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Powerful dilution refrigerator for use in the study of polarized liquid 3He and nuclear cooling
Powerful dilution refrigerator for use in the study of polarized liquid 3He and nuclear cooling G.A. Vermeulen* and G. Frossati Kamerlingh Onnes Laboratorium der Rijksuniversiteit Leiden, PO Box 9506, 2300 RA Leiden, The Netherlands Received 13 October 1986 A 3He-4He dilution refrigerator with a lowest temperature of 1.90 +__0.05 mK and a maximum circulation rate of 10 mmol s -I has been constructed. The apparatus is at present used for the study of 3He in high magnetic fields and as a precooling stage for nuclear demagnetization. The design and construction of the dilution refrigerator are described. Keywords: refrigerators; helium; dilution refrigerator; nuclear cooling
The study of polarized liquid 3He and the not yet discovered superfluidity of 3He diluted in 4He pose interesting challenges in the field of low temperature physics. The most promising way to produce highly polarized liquid 3He, which requires at equilibrium conditions at least a field of the order of knTpttt = 220 T, appears to be rapid melting of highly polarized solid i-4. The highest polarization in solid 3He has been reached by precooling liquid 3He, which has a much lower polarization and converting it to solid using a Pomeranchuk cell. To obtain 70-80% polarization in the solid, a temperature of 2-3 mK is necessary in a field of 9 T. The solidification rate and hence the cooling power and the minimum temperature are seriously limited by the spin lattice relaxation in the liquid. Too high a solidification rate will deplete the magnetization of the liquid and underpolarized solid will be formed. This shows itself as a higher melting pressure than the equilibrium melting pressure. The maximum solidification rate is = 5% h -~ at temperatures of = 5 mK and in a field of 7 T 5. However, there is evidence that the spin lattice relaxation time, x~, is reduced by a few orders of magnitude if the liquid is below the superfluid A 2 transition 6. Even in the A~ phase, a considerable decrease in x] is to be expected, although only a decrease by a factor of three has been observed 7. The presence of the superfluid will reduce the temperature gradients and the solid will collect at the bottom of the cell. The exposed walls will contribute to the magnetic relaxation. Hence, our aim was to have a dilution refrigerator, which could precool a Pomeranchuk cell below the superfluid transition of liquid 3He in a high magnetic field. Cooling 3 H e J H e mixtures to a temperature where the 3He quasigas might become superfluid (possibly in the low microkeivin range) requires nuclear adiabatic demagnetization. In a 9 T magnetic field the maximum specific heat of copper nuclear spins occurs at ~ 5 mK. Precooling to a lower temperature gives no great advantage with *Present address: Laboratoire de Physique des Solides, B&timent 510, 91405 Orsay Cedex, France
0011-2275/87/030139-09$03.00 © 1987 Butterworth & Co (Publishers)Ltd
respect to cooling power and the minimum temperature reached after demagnetization. However, a fairly large cooling power is needed to precool a copper nuclear demagnetization stage in a reasonably short time to 5 mK in 9 T. The minimum temperature which can be reached in liquid 3He or a liquid 3He-4He solution is mainly determined by the ratio of the heat leak into the sample and the Kapitza resistance between liquid and refrigerant. Therefore, it is of crucial importance to minimize all known sources of heat leaks. A dilution refrigerator with a very low base temperature allows sample cells to be immersed directly in the liquid of the mixing chamber. A simple mechanical or superconducting heat switch can be used to isolate the sample cell from the mixing chamber. The heat leak from the liquid of a mixing chamber at 2 mK to a cell with an area of 10 cm 2 is only = 1 pW (the cell being considered at T = 0 K). In view of these (and other) experiments we have decided to construct two dilution refrigerators (one has already been in operation for a few years and the other is still being completed) with a base temperature of 2 mK at a circulation rate of 1 mmol s -1. To increase the circulation rate and hence the cooling power, we have added the capacity to pump with the two pumping systems on one single dilution refrigerator. In this way, a circulation rate of > 10 mmol s -1 can be sustained. The epoxy mixing chamber is located in the centre of a 9 T magnet and is very large (300 cm3), providing enough space for several types of experiments.
Experimental
room
As a precaution against RF radiation, we have constructed a shielded room. The walls, floor and ceiling of our experimental room are covered with 0.3 mm thick copper sheets, which are soldered together. Two special doors and 1 m 2 of RF isolated windows have been purchased from Siemens. The electrical power is supplied through four lines, which are heavily filtered (Siemens model B84206-D22-E2, nominal current and voltage: 25 A and
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Powerful dilution refrigerator: G.A. Vermeulen and G. Frossati 380 V; the RF isolation is 90 dB up to 1 GHz). The computer, which is used to control some parts of the experiment (for instance NMR), generates a lot of RF noise. Therefore, we have placed it outside the shielded room together with its peripherals. We have limited ourselves to the use of the IEEE--488 bus for communication between the computer and the electronics inside the cage. This gives us the clean solution of decoupling the computer electrically from the experiment by means of two IEEE-488 converters, which transmit the signals through two optical fibres. Figure 1 shows a recorder trace of a carbon resistor at a temperature of < 10 mK with the door of the shielded room open and closed, which illustrates the effectiveness of the shielding. 1200 kg stainless steel reinforced concrete blocks on rubber dampers provide vibrational isolation of the cryostats. We have made provisions to mount air springs at the corner of the blocks in case the vibrational isolation is not sufficient. The cryostat is supported by a tripod of 200 mm diameter stainless steel tubes, which are screwed to one of the concrete blocks. These tubes can be eventually filled with sand or some viscous material to improve the damping or increase the mass, The total mass of concrete block, supports and cryostat is estimated to be 1700 kg. The tripod structure is very rigid. All pumping lines to the cryostat are vibrationally isolated by crossing two sets of compensated bellows, except for the 400 mm diameter 3He pumping lines, which are isolated by a tee with one set of very elastic plasma-welded bellows (Calorstat Industries, Dourdan, France). 3He-4He
gas handling Systems and pumps
Figure 2 shows a diagram of one of the gas handling systems. The 3He--4He gas handling systems and the pumps to circulate the "He are outside the shielded room. The storage tanks for the mixture to operate the dilution refrigerators consist of four vessels of 520 dm 3 and two of 154 dm 3. There is a separate set of pumps for each of the dilution refrigerators, but they can be set to work in parallel to increase the maximum flow rate in one refrigerator. With the two systems in parallel we can
>
IS, I
Rgure 2 Left part of the aHe--4He gas handling system (including one set of pumps and one of the cryostats). The system is symmetrical with respect to the dotted line and allows us to pump with two sets of pumps on one single cryostat. C, Cryostat; B, Edwards 18B4 booster pump; R, Edwards 1200 EH roots pump; A, Alcatel 2060H primary pump; P, small primary pump to clean the traps; Tt, Leybold Heraeus LH AF8-16 oil trap; T2, T3, home-made glass fibre filters; "1"4,carbon trap; "Is, palladium trap; St and $2, 520 dm 3 storage vessels; $3, 154 dm 3 storage vessel; M~, M2, Ma, manometers to monitor pressure in the storage vessels; M4, pressure monitor for the aHe pumping line; Ms, pressure sensor, which switches off A in case of overpressure (marked by a dashed line); Me, M7, pressure sensors, which open automatic valves in case of plugging of the traps (marked by dashed lines)
sustain a flow rate ~ 10 mmol s -~. A set of pumps consists of an Edwards 18B4 booster pump backed by an Edwards EH1200 roots pump and an Alcate12060H primary pump. The booster pumps are placed just outside the shielded room to decrease the length of the pumping lines as much as possible. Each booster pump is mounted on a 400 kg concrete block on rubber dampers for vibrational isolation. The backing pumps sit in another room on the other side of the corridor and are connected by ~ 10 m long, 100 mm diameter pumping lines. The backing pumps are mounted on one single concrete block on shock absorbers. The pumping lines between the booster and the roots pumps are rigidly anchored to the wall of the building and isolated from the pumps by bellows. As a precaution against plugging of the 3He condensing line we have put an oil trap (Leybold Heraeus model LH AF8-16) and a home-made filter of glass fibre (glass fibre FM004, Chemical Trading Co., London, UK) just after the primary pump. In addition, we have another identical charcoal filter, a trap and a palladium filter in the gas handling panel. Several litres of air are needed to saturate the charcoal traps and cause a blockage. The booster pumps are protected by thermal snap switches against a failure of the water cooling or high pressure on the pumping side. The primary pumps switch off automatically if the outlet pressure rises above 1.5 bar absolute pressure. The system is protected against plugging of the charcoal traps by valves, which are opened automatically if the pressure in front of the traps reaches = 1 bar.
Cryostat Figure I Recorder trace of a carbon resistor at T < 10 mK with the door of the shielded room open and then closed.
140
Cryogenics 1987 Vol 27 March
The maximum height of our experimental room, which is
Powerful dilution refrigerator: G.A. Vermeulen and G. Frossafi on the second floor, is 3.30 m. Between our floor and the ceiling of the floor below us, there is 1.20 m space for air conditioning, supplies for cooling water, compressed air and the central heating system, which made it possible to have 1.20 m deep holes in the floor. The maximum width of those holes is limited to 37 cm by parallel stretched beams. The cryostat was designed in view of the restrictions of the room and is shown in Figure 3. We have access to the mixing chamber by removing the tails of the outer vacuum can (OVC), nitrogen shield, helium can and inner vacuum can (IVC). The upper part of the cryostat which has an outer diameter of 0.8 m and contains the nitrogen reservoir and most of the volume of the helium reservoir, always stays in place. Except for a few current leads to operate the magnet and the liquid helium level gauge all the electrical wiring, capillaries, transfer tubes and connections to the low temperature valves enter the cryostat from the side. Flanges, which are demountable by means of indium joints, provide for leak-tight feed-throughs in the inner vacuum can as well as the outer vacuum can. All space at the top of the cryostat has been reserved for the 3He pumping line. The 3He pumping line is part of a conical concentric pumping line-heat exchanger assembly, which consists of three cones with a length of 1 m. At the top of the cryostat the diameter of the 3He pumping line is 300 mm and just above the still, 80 mm. The second cone encloses the SHe condensing line. Two spirals of 0.5 mm thick stainless steel tape have been spot-welded between the inner and the
A
B
't [ '= "i>>>x<<< "
II
--- ,l~>X<
m
LI
Figure 3 Schematic vertical cross-section of the cryostat. A, aHe pumping line; B, 1 K pot pumping line; C, outer vacuum can (OVC); D, liquid nitrogen reservoir; E, baffles inside the aHe pumping line; F, helium reservoir; G, removable tail of the OVC; H, removable tail of the nitrogen shield; I, removable tail of the nitrogen reservoir; J, inner vacuum can (IVC)
second cone. This increases the mechanical strength and the incoming 3He is forced down the spiral, so that the heat contact with the walls is improved. The 2 cm wide space between the outer cone and the second cone is the pumping line of the 1 K pot. Many rings of perforated copper plate have been soldered on the inside of the second cone to fulfil three purposes: 1, to act as radiation shields; 2, to improve the heat exchange between the incoming 3He gas and the outgoing 4He gas; and 3, to provide extra support for the outer cone (all cones are made out of 0.6 mm thick stainless steel plate). Inside the 3He pumping line there are four baffles which serve similar purposes. The useful helium charge above the inner vacuum can is = 80 dm 3 and the evaporation rate is between 1.4 and 1.8 dm 3 h -l. Thus, the time between two helium transfers is two days.
