The initiation and propagation of normal zones in a force-cooled tubular superconductor

A numerical analysis has been performed on the time-dependent equations of heat balance, gas convection, pressure drop, and mass-flow rate for supercritical helium gas flowing through a tubular superconductor. Three dimensional graphs of wall temperature, gas temperature, and mass-flow rate as functions of position and time are used to show the evolution of normal zones. In contrast to other methods of studying stability in superconductors by a quasi-steady-state analysis of critical-sized normal zones (minimum propagating zone), our analysis shows that stability is influenced by both the magnitude and the time dependence of the disturbance. As the current is increased in a system subjected to certain types of thermal disturbances, propagating normal zones may originate at positions well downstream from the site of the disturbance. At higher currents, propagating zones may originate both downstream and at the disturbed site, coalescing into a large propagating normal zone. With certain types of disturbances (such as an extraneous heat source over a short length of conductor), higher critical currents may be reached by fast current ramping, while with other types of disturbances (such as self heating in a degraded section of conductor), slow current ramping leads to higher critical currents.