Theoretical analysis of conduction-cooled current lead for superconducting magnet

Abstract

CCCL is a typical CL type to energise SC magnets from room to cryogenic temperatures (<100 K) for its simplicity and reliability, but causes a relatively large heat leak (∼50 W kA−1 from 300 K) compared to the heat leak (∼1.0 W kA−1 from 300 K to liquid helium) of VCCLs, which necessitates a comprehensive understanding of designers and users. However, systematic studies on CCCLs are still lacking up to now. This study starts from the differential equation governing heat conduction and generation in CCCLs and firstly derives a completely exact theoretical solution by adopting the WFL law for thermal conductivity and electrical resistivity with temperature dependence. The solution facilitates the CCCL design optimisation to achieve the minimum heat leak, which is determined only by the temperature range but independent of both materials and geometrical parameters. Practical optimum designs are concerned with material properties and approached by calculating a shape factor to determine the conductor length and cross-sectional area, which is detailed and illustrated in this paper. Furthermore, the practical behaviours at low and excess currents can also be mathematically deduced, and the corresponding heat leaks are found to rely on materials but not on geometrical parameters. This paper also describes the agreements between the theoretical analysis and the numerical simulation and comparison with material properties of the non-WFL law.