Cryocoolers near their low-temperature limit

• The very-low-temperature behavior of cryocoolers is analyzed.
• The observed time dependence of the temperature is explained.
• The importance of the zero thermal-expansion line (αα-line) is emphasized.
• Relationships are derived for thermodynamic diagrams of 4He and 3He.
• Performance improvements and further experiments are suggested.

This paper analyses the recently-observed temperature–time dependence in a GM-cooler near its low-temperature limit. The paper mainly focusses on GM-coolers with 4He as the working fluid, but some attention is also paid to pulse-tube refrigerators (PTR’s) using 3He and many features of the treatment equally apply to Stirling coolers. Ample attention is paid to the thermodynamics of the cycle by considering the isentropes in the Tp-diagrams of 4He and 3He. The role of the line, where the thermal expansion coefficient is zero, is emphasized. Some fundamental thermodynamic relationships are derived.