# Pulse tube refrigerator

The pulse tube refrigerator (PTR) or pulse tube cryocooler is a developing technology that emerged largely in the early 1980s with a series of other innovations in the broader field of thermoacoustics. In contrast with other cryocoolers (e.g. Stirling cryocooler and Gifford-McMahon cooler), this cryocooler can be made without moving parts in the low temperature part of the device, making the cooler suitable for a wide variety of applications.

## Uses

Pulse tube cryocoolers are used in industrial applications such as semiconductor fabrication and in military applications such as for the cooling of infrared sensors.[1] Pulse tubes are also being developed for cooling of astronomical detectors where liquid cryogens are typically used, such as the Atacama Cosmology Telescope[2] or the QUBIC experiment[3] (an interferometer for cosmology studies). PTR's are used as precoolers of dilution refrigerators. Pulse tubes will be particularly useful in space-based telescopes where it is not possible to replenish the cryogens as they are depleted. It has also been suggested that pulse tubes could be used to liquefy oxygen on Mars.[4]

## Description

Here the so-called Stirling-type single-orifice pulse-tube refrigerator will be treated operating with an ideal gas (helium) as the working fluid. Figure 1 represents the Stirling-type single-orifice Pulse-Tube Refrigerator (PTR). From left to right the components are:

• a compressor, with a piston moving back and forth at room temperature TH;
• a heat exchanger X1 where heat is released to the surroundings;
• a regenerator consisting of a porous medium with a large specific heat,The porous medium can be stainless steel wire mesh, copper wire mesh, phosphor bronze wire mesh or lead balls or lead shots or sometimes may be rarely earthen materials to produce very low temperature;
• a heat exchanger X2 where the useful cooling power $\dot{Q}_L$ is delivered at the low temperature TL;
• a tube, often called "the pulse tube";
• a heat exchanger X3 at room temperature where heat is released to the surroundings;
• a flow resistance (often called orifice);
• a buffer volume (a large closed volume at practically constant pressure).
Figure 1: Schematic drawing of a Stirling-type single-orifice PTR. From left to right: a compressor, a heat exchanger (X1), a regenerator, a heat exchanger (X2), a tube (often called "the pulse tube"), a heat exchanger (X3), a flow resistance (orifice), and a buffer volume. The cooling is generated at the low temperature TL. Room temperature is TH.

The part in between X1 and X3 is thermally insulated from the surroundings, usually by vacuum. The cooler is filled with helium at a pressure in the range from 10 to 30 bar. The pressure varies gradually and the velocities of the gas are low. So the name "pulse" tube cooler is very misleading since there are no pulses whatsoever in the system.

## How it operates

The piston moves periodically from left to right and back. As a result the gas also moves from left to right and back while the pressure within the system increases and decreases. If the gas from the compressor space moves to the right it enters the regenerator with temperature TH and leaves the regenerator at the cold end with temperature TL, hence heat is transferred into the regenerator material. On its return the heat stored within the regenerator is transferred back into the gas.

The thermal environment of a gas element near X2, that moves back and forth in the system, changes when it passes the heat exchanger. In the regenerator and in the heat exchanger the heat contact between the gas and its surrounding material is good. Here the temperature of the gas is practically the same as of the surrounding medium. However, in the pulse tube the gas element is thermally isolated (adiabatic), so, in the pulse tube, the temperature of the gas elements vary with the pressure.

Figure 2: Left: (near X2): a gas element enters the pulse tube with temperature TL and leaves it with a lower temperature. Right: (near X3): a gas element enters the tube with temperature TH and leaves it with a higher temperature.

Look at figure 1 and concentrate on gas elements close to X3 (at the hot end) which move in and out of the pulse tube. A gas element that flows into the tube does so when the pressure in the tube is low (it is sucked into the tube via X3 coming from the orifice and the buffer). At the moment it enters the tube it has the temperature TH . Later in the cycle it is pushed out the tube again when the pressure inside the tube is high. As a consequence its temperature will be higher than TH. In the heat exchanger X3 it releases heat and cools to the ambient temperature TH.

