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Advances in dilution refrigeration in high magnetic fields
PHYSICA Physica B 201 (1994) 597-600
ELSEVIER
Advances in dilution refrigeration in high magnetic fields J.D. Hutchins*, N.H. Balshaw, G.J. Batey, R. Ling, J.P. White, E.P. Whitehurst Oxford Instruments Ltd., Old Station Way, Eynsham, Witney, Oxon, OX8 1TL, UK
Abstract 3He/4He dilution refrigerators have become a standard laboratory tool used to cool experiments to the milli-kelvin temperature range. Many of these applications involve the use of high magnetic fields. One system includes a 20.7 T superconducting magnet (the highest field ever achieved using multi filamentary superconducting wire in compact magnet form) and it can cool samples to 20 mK. Other systems have been designed for use with rapidly sweeping superconducting magnets, and even for pulsed liquid nitrogen cooled magnets, with maximum fields up to 60 T,
1. Introduction A wide range of different dilution refrigerators has been built for applications involving high magnetic fields. The design of these refrigerators is profoundly influenced by the nature of the application. In particular, refrigerators optimised for operation in a static magnetic field are very different from those for sweeping or pulsed fields. We will describe several systems which operate with superconducting magnets (in static or sweeping fields) and one which is being used in a pulsed field.
2. Low eddy current sample holders Many experiments are carried out in static or slowly sweeping magnetic fields. Provided that vibrations are minimised, there is great advantage to be gained by putting the sample in vacuum in the centre of field of the magnet. It is easy to make wiring connections to the sample, and there is no need to break the low-temperature seals on the mixing chamber when the sample is changed. The sample can be mounted on a low eddy
* Corresponding author.
current sample holder made of a bundle of copper wires. The mixing chamber can be located in a cancelled field region, allowing field sensitive thermometers or experiments to be fitted. It is a common misconception among users of dilution refrigerator systems that the best thermal contact between their sample and the cold liquid in the mixing chamber can be made by immersing the sample in the liquid. However, at temperatures below 200inK the Kapitza resistance must not be neglected. This boundary resistance is caused by the phonon mis-match at the boundary between the liquid and solid, and varies with the speed of sound in the two media [1]. The following equation is said to be in reasonable agreement with most experimental results (for liquid helium to solid) in the temperature range from 10 to 200mK, dT 15h3psVs 3 Rk = d ~ = 292k 4 T3 Aphvh '
(1)
where Ps and vs are the density of the solid and transverse velocity of sound in the solid, and Ph and vh are for the liquid helium. If a sample is mounted inside the mixing chamber the thermal contact is usually very poor. A small amount of heat supplied to the sample can warm it to a temperature
0921-4526/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 4 ) 0 0 1 4 4 - K
598
J.D. Hutchins et al./ Physica B 201 (1994) 597 600
much higher than that of the 3He/~He liquid. For example, a heat load of 1 ~tW applied to a typical small sample may increase its temperature to 80 mK even if the liquid is at 30mK. Increasing the cooling power of the refrigerator does not help, but if the sample is carefully mounted it should be possible to reach a temperature close to 30 mK with the same heat load. In many cases the method of mounting the sample affects the performance of the system much more than the specified cooling power of the refrigerator. Increasing the surface area in contact with the liquid improves thermal contact. The sample can be thermally anchored to sintered silver heat exchanger fins within the mixing chamber. One gram of silver sinter typically has a surface area of 1 m 2, so it is possible to have tens of square metres in a very small volume. It is easier to get good thermal contact between solids because the phonon velocities are more closely matched. Some solids are better than others, and in particular some non-metallic materials have anomalously low Kapitza resistance which makes them useful for heat exchanger applications as described below. There are however, some situations where this is not the best approach, and it is sometimes necessary to compromise the thermal contact so that the amount of eddy current heating can be reduced to an acceptable level. If the field is sweeping more rapidly than about 1 T/min, other techniques have to be used.
possible to reduce the total heat load to around 2 or 3 ~tW. This type of dilution refrigerator is typically unaffected by magnetic fields sweeping at rates in excess of 2 T/min, and it is therefore appropriate for a variety of applications including quantum hall effect. It is also suitable for use in modulated magnetic fields, allowing other experiments to be carried out, including De Haas van Alphen, AC susceptibility and nuclear quadrapole resonance measurements. It is possible to make several top loading probes for one of these systems, to increase its flexibility. Each probe may be fitted with different services for the experiment. We have fitted twisted pair wiring, semi-rigid coaxial cables, light pipes and wave guides, and DC SQUIDS to these systems. We have also fitted mechanical drive rods, allowing a sample in the mixing chamber to be rotated about a vertical or horizontal axis with high precision. Similar refrigerator systems have also been built for operation in Bitter magnets and hybrid magnets (with and without top loading). Some of these magnets are capable of rapid sweep rates, but they also tend to have high vibration levels because of the cooling water flow. Therefore, it is important that non-metallic components are used in the high field regions to minimise eddy current heating. The room temperature bore of the magnet also tends to be small, so special cryostats have been built for these refrigerators with accurately aligned radiation shields. It is typically possible to get a sample space of 8 mm in a room temperature bore of 32 mm, and to cool samples to temperatures below 20 mK.
