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Top-loading high power dilution refrigerator for radiophysical studies at T ≲ 0.1 K
Top-loading high power dilution refrigerator for radiophysical studies at 0.1K A . V . Golik and S.I. Tarapov Institute of Radiophysics and Electronics, Academy of Sciences of the Ukrainian SSR, 310085 Kharkov, USSR
Received 29 May 199 I; revised 12 September 1991
The design of a top-loading high power 3He/4He dilution refrigerator for radiophysical studies at O. 1 K is described. Its construction is based on placing an experimental cell into a tapered stopper, which, in turn, is placed in a tube connecting the evaporation and mixing chambers. This construction allows one to position mechanically driven impedance matching transformers near the experimental cell.
magnetic fields, impedance transformers placed near the experimental cell and tuned by rods through vacuumtight leads-in placed at the top of the system are the most convenient• Devices for acoustic investigations in 4He or 3He evaporation refrigerators with such impedance transformers are described in References 4 and 5. Direct use of devices such as those described in References 1 - 3 in refrigerators is impossible because a power heat flow shunts the heat exchanges through a superflowing film using impedance transformers, coaxial feeders or waveguides. Below the construction is described of a top-loading dilution refrigerator for acoustic investigations near 0.1 K, in which mechanically tuned impedance transformers are placed near the experimental cell (see Figure 1). It contains a heat-insulating stopper (1), which consists of a thin-walled tubular body (2) made of stainless steel of thickness 0 . 3 - 0 • 5 mm and flanges (3 and 4). The flanges are coupled with the tubular body by indium self-tightening seals (5). The experimental cell
1CI
Keywords: refrigerators; dilution refrigerators transformers
Among the various types of dilution refrigerators, 3He/4He top-loading refrigerators t-3 have a leading role in practical physical experiments• One construction method for these refrigerators consists of using a tube • connecting a 3 H e /4H e mixing chamber and a 3He evaporation chamber. An experimental cell with the sample under investigation is placed on the lower end of the rod holder, which is inserted through a lock chamber placed at the top of the system. A tapered stopper is placed above the experimental cell; this pressurizes a tube connecting the evaporation and mixing chambers while in a working position. Using this set-up a connection between these chambers is provided only through the heat exchangers• When one needs to change the sample, the rod holder with the tapered stopper is taken out through the lock and the refrigerator goes into the 3He evaporation regime• With such a construction a sample change occurs without removing the refrigerator from the working regime and takes no more than 40 min. Conducting radiophysical experiments at low temperatures as a rule requires impedance matching of the load (e.g. resonator, acoustic transducer) with an electrodynamic feeder. This allows one to decrease the electromagnetic power supplied to the experimental cell and to realize the maximum sensitivity of the detecting devices. For radiophysical experiments in strong - 2 2 7 5 / 9 2 1 0 3 0 3 3 0 - 02 © 1992 Butterworth - Heinemann Ltd
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Cryogenics 1992 Vol 32, No 3
Figure 1 Diagram showing design of refrigerator. 1, Tapered stopper; 2, thin-walled body; 3, 4, flanges; 5, self-tightening seals; 6, experimental cell; 7, mixing chamber; 8, cold conductor; 9, heat exchanger; 10, feeder (coaxial); 11,12, tubes; 13, rod holder; 14, evaporation chamber; 15, tube, with a conical segment; 16, heat exchanger; 17, super-high frequency joints; 18, tight seals; 19, tie rods; 20, impedance transformers; 21, tie rod, 22, orientation mechanism; 23, upper flange of cryostat; 24, flexible coaxials
Research and technical notes