At the cold end of the pulse tube there is the opposite effect: here gas elements enter the tube via X2 when the pressure is high with temperature TL and return when the pressure is low with a temperature below TL. They take up heat from X2 : this gives the desired cooling power.

## Performance

The performance of the cooler is determined mainly by the quality of the regenerator. It has to satisfy conflicting requirements: it must have a low flow resistance (so it must be short with wide channels), but the heat exchange should also be good (so it must be long with narrow channels). The material must have a large heat capacity. At temperatures above 50 K practically all materials are suitable. Bronze or stainless steel is often used. For temperatures between 10 and 50 K lead is most suitable. Below 10 K one uses magnetic materials which are specially developed for this application.

The so-called Coefficient Of Performance $\xi$ (COP) of coolers is defined as the ratio between the cooling power $\dot{Q}_L$ and the compressor power P. In formula: $\xi = \dot{Q}_L/P$. For a perfectly reversible cooler, $\xi$ is given by the famous relation

 $\xi_C = \frac{T_L}{T_H - T_L}$ (1)

which is also called the Carnot COP. However, a pulse-tube refrigerator is not perfectly reversible due to the presence of the orifice, which has flow resistance. Therefore equation (1) does not hold. Instead, the COP of an ideal PTR is given by

 $\xi_{PTR} = \frac{T_L}{T_H}$. (2)

Comparing relations 1 and 2 shows that the COP of PTR’s is lower than that of ideal coolers.

## Comparison with other coolers

In most coolers gas is compressed and expanded periodically. Well-known coolers such as the Stirling coolers and the popular Gifford-McMahon coolers have a displacer that ensures that the cooling (due to expansion) takes place in a different region of the machine than the heating (due to compression). Due to its clever design the PTR does not have such a displacer. This means that the construction of a PTR is simpler, cheaper, and more reliable. Furthermore there are no mechanical vibrations and no electro-magnetic interferences. The basic operation of cryocoolers and related thermal machines is described by De Waele[5]

## History

W. E. Gifford and R. C. Longsworth, in 1960's, invented the so-called Basic Pulse Tube Refrigerator. The modern PTR was invented by Mikulin by introducing orifice in Basic pulse tube in 1984.[6] He reached a temperature of 105 K. Soon after that, PTR’s became better due to the invention of new variations.[7][8][9][10][11] This is shown in figure 3, where the lowest temperature for PTR’s is plotted as a function of time.

Figure 3: The temperature of PTR’s over the years. The temperature of 1.2 K is reached in a collaboration between the groups of Giessen and Eindhoven. They used a superfluid vortex cooler as an additional cooling stage to the PTR.

At the moment, the lowest temperature is below the boiling point of helium (4.2 K). Originally this was considered to be impossible. For some time it looked as if it would be impossible to cool below the lambda point of 4He (2.17 K), but the Low-Temperature group of the Eindhoven University of Technology managed to cool to a temperature of 1.73 K by replacing the usual 4He as refrigerant by its rare isotope 3He. Later this record was broken by the Giessen Group that managed to get even below 1.3 K. In a collaboration between the groups from Giessen and Eindhoven a temperature of 1.2 K was reached by combining a PTR with a superfluid vortex cooler.[12]

## Types of pulse-tube refrigerators

For getting the cooling, the source of the pressure variations is unimportant. PTR's for temperatures below 20 K usually operate at frequencies of 1 to 2 Hz and with pressure variations from 10 to 25 bar. The swept volume of the compressor would be very high (up to one liter and more). Therefore the compressor is uncoupled from the cooler. A system of valves (usually a rotating valve) alternatingly connects the high-pressure and the low-pressure side of the compressor to the hot end of the regenerator. As the high-temperature part of this type of PTR is the same as of GM-coolers this type of PTR is called a GM-type PTR. The gas flows through the valves are accompanied by losses which are absent in the Stirling-type PTR.

