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How Does a Dilution Refrigerator Work?

A cryogen-free dilution refrigerator is a closed-loop cooling system that provides cooling to temperatures of millikelvins – colder than outer space. The system is used to cool down samples and devices, which are attached to a metallic flange in the dilution refrigerator. The systems are used for instance in quantum computing, materials science, astrophysics, and fundamental research.

The dilution refrigerator systems can provide temperatures of < 10 millikelvin and can operate without moving parts at the low temperature stages. This is enabled by the dilution unit inside the system, which provides necessary cooling to reach these ultra-low temperatures. The cooling power of the dilution unit comes from the heat of mixing of the mixture of helium-3 (He-3) and helium-4 (He-4) isotopes. This is enabled by the peculiar property of helium, that its two isotopes can remain dissolved down to the lowest temperatures, whereas other fluids tend to separate completely at sufficiently low temperature.

Phase Separation of Helium Isotopes

He-3 and He-4 represent two different fundamental particles. He-3 is a fermion, while He-4 is a boson. Bosons can undergo a phenomenon called Bose-Einstein condensation, where multiple particles can occupy the lowest quantum mechanical energy state. This phenomenon is responsible for the onset of superfluidity of He-4 at 2.17 kelvin under saturated vapor pressure. For fermions, on the other hand, such phenomenon is not possible since only two fermions (with opposite spins) are allowed to occupy same quantum mechanical energy state. The superfluid state in He-3 is thus much more difficult to achieve, and it does not happen in the operational temperature range of the dilution refrigerator. The normal fluid He-3 is also called fermi fluid.

A dilution refrigerator uses the heat of mixing of those two isotopes of helium, He-3 and He-4, to obtain cooling. At temperatures below 0.87 kelvin (exact temperature depends on the He-3 concentration) the He-3– He-4 mixture will separate into two phases: an He-3 rich phase (concentrated phase) and an He-3 poor phase (dilute phase).

Phase diagram of helium-3—helium-4 mixture.

Approaching absolute zero temperature, the concentrated phase becomes pure He-3 while in the dilute He-4 rich phase there remains 6.6% of He-3. The enthalpy of He-3 in the dilute phase is larger than in the concentrated phase. Hence energy is required to move He-3 atoms from the concentrated to the dilute phase. In a dilution refrigerator this energy is taken from a well isolated environment so cooling will occur.

Essentially the cooling provided by the dilution unit is based on the He-3 requiring heat when pumped into the dilute phase, which provides cooling in the environment this happens in.

Operation of the Dilution Unit

In the dilution refrigerator, the isolated environment where the mixing of the isotopes happens is called the Mixing Chamber. That’s where the phase boundary is located, and where the cooling occurs when the He-3 is pumped through the phase boundary. Other essential parts of the dilution unit are the still chamber, the continuous flow heat exchanger (in the form of a spiral), and the step heat exchangers.

In a steady state operation, He-3 comes to the dilution unit pumped with a gas handling system. It enters the dilution unit precooled first by the pulse tube cryocooler down to about 3 kelvin, and through the main flow impedance in the still chamber. From there it proceeds to the continuous flow heat exchanger and then to the step heat exchangers, which cool the He-3 going to the mixing chamber. From the mixing chamber the He-3 goes into the still chamber and in a gas phase is evaporated through a still pumping line, eventually coming back to the start of the process. Below you can see a diagram of the cooling cycle.

Dilution refrigerator cooling cycle. 1. He-3-rich gas phase, 2. Still, 3. Heat exchangers, 4. He-3-poor phase, 5. Mixing Chamber, 6. Phase separation, and 7. He-3-rich phase.

The efficiency of the dilution refrigerator is determined by the efficiency of the heat-exchangers. The incoming He-3 should be cooled by the outgoing He-3 as much as possible.

The available cooling power is determined by the circulation rate of He-3. The larger the flow, the larger the cooling power, provided that the heat-exchangers are capable of handling the increased flow rate.

The temperature of the still and mixing chamber plate are controlled by heaters. The mixing chamber has a heater, which is there for diagnostics purposes; it can be used to characterize unit behaviour under various heat loads, i.e., simulate an installed experiment. The still heater on the other hand is essential to the unit operation. Without heating, the vapor pressure in the still chamber becomes so small, that pumps cannot effectively circulate He-3, resulting in reduced cooling power. Hence, heat must be applied to the still to increase evaporation. As He-3 has larger vapor pressure than He-4, this process distils He-3 out of the mixture (the He-3 concentration in the gas phase is ~90%)

After the He-3 gas evaporates from the still, it is pumped through a gas handling system (GHS), in which it is purified and then allowed back into the condensing line.

Dilution unit. 1. Still, 2. Continuous flow heat exchangers, 3. Step heat exchangers, and 4. Mixing chamber.

The entire dilution refrigerator consists of the different temperature stages, with the dilution unit located in the lowest stages. The stages are easily recognizable as they are made of large metallic plates. The stages are separated by non-conductive supports and heat switches, whose conductivity can be controlled. Using them the stages can be thermally connected or disconnected. The dilution unit is attached to three of these metallic plates. The still chamber of the dilution unit sits on top of the still flange, under that and after the continuous flow heat exchanger there is the cold plate, and the mixing chamber is located on top of the mixing chamber flange. Finally, below that there is the experimental space enabling measurements in millikelvin temperatures. All these stages will have temperature sensors to provide the user information about the temperatures at different stages.

Cooling With a Push of a Button

For the user of a dilution refrigerator all this cooling power is provided with a push of a button providing ease of use, with no need to understand all the mechanics proving this cooling. But for those that are curious, you now know that the dilution unit is the heart of the dilution refrigerator and enables it to provide the lowest temperatures for research and applications.

There are however numerous other components to the dilution refrigerator measurement system. Somehow all the helium in the system has to move around it and be precooled to the temperatures required for the dilution unit operations. We must also protect all of this from the outside environment to keep everything running efficiently. To learn about all that, read our blog on the components of the dilution refrigerator measurement system.