Refrigeration, dilution

Below about 0.5 K, the interactions between He and He in the superfluid Hquid phase becomes very small, and in many ways the He component behaves as a mechanical vacuum to the diffusional motion of He atoms. If He is added to the normal phase or removed from the superfluid phase, equiHbrium is restored by the transfer of He from a concentrated phase to a dilute phase. The effective He density is thereby decreased producing a heat-absorbing expansion analogous to the evaporation of He. The He density in the superfluid phase, and hence its mass-transfer rate, is much greater than that in He vapor at these low temperatures. Thus, the pseudoevaporative cooling effect can be sustained at practical rates down to very low temperatures in heHum-dilution refrigerators (72). 

Most of the measurements described in the fifth section have been carried out using a low-power dilution refrigerator. This apparent constraint obliged the authors of the experiments to look for original configurations which are fully discussed in the text. We avoided to make a list of the suppliers of cryogenic equipments as happens in most books, since this type of information is at present easily obtained through internet. 

A system of cascaded booster pumps has the characteristics of a medium-size rotary vane pump but does not present the drawback of the back-streaming. For this reason, it finds application in cryogenics, for example, for the circulation of the He mixture in dilution refrigerators. 

We wish also to mention that solid hydrogen is usually responsible for the block of capillaries in low-temperature apparatus, for example, dilution refrigerators. 

At milli-kelvin temperatures, the problem of contact resistance between helium and solids becomes more complex. Thermal transfer phenomena take place involving spins and thermal resistance of sintered materials. The understanding of the thermal transport at very low temperature is of the utmost importance, also from a technical point of view, since helium is the working substance in dilution refrigerators (see Chapter 6). 

In most applications, 3He refrigerators are now replaced by dilution refrigerators (see Chapter 6). They are still used in the range 0.3-1.3 K, when a very compact vibration-free system is required. 

In this section, we will describe the various types of mechanical coolers with reference to their working cycles. We shall start with a brief description of counterflow heat exchangers. This subject will be further dealt in Chapter 6 when treating dilution refrigerators. 

In this section, we will describe the so-called continuous heat exchangers which are used down to about 1K. For lower temperatures, due to the increasing importance of the Kapitza resistance (see Section 4.3) step exchangers are used. They will be described in Chapter 6 in connection with the dilution refrigerator. 

In this chapter, we will deal with the most powerful device used in refrigeration. The dilution refrigerator (DR), which uses for refrigeration a mixture of 4He and 3He, not only is capable of reaching temperatures of a few millikelvin, but can maintain such very low temperature for months (theoretically for ever), whereas all the other refrigerators are one shot . Hereafter we will describe four types of DR. 

We shall now describe the so-called classic dilution refrigerator. The main components of a classic DR are shown in Fig. 6.5. 

Fig. 6.6. Scheme of a counterflow heat exchanger for dilution refrigerator. 

Fig. 6.11. Scheme of a J-T dilution refrigerator made by Uhlig [32]. The R- represent the thermometers, while Z- represent the main flux impedances. 

Fig. 6.14. A recent Joule-Thomson dilution refrigerator (courtesy of Leiden Cryogenics).

Fig. 6.17. Schematic of the open cycle space dilution refrigerator.

Fig. 7.3. Comparison of the relative cooling powers Qlh of a Pomeranchuck refrigerator and of a dilution refrigerator. In the former case, die liquid is converted into solid at a rate of 10 fxmol/s in die latter case, 3He is removed from the mixing chamber at the same rate. 

In solenoid magnets, the clear bore diameter (the inner diameter of the innermost magnet former) is the usual information needed. The diameter may range from a few millimetres to a few metres. A diameter around 30-50 mm is typical for the use with a dilution refrigerator. 

To carry out measurements at a fixed temperature, the refrigerator temperature must be kept constant for a suitably long time. The problem of the temperature control depends not only on the refrigerator itself, but on the thermal characteristics of the experiment. Let us now consider an oversimplified case in which heat capacities are neglected the mixing chamber temperature of a dilute refrigerator (DR) is to be controlled by a resistive heater HR and a d.c. power supply. 

From Fig. 10.13, we see the latter condition is fulfilled in the first three cases, but not in the fourth case. The most stable situation is obtained with Rx. The choice R = RcosL is however usually adopted when the power supplied to the resistor must be measured. The control of temperature in the real (dynamic) case is much more complex. The problem is similar to that encountered in electronic or mechanical systems. The advantage in the cryogenic case is the absence of thermal inductors . Nevertheless, the heat capacities and heat resistances often show a steep dependence on temperature (i.e. 1 /T3 of Kapitza resistance) which makes the temperature control quite difficult. Moreover, some parameters vary from run to run for example, the cooling power of a dilution refrigerator depends on the residual pressure in the vacuum enclosure, on the quantity and ratio of 3He/4He mixture, etc. 

Figure 12.4 shows an example of experimental set up for a classical measurement of heat capacity the sample is glued onto a thin Si support slab. The thermometer is a doped silicon chip and the heater is made by a ( 60 nm thick) gold deposition pattern. Electrical wiring to the connect terminals are of superconductor (NbTi). The thermal conductance to the thermal bath (i.e. mixing chamber of a dilution refrigerator) is made with thin nylon thread. The Si slab, the thermometer and the heater represent the addendum whose heat... 

The frame was in good thermal contact with the mixing chamber of a dilution refrigerator. A Ru02 thermometer measured the temperature TB of the frame. A thermal shield at the same temperature TB of the mixing chamber was used. 

The delivery of SCUBA-2 instrument to the JCMT is due for the end 2006. SCUBA-2 cryogenics is based on a dry dilution refrigerator (DR) (see ref. [7]) the main cryostat cooled by pulse tube coolers with 60 and 4 K stages, and the 1K box and detector arrays with DR for 1 K and millikelvin stages. The PT system has a cooling power of 50W at 45K on the first stage and 1.0W at 4.2 K on the second stage. The coolers were chosen for their inherently low vibration levels. 

Fig. 16.3. Left Schematic picture of the damping system of MimiGRAIL. The suspension consists of seven stages, the upper four made of CuAl followed by three copper masses. The upper CuAl mass is suspended from the top flange of the cryostat by stainless steel cables hanging from helical springs. Mass number 5, the first copper mass, will be cooled by the dilution refrigerator. Right Picture of the four CuAl masses hanging from the top flange (courtesy of Leiden Cryogenics).

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