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Dilution refrigerator with closed cycle precooling

At the WMI, the construction of dilution refrigerators (DR) has a decade-long history. Traditional DRs are precooled with liquid helium (and nitrogen). But in the 1990s, in an experimental setup, we built a DR which was precooled by a Gifford-McMahon (GM) cryocooler. No cryogens were needed for the operation of this refrigerator; this was our first cryogen-free (CF) DR. Despite of the heavy vibrations of the GM cryocooler, a base temperature of 7.5 mK was reached in the mixing chamber by careful mechanical insulation of the dilution refrigeration unit from the closed cycle precooling circuit.

In 1999, pulse tube refrigerators (PTR) became commercially available. The vibrations of this new type of cryocooler were greatly reduced in comparison with other closed-cycle cryocoolers as there are no moving parts in the cold head of a PTR. Furthermore, there are no cold seals in the cold head, which results in long lifetimes of PTRs. Our pulse tube cryocooler, purchased in 1999, is still in use in our CF-DR. The use of PTRs to precool DRs was a pivotal improvement in the construction of cryogen-free DRs.

CF-DRs usually are made of three major components,

  1. a commercial 2-stage PTR
  2. a dilution refrigeration unit
  3. an intermediate cooling stage similar to a Joule Thomson (JT) stage.

Our PTR (Cryomech PT405 RM) is a 2-stage cryocooler with a base temperature of 2.5 K and a refrigeration capacity of 0.5 W at a temperature of the second stage of 4 K; the power consumption of the compressor is 4.6 kW. The rotary valve and its motor are separated from the cold head and only connected by a piece of flexible hose so that the vibrations of the compressor are blocked in the valve/motor assembly.

The dilution refrigeration unit was made at the WMI. It consists of a mixing chamber, three heat exchangers and a still. The bottom plate of the mixing chamber is equipped with a large silver sponge to provide good thermal contact to the 3,4He liquid inside. The heat exchangers are of a design that has proved of value for many years; they are made from solid silver blocks with flow channels and silver sponges inside.

The intermediate cooling stage consists of a counterflow heat exchanger and a flow restriction. The counterflow heat exchanger is made from capillaries which are wound to cones so they fit smugly into the pumping line of the still. The flow restriction is made from a piece of capillary with a wire inside, so its flow impedance is fixed.

In Fig. 1, a sketch of the cryostat setup is given which shows the main components of the apparatus. The pumps, the compressor of the pulse tube cryocooler and the helium storage tanks are placed in a utility room below the lab. Only the cryostat, its electronics and the gas handling board are in the lab. A cross section of the cryostat showing its most important parts is given in the insert of Fig. 1.



Fig.1. Setup of the cryostat, for details see text. Insert: Cross section of the fridge. a 1st stage of the PTR; b -charcoal trap; c 2nd stage of PTR; d counterflow heat exchanger; e flow restriction; f dilution unit (still, three heat exchangers, mixing chamber).


There are many applications where high cooling capacities of dilution refrigerators are needed. To increase the cooling capacity, the 3He flow has to be raised. In order to construct a high-capacity DR, the low temperature components of our fridge had to be re-designed to minimize viscous heating and avoid thermal shortages between the components of the DR.
Fig. 2 shows a graph of the cooling capacity of the cryostat in its status quo. In the experiment shown here, a dilution refrigeration unit was used which consisted of a mixing chamber, a still, a concentric tube heat exchanger and two concrete heat exchangers; we reached a base temperature of 10 mK with this setup. The cooling power had a value of up to 700 µ W @ 100 mK.



Fig. 2. Refrigeration capacity of the DR. The base temperature at a 3He flow rate of 230 µmol/s was 10 mK. The highest cooling capacity reached was 700 µmol/s at our highest flow rate of 1 mmol/s.

Recent developments

For our experiments on superconducting quantum circuits, but also for other types of applications, high cooling capacities at a temperature of ~ 1 K are desirable to cool amplifiers and coaxial lines. Recently, our DR was equipped with an additional cooling stage so that, in addition to the cooling capacity of the still, a considerable extra amount of refrigeration capacity is available at 1 K. This 1K-stage consists of a closed loop where 4He is circulated; it is similar to a JT-circuit. It can either be operated independently of the DR circuit or in combination with it. In Fig. 3, a cross section of our cryostat is depicted which shows how the PTR, the DR and the 1K-loop are combined in the newest setup. The 1K-loop on the left side of the sketch consists of a counterflow heat exchanger, a flow restriction and a vessel where 4Heliq can accumulate. The 4He is circulated with a rotary pump; a charcoal trap to purify the circulating 4He is attached to the 1st stage of the PTR.

In the vessel of the 1K-stage there is a heat exchanger where the 3He of the DR is cooled to ~1 K. Note that the counterflow heat exchanger between the still and the 2nd stage of the PTR (Fig. 2) has been omitted in the new design. This new concept has the following ramifications:

  1. The condensation rate of the 3,4He mixture prior to an experiment is about doubled compared to the former design (Fig. 2); it is now 110 std.l./h.
  2. The heat load Q into the 1K-circuit during continuous operation of the DR is given by Q = n3 x {H3(pin,TPT2) - H3(pin, TVESSEL)} where n3 is the 3He flow, H3 the enthalpy of 3He, pin its pressure, TPT2 the temperature of the 2nd stage of the PTR and TVESSEL the temperature of the 1K-stage. The 3He flow is liquefied in a heat exchanger at PT2; for n3 = 1 mmol/s, pin = 1 bar, TPT2 = 2.5 K and TVESSEL = 1.2 K we find a heat load of Q = 12.4 mW. The 3He flow of 1 mmol/s is the highest flow possible in our cryostat; the resulting heat load to the 1K-stage is small, but not negligible.
  3. The cooling capacity of the 1K-stage is as high as 100 mW (Fig. 4).
  4. The DR can still be run without the 1K-stage in operation [1]. Of course, the 1K-circuit can also be put into operation without running the DR.

The current setup has been tested in our design-and-development cryostat, so far. The findings will most likely be implemented in a new cryostat for research on superconducting quantum circuits. Results on the DR with 1K-stage are found in [2].



Fig. 3. Left side: Cross section of the DR with 1K-stage. The 1K-stage (green) is on the left. The 3He flow of the DR (pink) is pre-cooled by the PTR (1st stage and 2nd stage) and then cooled in a heat exchanger in the vessel of the 1K-stage. The dilution unit has no counterflow heat exchanger in the pumping line of the still. The photo on the right shows the dilution unit we presently use. a still; b counterflow hx; c step hx; d mixing chamber.



Fig 4. Refrigeration power of the 1K-stage (black curve, left scale) as a function of its temperature. The temperatures of the 2nd stage of the PTR (pink curve; "T2" in Fig. 3) and that of the 4He at the outlet of the counterflow heat exchanger (orange curve; "T3" in Fig. 3) are also depicted (right scale).



[1] Uhlig K. 3He/4He dilution refrigerator with high cooling capacity and direct pulse tube pre-cooling. Cryogenics 48 (2008) 511-514.
[2] Uhlig K. Concept of a powerful cryogen-free dilution refrigerator with separate 1K-stage. Cryocoolers 16 (2010) 509-513.