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.     

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.     

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.     

Theoretical Models for the Cooling Power and Base Temperature of Dilution Refrigerators

³He/⁴He dilution refrigerators are widely used for applications requiring continuous cooling at temperatures below approximately 300 mK. Despite of the popularity of these devices in low temperature physics, the thermodynamic relations underlying the cooling mechanism of ³He/⁴He refrigerators are very often incorrectly used. Several thermodynamic models of dilution refrigeration have been published in the past, sometimes contradicting each other. These models are reviewed and compared with each other over a range of different ³He flow rates. In addition, a new numerical method for the calculation of a dilution refrigerator’s cooling power at arbitrary flow rates is presented. This method has been developed at CERN’s Central Cryogenic Laboratory. It can be extended to include many effects that cannot easily be accounted for by any of the other models, including the degradation of heat exchanger performance due to the limited number of step heat exchanger elements, which can be considerable for some designs. Finally, the limitations of applying the results obtained with idealized thermodynamic models to actual dilution refrigeration systems 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 Capacity of Adsorbed Helium-3 at Ultra-Low Temperatures

We report on direct measurements of the heat capacity of monolayers of ³He adsorbed on the surface of a copper cell filled with superfluid ³He. We found that at ultra low temperatures the surface ³He heat capacity dominates over the heat capacity of the bulk liquid ³He. The replacement of adsorbed ³He by ⁴He changes the heat capacity of the sample by an order of magnitude. These investigations were made in the framework of the “ULTIMA” project, a dark matter detector based on superfluid ³He in the limit of ultra low temperatures.     

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.     

Specific heat of amorphous3He films and confined liquid3He

We have measured the heat capacities of³He films and liquid³He in porous Vycor glass at 10 to 600 mK. With increasing the film thickness from 1 to 3 atomic layers, the specific heat evolves gradually from that typical to solid to that of liquid³He. At about 2 atomic layers, however, its low-temperature part is nearly temperature-independent; we interpret this as a result of gradual freezing of spins in an amorphous solid³He film with decreasing the temperature. The contribution of liquid³He in the center of the Vycor pores can be described as the specific heat of bulk liquid³He at corresponding pressures in the range 0 to 28 bar. The thickness of amorphous solid on the pore walls increases with external pressure roughly linearly. Preplating the walls with⁴He allows to determine the positions of³He atoms contributing to the surface specific heat at 10 to 50 mK. In addition, the contribution from the specific heat of³ He -⁴He mixing at 100 to 600 mK is discussed as a function of pressure and amount of⁴He.0n leave from ISSP Acad. Sci. of Russia, Chernogolovka, Russia     

Observation of the Fermi Fluid in 3He-4He Mixture Films Formed in One-Dimensional 28 Å Pores

A ³He film formed in quite narrow pores is one of the possible model systems for a one-dimensional Fermi fluid. Here we report our new heat capacity resugts of ³He and ⁴He film adsorbed in a straight pore 28 Å in diameter down to 5 mK. The coverage and temperature dependence of the heat capacity indicates that a fluid phase appears between the second layer promotion and the complete filling of the pores. Since the heat capacity of ³He adsorbed on the bare substrate shows a large upturn due to the nuclear heat capacity of the localized ³He, it is difficugt to observe the true heat capacity of the fluid phase. By replacing the localized ³He, we can successfully suppress the upturn and observe the true heat capacity of the fluid phase.     

1-D transient numerical model of a regenerator in a novel sub Kelvin Active Magnetic Regenerative Refrigerator

A sub Kelvin Active Magnetic Regenerative Refrigerator (AMRR) is being developed at the University of Wisconsin – Madison. This AMRR consists of two circulators, two regenerators, one superleak, one cold heat exchanger, and two warm heat exchangers. The circulators are novel non-moving part pumps that reciprocate a superfluid mixture of ⁴He–³He in the system. Heat from the mixture is removed within the two regenerators of this tandem system. An accurate model of the regenerators in this AMRR is necessary in order to predict the performance of these components, which in turn helps predicting the overall performance of the AMRR system. This work presents modeling methodology along with results from a 1-D transient numerical model of the regenerators of an AMRR capable of removing 2.5 mW at 850 mK at cyclic steady state.     

Vapor Pressure and Heat Capacity Measurement of 3He Adsorbed on 18Å-Pores

We have measured the vapor pressure (0.84 K 3 He adsorbed on pores 18 Å in diameter. The results of the vapor pressure measurement indicate that ³ He film grows up to the second layer. In the first layer, the heat capacity of ³ He shows the same temperature and coverage dependence as ⁴ He, indicating a solid phase. Above a little higher coverage than second layer promotion, heat capacity isotherms for ³ He at several hundred mK increase with coverage while those for ⁴ He decrease. This large heat capacity of ³ He is the nuclear spin heat capacity of the second layer fluid ³ He.     

An apparatus for preparing isotopically pure He4

A cryostat has been constructed for extracting pure He⁴ from He II of natural isotopic composition by means of a heat flush technique. It is shown that the method is in principle capable of yielding He⁴ which is entirely devoid of He³ isotopic impurities. A secondary heat flush, operated in conjunction with a conical heat exchanger of novel design, was used to place an experimental lower bound of 2 × 10¹⁵ on the $\text{He}{}^4\text{He}{}^3$ ratio of the product, a standard sufficient for all present or projected applications requiring isotopically pure He⁴. The apparatus produces 2 000 1 (at standard temperature and pressure) of He⁴ per thermal cycle. The design of future purifiers is discussed.     

