Theoretical Models for the Cooling Power and Base Temperature of Dilution Refrigerators

He-3/He-4 dilution refrigerators are widely used for applications requiring continuous cooling at temperatures below approximately 300 mK. Despite of the popularity of these devices in low temperature physics, the thermodynamic relations underlying the cooling mechanism of He-3/He-4 refrigerators are very often incorrectly used. Several thermodynamic models of dilution refrigeration have been published in the past, sometimes contradicting each other. These models are reviewed and compared with each other over a range of different He-3 flow rates. In addition, a new numerical method for the calculation of a dilution refrigerator's cooling power at arbitrary flow rates is presented. This method has been developed at CERN's Central Cryogenic Laboratory. It can be extended to include many effects that cannot easily be accounted for by any of the other models, including the degradation of heat exchanger performance due to the limited number of step heat exchanger elements, which can be considerable for some designs. Finally, the limitations of applying the results obtained with idealized thermodynamic models to actual dilution refrigeration systems are discussed.