Dilution
refrigerator
The dilution refrigerator is an enlarged and improved version of the type developed by Frossati and coworkers 8"9. Figure 4 shows a vertical cross-section of the dilution refrigerator, 1 K pot, vacuum can and magnet. Before describing the heat exchangers, still chamber and mixing chamber in more detail, we will give an overview of all parts inside the vacuum can. The whole system hangs from the concentric 3He pumping line-heat exchanger assembly. From the conical heat exchanger the 3He enters a CuNi capillary (5 m x 1.0 mm x 1.5 mm) in the 3He pumping line just above the still, where it is further cooled before it enters a heat exchanger of similar size in the 1 K pot. The still is mounted to the bottom of the pumping line. The whole system of the vacuum can, 1 K pot and still is quite easily removed and demounted by means of indium joints. Eight flanges on top of the large flange of the inner vacuum can are reserved for feed-throughs. Gold plated copper plates are screwed to the bottom of the 1 K pot parallel to the large flange for thermal anchoring of the wires. An impedance, which is adjustable when the cryostat is open, is mounted on the still to condense the incoming SHe. This impedance is optionally bypassed by a valve, which is actuated from outside the cryostat. Opening the valve reduces the time needed to condense the 1500 dm 3 He gas used to operate the dilution refrigerator to ~ 2 h. Before entering the continuous tubular heat exchanger, the 3He may be optionally directed through a heat exchanger in the still. No significant improvement is found when the heat exchanger in the still is used. Below the still are the continuous tubular heat exchanger, the first sintered silver heat exchanger and a cold plate for thermal anchoring. One thermal radiation shield is anchored to the still and another to the cold plate. Six sintered silver heat exchangers and the mixing chamber are enclosed by the inner radiation shield and and the cold plate. The mixing chamber is made of Araldite and sits in the high field region of the magnet (9 T), while the heat exchangers are in the compensated low field region of the magnet. The radiation shields consist of a part made of copper plate in the zero field region and a part in the high field region, which is made of coil foil to reduce eddy current heating. The coil foil consists of 0.4 mm Cu wires glued on a Kapton foil with Stycast 1266. The foil is glued on a Kapton cylinder and a brass cap and copper flange are spot welded to it. The copper flange is screwed to the copper shield for good thermal contact. A coil (BII = 0.02 T/A) to sweep the
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Powerful dilution refrigerator: G.A. Vermeulen and G. Frossati Table 1 Physical properties of concentrated and diluted 3He
c
needed to design a dilution refrigerator: viscosity, q; heat conductivity, x; enthalpy, H; enthalpy along the phase separation curve,/-P; enthalpy at constant osmotic pressure, H°sin, and the mean Kapitza resistivity, rK~ = 2rK
DE
Concentrated
F
G H I
KJ L M N
R
T -2
5 x 10 - 8
7-.-2
r (WK -1 m - l ) a'a H(J mol-1) TM /'P (J mol-1) TM H°'m(J mo1-1)13
3.3 x 10-4 11.4 72
T -1
2.4 x 10-4
T -1
93 52
72 72 "/'-3
T -3
impedance but rather the area of the tube is the relevant parameter s-n°. This indicates that the flow in the tubular heat exchanger is diffusive. An explanation has been given by assuming mutual friction between the aHe quasipartides and the superfluid 4Henaal. Assuming diffusive flow, we expect no deviations from the linear relationship between power on the still and circulation rate up to 8 mmol s- ~ if we extrapolate a maximum flow rate of 800 l~mol s - l through a 2.5 mm diameter diluted channel 12. The sintered silver heat exchangers have been designed using the method described by Frossati et alfl "9. Essentially, this method consists of two steps, which will be summarized here:
U
V
2
Figure 4 Schematic vertical cross-section of the inner vacuum can and the dilution refrigerator. A, 3He pumping line; B, 1 K pot; C, umbrella to protect the still from backstreaming oil; D, space to collect the backstreaming oil (a conical plug to drain the oil is not shown); E, one of the eight small flanges for feed-throughs; F, IVC flange; G, copper plates connected to the 1 K pot for thermal anchoring; H, still with film burning device, heater and capacitive level gauge; I, flange for thermal anchoring of a radiation shield to 0.5 K; J, tubular heat exchanger; K, one of the four vespel rods to fix the 40 mK plate; L, first sintered silver heat exchanger; M, 40 mK plate (copper); N, channel to cool the 40 mK plate with the diluted stream; O, sintered silver heat exchangers; P, 0.5 K radiation shield; Q, 40 mK radiation shield; R, compensating windings of the magnet for a low field region; S, metal epoxy connection; T, exit tube of the mixing chamber (the input tube is not shown); U, mixing chamber; V, 9 T magnet
1.8 x 10 - 7
r~rn for: Brass/stainless steel (m2KW-1) 8.9 1.2 × 10-2 French silver powder (m2KW-1) e.a 8 x 10-2 Japanese silver powder (m2KW-1) a.9 28 T -2
o p Q
T
Diluted
11 (Pa s) a'a
given the design criteria (minimum temperature at optimum flow rate), estimate the total exchange area needed at a given heat leak; and optimize the size of the flow channels for a given length, so that the total heat leak due to axial conduction, Q~o., and viscous heating, Qvi~c, is minimized. If this heat leak, Qco. + Qvi~:, is larger than assumed in step 1, the length and the diameter of the channels have to be increased. (The exchanged.heat, Qexch, is assumed to be much larger than Q~o. + Qvi~:.)
To facilitate the design of heat exchangers, the quantities and formulae necessary to calculate the required exchangers are given in Table 1 and the Appendix. A cross-section of the heat exchangers is shown in Figure 5a. As compared to the former geometry 8"~, which is shown in Figure 5b, it has the advantage of having the capacity to leak test the pure 3He channel, before inserting
=
magnetic field has been wound on the inner coil foil and a gradient coil on the outer coil foil. Heat
_t
d
exchangers
The pure aHe channel of the continuous tubular heat exchanger is made by spiralling a brass tube (5.00 m x 3 m m x 3.5 mm) tightly around an 8 mm diameter metal rod to make it flatten. The spiral is put into a CuNi tube (1.00 m x 10.5 mm x 11 mm), which acts as the diluted channel. To make the heat exchanger as compact as possible it is filled with water, which is frozen with liquid nitrogen, to spiral it. The flow rate in a dilution refrigerator can be seriously limited by a capillary with a too small diameter in the diluted stream. Not the
142
1¢m
C r y o g e n i c s 1987 Vol 27 M a r c h
Co)
Cb)
Figure 5 Vertical cross-sections of the two models of sintered silver heat exchangers. (a) New design; (b) former design but scaled up to the size of (a). The concentrated channel is marked c and the diluted one d. The channels consist of annular boxes and lids made of 0.3 mm CuNi plate, which are closed by argon arc welds (denoted by small filled circles). The concentrated channel is fixed to the lid or the diluted channel by a few drops of tin solder. The hatched areas denote sintered silver
Powerful dilution refrigerator: G.A. Vermeulen and G. Frossati it in the external box (through which the diluted 3He flows). In addition, this design maximizes the thermal conduction between the helium and the sinter, while minimizing the amount of 3He used. Let us analyse how the heat is exchanged from the warmer concentrated phase to the diluted colder phase. In the new design the pure 3He channel is defined almost completely by the shape of the sinter. In the old design approximately one third of the sinter is directly in contact with the helium in the channels. The rest of the sinter makes contact through 0.3 mm thick slabs above and underneath the sinter. If we were to scale up this design to our dilution refrigerator, the slab would be 1 mm thick and the width of the slab 10 mm. If the heat resistance in the slabs is comparable to the total Kapitza resistance, the effective surface of the heat exchanger decreases. The Kapitza resistance for 1 cm length is given by RKap = 3.7/T2[K 3 W-l](RKap = rKm/O with o = 7.5 m 2 for 1 cm length) and the heat resistance due to conduction through the concentrated liquid by R .... = 7.5 x 105 T [ W -l] (Rco, = 0.25 A/Klwith A = 0.1 cm 2 for 1 cm length and I = 1 cm). Above 15 mK, Rco, is larger than RKap- In the high temperature heat exchangers, the height of the slabs in the older design cannot be < 1 mm, or this effect will become important. The total amount of 3He saved with the new design is 20-30 dm 3 NTP. The heat exchangers consist of annular metal boxes, which are made from 0.3 mm thick CuNi plate by deep drawing. A cross-section of a set of boxes and silver sinters is shown in Figure 6 and the dimensions are given in Table 2. Basically, there are three sizes of boxes and only the heigh, of the diluted channel can be changed by varying the depth of box, D. The exchange area and the amount of silver powder used for each heat exchanger are given in Table 3. The total amount of silver used is = 1.6 kg with a surface area of ~ 1000 m 2 at the concentrated side and 1300 m E at the diluted side. Because of the poor thermal conductivity of liquid 3He and 3He-4He mixtures at temperatures > 20 mK, in this temperature range we use the coarse 'French' powder (flakes of = 0.1 x 10 ttm),
°It
'
'i
ii W2
b - ~ - - ~1
,
C u Ni b o x C
C u Ni b o x D
f
It
tl
I I-',H~I I
I W2~ I
I
t
W 2 W 1
silver
sinter
D
silver
sinter
C
Figure 6
Definition of the sizes of the CuNi boxes and silver sinters of the heat exchangers. The dimensions are given in Table 2
which is presintered, crushed to 0.1 mm grains and then sintered again. Despite this precaution, experiments with only the first or the first and second sintered silver heat exchangers showed that a large part of the sinter in these exchangers is ineffective. A comparison of the temperatures reached with these exchangers with the theoretical predictions show that only = 50% of the sinter in the first and second heat exchangers is effective. However, this has a negligible effect on the performance of the dilution refrigerator. We have used brass dies to press the silver sinter. The dies are varnished with liquid Kapton to prevent sticking of the silver to the dies. First we press the sinter of
Table 2 Sizes of the boxes and sinters of the heat exchangers Boxes
Sinters
D
C
D
C
d
wl
w2
d
d~
d2
Wl
W2
0 1 2 3 4 5
8 8 8 8 10 11
13.5 15.0 17.0 17.0 24.0 26.0
31.0
6 6 6 6 8 9 9
4.0 4.0 4.0 4.0 8.7 9.5 9.5
13.8 13.8 13.8 13.8 17.6 20.0
11
6.6 6.6 6.6 6.6 8.6 11.0 11.0
4.0 4.0 4.0 4.0 2.3 2.5
6
8.6 8.6 8.6 8.6 11.0 14.2 14.2
2.5
20.0
12.4 12.4 12.4 12.4 14.4 17.6 17.6
r
W3
d
wI
w2
7 7 7 7 9 11 11
4 4 4 4 5 6 6
4.6 4.6 4.6 4.6 5.6 7.4 7.4
