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Techniques for the detection of second sound shock pulses and induced quantum turbulence in He II
Cryogenics 41 (2001) 347±353
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Techniques for the detection of second sound shock pulses and induced quantum turbulence in He II D.K. Hilton a,c,*, S.W. Van Sciver b,c a
c
Department of Physics, College of Arts and Sciences, Florida State University, Tallahassee, FL, USA b Mechanical Engineering Department, FAMU-FSU College of Engineering, Tallahassee, FL, USA National High Magnetic Field Laboratory, Florida State University, 1800 E. Paul Dirac Drive, Tallahassee, FL 32310, USA Received 8 January 2001; accepted 15 March 2001
Abstract This paper discusses the design and operation of thin-®lm thermometers and heaters for the detection and generation of second sound shock (SSS) pulses and second sound resonance (SSR) waves. The detection of quantum turbulence at multiple points along a channel is also discussed. An instrumentation package to simultaneously detect SSS pulses and induced quantum turbulence in He II has been developed. This system is able to generate and detect SSS pulses in a channel of He II while monitoring for induced quantum turbulence at multiple points along the channel. The system monitors for quantum turbulence by the attenuation of SSR waves. The experiments using this instrumentation package oer the ®rst opportunity to directly measure the quantum turbulence time and distance evolution of SSS pulses. These experiments have applications in transient heat transfer problems in He II, such as the cooling and stability of superconductors. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Temperature sensors; Thin ®lms; Heat transfer; Fluid dynamics; Super¯uid helium
1. Introduction Transient heat transfer problems in He II, such as the cooling and stability of superconductors, motivate continued research of second sound shock (SSS) pulse propagation. Solutions to such problems would be enhanced by a thorough understanding of the SSS pulse propagation. SSS pulses of sucient amplitude 2 (0:1±100 W=cm ) and short duration (0.01±10 ms) generate wakes of quantum vortex tangles, quantum turbulence, in He II, and are distorted by the quantum turbulence they induce. Nemirovskii and Tsoi presented a review and classi®cation of the existing experimental data [1]. Referring to Fig. 1, the parameter space de®ned by initial power ¯ux density and pulse duration, along with the He II bath temperature, reveals distinct regimes of qualitatively dierent transient heat transfer behaviors in He II, that require
*
Corresponding author. Tel.: +1-850-644-1708; fax: +1-850-6440867. E-mail address: [email protected] (D.K. Hilton).
further physical description. The region centered near 10 W=cm2 and 1 ms has not been extensively explored, and is perhaps the most interesting in that it is the intersection between three major regimes, developing quantum vorticity, fully developed vorticity, and ®lm boiling. The instrument package described in this paper will explore this region further than in previous experiments. All experiments of the type described here are performed in the lower temperature phase of liquid helium, He II, below the lambda point, Tk 2:176 K, on or near the saturation curve of liquid helium, and above T 1:40 K due to the existing equipment capability. Second sound manifests itself as temperature waves in He II. Consequently, second sound resonance (SSR) waves as well as SSS pulses require fast, compact thermometers and heaters for their detection and generation without distortion. Details requisite for an eective design of a SSS pulse research device have been outlined and veri®ed by experiment in a previous paper [2]. Here this discussion is extended to include the detection and generation of SSR waves. Further, the detection of induced quantum turbulence by the attenuation of SSR waves is also discussed.
0011-2275/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 1 - 2 2 7 5 ( 0 1 ) 0 0 0 9 1 - 1
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D.K. Hilton, S.W. Van Sciver / Cryogenics 41 (2001) 347±353
Fig. 2. Experimental schematic.
Fig. 1. Transient heat transfer regimes of He II [1].
