Principles and methods of dilution refrigeration

Abstract

Following a b r ie f introduction in Section T, the properties of pure He3 and of d ilu te solutions of He3 in superfluid He4 which are relevant to the design and understanding of d ilu tio n refrig erato rs are discussed in Section I I. In Section I I I the basic model fo r discussing the thermodynamics of the d ilu tio n process is developed and applied to both a continuously operating re frig e ra to r and to singlecycle refrig e ra to rs using both He3 flow and super f l u id He4 flow. The re la tiv e merits of He3 flow and super leak operated devices are also mentioned. In Section IV the thermodynamical properties of He* in the d ilu te phase of the re frig e ra to r are calculated, including the dependence of concentration on temperature and the e ffe ctiv e enthalpy function. The heat exchange problem is discussed in Section V, f i r s t by introducing new measurements of the Kapitza resistance fo r saturated d ilu te solutions and then by re la tin g these to the concept of a He*-phonon resistance in the d ilu te s o lu tio n s. F in a lly specific design estimates are made fo r the heat exchangers. In Section V I the physics of the He3 c irc u la tio n problem is discussed. The effects of circulated He4 and of viscous heating due to He3 flow are also emphasized. Both the effects of thermal conduction and viscosity lim it the low temperature attainable in a He3 flow type of d ilu tio n r e fr ig e r a to r. There is a lower lim it to 'the temperature attainable as a resu lt of these in trin s ic factors which is calculated in Section V II. The general characteristics of the re frig e ra tio n device i t s e lf are reviewed in Section V I I I. Section IX contains a d etailed description of two systems b u ilt and tested by us. Parts of the apparatus discussed are the s t i l l , the heat exchangers, the mixing chamber, the condenser and main impedance, interconnections, and mechanical support. The a u x ilia ry cryogenic and pumping systems are also described. In Section X the operational characteristics of two d ilu tio n refrig erato rs are d iscussed, both in regard to s ta rtin g them up and to th e ir steady state operating c h a ra c te ris tic s. The e ffec t of a heat load, of s t i l l power, and of the number of exchangers is given. Comparison with the thermodynamical treatment is made. Under suitable conditions a temperature of 10 m°K can be maintained continuously and a temperature of 4.5 m°K fo r short periods of time.

Indigenous Development of a Millikelvin Refrigerator at VECC, Kolkata

“…Because of the lower mass of the atom, 3 He has higher vapour pressure and therefore higher vaporization rate. Hence, we can reach further down to 0.3 K if we use 3 He instead of 4 He. Cooling below 0.3 K is not possible by conventional refrigeration technique; however, a dilution refrigerator can cool down to a few mK that can be maintained for several hours.…”

“…Of the several unique features exhibited by helium, one of the most convenient for a low temperature physicist is that at sufficiently low temperatures (about 0.8 K), a mixture of 3 He and 4 He will spontaneously separate into two phases, with the lighter 3 He rich fraction floating on top of the heavier 4 He rich fraction. Since there is an interface between two phases, extra energy is required for particles ( 3 He) to go from lighter phase to heavier phase.…”

“…The lowest temperature is limited by vapour pressure. Since vapour pressure decreases exponentially with falling temperature, cooling by evaporation of 4 He liquid can only reach about 1 K temperature. Below this temperature, the vapour is very small, and very little would evaporate.…”

“…Cooling below 0.3 K is not possible by conventional refrigeration technique; however, a dilution refrigerator can cool down to a few mK that can be maintained for several hours. It is based on the solution and separation of two isotopes of helium, 3 He and 4 He, and can produce a stable base temperature of few millikelvin to serve as a starting point for very low temperature experiments.…”

“…The heat load on the helium bath is estimated to be about 0.76 W at 4.2 K considering the effect of outer radiation from liquid nitrogen chamber and conduction through pumping lines, needle valves, etc. The cryostat was designed to obtain a long running time by having a sufficient volume of liquid 4 He and also by minimizing the heat leak by using a narrow neck. This IVC was housed within the helium bath of the cryostat with its top flange immersed in liquid helium.…”