3.4 3.4 3.4 3.4 4.0 5.8 5.8
Table 3 Amount and brand of silver powder used in the heat exchangers. The surface areas are estimated (Japanese silver powder 2 m 2 g - l , French silver powder -~ 0.1 m 2 g - l ) Percentage
Weight (g)
Heat exchanger Continuous 0a 1b 2 3 4 5 6
Surface area (mz)
French
Japanese
Concentrated
Diluted
Concentrated
Diluted
Mean
0 100 100 80 50 0 0 0
0 0 0 20 50 100 100 100
0 62 62 64 64 120 150 150
0 79 83 83 83 155 195 195
0.047 62 6.2 64 100 240 300 300
0.055 7.9 8.3 83 130 310 390 390
0.051 7 7.2 73 115 275 345 345
aPresintered and crushed silver powder; concentrated channel decreased by a spacer, so that all concentrated liquid is within 0.5 mm of the sinter bpresintered and crushed silver powder; all liquid in the concentrated channel is within 1 mm of the sinter
C r y o g e n i c s 1 9 8 7 V o l 27 M a r c h
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Powerful dilution refrigerator: G.A. Vermeulen and G. Frossati the diluted side and sinter it slightly, to make it stick together, so we can remove the die. Then we put box C in the sinter and press the concentrated side. The silver powder is sintered for 40 min at 220°C in a H2 atmosphere. The concentrated channel is closed by argon-arc welding a CuNi ring on top of it. A few centimetres have been cut from the pure 3He box and the ends have been closed by silver soldering copper plates. Inlet and outlet tubes are fitted and the concentrated 3He channel is tin soldered to the lid of the diluted channel after making holes for the interconnecting tubes. This assembly is argon-arc welded to the outer box, which is also provided with silversoldered copper end pieces. The heat exchangers are mounted by tin soldering them together, with the cold plate between the first and second sintered silver heat exchanger. The cold plate, which reaches a temperature of = 40 mK at a circulation rate of 1 mmol s -~ provides for thermal anchoring of a radiation shield and the capillaries to operate a Pomeranchuk cell, and so on. It is made by machining a thick copper plate, leaving a channel for the diluted phase. Thermal contact between liquid helium and copper is made by a 1 mm thick silver sinter. The channel was closed by soldering an annular plate on top of it. The cold plate is mechanically fixed to the still by three cylindrical hollow Vespel rods. The whole heat exchanger assembly is reinforced by 2 mm diameter CuNi tubes.
Still The still is shown in Figure 7. The body of the still is made of stainless steel and consists of two parts. Leak-tightness between the two parts is provi.ded for by an indium joint. The lower part of the still is soldered to the continuous heat exchanger and the outer radiation shield can be suspended from its top. The upper part of the still is mounted to the 3He pumping line. The space around the tube, which protrudes into the pumping line is meant as a collector of backstreaming oil and has to be drained every few experiments. Inside the still there is a heater, a carbon resistance thermometer, a film burning device, a capacitive level meter and a heat exchanger for the incoming
r~z~" ....
/ ~
DC E F
Rgure 7 Vertical cross-section of the still. A, Umbrella to block backstreaming oil; B, copper tubes, tin soldered to the top of the still; C, flange to mount the still to the 3He pumping line; D, glass tube, sealed to the copper tube by a leak-tight copper glass connection (a film burning heater is wound around the glass tube with cyanoacrilate glue); E, stainless steel condensing surface; F, capacitive level gauge; G, still heater; H, flange to mount the 0.5 K radiation shield; I, heat exchanger to cool the incoming aHe in the still, which can be optionally bypassed; J, carbon resistance thermometer; K, entrance of the diluted stream from the tubular heat exchanger
144 Cryogenics 1987 Vol 27 March
3He. The still heater is a twined spiralled constantan wire with a total resistance of 380 f} and an area of ~ 500 cm 2. The heat exchanger is a 1.2 m long spiralled CuNi tube ( 1.0 x 1.4 mm diameter). The level gauge consists of two cylindrical brass tubes, 22 mm high, I mm apart and with a mean diameter of 115 ram. The capacitance is ~ 100 pF at 4.2 K. The increase in capacitance from empty to full is 4%. The estimated resolution of the level gauge is ~ 5 ptm (measuring the capacitance with an HP 4274 A LCR meter). The level gauge is very useful for keeping the optimum amount of helium in the dilution refrigerator while readjusting the ratio of 3He and 4He or detecting an eventual loss of helium. The film burning device shown is the final result of many versions. The exit of the still is a glass tube, fixed by means of a leak-tight copper glass connection to a copper tube, which is tin soldered to the top of the still. The film burning heater is wound on the glass tube (17 x 19 mm diameter) and a condensing stainless steel surface is mounted around the heater. The gap between the glass tube and the condensing surface is 1.2 mm. The outlet of the still is protected from backstreaming oil by an umbrella. We have tried several different film burning devices, which never worked properly when we applied power (maybe because of the large perimeter). Nevertheless, the glass tube reduces the total 4He film flow to ~ 17 p.mol s - ' . Assuming a film flow of ,~ 3.2 ~tmol s -~ per centimetre of perimeter for a clean surface ~5, a film flow of 16 ~tmol s - ' is to be expected.
Mixing chamber The mixing chamber is large (300 cm2), to provide enough space for different experiments. It is made of epoxy and can be readily adapted for different types of experiments. A version of the mixing chamber, as it is used with experiments to study polarized liquid 3He, is shown in Figure 8, together with the long connecting tubes needed to position the mixing chamber in the centre of the magnetic field. The mixing chamber and the tubes can be easily removed by means of two epoxy conical joints at the low temperature side of the heat exchangers. The epoxy cones are glued to CuNi tubes, which are soldered to the last heat exchanger. The differential thermal expansion between epoxy and CuNi is taken care of by the use of an intermediate joint of talc-filled epoxy which has a thermal expansion coefficient closer to that of metals than nonfilled epoxy. The tubes for the diluted and concentrated stream have an inner diameter of 25 and 8 ram, respectively. A carbon resistance thermometer, a cerium magnesium nitrate (CMN) mutual inductance thermometer and a heater are in the inlet tube close to the heat exchangers to monitor the heat leak to the mixing chamber. In the outlet tube there is a quartz capacitance thermometer ~6 close to the mixing chamber and a CMN mutual inductance thermometer close to the heat exchangers. The CMN thermometers are in the region of the magnet of almost zero field and measure approximately the temperature of the mixing chamber in the high field region. The quartz thermometer is field independent but has to be calibrated for every run. The phase separation interface is adjusted so that it is contained by the hydrostatic pressure within the region enclosed by the Kapton cylinder. There are feed-throughs for four capillaries, six low frequency coaxial cables for capacitance measurements, six coaxial cables for NMR and 24 NbTi in CuNi matrix superconducting wires for thermometry and heaters.
Powerful dilution refrigerator: G.A. Vermeulen and G. Frossati /:/coppeP post
tube to neat excha'ngeP5 w~t~ heaten, ClMN mutual inductance and caPbon resistance thePmometeP
--/,tin soldee
~ ] i- stycast .1 1 1266
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-
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:emale pin 5MA connector stycast 2850 FT 9ross connecting piece
expem mental space
0.3mm innen conductor teflon spaghetti Genman silveP (2xl mm 9) Figure 8
Mixing chamber and the entrance and exit tubes
Electrical wiring To facilitate the removal of the dilution refrigerator, all the electrical wires running down into the 4.2 K are provided with connectors, which are thermally anchored via gold plated copper plates to the 1 K pot. It takes < 1 h to disconnect the wires, unsolder the incoming 3He line and the capillaries for the Pomeranchuk cell and remove the whole dilution unit below the 1 K pot. The wiring consists of: 1 72 NbTi in copper matrix wires (50 Ixm diameter) coming down from room temperature to 1.5 K for low frequency bridges and heaters. They are divided into six groups each with a home-made 12 pin connector, which consists of 12 gold plated pins (male pins; no. 1009; female pins, no. 530, OEC, Thomas-Betts, Ansley) in an 8 mm diameter Araldite support. Figure 9a shows a home-made connector. The Araldite support is mounted to the bottom of a cylindrical T-shaped copper piece. The wires are fed through a hole in the top of the 'T', wound around the narrow copper rod, soldered to the connector and cast into epoxy. The top of the copper 'T' is thermally anchored to the 1 K pot. The wiring between these connectors and feed-throughs in the dilution refrigerator (still and mixing chamber) and auxiliary thermometers consists of NbTi in CuNi matrix wires (55 rtm diameter). The wires are protected by running them through a PVC spaghetti. All connectors and feed-throughs are homemade. For instance, the feed-throughs in the mixing chamber, which are shown in Figure 9b, are made by soldering two female connectors back to back, inserting them in an Araidite cylinder and filling the cylinder with Stycast 1266; 2 four NbTi in copper matrix wires with commercial
Figure 9 Feed-throughs and connectors. (a) Connector, which is thermally anchored to the 1 K pot; (b) leak-tight feed-through; (c) leak-tight ~- 50 ~ connector
silver plated connectors (type B3N and 53N, MultiContact A G Basel, Allschwill, Switzerland) thermally anchored to the 1 K pot for the N M R sweep coil and the gradient coil. The copper matrix has been etched away on a 10 cm length to decrease the heat leak to the 1 K pot; and 3 18 coaxial cables. Six of these are RVS coaxial cables (UT-85-SS* Uniform Tubes, Inc., Pennsylvania, USA) running down from a position at room temperature to inside the helium bath. Figure 9c shows a leak-tight 50 f/coaxial feed-through in the IVC made of a coaxial cable filled with Stycast 2850 FF instead of Teflon. Thermal anchoring to the 1 K pot is done by clamping a female SMA connector to the gold plated copper plate. Home-made coaxial cables (NbTi wire in a Teflon spaghetti through a 0.6 x 0.9 mm diameter capillary) run down from the 1 K pot to the mixing chamber. They are thermally anchored to the heat exchangers by tin solder and terminate in a homemade 12 pin connector. For each cable one pin is soldered to the signal line and one to the ground. The remaining 12 cables are meant for capacitance measurements, low loss and are not matched to 50 f/.
