Evaluation of the refrigeration in the Gifford-McMahon-Cycle refrigerator based on the thermoacoustic theory

We have measured the refrigeration of the Gifford-McMahon-Cycle (G-M) refrigerator by using Pb, Er₃Ni and NdAg as regenerator materials. The magnetic intermetallic compounds Er₃Ni and NdAg exhibit a specific heat anomaly corresponding to the magnetic ordering at 7 and 22 K, respectively and possess a larger volumetric specific heat at low temperatures than that of the conventional regenerator materials Pb. We analyzed how the performance of the refrigerator is influenced by the differences in the specific heat of the regenerator materials based on the Tominaga thermoacoustic theory. We found that the refrigeration performance, as well as the lowest temperature reached in a given G-M refrigerator, is determined by the ratio of the specific heat of the regenerator material over that of the helium gas, and the volume expansion coefficient and mean temperature of the helium gas. We can predict the lowest temperature attainable by a given regenerator material in the ordinary G-M refrigerator only from the temperature dependence of the product of these parameters.