3. Top loading dilution refrigerators The top loading into mixture (TLM), design has been used successfully on many occasions [2]. The parts of the mixing chamber that are in the high field region are non-metallic, so the refrigerator is not affected by eddy current heating when the magnetic field sweeps rapidly. In 1992 we developed a smaller version of the TLM refrigerator with a compact pumping system, and this is more appropriate for the majority of laboratories. A 3.5 to 4 m high ceiling is typically required, depending on the size of the superconducting magnet. The sample is mounted on a top loading probe which is fitted with a vacuum lock to prevent the loss of the valuable 3He/4He mixture or the addition of air. This probe can be loaded into the refrigerator without warming the rest of the system above 4.2 K. It is possible to change samples and cool the new sample to 20 mK within 3 h. The design of this top loading probe is critical for successful operation of the system. It must be made of low thermal conductivity materials. It also has to be a very close fit in the dilution unit so that the heat load from the column of superfluid is minimised. It is typically
4. Non-metallic systems Pulsed magnetic fields are perhaps the most demanding environment for systems operating in the milli-kelvin range. Not only are higher fields available from pulsed magnets, but the field sweeps to a maximum value of 60 T or more in a few milli-seconds. The field pulse can induce large Lorentz forces in metallic components, and eddy currents induced in the system are dissipated as heat. Low conductivity metallic materials are used for parts of the refrigerator which operate at temperatures above 1 K, where the field is relatively low, and eddy current heating has less effect. All parts of the system which operate at temperatures below 1 K (the 'dilution unit') are non-metallic. Most of them are made from an engineering thermoplastic which can be accurately machined, and reliably bonded. This calls for an innovative approach to the technology of the heat exchangers, since the conventional systems use metal tubes and sintered metal powders, which are not allowed near the high field region. Fortunately, some plastic materials are found to
J.D, Hutchins et al./ Physica B 201 (1994) 597-600 18 way access for diagnostic wiring 18 way experimental • access 1K pot level -~ probe entry IVC pumping' line
599
1K pot needle valve ~-~---
~ ~
1K pot pumping line 3He return line ------- Syphon entry
-~
~_E / L - - - J
Helium level probe He oumoina line
Nitrogen exhaust Electrical access to cryostat Helium recover ~
Nitrogen fill
line
Liquid helium reservoir
1K pot Adjustable legs
refrigerator Removable extension tails
Pulsed magnet in liquid nitrogen reservoir
.i ./ Non metallic dilution refrigerator in pulsed magnet system
Fig. 1. A Kelvinox NT non-metallic dilution refrigerator in a pulsed field magnet.
600
J.D. Hutchins et al./ Physica B 201 (1994) 597-600
have anomalously low Kapitza resistances, so it is possible to build very effective heat exchangers, even though the thermal conductivity of the plastics is so low. Most pulsed field magnets have very limited access for the experiment, and tolerances are very tight. The sample region of the mixing chamber therefore has a very small diameter and since it is essential that it does not touch any of the warmer components around it, it has to be aligned carefully. The 3He is forced to flow past the sample, ensuring that it is cooled effectively. One of the most important features of the system is that it is easy to gain access to the wiring to modify it in the event of a change in the experiment. Fig. 1 shows a typical liquid nitrogen cooled pulsed magnet, with a non-metallic dilution refrigerator. This refrigerator requires a small liquid helium reservoir, and this is designed to fit into the liquid nitrogen space of the magnet cryostat. The system has a base temperature of 25mK, and a cooling power > 200laW at 100mK. The magnet will pulse to > 55 T in < 5 ms.
5. Conclusion
A wide range of techniques is already available to achieve low temperatures in high magnetic fields. We are continuously developing novel dilution refrigerator systems to extend the technology further. The combination of non-metallic dilution refrigerator technology with advances in pulsed field magnets will allow access to new physical environments. Easy access to B / T ratios in excess of 5 × 103 T / K should allow the discovery of many new and exciting phenomena in the next few years.
References
[1] F. Pobell, Matter and Methods at Low Temperatures (Springer, Berlin, 1992). [2] P.H.P. Reinders, M. Springford, P. Hilton, N. Kerley and N. Killoran, Cryogenics 27 (1987) 689.