Operation
and performance
In low temperature physics it is important to be able to cool down the cryostat and warm it up quickly. This time is much increased in cases where there is a leak or another defect. Less than 24 h are needed to cool the mixing chamber from room temperature to < 5 mK with the *UT-20-SS coaxial cable was useless because of leaks in the stainless steel tubes
Cryogenics 1987 Vol 27 M a r c h
145
Powerful dilution refrigerator: G.A. Vermeulen and G. Frossa ti procedure we are following. Precooling to 77 K is carried out by filling the helium and nitrogen reservoir with liquid N2, having 1 bar of H2 exchange gas in the IVC and a few mbar of He exchange gas in the dilution refrigerator. It takes 3 h from the beginning of the nitrogen transfer for the cryostat to reach thermal equilibrium. We transfer liquid He after the removal of the nitrogen out of the helium reservoir and the usual leak tests, whilekeeping 1 cm 3 NTP 3He exchange gas in the IVC can (in total another 4 h). Normally, we pump the IVC for 8 h to remove the 3He exchange gas. Then we close the IVC, start the 1 K pot and condense all the helium needed for the dilution refrigerator through the 3He condensing line, while we pump the still with the Edwards boosters ( ~ 3 h). It takes only 2 h for the mixing chamber to reach 5 mK after the beginning of the circulation. Warming up to room temperature is done by carefully admitting H2 exchange gas in the OVC, which isolates the helium bath, until the remaining liquid 4He starts to evaporate. It takes a night to warm up from 4.2 K to room temperature. Care must be taken to use as little H2 as possible and to pump it away before admitting air into the cryostat. Figure 10 shows the temperature of the mixing chamber, Tree, as a function of circulation rate, h, in three different cases: 1, with the first sintered silver heat exchanger only. The minimum temperature is slightly below 12 mK. Comparison with the theoretical cooling power s'9 shows that only 50% of the sinter is effective; 2, with all the heat exchangers and long (25 cm) entrance and exit tubes between the heat exchangers and the mixing chamber; and 3, the same as for 2 above, but with short (3 cm) entrance and exit tubes. The lowest temperature has been reached with short entrance and exit tubes (Tm~ = 1.90 + 0.05 mK at h = 850 ~mol s-~). The minimum temperatures reached with long tubes are a few tenths of a millikelvin higher. The temperatures are measured with a commercial platinum pulsed NMR thermometer ( P L M - 3 , IT Corporation) and a homemade pulsed NMR apparatus. Note that for high circula-
tion rates, Tree increases approximately as h 3/2, instead of as h (References 10 and 11). This unexpected behaviour could be explained by a heat leak Q(h), which varies as h a. However, we have measured Q(h) using the enthalpy balance and Q(h) increases approximately as h 2 (Q(h) 10 -7 W at h = 1000 ~tmol s -1) instead of linearly with h as has been found previously 8.9. A second explanation could be, that not all of the sinter is effective due to the large thickness of the sinter and the poor thermal conductivity inside the pores of the sinter, at higher temperatures, as compared to the Kapitza resistance ~7. Especially at high circulation rates and hence higher temperatures, the effective surface can be decreased significantly, which might explain the fast increase of Tmc with h. Figure 11 shows the coolin~ power, Qmc, versus temperature at h = 1540 Ixmol s -1 and h = 2600 ~tmol s -]. The performance of the dilution refrigerator in an actual experiment is very well illustrated by the time necessary to precool a nuclear copper demagnetization stage. The demagnetization stage is located in the mixing chamber and consists of a container filled with 200 g of ultrafine (400/~,*) copper powder. The container, made of quartz, is open at the top and can be closed by an optically flat quartz lid, which is actuated by bellows. If the space between the container and the lid is so narrow that only superfluid can go through, this acts as a mechanical heat switch (details will be given elsewhere). The time necessary to precool the nuclear stage to 5 mK in a magnetic field of 9 T is ~ 8 h and is mainly limited by the specific heat of the nuclear copper stage and the Kapitza resist-
*IA = 0.1 nm I
I
I
}1
I
I
500 200 100
20-
~
.
.-
50 20
10-- s
~
S~
/
I U
7
E ___J
E "0
5
10 5
2 0.5 11
I
~
,
0.5
,
,I
1
I
2
~
,
I
5
,
, , ,I
I0
[m ol/s] Figure 10 Temperature of the mixing c h a m b e r as a function of circulation rate. The lowest t e m p e r a t u r e was 1.90 + 0.05 mK at a circulation rate of 850 limol s -~. O, El, Short entrance and exit tubes and long tubes, respectively; ~7, first sintered heat exchanger only. - - - , Theoretical curve (Equation (3A) of Appendix) with o = 7 m z and Q/h = 10 -3 J tool -1
146
Cryogenics
1987
Vol 27 March
0.2 0.1
I
2
5 10 20 Tmc (inK)
I
50 100
Figure 11 Cooling power of the dilution refrigerator as a function of t e m p e r a t u r e of the mixing c h a m b e r for different circulation rates. O, h = 1540 limol s - l ; ~7, h = 2600 I~mol s =1
Powerful dilution refrigerator: G.A. Vermeulen and G. Frossati ance between the liquid and the copper. This precooling time is an order of magnitude shorter than that obtained in a similar experiment with immersed refrigeran¢ 8't9. A Pomeranchuk cell was precooled below TA in a field of 25 mT and experiments are now proceeding to reach at least the superfluid A ~transition in a 9 T magnetic field. A PrNi5 nuclear demagnetization stage will be inserted inside the empty space left by the heat exchangers to provide ~ 0.5 mK in a high magnetic field.
Acknowledgements We wish to thank Professor W.J. Huiskamp for his important support during the early stages of our work. We are very much indebted to Professor F. Pobell for providing the 1 m diameter flanges of our cryostat, which could not be made in our laboratory. We would like to thank Mr J.P. Hemerik and Mr A.J. Kamper for their excellent technical support during the construction of the cryostat and dilution refrigerator. We also thank Mr A.J.J. Kuyt for his technical support and Mr P.P.M. Vreeburg for the capacitive quartz thermometer, film burning device and nuclear demagnetization cell. The contribution of G.J. D e k k e r , W. Griffioen, C.C. Kranenburg, P.J. Reijntjes and H.L. Stipdonk during the construction and testing of the dilution refrigerator is kindly acknowledged. This work has been supported by the Stichting voor Fundamenteel Onderzoek der Materie (FOM), which is financially supported by the Nederlandse Organisatie voor zuiver Wetenschappelijk Onderzoek (ZWO).
References 1 Castaing, B. and Nozii~res, P. J Phys (Paris) (1979) 40 257 2 Schumacher, G., Thoulouze, D., Castaing, B., Chabre, Y., Segransan, P. and Joffrin, J. J Phys Lett (Paris) (1979) 40 L-143 3 Chapellier,M., Frossati, G. and Rasmussen, F.B. Phys Rev Lett (1979) 42 904 4 F r ~ t i , G. J Phys (1980) 41 C7-95 5 Godfrin, H., Frossati, G., Greenberg, A.S., Hebral, B. and Thoulouze D. Phys Rev Lett (1980) 44 1695 6 Yu, C. and Anderson, P.W. Phys Lett (1979) "74A 236 7 Corruccini, L.R. and Osheroff, D.D. Phys Rev (1978) BI7 126 8 Frossati, G., Godfrin, H., Hebral, B., Schumacher, G. and Thoulouze, D. Proc UL T Hakone Symp The Physical Society of
Japan (1977) 205 9 Frossati, G. J Phys (1978) 39 C6-1578 10 Castelijns, C.A.M., Kuerten, J.G.M., de Waele, A.T.A.M. and Gijsman, H.M. Phys Rev (1985) B32 2286 11 Knerten, J.G.M., Castelijns, C.A.M., de Waele A.T.A.M. and Gijsraan, H.M. Phys Rev Left (1986) 56 2288 12 Schumacher, G. PhD Thesis Grenoble, France (1978) 13 Knerten, J.G.M., Castelijns, C.A.M., de Waele, A.T.A.M. and Gijsman, H.M. Cryogenics (1985) 25 419
14 Greywall, D.S. Phys Rev (1985) B29 4933 15 Wilks,J. The Properties of Liquid and Solid Helium Clarendon Press, UK (1967) 16 Reijntjes, P.J., van Rijswijk, W., Vermenlen, G.A. and Frossati, G. Rev Sci lnstrum (1986) 57 1413 17 Radebaugh, R., Siegwarth, J.D. and Holste, J.C. Proc ICEC 5 IPC Science and Technology Press, Guildford, UK (1974) 242 18 Dow, R.C.M., Guenault, A.M. and Pickett, G.R. J Low Temp Phys (1982) 47 477 19 Bradley, D.L, Guenanlt, A.M., Keith, V., Kennedy, C.J., Miller, I.E., Mussett, S.G., Pickett, G.R. and Pratt, W.P., Jr J Low Temp Phys (1984) 57 359
Appendix Formulae to design the heat exchangers of a dilution refrigerator (formulae 2-8 are found in References 8 and 9): rule of thumb for the diameter of the diluted flow channel of the tubular heat exchanger, Equation (A1); relation between the temperature of the mixing chamber, circulation rate, exchange area and external heat leak for a quadratic rKm (a good approximation is to assume Q/h to be a constant), Equation (A2); same as Equation (A2) but for a cubic rKm, Equation (A3); the ratio between the temperature of the diluted and the concentrated stream is assumed to be constant, Equation (A4); heat leak due to viscous flow for a cylindrical flow channel 01 = rh/T2), Equation (A5); heat leak due to axial conduction for a cylindrical flow channel (K = K~/T), Equation (A6); general dependence on the diameter, D, of Qvi~ + Q¢o, (A and B are defined by Equations (A5) and (A6)), Equation (A7); and the •optimum diameter, D, and optimum value of Qvis¢ + Q .... Equation (A8). d = (chf~- with c = 8 x 10 -3 m2s mol -~ for 1 m length (A1) Tmc = 28.7--~rKm + 0.11 (Q/h)"-
(A2)
O_/h
(A3)
TZm~= 6.73 ~rKm h + 0.0122 Tc = 2.86 To
(A4)
0visc = Z 4rh)[hVm]2 with Z = 128L [Th + TI] 2 ~D 4
(AS)
• Qco. = S Koln[Th/T,] with S = ~~ D :
(A6)
arise + 0 .... = A/D4 + BD2
(A7)
• Dop, = (2A/B) 1/6 and Q,,pt = 3 (2AB2)1/3
(A8)
Cryogenics 1987 Vol 27 March
147
The study of polarized liquid 3He and the not yet discovered superfluidity of 3He diluted in 4He pose interesting challenges in the field of low temperature physics. The most promising way to produce highly polarized liquid 3He, which requires at equilibrium conditions at least a field of the order of knTpttt = 220 T, appears to be rapid melting of highly polarized solid i-4. The highest polarization in solid 3He has been reached by precooling liquid 3He, which has a much lower polarization and converting it to solid using a Pomeranchuk cell. To obtain 70-80% polarization in the solid, a temperature of 2-3 mK is necessary in a field of 9 T. The solidification rate and hence the cooling power and the minimum temperature are seriously limited by the spin lattice relaxation in the liquid. Too high a solidification rate will deplete the magnetization of the liquid and underpolarized solid will be formed. This shows itself as a higher melting pressure than the equilibrium melting pressure. The maximum solidification rate is = 5% h -~ at temperatures of = 5 mK and in a field of 7 T 5. However, there is evidence that the spin lattice relaxation time, x~, is reduced by a few orders of magnitude if the liquid is below the superfluid A 2 transition 6. Even in the A~ phase, a considerable decrease in x] is to be expected, although only a decrease by a factor of three has been observed 7. The presence of the superfluid will reduce the temperature gradients and the solid will collect at the bottom of the cell. The exposed walls will contribute to the magnetic relaxation. Hence, our aim was to have a dilution refrigerator, which could precool a Pomeranchuk cell below the superfluid transition of liquid 3He in a high magnetic field. Cooling 3 H e J H e mixtures to a temperature where the 3He quasigas might become superfluid (possibly in the low microkeivin range) requires nuclear adiabatic demagnetization. In a 9 T magnetic field the maximum specific heat of copper nuclear spins occurs at ~ 5 mK. Precooling to a lower temperature gives no great advantage with *Present address: Laboratoire de Physique des Solides, B&timent 510, 91405 Orsay Cedex, France
