Optimum intermediate temperatures of two-stage Gifford-McMahon type coolers

Optimum intermediate temperatures are evaluated for two-stage Gifford-McMahon (GM) coolers including shield coolers protecting cryostats with low-boiling-point liquids, e.g. liquid Helium-4 (He 1) baths near 4 K. Recent cooler progress has raised refrigeration loads to the 1-watt order of magnitude at 4 K. Thus, present three-stage systems with two-stage GM and single-stage Joule-Thomson (JT) expanders are potentially replaceable as two-stage GMs reach the refrigeration power of the three-stage GM/JT systems. We have extended earlier studies with the objective of evaluating realistic optimum intermediate temperatures, e.g. of two-stage GMs, in order to replace previous ideal limits. Our present extended model includes previous components such as the cascade-shunt model. Its optimum temperatures are found to be lower than ideal values, consistent with cooler data, in the range of parameters covered. This feature relates in part to higher loss parameters in the low temperature stage exceeding those of the elevated temperature stage.