Dilution refrigerator
A 3He/4He dilution refrigerator is a
isotopes.The dilution refrigerator was first proposed by Heinz London in the early 1950s, and was experimentally realized in 1964 in the Kamerlingh Onnes Laboratorium at Leiden University.[3] The field of dilution refrigeration is reviewed by Zu et al.[4]
Theory of operation
The refrigeration process uses a mixture of two isotopes of helium: helium-3 and helium-4. When cooled below approximately 870 millikelvins, the mixture undergoes spontaneous phase separation to form a 3He-rich phase (the concentrated phase) and a 3He-poor phase (the dilute phase). As shown in the phase diagram, at very low temperatures the concentrated phase is essentially pure 3He, while the dilute phase contains about 6.6% 3He and 93.4% 4He. The working fluid is 3He, which is circulated by vacuum pumps at room temperature.
The 3He enters the cryostat at a pressure of a few hundred
In the mixing chamber, two phases of the 3He–4He mixture, the concentrated phase (practically 100% 3He) and the dilute phase (about 6.6% 3He and 93.4% 4He), are in equilibrium and separated by a phase boundary. Inside the chamber, the 3He is diluted as it flows from the concentrated phase through the phase boundary into the dilute phase. The heat necessary for the dilution is the useful cooling power of the refrigerator, as the process of moving the 3He through the phase boundary is endothermic and removes heat from the mixing chamber environment. The 3He then leaves the mixing chamber in the dilute phase. On the dilute side and in the still the 3He flows through
Cryogen-free dilution refrigerators
Modern dilution refrigerators can precool the 3He with a cryocooler in place of liquid nitrogen, liquid helium, and a 1 K bath.[6] No external supply of cryogenic liquids is needed in these "dry cryostats" and operation can be highly automated. However, dry cryostats have high energy requirements and are subject to mechanical vibrations, such as those produced by pulse tube refrigerators. The first experimental machines were built in the 1990s, when (commercial) cryocoolers became available, capable of reaching a temperature lower than that of liquid helium and having sufficient cooling power (on the order of 1 Watt at 4.2 K).[7] Pulse tube coolers are commonly used cryocoolers in dry dilution refrigerators.
Dry dilution refrigerators generally follow one of two designs. One design incorporates an inner vacuum can, which is used to initially precool the machine from room temperature down to the base temperature of the pulse tube cooler (using heat-exchange gas). However, every time the refrigerator is cooled down, a vacuum seal that holds at cryogenic temperatures needs to be made, and low temperature vacuum feed-throughs must be used for the experimental wiring. The other design is more demanding to realize, requiring heat switches that are necessary for precooling, but no inner vacuum can is needed, greatly reducing the complexity of the experimental wiring.
Cooling power
The cooling power (in watts) at the mixing chamber is approximately given by
where is the 3He molar circulation rate, Tm is the mixing-chamber temperature, and Ti the temperature of the 3He entering the mixing chamber. There will only be useful cooling when
This sets a maximum temperature of the last heat exchanger, as above this all cooling power is used up only cooling the incident 3He.
Inside of a mixing chamber there is negligible thermal resistance between the pure and dilute phases, and the cooling power reduces to
A low Tm can only be reached if Ti is low. In dilution refrigerators, Ti is reduced by using heat exchangers as shown in the schematic diagram of the low-temperature region above. However, at very low temperatures this becomes more and more difficult due to the so-called
Limitations
There is no fundamental limiting low temperature of dilution refrigerators. Yet the temperature range is limited to about 2 mK for practical reasons. At very low temperatures both the viscosity and the thermal conductivity of the circulating fluid become larger if the temperature is lowered. To reduce the viscous heating the diameters of the inlet and outlet tubes of the mixing chamber must go as T−3
m and to get low heat flow the lengths of the tubes should go as T−8
m. That means that, to reduce the temperature by a factor 2, one needs to increase the diameter by a factor 8 and the length by a factor 256. Hence the volume should be increased by a factor 214 = 16,384. In other words: every cm3 at 2 mK would become 16,384 cm3 at 1 mK. The machines would become very big and very expensive. There is a powerful alternative for cooling below 2 mK: nuclear demagnetization.
See also
- Adiabatic demagnetization
- Magnetic refrigeration
- Helium-3 refrigerator
- Refrigerated transport Dewar
- Timeline of low-temperature technology
References
- ISBN 978-0-12-455950-9.
- ISBN 978-3-540-46360-3.
- ISBN 978-1-4899-6217-1.
- S2CID 244005391.
- ISBN 978-0-08-087308-4.
- .
- .
- H. E. Hall; P. J. Ford; K. Thomson (1966). "A helium-3 dilution refrigerator". Cryogenics. 6 (2): 80–88. .
- J. C. Wheatley; O. E. Vilches; W. R. Abel (1968). "Principles and methods of dilution refrigeration". Journal of Low Temperature Physics. 4: 1–64. S2CID 123091791.
- T. O. Niinikoski (1971). "A horizontal dilution refrigerator with very high cooling power". Nuclear Instruments and Methods. 97 (1): 95–101. .
- G. J. Frossati (1992). "Experimental techniques: methods for cooling below 300 mK". Journal of Low Temperature Physics. 87 (3–4): 595–633. S2CID 120814643.
External links
- Lancaster University, Ultra Low Temperature Physics - Description of dilution refrigeration.
- Harvard University, Marcus Lab - Hitchhiker's Guide to the Dilution Refrigerator.