0011-2275/87/030139-09$03.00 © 1987 Butterworth & Co (Publishers)Ltd
respect to cooling power and the minimum temperature reached after demagnetization. However, a fairly large cooling power is needed to precool a copper nuclear demagnetization stage in a reasonably short time to 5 mK in 9 T. The minimum temperature which can be reached in liquid 3He or a liquid 3He-4He solution is mainly determined by the ratio of the heat leak into the sample and the Kapitza resistance between liquid and refrigerant. Therefore, it is of crucial importance to minimize all known sources of heat leaks. A dilution refrigerator with a very low base temperature allows sample cells to be immersed directly in the liquid of the mixing chamber. A simple mechanical or superconducting heat switch can be used to isolate the sample cell from the mixing chamber. The heat leak from the liquid of a mixing chamber at 2 mK to a cell with an area of 10 cm 2 is only = 1 pW (the cell being considered at T = 0 K). In view of these (and other) experiments we have decided to construct two dilution refrigerators (one has already been in operation for a few years and the other is still being completed) with a base temperature of 2 mK at a circulation rate of 1 mmol s -1. To increase the circulation rate and hence the cooling power, we have added the capacity to pump with the two pumping systems on one single dilution refrigerator. In this way, a circulation rate of > 10 mmol s -1 can be sustained. The epoxy mixing chamber is located in the centre of a 9 T magnet and is very large (300 cm3), providing enough space for several types of experiments.
Experimental
room
As a precaution against RF radiation, we have constructed a shielded room. The walls, floor and ceiling of our experimental room are covered with 0.3 mm thick copper sheets, which are soldered together. Two special doors and 1 m 2 of RF isolated windows have been purchased from Siemens. The electrical power is supplied through four lines, which are heavily filtered (Siemens model B84206-D22-E2, nominal current and voltage: 25 A and
Cryogenics 1987 Vol 27 March
139
Powerful dilution refrigerator: G.A. Vermeulen and G. Frossati 380 V; the RF isolation is 90 dB up to 1 GHz). The computer, which is used to control some parts of the experiment (for instance NMR), generates a lot of RF noise. Therefore, we have placed it outside the shielded room together with its peripherals. We have limited ourselves to the use of the IEEE--488 bus for communication between the computer and the electronics inside the cage. This gives us the clean solution of decoupling the computer electrically from the experiment by means of two IEEE-488 converters, which transmit the signals through two optical fibres. Figure 1 shows a recorder trace of a carbon resistor at a temperature of < 10 mK with the door of the shielded room open and closed, which illustrates the effectiveness of the shielding. 1200 kg stainless steel reinforced concrete blocks on rubber dampers provide vibrational isolation of the cryostats. We have made provisions to mount air springs at the corner of the blocks in case the vibrational isolation is not sufficient. The cryostat is supported by a tripod of 200 mm diameter stainless steel tubes, which are screwed to one of the concrete blocks. These tubes can be eventually filled with sand or some viscous material to improve the damping or increase the mass, The total mass of concrete block, supports and cryostat is estimated to be 1700 kg. The tripod structure is very rigid. All pumping lines to the cryostat are vibrationally isolated by crossing two sets of compensated bellows, except for the 400 mm diameter 3He pumping lines, which are isolated by a tee with one set of very elastic plasma-welded bellows (Calorstat Industries, Dourdan, France). 3He-4He
gas handling Systems and pumps
Figure 2 shows a diagram of one of the gas handling systems. The 3He--4He gas handling systems and the pumps to circulate the "He are outside the shielded room. The storage tanks for the mixture to operate the dilution refrigerators consist of four vessels of 520 dm 3 and two of 154 dm 3. There is a separate set of pumps for each of the dilution refrigerators, but they can be set to work in parallel to increase the maximum flow rate in one refrigerator. With the two systems in parallel we can
>
IS, I
Rgure 2 Left part of the aHe--4He gas handling system (including one set of pumps and one of the cryostats). The system is symmetrical with respect to the dotted line and allows us to pump with two sets of pumps on one single cryostat. C, Cryostat; B, Edwards 18B4 booster pump; R, Edwards 1200 EH roots pump; A, Alcatel 2060H primary pump; P, small primary pump to clean the traps; Tt, Leybold Heraeus LH AF8-16 oil trap; T2, T3, home-made glass fibre filters; "1"4,carbon trap; "Is, palladium trap; St and $2, 520 dm 3 storage vessels; $3, 154 dm 3 storage vessel; M~, M2, Ma, manometers to monitor pressure in the storage vessels; M4, pressure monitor for the aHe pumping line; Ms, pressure sensor, which switches off A in case of overpressure (marked by a dashed line); Me, M7, pressure sensors, which open automatic valves in case of plugging of the traps (marked by dashed lines)
sustain a flow rate ~ 10 mmol s -~. A set of pumps consists of an Edwards 18B4 booster pump backed by an Edwards EH1200 roots pump and an Alcate12060H primary pump. The booster pumps are placed just outside the shielded room to decrease the length of the pumping lines as much as possible. Each booster pump is mounted on a 400 kg concrete block on rubber dampers for vibrational isolation. The backing pumps sit in another room on the other side of the corridor and are connected by ~ 10 m long, 100 mm diameter pumping lines. The backing pumps are mounted on one single concrete block on shock absorbers. The pumping lines between the booster and the roots pumps are rigidly anchored to the wall of the building and isolated from the pumps by bellows. As a precaution against plugging of the 3He condensing line we have put an oil trap (Leybold Heraeus model LH AF8-16) and a home-made filter of glass fibre (glass fibre FM004, Chemical Trading Co., London, UK) just after the primary pump. In addition, we have another identical charcoal filter, a trap and a palladium filter in the gas handling panel. Several litres of air are needed to saturate the charcoal traps and cause a blockage. The booster pumps are protected by thermal snap switches against a failure of the water cooling or high pressure on the pumping side. The primary pumps switch off automatically if the outlet pressure rises above 1.5 bar absolute pressure. The system is protected against plugging of the charcoal traps by valves, which are opened automatically if the pressure in front of the traps reaches = 1 bar.
Cryostat Figure I Recorder trace of a carbon resistor at T < 10 mK with the door of the shielded room open and then closed.
140
Cryogenics 1987 Vol 27 March
The maximum height of our experimental room, which is
Powerful dilution refrigerator: G.A. Vermeulen and G. Frossafi on the second floor, is 3.30 m. Between our floor and the ceiling of the floor below us, there is 1.20 m space for air conditioning, supplies for cooling water, compressed air and the central heating system, which made it possible to have 1.20 m deep holes in the floor. The maximum width of those holes is limited to 37 cm by parallel stretched beams. The cryostat was designed in view of the restrictions of the room and is shown in Figure 3. We have access to the mixing chamber by removing the tails of the outer vacuum can (OVC), nitrogen shield, helium can and inner vacuum can (IVC). The upper part of the cryostat which has an outer diameter of 0.8 m and contains the nitrogen reservoir and most of the volume of the helium reservoir, always stays in place. Except for a few current leads to operate the magnet and the liquid helium level gauge all the electrical wiring, capillaries, transfer tubes and connections to the low temperature valves enter the cryostat from the side. Flanges, which are demountable by means of indium joints, provide for leak-tight feed-throughs in the inner vacuum can as well as the outer vacuum can. All space at the top of the cryostat has been reserved for the 3He pumping line. The 3He pumping line is part of a conical concentric pumping line-heat exchanger assembly, which consists of three cones with a length of 1 m. At the top of the cryostat the diameter of the 3He pumping line is 300 mm and just above the still, 80 mm. The second cone encloses the SHe condensing line. Two spirals of 0.5 mm thick stainless steel tape have been spot-welded between the inner and the
A
B
't [ '= "i>>>x<<< "
II
--- ,l~>X<
m
LI
Figure 3 Schematic vertical cross-section of the cryostat. A, aHe pumping line; B, 1 K pot pumping line; C, outer vacuum can (OVC); D, liquid nitrogen reservoir; E, baffles inside the aHe pumping line; F, helium reservoir; G, removable tail of the OVC; H, removable tail of the nitrogen shield; I, removable tail of the nitrogen reservoir; J, inner vacuum can (IVC)
second cone. This increases the mechanical strength and the incoming 3He is forced down the spiral, so that the heat contact with the walls is improved. The 2 cm wide space between the outer cone and the second cone is the pumping line of the 1 K pot. Many rings of perforated copper plate have been soldered on the inside of the second cone to fulfil three purposes: 1, to act as radiation shields; 2, to improve the heat exchange between the incoming 3He gas and the outgoing 4He gas; and 3, to provide extra support for the outer cone (all cones are made out of 0.6 mm thick stainless steel plate). Inside the 3He pumping line there are four baffles which serve similar purposes. The useful helium charge above the inner vacuum can is = 80 dm 3 and the evaporation rate is between 1.4 and 1.8 dm 3 h -l. Thus, the time between two helium transfers is two days.