2. Instrumentation package The focus of the instrument package is the SSS channel, a G-10 channel 178 mm long, with a 19:1 mm 12:7 mm rectangular interior cross-section. To minimize the electrical noise, the exterior lateral surface of the channel is layered in lead sheet, electrically grounded, forming a superconductive shield (Pb, Tc 7:2 K). The smoothness of the channel interior surface is as-received. Reviewing selections by previous researchers, neither the surface smoothness nor the material choice of the channel seems to introduce signi®cant artifacts during SSS pulse propagation [3±5]. The maximum duration pulse that can be investigated is determined by the length of the channel and the speed of second sound, of the order of 20 m/s in He II between 1 and 2 K. Shown in Fig. 2 is the experimental schematic, giving the essential spatial con®guration of the required thermometers and heaters. The bottom end holds the primary SSS heater, consisting of a fused silica (amorphous SiO2 ) substrate, 25:4 mm 19:1 mm, 0.83 mm thick, with both faces
ground and the upper active face polished. Upon the upper face is deposited by physical vapor deposition (PVD) a 16.5 nm thin-®lm of nichrome (80% Ni/20% Cr by weight), a centered 19.1 mm square. Nichrome has a nearly constant resistivity of 1:05 10 4 X cm at T < 4:2 K, and this resistivity does not vary signi®cantly over the range of interest up to room temperature. Electrical power pulse contacts are made to the primary heater at opposite edges through 150 nm thin-®lm strips of pure silver deposited by PVD, each 6.35 mm wide. Two brass plates, each 0.38 mm thick and with a superconducting indium (In) interface, are pressed into position to make cold-weld electrical contacts. Above the SSS heater along the longitudinal axis of the channel is the primary SSS thermometer, consisting of an S-glass ®lament of the order of 5±7 lm in diameter, such as the kind used in composites. Following similar work by Laguna [6], a 100 nm thin-®lm of tin (Sn) on top of a 25 nm thin-®lm of gold (Au) is deposited by PVD on one side of the ®lament. Tin is an elemental, Type-I superconductor (Sn, Tc 3:7 K). The layered thin-®lm system of Aux Sn1 x forms a proximity superconductor with an adjustable critical temperature (2:0 K < Tc < 3:7 K) and corresponding transition width. For x 0:2, Tc 2:1 K for this superconductor in zero magnetic ®eld [6]. Furthermore, the transition curve of this superconductor can be shifted down in temperature by the introduction of a low external magnetic ®eld. For example, a magnetic ®eld, B 0:02
D.K. Hilton, S.W. Van Sciver / Cryogenics 41 (2001) 347±353
T corresponds to a critical temperature, Tc 1:7 K according to the results of Laguna [6]. Thus, just above the SSS thermometer, mounted on a G-10 support tube for both is a small solenoid electromagnet. The electromagnet consists of a brass coil form, 11.13 mm in diameter, with four layers of 200 turns each of wire to form a solenoid 20.32 mm long. The wire, 0.102 mm in diameter, is a superconducting niobium±titanium/copper composite. At an operating current, I 3 A, this electromagnet can generate a fringe axial magnetic ®eld, B 0:03 T at a distance of 3.5 mm from the end of the solenoid, where the SSS thermometer is placed. Since the electromagnet is an integral component of the primary SSS thermometer, and Fig. 2 is a schematic, the electromagnet is not shown in this ®gure. Along the side walls, across the narrow span of the SSS channel, are heater and thermometer pairs for the generation and detection of SSR waves. The presence of quantum turbulence attenuates the SSR waves. Thus, the SSR waves, once established between each heater and thermometer pair, will continuously monitor at this position for quantum turbulence induced in conjunction with the SSS pulses being propagated. Six port pairs are provided along the channel, spaced 25.4 mm apart above the SSS heater. Three heater and thermometer pairs are installed for any given experiment, with the other ports closed o with blank G-10 plugs. Each side wall SSR heater consists of a fused silica (amorphous SiO2 ) disk substrate, 12.37 mm in diameter, 0.83 mm thick, with both faces ground and the interior active face polished. Upon the interior face is deposited by PVD a 34.7 nm thin-®lm of nichrome (80% Ni/20% Cr by weight). Two gold-plated needles 9.63 mm apart center-to-center at opposite edges with indium interfaces are pressed into position to make electrical contacts. Each side wall heater is assembled into a self-contained G-10 port plug machined for the purpose. Each side wall thermometer is also assembled into a similar G-10 port plug. The active interior face of the plug, 12.60 mm in diameter, is abraded in every direction of its surface with medium grit (240 grit) sandpaper to insure retention of a graphite thin-®lm that is the SSR thermometer. The abrasion cuts micro-channels into the surface, forming parallel, temperature-sensitive graphite resistors in the direction of the abrasion, when the graphite is later applied. Thus, the direction of abrasion in part determines the ®nal mean resistance of the thermometer, which in turn determines the electrical time constant [2]. The source of the graphite is a particular brand of pencil lead (Pentel, 0.5 mm, hardness B). The ®nal mean operating resistance and sensitivity of the thermometer is strongly dependent on the graphite source and hardness, graphite being a semi-metal whose resistivity is strongly dependent on its doping and impurity [2]. After surface treatment of the active interior face of the G-10 port plug, the graphite thin-®lm is
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formed also by abrasion. Electrical contact is secured at opposite edges of the thin-®lm using two gold-plated needles 9.63 mm apart center-to-center, and a twocomponent, electrically conductive, silver-®lled epoxy, Epo-Tek H20E. Shown in Fig. 3 is a thermometer of the same type, used in previous, related second sound experiments [2]. The two gold-plated needles are 3.43 mm apart center-to-center in the ®gure. The experiments are initiated, monitored, and documented by a Macintosh computer running LabVIEW software. Shown in Fig. 4 is a ¯ow chart of the electronic apparatus that enables the transfer of SSS pulses along the channel. The computer initiates a square voltage pulse from the pulse generator (HP 8116 A), which is immediately converted to a power pulse by the highspeed power ampli®er (NF 4015). This power is transferred by RG-58/U coax cable and 24 A.W.G. stranded copper wire twisted pair to the SSS heater. The resulting voltage signal from the SSS thermometer is transferred by Lake Shore SC and RG-178 B/U coax cable to a high-speed, high-gain preampli®er. The preampli®er is comprised of three high-precision operational ampli®er stages (PMI OP 27 EP), each set to a gain of about 10, and each with a gain-bandwidth product of about 5 MHz. This gain-bandwidth was chosen to allow the signal to pass without signi®cant distortion and without excessive noise. The digitizing oscilloscope (TDS 744 A)
Fig. 3. Second sound thermometer GFT-G10 consisting of a graphite thin-®lm deposited onto G-10 by abrasion [2]. The two gold-plated needles are 3.43 mm apart center-to-center.
