely avoid quench. This request sharp comparison of local, transient conductor temperature and current transport density with local values of critical superconductor temperature, TCrit, and critical current density, JCrit, and the latter is a strong function of temperature. Numerical, Finite Element simulations reported previously and in this paper have provided the requested, transient temperature distribution; under disturbances, this distribution may strongly be non-uniform. But what happens if the other variable, TCrit, might not uniquely be defined? A multi-physics model (fractional parentage, Pauli selection rule, time of flight-concept with a mediating Boson, the Yukawa model and the uncertainty principle) provides relaxation time at which TCrit, as the thermodynamic, equilibrium state, finally would be obtained. But relaxation time diverges the closer the electron system approaches the phase transition, which questions existence of uniquely defined TCrit within finite process time. In this paper, focus is on multiple internal heat transfer (solid conduction and, in thin films, radiation), a suggested operator method to solve the incompleteness problem of radiative transfer, and time dependence of the order parameter obtained from the quantum-mechanical model. Traditional stability models cannot provide this information., Comment: Manuscript 54 p. (including refs list), 14 Figs (1a-c to 14, of which Figs 10a-c to 14 in Appendices 1 to 4, 23 Refs. No changes of Metadata and Categories. Results and conclusions same as before. No errors to be corrected; no changes within manuscript except for more comments, stylistic improvements. Paper originally submitted to Cryogenics, after requested (minor) revisions still under review