Dilution
refrigerator
The dilution refrigerator is an enlarged and improved version of the type developed by Frossati and coworkers 8"9. Figure 4 shows a vertical cross-section of the dilution refrigerator, 1 K pot, vacuum can and magnet. Before describing the heat exchangers, still chamber and mixing chamber in more detail, we will give an overview of all parts inside the vacuum can. The whole system hangs from the concentric 3He pumping line-heat exchanger assembly. From the conical heat exchanger the 3He enters a CuNi capillary (5 m x 1.0 mm x 1.5 mm) in the 3He pumping line just above the still, where it is further cooled before it enters a heat exchanger of similar size in the 1 K pot. The still is mounted to the bottom of the pumping line. The whole system of the vacuum can, 1 K pot and still is quite easily removed and demounted by means of indium joints. Eight flanges on top of the large flange of the inner vacuum can are reserved for feed-throughs. Gold plated copper plates are screwed to the bottom of the 1 K pot parallel to the large flange for thermal anchoring of the wires. An impedance, which is adjustable when the cryostat is open, is mounted on the still to condense the incoming SHe. This impedance is optionally bypassed by a valve, which is actuated from outside the cryostat. Opening the valve reduces the time needed to condense the 1500 dm 3 He gas used to operate the dilution refrigerator to ~ 2 h. Before entering the continuous tubular heat exchanger, the 3He may be optionally directed through a heat exchanger in the still. No significant improvement is found when the heat exchanger in the still is used. Below the still are the continuous tubular heat exchanger, the first sintered silver heat exchanger and a cold plate for thermal anchoring. One thermal radiation shield is anchored to the still and another to the cold plate. Six sintered silver heat exchangers and the mixing chamber are enclosed by the inner radiation shield and and the cold plate. The mixing chamber is made of Araldite and sits in the high field region of the magnet (9 T), while the heat exchangers are in the compensated low field region of the magnet. The radiation shields consist of a part made of copper plate in the zero field region and a part in the high field region, which is made of coil foil to reduce eddy current heating. The coil foil consists of 0.4 mm Cu wires glued on a Kapton foil with Stycast 1266. The foil is glued on a Kapton cylinder and a brass cap and copper flange are spot welded to it. The copper flange is screwed to the copper shield for good thermal contact. A coil (BII = 0.02 T/A) to sweep the
C r y o g e n i c s 1987 Vol 27 M a r c h
141
Powerful dilution refrigerator: G.A. Vermeulen and G. Frossati Table 1 Physical properties of concentrated and diluted 3He
c
needed to design a dilution refrigerator: viscosity, q; heat conductivity, x; enthalpy, H; enthalpy along the phase separation curve,/-P; enthalpy at constant osmotic pressure, H°sin, and the mean Kapitza resistivity, rK~ = 2rK
DE
Concentrated
F
G H I
KJ L M N
R
T -2
5 x 10 - 8
7-.-2
r (WK -1 m - l ) a'a H(J mol-1) TM /'P (J mol-1) TM H°'m(J mo1-1)13
3.3 x 10-4 11.4 72
T -1
2.4 x 10-4
T -1
93 52
72 72 "/'-3
T -3
impedance but rather the area of the tube is the relevant parameter s-n°. This indicates that the flow in the tubular heat exchanger is diffusive. An explanation has been given by assuming mutual friction between the aHe quasipartides and the superfluid 4Henaal. Assuming diffusive flow, we expect no deviations from the linear relationship between power on the still and circulation rate up to 8 mmol s- ~ if we extrapolate a maximum flow rate of 800 l~mol s - l through a 2.5 mm diameter diluted channel 12. The sintered silver heat exchangers have been designed using the method described by Frossati et alfl "9. Essentially, this method consists of two steps, which will be summarized here:
U
V
2
Figure 4 Schematic vertical cross-section of the inner vacuum can and the dilution refrigerator. A, 3He pumping line; B, 1 K pot; C, umbrella to protect the still from backstreaming oil; D, space to collect the backstreaming oil (a conical plug to drain the oil is not shown); E, one of the eight small flanges for feed-throughs; F, IVC flange; G, copper plates connected to the 1 K pot for thermal anchoring; H, still with film burning device, heater and capacitive level gauge; I, flange for thermal anchoring of a radiation shield to 0.5 K; J, tubular heat exchanger; K, one of the four vespel rods to fix the 40 mK plate; L, first sintered silver heat exchanger; M, 40 mK plate (copper); N, channel to cool the 40 mK plate with the diluted stream; O, sintered silver heat exchangers; P, 0.5 K radiation shield; Q, 40 mK radiation shield; R, compensating windings of the magnet for a low field region; S, metal epoxy connection; T, exit tube of the mixing chamber (the input tube is not shown); U, mixing chamber; V, 9 T magnet
1.8 x 10 - 7
r~rn for: Brass/stainless steel (m2KW-1) 8.9 1.2 × 10-2 French silver powder (m2KW-1) e.a 8 x 10-2 Japanese silver powder (m2KW-1) a.9 28 T -2
o p Q
T
Diluted
11 (Pa s) a'a
given the design criteria (minimum temperature at optimum flow rate), estimate the total exchange area needed at a given heat leak; and optimize the size of the flow channels for a given length, so that the total heat leak due to axial conduction, Q~o., and viscous heating, Qvi~c, is minimized. If this heat leak, Qco. + Qvi~:, is larger than assumed in step 1, the length and the diameter of the channels have to be increased. (The exchanged.heat, Qexch, is assumed to be much larger than Q~o. + Qvi~:.)
To facilitate the design of heat exchangers, the quantities and formulae necessary to calculate the required exchangers are given in Table 1 and the Appendix. A cross-section of the heat exchangers is shown in Figure 5a. As compared to the former geometry 8"~, which is shown in Figure 5b, it has the advantage of having the capacity to leak test the pure 3He channel, before inserting
=
magnetic field has been wound on the inner coil foil and a gradient coil on the outer coil foil. Heat
_t
d
exchangers
The pure aHe channel of the continuous tubular heat exchanger is made by spiralling a brass tube (5.00 m x 3 m m x 3.5 mm) tightly around an 8 mm diameter metal rod to make it flatten. The spiral is put into a CuNi tube (1.00 m x 10.5 mm x 11 mm), which acts as the diluted channel. To make the heat exchanger as compact as possible it is filled with water, which is frozen with liquid nitrogen, to spiral it. The flow rate in a dilution refrigerator can be seriously limited by a capillary with a too small diameter in the diluted stream. Not the
142
1¢m
C r y o g e n i c s 1987 Vol 27 M a r c h
Co)
Cb)
Figure 5 Vertical cross-sections of the two models of sintered silver heat exchangers. (a) New design; (b) former design but scaled up to the size of (a). The concentrated channel is marked c and the diluted one d. The channels consist of annular boxes and lids made of 0.3 mm CuNi plate, which are closed by argon arc welds (denoted by small filled circles). The concentrated channel is fixed to the lid or the diluted channel by a few drops of tin solder. The hatched areas denote sintered silver
Powerful dilution refrigerator: G.A. Vermeulen and G. Frossati it in the external box (through which the diluted 3He flows). In addition, this design maximizes the thermal conduction between the helium and the sinter, while minimizing the amount of 3He used. Let us analyse how the heat is exchanged from the warmer concentrated phase to the diluted colder phase. In the new design the pure 3He channel is defined almost completely by the shape of the sinter. In the old design approximately one third of the sinter is directly in contact with the helium in the channels. The rest of the sinter makes contact through 0.3 mm thick slabs above and underneath the sinter. If we were to scale up this design to our dilution refrigerator, the slab would be 1 mm thick and the width of the slab 10 mm. If the heat resistance in the slabs is comparable to the total Kapitza resistance, the effective surface of the heat exchanger decreases. The Kapitza resistance for 1 cm length is given by RKap = 3.7/T2[K 3 W-l](RKap = rKm/O with o = 7.5 m 2 for 1 cm length) and the heat resistance due to conduction through the concentrated liquid by R .... = 7.5 x 105 T [ W -l] (Rco, = 0.25 A/Klwith A = 0.1 cm 2 for 1 cm length and I = 1 cm). Above 15 mK, Rco, is larger than RKap- In the high temperature heat exchangers, the height of the slabs in the older design cannot be < 1 mm, or this effect will become important. The total amount of 3He saved with the new design is 20-30 dm 3 NTP. The heat exchangers consist of annular metal boxes, which are made from 0.3 mm thick CuNi plate by deep drawing. A cross-section of a set of boxes and silver sinters is shown in Figure 6 and the dimensions are given in Table 2. Basically, there are three sizes of boxes and only the heigh, of the diluted channel can be changed by varying the depth of box, D. The exchange area and the amount of silver powder used for each heat exchanger are given in Table 3. The total amount of silver used is = 1.6 kg with a surface area of ~ 1000 m 2 at the concentrated side and 1300 m E at the diluted side. Because of the poor thermal conductivity of liquid 3He and 3He-4He mixtures at temperatures > 20 mK, in this temperature range we use the coarse 'French' powder (flakes of = 0.1 x 10 ttm),
°It
'
'i
ii W2
b - ~ - - ~1
,
C u Ni b o x C
C u Ni b o x D
f
It
tl
I I-',H~I I
I W2~ I
I
t
W 2 W 1
silver
sinter
D
silver
sinter
C
Figure 6
Definition of the sizes of the CuNi boxes and silver sinters of the heat exchangers. The dimensions are given in Table 2
which is presintered, crushed to 0.1 mm grains and then sintered again. Despite this precaution, experiments with only the first or the first and second sintered silver heat exchangers showed that a large part of the sinter in these exchangers is ineffective. A comparison of the temperatures reached with these exchangers with the theoretical predictions show that only = 50% of the sinter in the first and second heat exchangers is effective. However, this has a negligible effect on the performance of the dilution refrigerator. We have used brass dies to press the silver sinter. The dies are varnished with liquid Kapton to prevent sticking of the silver to the dies. First we press the sinter of
Table 2 Sizes of the boxes and sinters of the heat exchangers Boxes
Sinters
D
C
D
C
d
wl
w2
d
d~
d2
Wl
W2
0 1 2 3 4 5
8 8 8 8 10 11
13.5 15.0 17.0 17.0 24.0 26.0
31.0
6 6 6 6 8 9 9
4.0 4.0 4.0 4.0 8.7 9.5 9.5
13.8 13.8 13.8 13.8 17.6 20.0
11
6.6 6.6 6.6 6.6 8.6 11.0 11.0
4.0 4.0 4.0 4.0 2.3 2.5
6
8.6 8.6 8.6 8.6 11.0 14.2 14.2
2.5
20.0
12.4 12.4 12.4 12.4 14.4 17.6 17.6
r
W3
d
wI
w2
7 7 7 7 9 11 11
4 4 4 4 5 6 6
4.6 4.6 4.6 4.6 5.6 7.4 7.4
3.4 3.4 3.4 3.4 4.0 5.8 5.8
Table 3 Amount and brand of silver powder used in the heat exchangers. The surface areas are estimated (Japanese silver powder 2 m 2 g - l , French silver powder -~ 0.1 m 2 g - l ) Percentage
Weight (g)
Heat exchanger Continuous 0a 1b 2 3 4 5 6
Surface area (mz)
French
Japanese
Concentrated
Diluted
Concentrated
Diluted
Mean
0 100 100 80 50 0 0 0
0 0 0 20 50 100 100 100
0 62 62 64 64 120 150 150
0 79 83 83 83 155 195 195
0.047 62 6.2 64 100 240 300 300
0.055 7.9 8.3 83 130 310 390 390
0.051 7 7.2 73 115 275 345 345
aPresintered and crushed silver powder; concentrated channel decreased by a spacer, so that all concentrated liquid is within 0.5 mm of the sinter bpresintered and crushed silver powder; all liquid in the concentrated channel is within 1 mm of the sinter
C r y o g e n i c s 1 9 8 7 V o l 27 M a r c h
143
Powerful dilution refrigerator: G.A. Vermeulen and G. Frossati the diluted side and sinter it slightly, to make it stick together, so we can remove the die. Then we put box C in the sinter and press the concentrated side. The silver powder is sintered for 40 min at 220°C in a H2 atmosphere. The concentrated channel is closed by argon-arc welding a CuNi ring on top of it. A few centimetres have been cut from the pure 3He box and the ends have been closed by silver soldering copper plates. Inlet and outlet tubes are fitted and the concentrated 3He channel is tin soldered to the lid of the diluted channel after making holes for the interconnecting tubes. This assembly is argon-arc welded to the outer box, which is also provided with silversoldered copper end pieces. The heat exchangers are mounted by tin soldering them together, with the cold plate between the first and second sintered silver heat exchanger. The cold plate, which reaches a temperature of = 40 mK at a circulation rate of 1 mmol s -~ provides for thermal anchoring of a radiation shield and the capillaries to operate a Pomeranchuk cell, and so on. It is made by machining a thick copper plate, leaving a channel for the diluted phase. Thermal contact between liquid helium and copper is made by a 1 mm thick silver sinter. The channel was closed by soldering an annular plate on top of it. The cold plate is mechanically fixed to the still by three cylindrical hollow Vespel rods. The whole heat exchanger assembly is reinforced by 2 mm diameter CuNi tubes.
