Dilution Refrigerator - Limitations

Limitations

There is no fundamental limiting low temperature of dilution refrigerators. Yet the temperature range is limited to about 2 mK for practical reasons. At very low temperatures both the viscosity and the thermal conductivity of the circulating fluid become larger if the temperature is lowered. To reduce the viscous heating the diameters of the inlet and outlet tubes of the mixing chamber must go as T_m-3 and to get low heat flow the lengths of the tubes should go as T_m-8. That means that, to reduce the temperature by a factor 2, one needs to increase the diameter by a factor 8 and the length by a factor 256. Hence the volume should be increased by a factor 214=16384. In other words: every cm3 at 2 mK would become 16.384 liter at 1 mK. The machines would become very big and very expensive. Fortunately there is a very powerful alternative for cooling below 2 mK and that is nuclear demagnetization.