(6) is installed at the lower flange (4). Heat contact between the cell (6) and a mixing chamber (7) is provided by a cold conductor (8) made of a bunch of copper wires brazed into the flange (4). The lower end of the bunch is sintered with a heat exchanger (9) which is a block of sintered copper powder with a grain size d = 7/~m. The surface area of the heat exchanger S --- 2 m 2. Electrodynamic feeders (10) and the tubes (11 and 12) entering the stopper through the flange (3) are placed inside the thin-wailed rod holder (13). The rod holder (13) is intended to facilitate input of the stopper into the mixing chamber (7). The flange (3) is in the 3He evaporation chamber (14). The evaporation chamber (14) is connected with the mixing chamber by a tube (15) with a conical segment and continuous and discrete heat exchangers (16). Vacuum-tight super-high frequency (SHF) ( 3 - 3 0 GHz)joints (17) and tight seals (18) of tie rods (19) for impedance transformer tuning (20) and a tie rod (21) for orientation (22) of the experimental cell (6) are placed over the upper flange (23) of the cryostat. The lock is not shown in Figure 1. The experimental cell is electrically connected with the impedance transformers by flexible coaxials (24). Construction types of coaxial impedance transformers produced in recent years which showed high operation characteristics are described in Reference 5. One tube (12) serves to evacuate gas from the stopper and the tie rod (11) controls the mechanism for cell orientation. Such an arrangement of the refrigerator, as well as allowing the possibility of knocking down the stopper, allows the transference of mechanical motion of the tie rods to the cavity placed over the mixing chamber. This construction is very advanced for conducting electrodynamic investigations using open resonators 6'7. In this case, a sample with a lower resonator mirror is closely attached to the cold conductor (8) and has no heat contact with the upper mirror, connected to a waveguide. Due to this arrangement, the heat power absorbed in the mirrors at the expense of the SHF heat losses falls by a factor of almost two and amounts to W=5x10 -4-1 x10 -3W. The circulation rate of 3He, i3 = 5 x 10-3 _ 10-2 mol s- 1, is maintained by a pumping system with a pump capacity of v = 2500 dm 3 s -I. A block of super-low temperature heat exchangers includes a continuous countercurrent heat exchanger having a heat exchange area A = 1 m 2 and three coaxial discrete heat exchangers of sintered copper powder (d = 7 #m) with a heat exchange area Ad = 8 m 2. This system provides cooling power W = 1.5 x 10 -1 W at a mixing chamber temperature Tm.c. = 0.5 K. Such a high capacity with the given construction enables one to install adjustable throttles for 4He and 3He/aHe dilutions that give the ability first, to maintain the working temperature for 20 min (beginning at 4.2 K) and second, to practically exclude the small quantity of compressed air (used to plug the seal throttle), which inevitably comes into the refrigerator through the lock chamber. It is necessary to note that the arrangement of the experimental cell inside the stopper must satisfy the next thermodynamic condition, i.e. the total heat flow to the experimental cell must not exceed the heat removal at the expense of the mixing chamber. Where Te is the temperature of the 3He evaporation chamber and Tm is
the temperature of the mixing chamber, AT is the difference between the temperatures of the experimental cell and mixing chamber. Known calculation methods and thermodynamic relations (see, for example, Reference 8) allow us to express this condition as follows (
H _ 1 < / ( T e - Tm - AT)[(R1 + Rz)X2Az + H]
-X2A2An3/fX2A2aT
+ (To-
/ \)~TAT,]
T m -
AT)I
(1)
where: H is the distance from the bottom of the evaporation chamber to the top of the mixing chamber; l is the distance from the bottom of the evaporation chamber to the experimental cell; R1 is the Kapitza resistance at the boundary between the 3He/4He dilution and the copper heat exchanger placed in the mixing chamber; R2 is the Kapitza resistance at the boundary between the cold conductor and the experimental cell; R 3 is the Kapitza resistance at the intersection of the electrodynamic feeder and the experimental cell; )~2 is the heat conductivity of the cold conductor material; A2 is the crosssectional area of the cold conductor; XT is the heat conductivity of the material of the electrodynamic feeders; and AT is the cross-sectional area of the electrodynamic feeders. The case of equality of the right-hand side of Equation (1) corresponds to the equality of the external heat flow to the experimental cell with the refrigerating capacity of the mixing chamber. A change in the sign of the equality in the right-hand side of Equation (1) denotes a departure from the above thermodynamic condition. A limiting case H = l corresponds to the mounting of the experimental cell on the bottom of the stopper (lower flange) and, naturally, this is the best situation from the thermodynamic point of view. From another part of the equation one may obtain the limit of the minimum value of H. Practically, H = 8 - 1 0 cm in the working temperature range of the sample Tsample = 70--100 mK.
