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The analysis of cooling of a binary HTS 20 kA current lead (CL) operating between 4.5 and 300 K has been carried out. Assuming that the HTS module is conduction-cooled, two cooling options for the copper heat exchanger (HEX) part of the CL have been considered, i.e. (1) cooling with a single flow of gaseous helium and (2) cooling with two flows of gaseous helium. The ideal refrigerator power required to cool the whole HTS CL has been calculated for both cooling scenarios and different values of input parameters and the thermodynamic optimization has been performed for both cooling options. The obtained results indicate that the cooling Option 2 cannot provide significant savings of the refrigerator power, as compared to the Option I. However, it has been observed that at the same helium inlet temperature the temperature at the warm end of the HTS part, and the resulting number of HTS tapes, can be reduced in the Option 2 with respect to the Option 1. (C) 2012 Elsevier Ltd. All rights reserved.