Abstract
Analysis is performed to determine the optimal lengths or cross-sectional areas of refrigerator-cooled current leads that can be applied to the conduction-cooled superconducting systems. The binary current lead is composed of the series combination of a normal metal at the upper(warm) part and a high $T_c$ superconductor(HTS) at the lower(cold) part. The heat conduction toward the cold end of HTS part constitutes a major refrigeration load. In addition, the joint between the parts should be cooled by a refrigerator in order to reduce the load at the low end and maintain the HTS part in a superconducting state. The sum of the work inputs required for the two refrigeration loads needs to be minimized for an optimal operation. In this design, three simple models that depict the refrigeration performance as functions of cooling temperature are developed based on some of the existing refrigerators. By solving one-dimensional conduction equation that take into account the temperature-dependent properties of the materials, the refrigeration works are numerically calculated for various values of the joint temperature and the sizes of two parts. The results show that for given size of HTS, there exist the optimal values for the joint temperature and the size of the normal metal. It is also found that the refrigeration work decreases as the length of HTS increases and that the optimal size of normal metal is quite independent of the size of HTS. For a given length of HTS, there is an optimal cross-sectional area and it increases as the length increases. The dependence of the optimal sizes on the refrigerator models employed are presented for 1kA leads.