References 1 Direkt ladbarer Mischkryostat mit Proben-Schnellwechsel BRD Patent No. 2744346; F 25D 3/10; B 01 L 11/60 (1977) 2 Neganov, V.S., Parlor, W.N. and Borisov, N.S., Ustrojstvo dlja poluchenija nizkich temperatur, A.S. USSR No. 5 79508; F 25 j I/009, F 25D 3/10, Bull oipoiz (1977) 41 3 Reinders, P.H.P., Springford, M., Hilton, P., Kerley, N. and Killoran, N. Novel top-loading 20 mK/IST cryomagnetic system Cryogenics (1987) 27 689-642 4 Korolyuk, A.P., Roi, V.F., Golik, A.V. et al. A low temperature device for magnetoacoustic studies Cryogenics (1975) 10 146-147 and Prib i Tekh Eksp (1974) 4 208-209 5 Golik, A.V., Korolyuk, A.P. and Khizhnyi, V.I. Nizkotemperaturnoe soglasujuschee ustrojstvo Prib i Tekh Eksp (1987) 2 213-215 6 Vertiy, A.A., Ivanehenko, I.V., Tarapov, S.I. et al. Radiophuzicheskij blok sverhnizkotemperaturnogo spectrometra mm diapazona Prib i Tekh Eksp (1988) 2 107-111 7 Vertiy, A.A., Golik, A.V., Tarapov, S.I., Korolyuk, A.P. et al. Magnetic resonance in amorphous metals based on Fe in millimeter radiowave range In J Infrared Millimeter Waves (1989) 10 1451 - 1457 8 Lounasmaa, O.V. Experimental Principles and Methods Below 1 K Academic Press, London, UK (1974) 38
Cryogenics 1992 Vol 32, No 3
331
Received 29 May 199 I; revised 12 September 1991
The design of a top-loading high power 3He/4He dilution refrigerator for radiophysical studies at O. 1 K is described. Its construction is based on placing an experimental cell into a tapered stopper, which, in turn, is placed in a tube connecting the evaporation and mixing chambers. This construction allows one to position mechanically driven impedance matching transformers near the experimental cell.
magnetic fields, impedance transformers placed near the experimental cell and tuned by rods through vacuumtight leads-in placed at the top of the system are the most convenient• Devices for acoustic investigations in 4He or 3He evaporation refrigerators with such impedance transformers are described in References 4 and 5. Direct use of devices such as those described in References 1 - 3 in refrigerators is impossible because a power heat flow shunts the heat exchanges through a superflowing film using impedance transformers, coaxial feeders or waveguides. Below the construction is described of a top-loading dilution refrigerator for acoustic investigations near 0.1 K, in which mechanically tuned impedance transformers are placed near the experimental cell (see Figure 1). It contains a heat-insulating stopper (1), which consists of a thin-walled tubular body (2) made of stainless steel of thickness 0 . 3 - 0 • 5 mm and flanges (3 and 4). The flanges are coupled with the tubular body by indium self-tightening seals (5). The experimental cell
1CI
Keywords: refrigerators; dilution refrigerators transformers
Among the various types of dilution refrigerators, 3He/4He top-loading refrigerators t-3 have a leading role in practical physical experiments• One construction method for these refrigerators consists of using a tube • connecting a 3 H e /4H e mixing chamber and a 3He evaporation chamber. An experimental cell with the sample under investigation is placed on the lower end of the rod holder, which is inserted through a lock chamber placed at the top of the system. A tapered stopper is placed above the experimental cell; this pressurizes a tube connecting the evaporation and mixing chambers while in a working position. Using this set-up a connection between these chambers is provided only through the heat exchangers• When one needs to change the sample, the rod holder with the tapered stopper is taken out through the lock and the refrigerator goes into the 3He evaporation regime• With such a construction a sample change occurs without removing the refrigerator from the working regime and takes no more than 40 min. Conducting radiophysical experiments at low temperatures as a rule requires impedance matching of the load (e.g. resonator, acoustic transducer) with an electrodynamic feeder. This allows one to decrease the electromagnetic power supplied to the experimental cell and to realize the maximum sensitivity of the detecting devices. For radiophysical experiments in strong - 2 2 7 5 / 9 2 1 0 3 0 3 3 0 - 02 © 1992 Butterworth - Heinemann Ltd
