Dry dilution refrigerator with 4He-1 K-loop

In this article we summarize experimental work on cryogen-free ³He/⁴He dilution refrigerators which, in addition to the dilution refrigeration circuit, are equipped with a ⁴He-1 K-stage. This type of DR becomes worth considering when high cooling capacities are needed at T ∼ 1 K to cool cold amplifiers and heat sink cables. In our application, the motivation for the construction of this type of cryostat was to do experiments on superconducting quantum circuits for quantum information technology and quantum simulations. In other work, DRs with 1 K-stage were proposed for astro-physical cryostats. For neutron scattering research, a top-loading cryogen-free DR with 1 K-stage was built which was equipped with a standard commercial dilution refrigeration insert.Cooling powers of up to 100 mW have been reached with our 1 K-stage, but higher refrigeration powers were achieved with more powerful pulse tube cryocoolers and higher ⁴He circulation rates in the 1 K-loop. Several different versions of a 1 K-loop have been tested in combination with a dilution refrigeration circuit.The lowest temperature of our DR was 4.3 mK.     

Condensation stage of a pulse tube pre-cooled dilution refrigerator

In our article, experiments with a pulse tube (PTR) pre-cooled dilution refrigerator (DR) are presented, where an upgraded ³He condensation stage has been tested. The DR had a ³He flow rate of up to 1.1 mmol/s. The ³He gas entering the refrigerator was first pre-cooled to a temperature of ～50 K at the first stage of the PTR. In the next cooling step, the ³He was run through a recently installed heat exchanger, which was attached to the regenerator of the second stage of the pulse tube cryocooler; at the outlet of this heat exchanger the temperature of the ³He was as low as ～4 K. Due to the non-ideality of the helium gas, the second regenerator of a two stage PTR has excess cooling power which can be made use of without affecting the base temperature of this stage, and it is this effect which was put to work, here. Finally, the ³He was further cooled in a heat exchanger, mounted at the second stage of the PTR, before it entered the dilution unit of the cryostat.The installation of a heat exchanger at the regenerator of the second stage of the PTR is especially important for the construction of DRs with high refrigeration capacities; in addition, it allows for a plain design of the subsequent Joule–Thomson (JT) stage, and herewith facilitates considerably the construction of “dry” DRs. The condensation rate of the ^3,4He mash prior to an experiment was increased. The pressure during condensation could be kept near 1 bar, and thus a compressor was no longer necessary with the modified apparatus.     

Dilution refrigeration

The history of dilution refrigeration is traced back to 1951 when H. London suggested the possibility of cooling by mixing He³ and He⁴. The first dilution and cascade refrigerators are described, followed by continuous refrigerators and Lyden dilution referation. Finally the Kamerling Onnes Laboratory Pomeranchuk cooling device is described.     

3He/4He dilution refrigerator with high cooling capacity and direct pulse tube pre-cooling

In the article, a ³He/⁴He dilution refrigerator (DR) is described which is pre-cooled by a commercial two-stage pulse tube refrigerator (PTR); cryo-liquids are not necessary with this type of milli-kelvin refrigerator. The simple design of the condensation stage of this so-called dry DR is novel and explained in detail. In most dry DRs the circulating ³He gas is cooled by a two-stage PTR to a temperature of about 4 K. In the next cooling step, the ³He flow is cooled and partially liquefied in a Joule–Thomson circuit, before it is run to the dilution refrigeration unit. The counterflow heat exchanger of the Joule–Thomson circuit is cooled by the cold ³He gas pumped from the still of the DR. In the DR described here, the heat exchanger of the Joule–Thomson stage was omitted entirely; in the present design, the ³He gas is cooled by the PTR in three different heat exchangers, with the first one mounted on the first stage of the PTR, the second one on the regenerator of the second stage, and the third one on the cold end of the second stage. The heat load caused by the ³He flow is mostly absorbed by the first two heat exchangers. Thus the ³He flow presents only a small heat load to the second stage of the PTR, which therefore operates close to its base temperature of 2.5 K at all times. A pre-cooling temperature of 2.5 K of the ³He flow is sufficiently low to run a DR without further pre-cooling. The simplified condensation system allows for a shorter, compacter and more economical design of the DR. Additionally, the pumping speed of the turbo pump is no longer obstructed by the counterflow heat exchanger of the Joule Thomson stage as in our earlier DR design.     

Development of a proof of concept low temperature 4He Superfluid Magnetic Pump

We describe the development and experimental results of a proof of concept Superfluid Magnetic Pump in this work. This novel low temperature, no moving part pump can replace the existing bellows-piston driven ⁴He or ³He-⁴He mixture compressor/circulators used in various sub Kelvin refrigeration systems such as dilution, Superfluid pulse tube, Stirling, or active magnetic regenerative refrigerators. Due to the superior thermal transport properties of sub-Lambda ⁴He this pump can also be used as a simple circulator to distribute cooling over large surface areas. Our pump was experimentally shown to produce a maximum flow rate of 440 mg/s (averaged over cycle), 665 mg/s (peak) and produced a maximum pressure difference of 2323 Pa using only the more common isotope of helium, ⁴He. This pump worked in an “ideal” thermodynamic state: The experimental results matched with the theoretical values predicted by a computer model. Pump curves were developed to map the performance of this pump. This successful demonstration will enable this novel pump to be implemented in suitable sub Kelvin refrigeration systems.     

