A 3He circulating dilution refrigerator with two mixing chambers

Physrca 81B (1976) 323-324 0 North-Holland Pubhshmg Company

LETTER TO THE EDITOR

A 3He CIRCULATING

DILUTION REFRIGERATOR

WITH TWO MIXING CHAMBERS

A.Th.A.M. DE WAELE, A.B. REEKERS and H.M. GIJSMAN Ezndhoven

Unzverszty of Technology,

Ezndhoven,

The Netherlands

Recetved 19 November 1975

A drlutron refrrgerator with two mrxmg chambers is descrrbed. When compared with a drlutron refrigerator wrth only one mrxing chamber the temperature range 1s extended to lower temperatures The temperature reduction factor can be up to a factor 2.8. The results of an experiment are reported m which a magnetic temperature of 5 5 mK was obtained m the continuous mode and 3.5 mK m the smgle cycle mode, using a drlutron refrigerator that reaches 13 mK in the contmuous mode with one mrxmg chamber

A standard 3He crrculating dilution refrigerator [ 1,2] consists essenttally of a set of heat exchangers, a mixing chamber and a still. The lowest temperature that can be obtained m the contmuous mode depends on the number of heat exchangers and on then surface area. Their efficiency at low temperatures is limited by the Kapitza resistance. If one wants to obtain temperatures on the order of 5-6 mK many step exchangers are necessary [3]. One can avoid this problem by circulating 4He mstead of 3He m the dilution refrigerator [4]. In the dilution refrigerator described in this letter 3He is circulated. The problems arising from the Kapitza resistance are solved here by the installation of a second mrxing chamber. In this way a double mixmg chamber is obtained. The flow of 3He m this double mixmg chamber is depicted in fig. 1. The concentrated 3He from the coldest heat exchanger flows into the first mixing chamber (MC-l) with a flow rate of ht moles per second, but only part of it (fiI) is diluted here. The cooling produced by the dilution of fil is used to cool the portion ti2 = it - til of the 3He that is not diluted in MC-I. This undiluted portion then leaves MC-I, flows into the second mixing chamber (MC-2) and is diluted there. In MC-2 the lowest temperature is reached. The purpose of MC-l is to lower the temperature of the 3He flowing mto MC-2. From the enthalpy balances of MC-I and MC-2 follows that

I

MC-2

MC-I

Fig. 1. Flow of 3He m the two mixing chambers. The symbols are explained in the text

1 T2=$1

1 Tr =Gf

and

f=>T, where T, , T2 and Tl are the temperatures of MC-l, MC-2 and of the 3He leaving the coldest heat exchanger respectively, r = ir 1/ri t and f is the temperature reduction factor of MC-l. The value off ranges from 1 (when no dilution takes place in MC-l) to 2.8 (when almost all 3He is diluted in MC-l). In a normal dilution refrig323

324

A Th A M de Waele et al /A dlluhon refrrgerator with two mlxmg chambers

erator with only one mtxmg chamber the temperature of the mtxing chamber 1s given by T. TM=+ The value of T, IS mdependent of whether the dilutron refrigerator has one or two mixmg chambers. Hence the mstallation of a second mixing chamber can lower the temperature. In practtce the behaviour of the double mrxmg chamber 1s influenced by the osmotrc-pressure difference between MC-l and MC-2. At low temperatures this osmotrc-pressure difference All is given by [2] AR = ff, -- fI2 = 1 .O X 10’ (Tf - Ti)

(Sl units)

In a stationary srtuatron ATTwtll (m first approxrmanon) be balanced by a hydrostattc-pressure difference resulting m a level difference Ah of the two phase boundartes (see fig. 1) given by:

2.6 mm, height 8 mm), calibrated against a superconducting fixed-point device [5]. With the values of Z = 14 X lo6 cmP3 and tit = 40 pmol/s we obtained m the contmuous mode a magnetic temperature Tz = 5 ..5 mK, usmg a dilution refrigerator that reaches 13 mK when only one mtxmg chamber IS installed. This result shows that the temperature range of a standard dllutton refrigerator can be extended considerably when the mrxmg chamber 1s replaced by a double mixing chamber Taking 5 5 mK as the starting temperature for a single cycle we obtained a magnetic temperature T,* = 3.5 mK. It seems likely that this temperature can also be reached m the contmuous mode when more mrxmg chambers are used to precool the 3He flowing into the final mtxmg chamber

References [ 1] J.C Wheatley,

m which pd and pc are the densities of the dilute and the concentrated phases respectrvely, and g 1s the gravrtattonal acceleration. Thrs pressure difference drives an internal circulatron of 3He m the double mrxmg chamber As a consequence the direction of the flow h2 might become negative or zero in certam situations. The impendance Z at the dilute outlet of MC-1 forces IQ in the drrectton as given m fig. 1. Another posstble consequence of AIl f 0 is that Ah can be comparable with the height h of the mrxmg chambers With h = 5 cm and T, = 2.8 T2 the opttmal performance of the double mrxing chamber 1s achieved only when T, < 18 mK. In our experiment the temperatures T, and T2 were measured with thermometers, consisting of 50 mg of powdered CMN m the shape of a cyhnder (diameter

[2] [3] [4]

(51

0 E. Vilches

and W R Abel, Phys

4 (1968)

1, J.C Wheatly, R.E Rapp and R T Johnson, J. Low Temp Phys 4 (1971) 1. R. Radebaugh, Nat Bur Stand (U.S.), Tech. Note, No 362 (1967). K N Zmovyeva, J Phystque (Parts), 31 (1970) C3-91 K.W. Tacoms, N H. Pennings, P Das and R de Bruyn Oubbter, Phystca 56 (1971) 168, N H. Pennings, K W Tacoms and R. de Bruyn Ouboter, Cryogemcs 14 (1974) 53. N H. Pennings, R de Bruyn Ouboter and K W. Taconis, Phystca 818 (1976) 101 (Commun Kamerlmgh Onnes Lab, Letden No 418d), G Frossatr, G Schumacher and D. Thoulouze, Proc. 14th Int Conf on Low Temp Phys, Vol 4 (North-Holland Publ. Comp., Amsterdam, 1975) p 13. F A Staas and H C M van der Waerden, Proc 14th Int Conf on Low Temp Phys., Vol 4 (North-Holland Publ. Comp., Amsterdam, 1975) p 17 J F Schooley, R J. Soulen and G.A. Evans, Jr, Nat Bur Stand (US ), Specral Pubhcatton 260-44