0011
330
Cryogenics 1992 Vol 32, No 3
Figure 1 Diagram showing design of refrigerator. 1, Tapered stopper; 2, thin-walled body; 3, 4, flanges; 5, self-tightening seals; 6, experimental cell; 7, mixing chamber; 8, cold conductor; 9, heat exchanger; 10, feeder (coaxial); 11,12, tubes; 13, rod holder; 14, evaporation chamber; 15, tube, with a conical segment; 16, heat exchanger; 17, super-high frequency joints; 18, tight seals; 19, tie rods; 20, impedance transformers; 21, tie rod, 22, orientation mechanism; 23, upper flange of cryostat; 24, flexible coaxials
Research and technical notes
(6) is installed at the lower flange (4). Heat contact between the cell (6) and a mixing chamber (7) is provided by a cold conductor (8) made of a bunch of copper wires brazed into the flange (4). The lower end of the bunch is sintered with a heat exchanger (9) which is a block of sintered copper powder with a grain size d = 7/~m. The surface area of the heat exchanger S --- 2 m 2. Electrodynamic feeders (10) and the tubes (11 and 12) entering the stopper through the flange (3) are placed inside the thin-wailed rod holder (13). The rod holder (13) is intended to facilitate input of the stopper into the mixing chamber (7). The flange (3) is in the 3He evaporation chamber (14). The evaporation chamber (14) is connected with the mixing chamber by a tube (15) with a conical segment and continuous and discrete heat exchangers (16). Vacuum-tight super-high frequency (SHF) ( 3 - 3 0 GHz)joints (17) and tight seals (18) of tie rods (19) for impedance transformer tuning (20) and a tie rod (21) for orientation (22) of the experimental cell (6) are placed over the upper flange (23) of the cryostat. The lock is not shown in Figure 1. The experimental cell is electrically connected with the impedance transformers by flexible coaxials (24). Construction types of coaxial impedance transformers produced in recent years which showed high operation characteristics are described in Reference 5. One tube (12) serves to evacuate gas from the stopper and the tie rod (11) controls the mechanism for cell orientation. Such an arrangement of the refrigerator, as well as allowing the possibility of knocking down the stopper, allows the transference of mechanical motion of the tie rods to the cavity placed over the mixing chamber. This construction is very advanced for conducting electrodynamic investigations using open resonators 6'7. In this case, a sample with a lower resonator mirror is closely attached to the cold conductor (8) and has no heat contact with the upper mirror, connected to a waveguide. Due to this arrangement, the heat power absorbed in the mirrors at the expense of the SHF heat losses falls by a factor of almost two and amounts to W=5x10 -4-1 x10 -3W. The circulation rate of 3He, i3 = 5 x 10-3 _ 10-2 mol s- 1, is maintained by a pumping system with a pump capacity of v = 2500 dm 3 s -I. A block of super-low temperature heat exchangers includes a continuous countercurrent heat exchanger having a heat exchange area A = 1 m 2 and three coaxial discrete heat exchangers of sintered copper powder (d = 7 #m) with a heat exchange area Ad = 8 m 2. This system provides cooling power W = 1.5 x 10 -1 W at a mixing chamber temperature Tm.c. = 0.5 K. Such a high capacity with the given