PTR's can be classified according to their shape. If the regenerator and the tube are in line (as in Fig.1) we talk about a linear PTR. The disadvantage of the linear PTR is that the cold spot is in the middle of the cooler. For many applications it is preferable that the cooling is produced at the end of the cooler. By bending the PTR we get a U-shaped cooler. Both hot ends can be mounted on the flange of the vacuum chamber at room temperature. This is the most common shape of PTR's. For some applications it is preferable to have a cylindrical geometry. In that case the PTR can be constructed in a coaxial way so that the regenerator becomes a ring-shaped space surrounding the tube.

The lowest temperature, reached with single-stage PTR's, is just above 10 K.[13] However, one PTR can be used to precool the other. The hot end of the second tube is connected to room temperature and not to the cold end of the first stage. In this clever way it is avoided that the heat, released at the hot end of the second tube, is a load on the first stage. In applications the first stage also operates as a temperature-anchoring platform for e.g. shield cooling of superconducting-magnet cryostats. Matsubara and Gao were the first to cool below 4K with a three-stage PTR.[14] With two-stage PTR's temperatures of 2.1 K, so just above the λ-point of helium, have been obtained. With a three-stage PTR 1.73 K has been reached using 3He as the working fluid.[15]

## Prospects

The COP of PTR’s at room temperature is low, so it is not likely that they will play a role in domestic cooling. However, below about 80 K the COP is comparable with other coolers (compare Eqs.(1) and (2)) and in the low-temperature region the advantages get the upper hand. For the 70K- and the 4K temperature regions PTR’s are commercially available. They are applied in infrared detection systems, for reduction of thermal noise in devices based on (high-Tc) superconductivity such as SQUID's, and filters for telecommunication. PTR’s are also suitable for cooling MRI-systems and energy-related systems using superconducting magnets. In so-called dry magnets, coolers are used so that no cryoliquid is needed at all or for the recondensation of the evaporated helium. Also the combination of cryocoolers with 3He-4He dilution refrigerators for the temperature region down to 2 mK is attractive since in this way the whole temperature range from room temperature to 2 mK is easier to access.

## References

1. ^ Development of the Pulse Tube Refrigerator as an Efficient and Reliable Cryocooler (2000)
2. ^ About ACT (official site)
3. ^ QUBIC Bolometric interferometry: the concept (official site)
4. ^ Pulse Tube Oxygen Liquefier
5. ^ A.T.A.M. de Waele, Basic operation of cryocoolers and related thermal machines, Review article, J Low Temp Phys., Vol.164, pp. 179-236, (2011), DOI: 10.1007/s10909-011-0373-x.
6. ^ E.I. Mikulin, A.A. Tarasov, and M.P. Shkrebyonock, Low-temperature expansion pulse tubes, Adv. Cryo. Eng., 31 (1984) 629
7. ^ S. Zhu, P. Wu, and Z. Chen, Double inlet pulse tube refrigerators: an important improvement, Cryogenics, 30 (1990) 514-520;
8. ^ Y. Matsubara and J.L. Gao, Novel configuration of three-stage pulse tube refrigerator for temperatures below 4 K, Cryogenics, 34 (1994) 259;
9. ^ G. Thummes, C. Wang, S. Bender, and C. Heiden, DKV-Tagungsbericht 23, Jahrgang Band I , (1996) 147;
10. ^ M.Y. Xu, A.T.A.M. de Waele, and Y.L. Ju, A pulse-tube refrigerator below 2 K, Cryogenics, 39 (1999) 865;
11. ^ Y. Matsubara, Proc. of the 17th Int. Cryogenic Eng. Conf.,(Institute of Physics Publishing, 1998) 11.
12. ^ I.A. Tanaeva, U. Lindemann, N. Jiang, A.T.A.M. de Waele and G. Thummes, Superfluid Vortex Cooler, Advances in Cryogenic Engineering 49B, 1906-1913 (2004)
13. ^ Z.H. Gan, W.Q. Dong, L.M. Qiu, X.B. Zhang, H. Sun, Y.L. He, and R. Radebaugh, Cryogenics 49, 198 (2009)
14. ^ Y. Matsubara and J.L. Gao, Cryogenics 34, 259 (1994)
15. ^ M.Y. Xu, A.T.A.M. de Waele, and Y.L. Ju, Cryogenics 39, 865 (1999)