ELSEVIER
Advances in dilution refrigeration in high magnetic fields J.D. Hutchins*, N.H. Balshaw, G.J. Batey, R. Ling, J.P. White, E.P. Whitehurst Oxford Instruments Ltd., Old Station Way, Eynsham, Witney, Oxon, OX8 1TL, UK
Abstract 3He/4He dilution refrigerators have become a standard laboratory tool used to cool experiments to the milli-kelvin temperature range. Many of these applications involve the use of high magnetic fields. One system includes a 20.7 T superconducting magnet (the highest field ever achieved using multi filamentary superconducting wire in compact magnet form) and it can cool samples to 20 mK. Other systems have been designed for use with rapidly sweeping superconducting magnets, and even for pulsed liquid nitrogen cooled magnets, with maximum fields up to 60 T,
1. Introduction A wide range of different dilution refrigerators has been built for applications involving high magnetic fields. The design of these refrigerators is profoundly influenced by the nature of the application. In particular, refrigerators optimised for operation in a static magnetic field are very different from those for sweeping or pulsed fields. We will describe several systems which operate with superconducting magnets (in static or sweeping fields) and one which is being used in a pulsed field.
2. Low eddy current sample holders Many experiments are carried out in static or slowly sweeping magnetic fields. Provided that vibrations are minimised, there is great advantage to be gained by putting the sample in vacuum in the centre of field of the magnet. It is easy to make wiring connections to the sample, and there is no need to break the low-temperature seals on the mixing chamber when the sample is changed. The sample can be mounted on a low eddy
* Corresponding author.
current sample holder made of a bundle of copper wires. The mixing chamber can be located in a cancelled field region, allowing field sensitive thermometers or experiments to be fitted. It is a common misconception among users of dilution refrigerator systems that the best thermal contact between their sample and the cold liquid in the mixing chamber can be made by immersing the sample in the liquid. However, at temperatures below 200inK the Kapitza resistance must not be neglected. This boundary resistance is caused by the phonon mis-match at the boundary between the liquid and solid, and varies with the speed of sound in the two media [1]. The following equation is said to be in reasonable agreement with most experimental results (for liquid helium to solid) in the temperature range from 10 to 200mK, dT 15h3psVs 3 Rk = d ~ = 292k 4 T3 Aphvh '
(1)
where Ps and vs are the density of the solid and transverse velocity of sound in the solid, and Ph and vh are for the liquid helium. If a sample is mounted inside the mixing chamber the thermal contact is usually very poor. A small amount of heat supplied to the sample can warm it to a temperature
0921-4526/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 4 ) 0 0 1 4 4 - K
598
J.D. Hutchins et al./ Physica B 201 (1994) 597 600
much higher than that of the 3He/~He liquid. For example, a heat load of 1 ~tW applied to a typical small sample may increase its temperature to 80 mK even if the liquid is at 30mK. Increasing the cooling power of the refrigerator does not help, but if the sample is carefully mounted it should be possible to reach a temperature close to 30 mK with the same heat load. In many cases the method of mounting the sample affects the performance of the system much more than the specified cooling power of the refrigerator. Increasing the surface area in contact with the liquid improves thermal contact. The sample can be thermally anchored to sintered silver heat exchanger fins within the mixing chamber. One gram of silver sinter typically has a surface area of 1 m 2, so it is possible to have tens of square metres in a very small volume. It is easier to get good thermal contact between solids because the phonon velocities are more closely matched. Some solids are better than others, and in particular some non-metallic materials have anomalously low Kapitza resistance which makes them useful for heat exchanger applications as described below. There are however, some situations where this is not the best approach, and it is sometimes necessary to compromise the thermal contact so that the amount of eddy current heating can be reduced to an acceptable level. If the field is sweeping more rapidly than about 1 T/min, other techniques have to be used.
possible to reduce the total heat load to around 2 or 3 ~tW. This type of dilution refrigerator is typically unaffected by magnetic fields sweeping at rates in excess of 2 T/min, and it is therefore appropriate for a variety of applications including quantum hall effect. It is also suitable for use in modulated magnetic fields, allowing other experiments to be carried out, including De Haas van Alphen, AC susceptibility and nuclear quadrapole resonance measurements. It is possible to make several top loading probes for one of these systems, to increase its flexibility. Each probe may be fitted with different services for the experiment. We have fitted twisted pair wiring, semi-rigid coaxial cables, light pipes and wave guides, and DC SQUIDS to these systems. We have also fitted mechanical drive rods, allowing a sample in the mixing chamber to be rotated about a vertical or horizontal axis with high precision. Similar refrigerator systems have also been built for operation in Bitter magnets and hybrid magnets (with and without top loading). Some of these magnets are capable of rapid sweep rates, but they also tend to have high vibration levels because of the cooling water flow. Therefore, it is important that non-metallic components are used in the high field regions to minimise eddy current heating. The room temperature bore of the magnet also tends to be small, so special cryostats have been built for these refrigerators with accurately aligned radiation shields. It is typically possible to get a sample space of 8 mm in a room temperature bore of 32 mm, and to cool samples to temperatures below 20 mK.