A tiltable single-shot miniature dilution refrigerator for astrophysical applications

We present a ³He/⁴He dilution refrigerator designed for cooling astronomical mm-wave telescope receivers to around 100 mK. Used in combination with a Gifford–McMahon closed-cycle refrigerator, ⁴He and ³He sorption-pumped refrigerators, our cryogen-free system is capable of achieving 2 μW cooling power at 87 mK. A receiver attached directly to the telescope optics is required to rotate with respect to the downward direction. This scenario, of variable tilt, has proved difficult for typical dilution refrigerators, but our design has a geometry chosen to allow tilt to 45° and beyond.     

Flow impedance construction for liquid helium continuous refrigerators

Continuous refrigeration below 1 K implies the circulation of a cooling fluid. This requires some kind of constriction to limit the flow and allow the build-up of the pressure difference which gives rise to the enthalpy difference on which the cooling process depends. This situation is met by cooling with helium-4 to 1 K,^1,2 with helium-3, to 0.3 K, and also in dilution refrigerators; these flow impedances have to be small, rugged, and hard to plug with dust and oil mist.     

4He-circulating dilution refrigerator

Investigations are reported on a dilution refrigerator through which superfluid⁴He is circulated. First, discussions are given about the effectiveness of a counterflow tube heat exchanger in which the phase-separated concentrated and dilute phases directly contact each other. Then experimental results of the cooling behavior of our⁴He-circulating dilution refrigerator are presented. It is found that the cooling characteristic of the machine changes abruptly when the⁴He-circulating rate exceeds a certain critical value. In the circulation rate region above this critical value, a lowest temperature of 3.4 mK has been attained. On the basis of various experimental results such as the effect of heat input, effect of tilting the cryostat, and visual observation with a machine made of glass, discussions are given of the flow state of the descending cold dilute mixture in the counterflow tube.     

Small heat exchanger using silver powder

A simple heat exchanger using silver powder for cooling pure liquid ³He is described. The temperature difference across the heat exchanger was less than 5μK at the superfluid transition of ³He with a thermal flux of 0.06 nW.     

Development of a thermodynamic model for a cold cycle 3He-4He dilution refrigerator

A thermodynamic model of a ³He-⁴He cold cycle dilution refrigerator with no actively-driven mechanical components is developed and investigated. The refrigerator employs a reversible superfluid magnetic pump, passive check valves, a phase separation chamber, and a series of recuperative heat exchangers to continuously circulate ³He-⁴He and maintain a ³He concentration gradient across the mixing chamber. The model predicts cooling power and mixing chamber temperature for a range of design and operating parameters, allowing an evaluation of feasibility for potential ³He-⁴He cold cycle dilution refrigerator prototype designs. Model simulations for a prototype refrigerator design are presented.     

Experimental techniques: Methods for cooling below 300 mK

There are at present three methods for cooling samples to temperatures below 300 mK: dilution, Pomeranchuk, and nuclear refrigeration. We give the basic principles of these methods with more details concerning dilutions refrigerators. This should allow the construction of a simple all plastic refrigerator for temperatures lower than 15 mK, or an even simpler Pomeranchuk cell. The source of heat leaks and other important points for reaching temperatures in the microkelvin range with nuclear refrigerators are given in the lecture by F. Pobell     

Development of a low-temperature He compressor for superfluid He-He mixtures

The development, testing and modeling of a “compressor” that is capable of increasing the concentration of the ³He component of a liquid superfluid ³He-⁴He mixture is discussed. This compressor was developed to drive refrigeration cycles for cooling below 1 K. The compressor design and performance testing is described in detail. The compressor was operated at 1.2 K and ³He molar flow rates of 130 μmol/s were achieved. Compression ratios in excess of 6 were also demonstrated. The theoretical models presented are used to estimate the expected efficiencies of the compressor as well as the effect of the ⁴He component on the power required to drive the compressor.     