Possible 3He Boltzmann Gas Formed on Three-Dimensional Nanopores Preplated with 4He

We have measured the heat capacity of ³He adsorbed on three-dimensionally connected nanopores, 2.7 nm in diameter, preplated with about 1.3 atomic layers of ⁴He. At low coverages of ³He, the ³He heat capacity is roughly constant at the measured temperatures between 0.1 and 1 K. Its molar heat capacity is on the order of the gas constant R, between 1.1R and 1.8R. This suggests a Boltzmann gas state of the adsorbed ³He. At high coverages, the heat capacity is likely approaching linear in T at low temperatures, which suggests a degenerate state at further lower temperatures.     

Heat Capacity Measurements of 3He-4He Mixture Films

We report heat capacity measurements from our on-going experiments on two-dimensional liquid ³He on superfluid ⁴He thin films absorbed on Nuclepore. The ³He coverage dependence of the heat capacity for 0.02–0.50 bulk-density layers of ³He with 3.10 bulk-density layers of ⁴He over the temperature range 40≤T≤200 mK is presented. We find the effective mass of ³He on 3.10 layers of ⁴He is greater than that on 4.33 layers of ⁴He, consistent with our previous magnetic susceptibility measurements.     

Polarized liquid3He in a4He circulating dilution refrigerator

We have used a⁴He circulating dilution refrigerator to produce cold liquid³He with a steady state out-of-equilibrium nuclear spin polarization. Polarizations on the order of 15% (more than 7 times higher than the equilibrium polarization in the external field of 6.6 T) have been obtained in the mixing chamber of the refrigerator at temperatures between 10 and 15 mK. The polarization is enhanced at high pressure because the molar susceptibility of concentrated³He is larger than that of the dilute phase. The polarization exchange between the dilute and concentrated phases (in direct contact in the heat exchanger of the refrigerator) amplifies the enhancement. The polarization diminishes below a pressure of 2.6 bar. This allows us to scale and reinterpret susceptibility data of the dilute phase¹ in combination with the effective mass deduced from osmotic pressure measurements². We find 1+F ₀ ^a = 0.89±1% on the phase separation line in the pressure range 0–20 bar.We would like to thank Profs. D.M. Lee and M.S. Tagirov for the many discussions during their visits.     

Visualization of Bubble Nucleation in Boiling 3He

The heat transfer properties of ³He bubbles in the nucleate boiling state have been investigated in liquid ³He below 1.0 K by using the shadowgraph method. The temperature difference between the copper surface and liquid ³He temperature was also measured as a function of heat flux in steady state. The size and number of bubbles departing from the surface in a specific time were compared using photograph recorded by a high-speed video camera at various heat flux and liquid ³He temperature of 0.5, 0.7 and 1.0 K.     

3He-4He mixture films in Anopore membranes

We report recent heat capacity and phase shift measurements on a⁴He and a³He-⁴He mixture film adsorbed in Anopore membranes We discuss the effects of a 1.1%³He concentration at a heat capacity signature found for a pure⁴He film.     

Heat Capacity of Dilute 3He–4He Films on Graphite

The heat capacity of dilute ³He–⁴He films is measured to clarify whether the second adsorbed layer of ⁴He films on graphite solidify into the so-called “4/7 phase.” The ³He areal density is fixed at 0.2 nm^?2, whereas the ⁴He areal density is gradually increased. The measured heat capacities suddenly decrease with an increasing areal density approaching that of the 4/7 phase. Above the areal density of the 4/7 phase, the heat capacities do not reduce completely to zero and have finite values. The behavior of the heat capacity does not change over a rather wide areal density regime, although it suddenly increases or recovers at around the areal density of the third-layer promotion. These behaviors can be interpreted as the separation of ³He–⁴He mixture films into a ³He-rich phase and a ⁴He-rich phase, with the ³He-rich phase solidifying into the 4/7 phase and the ⁴He-rich phase remaining fluid below the areal density of the third-layer promotion. These observations strongly suggest that a ⁴He film adsorbed on a graphite surface does not solidify into the 4/7 phase.     

3He and 4He Coverage Dependence of FA 0 and FS 1 in Thin Mixture Films

No Heading We report additional heat capacity measurements and analysis from our experiments on two-dimensional liquid. ³He on superfluid ⁴He thin films absorbed on Nuclepore. The ³He heat capacity for sub-monolayer coverages of ³He with 3.10 bulk-density layers of ⁴He for T 40 mK is discussed. We incorporate these measurements with earlier NMR work in similar coverage ranges and deduce preliminary values for the two-dimensional Fermi Liquid parameters for the ³He for 3.10 layers of ⁴He.PACS numbers: 67.60.Fp, 67.65.+z.     

Possible Phase Transition at Low mK Temperatures in Liquid Helium Mixture Films Adsorbed on Graphite

We report heat capacity and magnetisation measurements of ³He adsorbed on the surface of graphite plated with three atomic layers of ⁴He. For ³He coverages n ₃>4 nm^?2 the heat capacity corresponds to a 2D Fermi fluid. The inferred hydrodynamic mass of the ³He quasiparticles is 1.38±0.05 m₃. The ³He effective mass ratio increases with coverage to 2.4 at n ₃=4 nm^?2, due to Fermi liquid interactions. The heat capacity isotherm exhibits a steplike increase centred on n ₃=4.5 nm^?2, similar to that previously observed on four layers of ⁴He. This is associated with the population of the first excited Andreev surface bound state. However, in the present case, as n ₃ is increased through the step a pronounced anomalous feature develops in the temperature dependence of the heat capacity, around 10 mK. Below 5 mK the heat capacity is approximately linear in temperature. With n ₃=7 nm^?2, we find that this behaviour is very sensitive to small changes in the ⁴He third layer coverage, around the completed third layer. Measurements of the ³He magnetisation,, by continuous wave NMR methods, find a significant increase with decreasing temperature below around 20 mK. Together the data suggest that a phase transition takes place in the film at low mK temperatures.