Quench energies of composite superconductors

The minimum energy of a local heat pulse Qo, initiating normal zone propagation is an important characteristic of the stability of a superconducting composite. There are many papers concerning, both experimentally and theoretically (usually numerically), the value of Qc for composite superconductors (see, e.g., References 1-3 and references therein). In particular, simple analytical formulae for quench energy of a local heat pulse were obtained by Pasztor and Schmidt 4 and Dresner 5. In these papers ~'5 the model of anisotropic effective continuum was treated, the dependence of specific heat and thermal conductivity of the superconductor on temperature and the heat transfer to the coolant being neglected. The latter assumption restricted these results either by the case of thermally insulated composites or by currents I which are substantially greater than the minimum propagating current I w In the present paper the formulae for Qc have been obtained for the cases of one-, twoand threedimensional heat propagation, which take into account heat transfer to the coolant. We consider the model of anisotropic effective continuum disregarding the current sharing, which allows us to obtain the universal formulae for Qo(I) in the whole region Ip < I < I¢, where Ic is the critical current of the superconductor. The heat balance equation describing the temperature distribution in the superconducting composite is