Operational stability analysis for superconductors under thermal disturbances
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The first objective of this study is to develop a complete method of operational stability analysis for superconductors under thermal disturbances. The second objective is to demonstrate the use of the method, through applications to the physical systems for the design and performance characterization purposes. Thermal stability is one of the major issues in the design and operation of superconducting devices. A superconductor in operation can experience a transition from the superconducting state to the normal resistive state, due to thermal disturbances. Following the quenching, a normal zone forms within the superconductor, which may grow or collapse depending on the disturbance energy, thermophysical and electronic properties, operating conditions, and the geometrical configuration of the superconductor. In this study, the operational behavior of pure superconductors subjected to thermal disturbances is investigated. Based on the existing intrinsic thermal stability theory and the cryogenic stability concept, a quenching-recovery criterion is developed. The criterion involves comparison of two critical current density ratios: one concerning intrinsic stability, the other concerning recovery. Based on the quenching-recovery criterion, a complete method for the prediction of quenching-recovery behavior is presented. In the first part of the study, the development of the method is presented through analysis conducted on both tape/film-type and cylinder/wire-type superconductors that are subjected to infinite line heat sources. In the second part of the analysis, the effect of the heat source length on the quenching-recovery behavior is investigated by considering finite length heat sources for both cylinder/wire and tape/film configurations. The effects of the wire diameter for cylinder/wire-type superconductors, and aspect ratio for tape/film-type superconductors, on the quenching-recovery behavior are also investigated in the second part of the analysis. Throughout the analysis, the governing heat transfer equations corresponding to the special cases presented are solved analytically whenever analytical solutions are possible, and numerically using the finite difference method whenever analytical solutions are not available.