3. Top loading dilution refrigerators The top loading into mixture (TLM), design has been used successfully on many occasions [2]. The parts of the mixing chamber that are in the high field region are non-metallic, so the refrigerator is not affected by eddy current heating when the magnetic field sweeps rapidly. In 1992 we developed a smaller version of the TLM refrigerator with a compact pumping system, and this is more appropriate for the majority of laboratories. A 3.5 to 4 m high ceiling is typically required, depending on the size of the superconducting magnet. The sample is mounted on a top loading probe which is fitted with a vacuum lock to prevent the loss of the valuable 3He/4He mixture or the addition of air. This probe can be loaded into the refrigerator without warming the rest of the system above 4.2 K. It is possible to change samples and cool the new sample to 20 mK within 3 h. The design of this top loading probe is critical for successful operation of the system. It must be made of low thermal conductivity materials. It also has to be a very close fit in the dilution unit so that the heat load from the column of superfluid is minimised. It is typically
4. Non-metallic systems Pulsed magnetic fields are perhaps the most demanding environment for systems operating in the milli-kelvin range. Not only are higher fields available from pulsed magnets, but the field sweeps to a maximum value of 60 T or more in a few milli-seconds. The field pulse can induce large Lorentz forces in metallic components, and eddy currents induced in the system are dissipated as heat. Low conductivity metallic materials are used for parts of the refrigerator which operate at temperatures above 1 K, where the field is relatively low, and eddy current heating has less effect. All parts of the system which operate at temperatures below 1 K (the 'dilution unit') are non-metallic. Most of them are made from an engineering thermoplastic which can be accurately machined, and reliably bonded. This calls for an innovative approach to the technology of the heat exchangers, since the conventional systems use metal tubes and sintered metal powders, which are not allowed near the high field region. Fortunately, some plastic materials are found to
J.D, Hutchins et al./ Physica B 201 (1994) 597-600 18 way access for diagnostic wiring 18 way experimental • access 1K pot level -~ probe entry IVC pumping' line
599
1K pot needle valve ~-~---
~ ~
1K pot pumping line 3He return line ------- Syphon entry
-~
~_E / L - - - J
Helium level probe He oumoina line
Nitrogen exhaust Electrical access to cryostat Helium recover ~
Nitrogen fill
line
Liquid helium reservoir
1K pot Adjustable legs
refrigerator Removable extension tails
Pulsed magnet in liquid nitrogen reservoir
.i ./ Non metallic dilution refrigerator in pulsed magnet system
Fig. 1. A Kelvinox NT non-metallic dilution refrigerator in a pulsed field magnet.
600
J.D. Hutchins et al./ Physica B 201 (1994) 597-600
have anomalously low Kapitza resistances, so it is possible to build very effective heat exchangers, even though the thermal conductivity of the plastics is so low. Most pulsed field magnets have very limited access for the experiment, and tolerances are very tight. The sample region of the mixing chamber therefore has a very small diameter and since it is essential that it does not touch any of the warmer components around it, it has to be aligned carefully. The 3He is forced to flow past the sample, ensuring that it is cooled effectively. One of the most important features of the system is that it is easy to gain access to the wiring to modify it in the event of a change in the experiment. Fig. 1 shows a typical liquid nitrogen cooled pulsed magnet, with a non-metallic dilution refrigerator. This refrigerator requires a small liquid helium reservoir, and this is designed to fit into the liquid nitrogen space of the magnet cryostat. The system has a base temperature of 25mK, and a cooling power > 200laW at 100mK. The magnet will pulse to > 55 T in < 5 ms.
5. Conclusion
A wide range of techniques is already available to achieve low temperatures in high magnetic fields. We are continuously developing novel dilution refrigerator systems to extend the technology further. The combination of non-metallic dilution refrigerator technology with advances in pulsed field magnets will allow access to new physical environments. Easy access to B / T ratios in excess of 5 × 103 T / K should allow the discovery of many new and exciting phenomena in the next few years.
References
[1] F. Pobell, Matter and Methods at Low Temperatures (Springer, Berlin, 1992). [2] P.H.P. Reinders, M. Springford, P. Hilton, N. Kerley and N. Killoran, Cryogenics 27 (1987) 689.