Compact current leads have been developed for a superconducting thin solenoid magnet at KEK. A disk fin of a special type (straight-cut disk fin) is devised which is suited to be cut straight with numerically controlled machines such as a wire cutter or a milling machine. Since the straight-cut disk fins increase both the heat exchange efficiency and the thermal inertia of current-carrying conductor, they enable us to construct the current lead compactly. The length of the current lead fabricated is as short as 60 cm for its operating current of 4.1 kA. Good results have been achieved experimentally on the heat leakage into the cold region and on the pressure drop of cooling gas. The reliability of this current lead is estimated to be equivalent to that of the current lead twice in length without the cooling fin.
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