construction enables one to install adjustable throttles for 4He and 3He/aHe dilutions that give the ability first, to maintain the working temperature for 20 min (beginning at 4.2 K) and second, to practically exclude the small quantity of compressed air (used to plug the seal throttle), which inevitably comes into the refrigerator through the lock chamber. It is necessary to note that the arrangement of the experimental cell inside the stopper must satisfy the next thermodynamic condition, i.e. the total heat flow to the experimental cell must not exceed the heat removal at the expense of the mixing chamber. Where Te is the temperature of the 3He evaporation chamber and Tm is
the temperature of the mixing chamber, AT is the difference between the temperatures of the experimental cell and mixing chamber. Known calculation methods and thermodynamic relations (see, for example, Reference 8) allow us to express this condition as follows (
H _ 1 < / ( T e - Tm - AT)[(R1 + Rz)X2Az + H]
-X2A2An3/fX2A2aT
+ (To-
/ \)~TAT,]
T m -
AT)I
(1)
where: H is the distance from the bottom of the evaporation chamber to the top of the mixing chamber; l is the distance from the bottom of the evaporation chamber to the experimental cell; R1 is the Kapitza resistance at the boundary between the 3He/4He dilution and the copper heat exchanger placed in the mixing chamber; R2 is the Kapitza resistance at the boundary between the cold conductor and the experimental cell; R 3 is the Kapitza resistance at the intersection of the electrodynamic feeder and the experimental cell; )~2 is the heat conductivity of the cold conductor material; A2 is the crosssectional area of the cold conductor; XT is the heat conductivity of the material of the electrodynamic feeders; and AT is the cross-sectional area of the electrodynamic feeders. The case of equality of the right-hand side of Equation (1) corresponds to the equality of the external heat flow to the experimental cell with the refrigerating capacity of the mixing chamber. A change in the sign of the equality in the right-hand side of Equation (1) denotes a departure from the above thermodynamic condition. A limiting case H = l corresponds to the mounting of the experimental cell on the bottom of the stopper (lower flange) and, naturally, this is the best situation from the thermodynamic point of view. From another part of the equation one may obtain the limit of the minimum value of H. Practically, H = 8 - 1 0 cm in the working temperature range of the sample Tsample = 70--100 mK.
References 1 Direkt ladbarer Mischkryostat mit Proben-Schnellwechsel BRD Patent No. 2744346; F 25D 3/10; B 01 L 11/60 (1977) 2 Neganov, V.S., Parlor, W.N. and Borisov, N.S., Ustrojstvo dlja poluchenija nizkich temperatur, A.S. USSR No. 5 79508; F 25 j I/009, F 25D 3/10, Bull oipoiz (1977) 41 3 Reinders, P.H.P., Springford, M., Hilton, P., Kerley, N. and Killoran, N. Novel top-loading 20 mK/IST cryomagnetic system Cryogenics (1987) 27 689-642 4 Korolyuk, A.P., Roi, V.F., Golik, A.V. et al. A low temperature device for magnetoacoustic studies Cryogenics (1975) 10 146-147 and Prib i Tekh Eksp (1974) 4 208-209 5 Golik, A.V., Korolyuk, A.P. and Khizhnyi, V.I. Nizkotemperaturnoe soglasujuschee ustrojstvo Prib i Tekh Eksp (1987) 2 213-215 6 Vertiy, A.A., Ivanehenko, I.V., Tarapov, S.I. et al. Radiophuzicheskij blok sverhnizkotemperaturnogo spectrometra mm diapazona Prib i Tekh Eksp (1988) 2 107-111 7 Vertiy, A.A., Golik, A.V., Tarapov, S.I., Korolyuk, A.P. et al. Magnetic resonance in amorphous metals based on Fe in millimeter radiowave range In J Infrared Millimeter Waves (1989) 10 1451 - 1457 8 Lounasmaa, O.V. Experimental Principles and Methods Below 1 K Academic Press, London, UK (1974) 38
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