Proposed designs for a “dry” dilution refrigerator with a 1 K condenser

Recent development of “dry” dilution refrigerators has used mechanical cryocoolers and Joule-Thomson expansion stages to cool and liquefy the circulating ³He. While this approach has been highly successful, we propose three alternative designs that use independently-cooled condensers. In the first, the circulating helium is precooled by a mechanical cooler, and liquified by self-contained ⁴He sorption coolers. In the second, the helium is liquefied by a closed-cycle, continuous flow ⁴He refrigerator operating from a room temperature pump. Finally, the third scheme uses a separate ⁴He Joule-Thomson stage to cool the ³He condenser. The condensers in all these schemes are analogous to the “1-K pot” in a conventional dilution refrigerator. Such an approach would be advantageous in certain applications, such as instrumentation for astronomy and particle physics experiment, where a thermal stage at approximately 1 K would allow an alternative heat sink to the still for electronics and radiation shielding, or quantum computer research where a large number of coaxial cables must be heat sunk in the cryostat. Furthermore, the behaviour of such a refrigerator is simplified due to the separation of the condenser stage from the dilution circuit, removing the complex interaction between the 4-K, Joule-Thomson, still and mixing chamber stages found in current dry DR designs.     

Plastic dilution refrigerators

A new design for conventional,³He re-circulating, dilution refrigerators has been developed and tested. The units are made out of plastic and can be designed to have very small diameters (<15mm). These characteristics make them ideal to cool samples below 100 mK in high or time-varying magnetic fields. Furthermore, they are inexpensive, reliable and easily constructed. The best refrigerators reach continuous temperatures of around 10 mK at low circulation rates ( 100 mol/s). The cooling power at high temperatures is limited by the speed of the circulation pump and not by the refrigerator itself. The basic design and construction methods are discussed.     

Measurements of the Superfluid Joule–Thomson Refrigerator Using High Concentration 3He–4He Mixtures

The superfluid Joule–Thomson refrigerator (SJTR) uses a liquid superfluid ³He–⁴He mixture to provide cooling below 1 K. Performance measurements of the SJTR using 5% and 11% ³He concentration mixtures are reported. High concentration operation shows higher cooling powers at high temperature. Ultimate temperatures are seen to increase with increasing concentration due to a pinching of the temperature defect in the recuperative heat exchanger. This pinching effect is due to the variation of the heat capacity of the ³He–⁴He mixture with temperature and concentration and is discussed in detail and design changes are suggested to mitigate it.     

Heat exchangers for he II cooling loops with self-sustained fountain effect pumps

A cooling cycle with He II convection driven by self-sustained fountain effect pumps is being investigated. Special attention is drawn to the problem of heat transfer at both ends of the superfilter of this loop. The heat exchanger requirements are derived from theoretical considerations on the degradation of the cooling characteristic effected by non-perfect heat exchangers. A shell and tube type heat exchanger, optimized for the warm end of the filter has been operated in this loop with a thermal load of up to 9 W, with 2.8 g s⁻¹ maximum helium flow rate and with inlet temperatures between 1.8 and 3.4 K. Its performance is well described by computations. A different heat exchanger design with finned Cu walls is suggested for the cold end of the pump. Some considerations on its optimization are given.     

A high capacity completely closed-cycle 250 mK He refrigeration system based on a pulse tube cooler

We present the design of a completely closed-cycle refrigeration system. The system consists of four stages; the first two, 40.5 and 2.7 K, are provided by a pulse tube cooler, the third and fourth stages by helium adsorption refrigerators. The adsorption refrigerators use ⁴He and ³He with base temperatures of 700 and 250 mK, respectively. Performance tests including some with the cooler rotated from the vertical showed that with a load of 15 μK, a temperature below 286 mK can be maintained for 72 h.     

3He/4He dilution refrigerator without a pumped 4He stage

A ³He/⁴He dilution refrigerator is described where the instreaming ³He is precooled and liquefied by a counterflow heat exchanger which makes use of the enthalpy of the cold ³He gas pumped out of the still, and by subsequent Joule-Thomson expansion. This condenser replaces the usual ⁴He condenser.     

Cryocoolers near their low-temperature limit

This paper analyses the recently-observed temperature–time dependence in a GM-cooler near its low-temperature limit. The paper mainly focusses on GM-coolers with ⁴He as the working fluid, but some attention is also paid to pulse-tube refrigerators (PTR’s) using ³He and many features of the treatment equally apply to Stirling coolers. Ample attention is paid to the thermodynamics of the cycle by considering the isentropes in the Tp-diagrams of ⁴He and ³He. The role of the line, where the thermal expansion coefficient is zero, is emphasized. Some fundamental thermodynamic relationships are derived.     

Calculation of cooling of3He by adiabatic demagnetization of a paramagnetic salt

In an effort to better understand the various factors involved in refrigeration by adiabatic demagnetization, we have set up a computer model of a paramagnetic salt in contact with liquid³He. This model has been used to study the cooling of the³He from an initial temperature of 20 mK, which is typical of the temperature achieved in a dilution refrigerator. The effects of various demagnetization schedules, heat leaks, and varying ratios of salt to liquid have been studied. The model was used to simulate an actual demagnetization and gave excellent agreement with measured temperatures. We also show how the model can be extended to the case of nuclear demagnetization.Based on work performed under the auspices of the U.S. Energy Research and Development Administration.