“…Its thermophysical properties including equation of state are well known. However, due to a small thermal expansion coefficient, the cooling capacity of 4 He regenerative cryocoolers diminishes quickly at liquid helium temperatures close to the lambda transition line of this fluid. The lowest non-load cooling temperatures achieved by commercial regenerative cryocoolers are of order 2.3 K, while the cooling power at 4.2 K can reach 1-1.5 W. Much of the research on cryocoolers has focused on such issues as 1) improving heat transfer at the cold end, 2) modifying the structures, *Corresponding author (email: huangyh@sjtu.edu.cn) and 3) adjusting the phase shifter.…”