Still The still is shown in Figure 7. The body of the still is made of stainless steel and consists of two parts. Leak-tightness between the two parts is provi.ded for by an indium joint. The lower part of the still is soldered to the continuous heat exchanger and the outer radiation shield can be suspended from its top. The upper part of the still is mounted to the 3He pumping line. The space around the tube, which protrudes into the pumping line is meant as a collector of backstreaming oil and has to be drained every few experiments. Inside the still there is a heater, a carbon resistance thermometer, a film burning device, a capacitive level meter and a heat exchanger for the incoming
r~z~" ....
/ ~
DC E F
Rgure 7 Vertical cross-section of the still. A, Umbrella to block backstreaming oil; B, copper tubes, tin soldered to the top of the still; C, flange to mount the still to the 3He pumping line; D, glass tube, sealed to the copper tube by a leak-tight copper glass connection (a film burning heater is wound around the glass tube with cyanoacrilate glue); E, stainless steel condensing surface; F, capacitive level gauge; G, still heater; H, flange to mount the 0.5 K radiation shield; I, heat exchanger to cool the incoming aHe in the still, which can be optionally bypassed; J, carbon resistance thermometer; K, entrance of the diluted stream from the tubular heat exchanger
144 Cryogenics 1987 Vol 27 March
3He. The still heater is a twined spiralled constantan wire with a total resistance of 380 f} and an area of ~ 500 cm 2. The heat exchanger is a 1.2 m long spiralled CuNi tube ( 1.0 x 1.4 mm diameter). The level gauge consists of two cylindrical brass tubes, 22 mm high, I mm apart and with a mean diameter of 115 ram. The capacitance is ~ 100 pF at 4.2 K. The increase in capacitance from empty to full is 4%. The estimated resolution of the level gauge is ~ 5 ptm (measuring the capacitance with an HP 4274 A LCR meter). The level gauge is very useful for keeping the optimum amount of helium in the dilution refrigerator while readjusting the ratio of 3He and 4He or detecting an eventual loss of helium. The film burning device shown is the final result of many versions. The exit of the still is a glass tube, fixed by means of a leak-tight copper glass connection to a copper tube, which is tin soldered to the top of the still. The film burning heater is wound on the glass tube (17 x 19 mm diameter) and a condensing stainless steel surface is mounted around the heater. The gap between the glass tube and the condensing surface is 1.2 mm. The outlet of the still is protected from backstreaming oil by an umbrella. We have tried several different film burning devices, which never worked properly when we applied power (maybe because of the large perimeter). Nevertheless, the glass tube reduces the total 4He film flow to ~ 17 p.mol s - ' . Assuming a film flow of ,~ 3.2 ~tmol s -~ per centimetre of perimeter for a clean surface ~5, a film flow of 16 ~tmol s - ' is to be expected.
Mixing chamber The mixing chamber is large (300 cm2), to provide enough space for different experiments. It is made of epoxy and can be readily adapted for different types of experiments. A version of the mixing chamber, as it is used with experiments to study polarized liquid 3He, is shown in Figure 8, together with the long connecting tubes needed to position the mixing chamber in the centre of the magnetic field. The mixing chamber and the tubes can be easily removed by means of two epoxy conical joints at the low temperature side of the heat exchangers. The epoxy cones are glued to CuNi tubes, which are soldered to the last heat exchanger. The differential thermal expansion between epoxy and CuNi is taken care of by the use of an intermediate joint of talc-filled epoxy which has a thermal expansion coefficient closer to that of metals than nonfilled epoxy. The tubes for the diluted and concentrated stream have an inner diameter of 25 and 8 ram, respectively. A carbon resistance thermometer, a cerium magnesium nitrate (CMN) mutual inductance thermometer and a heater are in the inlet tube close to the heat exchangers to monitor the heat leak to the mixing chamber. In the outlet tube there is a quartz capacitance thermometer ~6 close to the mixing chamber and a CMN mutual inductance thermometer close to the heat exchangers. The CMN thermometers are in the region of the magnet of almost zero field and measure approximately the temperature of the mixing chamber in the high field region. The quartz thermometer is field independent but has to be calibrated for every run. The phase separation interface is adjusted so that it is contained by the hydrostatic pressure within the region enclosed by the Kapton cylinder. There are feed-throughs for four capillaries, six low frequency coaxial cables for capacitance measurements, six coaxial cables for NMR and 24 NbTi in CuNi matrix superconducting wires for thermometry and heaters.
Powerful dilution refrigerator: G.A. Vermeulen and G. Frossati /:/coppeP post
tube to neat excha'ngeP5 w~t~ heaten, ClMN mutual inductance and caPbon resistance thePmometeP
--/,tin soldee
~ ] i- stycast .1 1 1266
,/
-tube to heat exchangers w i t h CMN m u t u a l inductance and capbon Pesistance thePmometeP
-
1 cm
!
glass t h e P m o m e t e r
a)
(b/
:~flon piece to )rotect the female pin
! cm
lcm
:emale pin 5MA connector stycast 2850 FT 9ross connecting piece
expem mental space
0.3mm innen conductor teflon spaghetti Genman silveP (2xl mm 9) Figure 8
Mixing chamber and the entrance and exit tubes
Electrical wiring To facilitate the removal of the dilution refrigerator, all the electrical wires running down into the 4.2 K are provided with connectors, which are thermally anchored via gold plated copper plates to the 1 K pot. It takes < 1 h to disconnect the wires, unsolder the incoming 3He line and the capillaries for the Pomeranchuk cell and remove the whole dilution unit below the 1 K pot. The wiring consists of: 1 72 NbTi in copper matrix wires (50 Ixm diameter) coming down from room temperature to 1.5 K for low frequency bridges and heaters. They are divided into six groups each with a home-made 12 pin connector, which consists of 12 gold plated pins (male pins; no. 1009; female pins, no. 530, OEC, Thomas-Betts, Ansley) in an 8 mm diameter Araldite support. Figure 9a shows a home-made connector. The Araldite support is mounted to the bottom of a cylindrical T-shaped copper piece. The wires are fed through a hole in the top of the 'T', wound around the narrow copper rod, soldered to the connector and cast into epoxy. The top of the copper 'T' is thermally anchored to the 1 K pot. The wiring between these connectors and feed-throughs in the dilution refrigerator (still and mixing chamber) and auxiliary thermometers consists of NbTi in CuNi matrix wires (55 rtm diameter). The wires are protected by running them through a PVC spaghetti. All connectors and feed-throughs are homemade. For instance, the feed-throughs in the mixing chamber, which are shown in Figure 9b, are made by soldering two female connectors back to back, inserting them in an Araidite cylinder and filling the cylinder with Stycast 1266; 2 four NbTi in copper matrix wires with commercial
Figure 9 Feed-throughs and connectors. (a) Connector, which is thermally anchored to the 1 K pot; (b) leak-tight feed-through; (c) leak-tight ~- 50 ~ connector
silver plated connectors (type B3N and 53N, MultiContact A G Basel, Allschwill, Switzerland) thermally anchored to the 1 K pot for the N M R sweep coil and the gradient coil. The copper matrix has been etched away on a 10 cm length to decrease the heat leak to the 1 K pot; and 3 18 coaxial cables. Six of these are RVS coaxial cables (UT-85-SS* Uniform Tubes, Inc., Pennsylvania, USA) running down from a position at room temperature to inside the helium bath. Figure 9c shows a leak-tight 50 f/coaxial feed-through in the IVC made of a coaxial cable filled with Stycast 2850 FF instead of Teflon. Thermal anchoring to the 1 K pot is done by clamping a female SMA connector to the gold plated copper plate. Home-made coaxial cables (NbTi wire in a Teflon spaghetti through a 0.6 x 0.9 mm diameter capillary) run down from the 1 K pot to the mixing chamber. They are thermally anchored to the heat exchangers by tin solder and terminate in a homemade 12 pin connector. For each cable one pin is soldered to the signal line and one to the ground. The remaining 12 cables are meant for capacitance measurements, low loss and are not matched to 50 f/.
