Effect of axial conduction and metal-helium heat transfer on the local stability of superconducting composite media

The growth or collapse of a local normal zone in a superconducting winding structure saturated with single phase liquid helium (composite superconductor) is studied analytically. The history of a given temperature disturbance is derived from the solution to the transient heat conduction equation in a one-dimensional infinite solid with temperature dependent rate of internal heat generation, communicating laterally with a channel filled with stagnant helium. The combined diffusion by axial heat conduction and lateral heat transfer to the helium channel and its effect on the collapse or growth behaviour of a local disturbance is presented analytically. The paper develops a theoretical criterion for local stability (recovery) expressed in terms of dimensionless groups accounting for heat generation in the normal zone, metal axial conduction cooling, lateral cooling provided by the helium channel and, most importantly, the amount and spatial extent of the sudden release of energy responsible for the local disturbance.