LIQUID He3, LIQUID MIXTURES OF He3 AND He4, AND DILUTION REFRIGERATION

Abstract

Basic properties of pure liquid He3 and of dilute solutions of He3 in superfluid He4 are reviewed as they relate to the design and operation of dilution refrigerators. Brief discussions are given both of the intrinsic limitations of the dilution refrigerator and of instabilities which can degrade performance. Finally some characteristics of a new generation of practical dilution refrigerators are displayed and discussed. I. Basic Properties of Liquid ~e~ and of Dilute Mixtures of He3 and He4 as They Relate to the Dilution Refrigerator. We have already discussed elsewhere [I] the essence of this section, so we will confine ourselves to a few remarks in review. Pure, or concentrated, liquid He3 can be regarded as a normal Fermi liquid with sufficient accuracy for the present purposes. That is, we can ignore the very interesting departures [2] at low temperatures of the specific heat from a linear dependence on T, of the thermal conductivity from a T-' law, and of the viscosity from a T ~ law. Dilute solutions of He3 in superfluid He4 have thermal properties very similar to those of the ideal FermiDirac gas. Transport phenomena in the dilute solutions at temperatures below 10 to 20 m OK are also rather like those in a dilute Fermi gas. They may be deduced from an effective interaction [3] dependent on momentum transfer in a mutual collision of quasiparticles and attractive for low values of momentum transfer. Above about 10 m OK the contribution of He4 phonons to the thermal conduction in dilute solutions is already important. By 100 m OK He4 phonons, scattered by He3 quasiparticules and by boundaries, carry essentially allthe heat [4]. There are no measurements of capillary viscosity at low temperatures in dilute solutions. At low temperatures the capillary viscosity has been estimated by Roach [5]. Above 100 m OK we can use the effective viscosity measured by Webeler and Allen [6] to estimate viscosity as a function of temperature and concentration. In addition to the properties individually of concentrated He3 and dilute solutions, the solubility of He3 in He4, and vice versa, is of great importance. A number of measurements have been made, particularly by Edwards and collaborators, [7] and these have been reviewed in reference 2. The principal qualitative point is that at T = 0 a single He3 atom is more strongly bound to liquid He4 than it is to liquid He3, so that even at T = 0 He3 will dissolve in He4. The solubility is limited, however, by the Fermion nature of ~e~ quasiparticles in superfluid He4 which requires additional He3 atoms to enter the liquid in higher translational energy states. Similarly, a single He4 atom is also more strongly bound to liquid ~e~ than to liquid He3 so that as T approaches zero the concentration of He4 in He3 tends rapidly to zero. Certainly below 100 m OK an accurate picture of a mixture of He3 and He4 is that, assuming excess He3, essentially pure He3 will float over a dilute solution containing near T = 0 a He3 molar concentration of about 6.5 %. At higher temperatures the increase in solubility of He3 in superfluid is proportional to T 2 . In the most common type of dilution refrigerator, the refrigeration is produced by dilution of He3 by the superfluid in the mixing chamber. The refrigeration rate at constant temperature is of the form n3 TAs , or