Thermal analysis for the recovery and quenching of disturbed composite superconductors

Thermal stability is one of the major issues in the design and operation of superconducting devices. Due to a thermal disturbance, the superconductor may experience a transition from the superconducting state to the normal resistive state a phenomenon known as quenching. The high electrical resistivity of the normal state superconductor and large energy stored in magnetic field contribute to an excessive amount of heat generation which may cause an irrecoverable damage. In a composite superconductor, a stabilizer is provided to alleviate the problem through a current sharing process. For a low disturbance energy, the conductor can reinstate its superconducting state. However for a large disturbance energy, irrecoverable quenching stiU occurs. The critical energy is referred to as a maximum energy required to initiate quenching. The one-dimensional heat balance equation based on the assumption of uniform cross-sectional temperature distribution has been used to calculate the critical energy in previous studies. Cryogenic stability criterion and the Minimum Propagation Zone (MPZ) theory have been typical tools to analyze the stabihty of composite superconductors.

The present study investigates the effect of non-uniform temperature distribution in a cross-section of a composite superconductor. Mathematical models of current sharing and Joule heat generation in the superconductor and the stabilizer are formulated. The transient solution by finite-difference method reveals the scenario of the behavior of the conductor, starting from the deposition of initial disturbance energy, current sharing, quenching, and possible recoveryo f superconductivity. The analytical solutions of the critical energies in the superconductor and the stabilizer are also obtained for special geometries, such as a tape/film superconductor sandwiched between two stabilizers, and a wire superconductor imbedded in a stabilizer. Based on the analytical calculation of the critical energies, a new stabihty criterion for the composite superconductor is proposed. In addition, a new approach to the one-dimensional stabihty analysis has been conducted by analyzing the effect of disturbance temperature profile. The concept of critical Joule heat generation is introduced to remedy the drawback of existing critical energy theory. To achieve a low hehum boiloff in the high-temperature superconducting current lead without danger of burnout the analytical and numerical analyses are performed.