Cooling liquid He-3 below 1 mK by nuclear demagnetization

The design and construction of a nuclear adiabatic demagnetization cryostat is detailed and the cooling of approximately 20 cc of liquid He-3 to a temperature of 0.4 mK is discussed. The net heat leak to the nuclear stage was only 5 nW and the run time being 1 mK was in excess of two days. The thermal resistances between the liquid He-3 and the nuclear spins of the copper bundle are examined. Extensive calculations and measurements show that the Kapitza resistance between the palladium heat exchanger and the He-3 is the dominant factor. A single mathematical approach to optimizing the cooling of the He-3 by minimizing the entropy production in the bundle is also presented. The results of this optimization can be used with a microprocessor based controller to automate the demagnetization process and to evaluate the effects of making changes in the apparatus.