Operation
and performance
In low temperature physics it is important to be able to cool down the cryostat and warm it up quickly. This time is much increased in cases where there is a leak or another defect. Less than 24 h are needed to cool the mixing chamber from room temperature to < 5 mK with the *UT-20-SS coaxial cable was useless because of leaks in the stainless steel tubes
Cryogenics 1987 Vol 27 M a r c h
145
Powerful dilution refrigerator: G.A. Vermeulen and G. Frossa ti procedure we are following. Precooling to 77 K is carried out by filling the helium and nitrogen reservoir with liquid N2, having 1 bar of H2 exchange gas in the IVC and a few mbar of He exchange gas in the dilution refrigerator. It takes 3 h from the beginning of the nitrogen transfer for the cryostat to reach thermal equilibrium. We transfer liquid He after the removal of the nitrogen out of the helium reservoir and the usual leak tests, whilekeeping 1 cm 3 NTP 3He exchange gas in the IVC can (in total another 4 h). Normally, we pump the IVC for 8 h to remove the 3He exchange gas. Then we close the IVC, start the 1 K pot and condense all the helium needed for the dilution refrigerator through the 3He condensing line, while we pump the still with the Edwards boosters ( ~ 3 h). It takes only 2 h for the mixing chamber to reach 5 mK after the beginning of the circulation. Warming up to room temperature is done by carefully admitting H2 exchange gas in the OVC, which isolates the helium bath, until the remaining liquid 4He starts to evaporate. It takes a night to warm up from 4.2 K to room temperature. Care must be taken to use as little H2 as possible and to pump it away before admitting air into the cryostat. Figure 10 shows the temperature of the mixing chamber, Tree, as a function of circulation rate, h, in three different cases: 1, with the first sintered silver heat exchanger only. The minimum temperature is slightly below 12 mK. Comparison with the theoretical cooling power s'9 shows that only 50% of the sinter is effective; 2, with all the heat exchangers and long (25 cm) entrance and exit tubes between the heat exchangers and the mixing chamber; and 3, the same as for 2 above, but with short (3 cm) entrance and exit tubes. The lowest temperature has been reached with short entrance and exit tubes (Tm~ = 1.90 + 0.05 mK at h = 850 ~mol s-~). The minimum temperatures reached with long tubes are a few tenths of a millikelvin higher. The temperatures are measured with a commercial platinum pulsed NMR thermometer ( P L M - 3 , IT Corporation) and a homemade pulsed NMR apparatus. Note that for high circula-
tion rates, Tree increases approximately as h 3/2, instead of as h (References 10 and 11). This unexpected behaviour could be explained by a heat leak Q(h), which varies as h a. However, we have measured Q(h) using the enthalpy balance and Q(h) increases approximately as h 2 (Q(h) 10 -7 W at h = 1000 ~tmol s -1) instead of linearly with h as has been found previously 8.9. A second explanation could be, that not all of the sinter is effective due to the large thickness of the sinter and the poor thermal conductivity inside the pores of the sinter, at higher temperatures, as compared to the Kapitza resistance ~7. Especially at high circulation rates and hence higher temperatures, the effective surface can be decreased significantly, which might explain the fast increase of Tmc with h. Figure 11 shows the coolin~ power, Qmc, versus temperature at h = 1540 Ixmol s -1 and h = 2600 ~tmol s -]. The performance of the dilution refrigerator in an actual experiment is very well illustrated by the time necessary to precool a nuclear copper demagnetization stage. The demagnetization stage is located in the mixing chamber and consists of a container filled with 200 g of ultrafine (400/~,*) copper powder. The container, made of quartz, is open at the top and can be closed by an optically flat quartz lid, which is actuated by bellows. If the space between the container and the lid is so narrow that only superfluid can go through, this acts as a mechanical heat switch (details will be given elsewhere). The time necessary to precool the nuclear stage to 5 mK in a magnetic field of 9 T is ~ 8 h and is mainly limited by the specific heat of the nuclear copper stage and the Kapitza resist-
*IA = 0.1 nm I
I
I
}1
I
I
500 200 100
20-
~
.
.-
50 20
10-- s
~
S~
/
I U
7
E ___J
E "0
5
10 5
2 0.5 11
I
~
,
0.5
,
,I
1
I
2
~
,
I
5
,
, , ,I
I0
[m ol/s] Figure 10 Temperature of the mixing c h a m b e r as a function of circulation rate. The lowest t e m p e r a t u r e was 1.90 + 0.05 mK at a circulation rate of 850 limol s -~. O, El, Short entrance and exit tubes and long tubes, respectively; ~7, first sintered heat exchanger only. - - - , Theoretical curve (Equation (3A) of Appendix) with o = 7 m z and Q/h = 10 -3 J tool -1
146
Cryogenics
1987
Vol 27 March
0.2 0.1
I
2
5 10 20 Tmc (inK)
I
50 100
Figure 11 Cooling power of the dilution refrigerator as a function of t e m p e r a t u r e of the mixing c h a m b e r for different circulation rates. O, h = 1540 limol s - l ; ~7, h = 2600 I~mol s =1
Powerful dilution refrigerator: G.A. Vermeulen and G. Frossati ance between the liquid and the copper. This precooling time is an order of magnitude shorter than that obtained in a similar experiment with immersed refrigeran¢ 8't9. A Pomeranchuk cell was precooled below TA in a field of 25 mT and experiments are now proceeding to reach at least the superfluid A ~transition in a 9 T magnetic field. A PrNi5 nuclear demagnetization stage will be inserted inside the empty space left by the heat exchangers to provide ~ 0.5 mK in a high magnetic field.
Acknowledgements We wish to thank Professor W.J. Huiskamp for his important support during the early stages of our work. We are very much indebted to Professor F. Pobell for providing the 1 m diameter flanges of our cryostat, which could not be made in our laboratory. We would like to thank Mr J.P. Hemerik and Mr A.J. Kamper for their excellent technical support during the construction of the cryostat and dilution refrigerator. We also thank Mr A.J.J. Kuyt for his technical support and Mr P.P.M. Vreeburg for the capacitive quartz thermometer, film burning device and nuclear demagnetization cell. The contribution of G.J. D e k k e r , W. Griffioen, C.C. Kranenburg, P.J. Reijntjes and H.L. Stipdonk during the construction and testing of the dilution refrigerator is kindly acknowledged. This work has been supported by the Stichting voor Fundamenteel Onderzoek der Materie (FOM), which is financially supported by the Nederlandse Organisatie voor zuiver Wetenschappelijk Onderzoek (ZWO).
References 1 Castaing, B. and Nozii~res, P. J Phys (Paris) (1979) 40 257 2 Schumacher, G., Thoulouze, D., Castaing, B., Chabre, Y., Segransan, P. and Joffrin, J. J Phys Lett (Paris) (1979) 40 L-143 3 Chapellier,M., Frossati, G. and Rasmussen, F.B. Phys Rev Lett (1979) 42 904 4 F r ~ t i , G. J Phys (1980) 41 C7-95 5 Godfrin, H., Frossati, G., Greenberg, A.S., Hebral, B. and Thoulouze D. Phys Rev Lett (1980) 44 1695 6 Yu, C. and Anderson, P.W. Phys Lett (1979) "74A 236 7 Corruccini, L.R. and Osheroff, D.D. Phys Rev (1978) BI7 126 8 Frossati, G., Godfrin, H., Hebral, B., Schumacher, G. and Thoulouze, D. Proc UL T Hakone Symp The Physical Society of
Japan (1977) 205 9 Frossati, G. J Phys (1978) 39 C6-1578 10 Castelijns, C.A.M., Kuerten, J.G.M., de Waele, A.T.A.M. and Gijsman, H.M. Phys Rev (1985) B32 2286 11 Knerten, J.G.M., Castelijns, C.A.M., de Waele A.T.A.M. and Gijsraan, H.M. Phys Rev Left (1986) 56 2288 12 Schumacher, G. PhD Thesis Grenoble, France (1978) 13 Knerten, J.G.M., Castelijns, C.A.M., de Waele, A.T.A.M. and Gijsman, H.M. Cryogenics (1985) 25 419
14 Greywall, D.S. Phys Rev (1985) B29 4933 15 Wilks,J. The Properties of Liquid and Solid Helium Clarendon Press, UK (1967) 16 Reijntjes, P.J., van Rijswijk, W., Vermenlen, G.A. and Frossati, G. Rev Sci lnstrum (1986) 57 1413 17 Radebaugh, R., Siegwarth, J.D. and Holste, J.C. Proc ICEC 5 IPC Science and Technology Press, Guildford, UK (1974) 242 18 Dow, R.C.M., Guenault, A.M. and Pickett, G.R. J Low Temp Phys (1982) 47 477 19 Bradley, D.L, Guenanlt, A.M., Keith, V., Kennedy, C.J., Miller, I.E., Mussett, S.G., Pickett, G.R. and Pratt, W.P., Jr J Low Temp Phys (1984) 57 359
Appendix Formulae to design the heat exchangers of a dilution refrigerator (formulae 2-8 are found in References 8 and 9): rule of thumb for the diameter of the diluted flow channel of the tubular heat exchanger, Equation (A1); relation between the temperature of the mixing chamber, circulation rate, exchange area and external heat leak for a quadratic rKm (a good approximation is to assume Q/h to be a constant), Equation (A2); same as Equation (A2) but for a cubic rKm, Equation (A3); the ratio between the temperature of the diluted and the concentrated stream is assumed to be constant, Equation (A4); heat leak due to viscous flow for a cylindrical flow channel 01 = rh/T2), Equation (A5); heat leak due to axial conduction for a cylindrical flow channel (K = K~/T), Equation (A6); general dependence on the diameter, D, of Qvi~ + Q¢o, (A and B are defined by Equations (A5) and (A6)), Equation (A7); and the •optimum diameter, D, and optimum value of Qvis¢ + Q .... Equation (A8). d = (chf~- with c = 8 x 10 -3 m2s mol -~ for 1 m length (A1) Tmc = 28.7--~rKm + 0.11 (Q/h)"-
(A2)
O_/h
(A3)
TZm~= 6.73 ~rKm h + 0.0122 Tc = 2.86 To
(A4)
0visc = Z 4rh)[hVm]2 with Z = 128L [Th + TI] 2 ~D 4
(AS)
• Qco. = S Koln[Th/T,] with S = ~~ D :
(A6)
arise + 0 .... = A/D4 + BD2
(A7)
• Dop, = (2A/B) 1/6 and Q,,pt = 3 (2AB2)1/3
(A8)
Cryogenics 1987 Vol 27 March
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