Analysis of self-cooled binary current leads containing high temperature superconductors

The steady-state thermal performance of a cryostat current lead composed of a normal conductor upper part and a superconductor lower part is analysed. The upper end of the lead is at ambient temperature, the lower end is immersed in liquid helium, and the cooling for the lead is totally provided by the vapour generated by the heat flux from the lead into the helium. In the limit of high heat transfer rate between the lead and the helium vapour, there is a universal relationship between mass flow rate and superconductor transition temperature that is indpendent of the thermophysical properties or geometric details of either the superconductor or the normal conductor. This relationship shows that the reduction in heat flux to the helium with self-cooled binary leads, compared to that of the best copper leads, is limited to about 20% with critical temperatures (< 130 K) of existing high temperature superconductors. In general, helium boiloff with binary leads increases with decreasing heat transfer coefficient between lead and vapour. However, for some designs, based around a nominal heat-transfer rate, an increase in heat transfer results in higher temperatures along most of the lead.