Fig. 4. SSS pulse electronic apparatus ¯ow chart [2].
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Fig. 5. SSR wave electronic apparatus ¯ow chart.
displays the signals, and stores them for later retrieval by the computer [2]. Shown in Fig. 5 is a ¯ow chart of the electronic apparatus that enables the establishment of SSR waves across the channel. Sinusoidal rather than pulse power is delivered to each SSR heater from a dedicated power waveform generator. Each waveform generator is based on an XR-2206 monolithic function generator. The resulting voltage signal from each SSR thermometer is processed by a dedicated analog lock-in ampli®er. Each lock-in ampli®er is based on an MPY 634 precision analog multiplier. The digitizing oscilloscope displays these signals synchronously with the SSS pulse signal, and stores them also for later retrieval by the computer. The present design is capable of generating and detecting SSS pulses with durations between 10 ls and 10 ms approximately, and with initial power ¯ux densities up 2 to about 85 W=cm . 3. Thermometer and heater design A summary of the selection and design of the installed thermometers and heaters is given here. More details are presented in [2]. Second sound thermometers and heaters have similar requirements due to an analog of electromagnetic reciprocity. Their Biot numbers (Bi hL=k) must be less than 0.1 for them to respond at high speed without signi®cant transient internal temperature gradients. Here L in the Biot number de®nition is the active thickness. Active thickness is the thickness in the direction of the thermal power ¯ux, either out of the heater, or into the thermometer. Here the direction of the thermal power ¯ux is the direction of second sound propagation. Also, k is the thermal conductivity of the heater or the thermometer, and in He II, h is the Kapitza conductance. With their Biot numbers less than 0.1, the thermometer and the heater can then be described by lumped parameter ®rst-order ordinary dierential
equations for thermal transport. However, they can also be described by lumped parameter ®rst-order ordinary dierential equations for electrical transport also, because they are embedded in an electronic instrumentation system. How they interact with this system as well as how they behave in the He II bath are both important for their operation. The time constants in both cases must be considered with respect to the required minimum pulse duration or maximum sinusoid frequency to arrive at a correct design for the thermometer and the heater. A thermometer and heater are considered to be correctly designed when they are suciently thin in the direction of the thermal power ¯ux that their thermal time constants are minimized without inducing a signi®cant electrical impedance mismatch. However, in a correct design, the electrical time constant sE RC is comparable to or larger than the thermal time constant sh qVc=hA for the thermometer and the heater, and in fact, may determine the high-speed performance. Here R is the electrical resistance of the thermometer or the heater, and C is the electrical capacitance of the connecting cables. Also, q is the mass density and c is the speci®c heat of the thermometer or the heater, respectively. Also, the heater must have a resistance comparable to the impedance of its power source for maximum power transfer, and an active area small enough to give the required thermal power ¯ux density. Active area is the area of the thermal power ¯ux, either out of the heater, or into the thermometer. The cross-section of the SSS channel is determined by the active area of the SSS heater. The thermometer current must be as high as possible without inducing signi®cant self-heating for the thermometer to deliver the maximum possible voltage signal. A thin thermometer with a large active area experiences less self-heating than one with a small active area, because the self-heating is primarily dependent on the active area with the thickness determined, whereas the thermal time constant is primarily dependent on the characteristic length, active thickness. The thermal time constant and the Biot number of the thermometer or the heater are determined by their active thickness. The thermometer and the heater must be approximately matched in impedance to their respective coaxial cables. The assumed power-law relationship between the bath temperature, T1 , and the mean resistance of the thers mometer, R1 aT1 ; de®nes the meaning of thermometer operating sensitivity, s dlnR=dlnT , with a a proportionality constant. The thermal and electrical performance of a thermometer can thus be speci®ed by its mean operating resistance, sensitivity, Biot number, operating current, electrical time constant, thermal time constant, and the bath operating temperature. In Table 1 is a summary of the thermal and electrical performance of dierent resistive ®lament or ®lm thermometer (RFT) types tested as potential SSS thermometers [2].
D.K. Hilton, S.W. Van Sciver / Cryogenics 41 (2001) 347±353 Table 1 Resistive ®lament/®lm thermometer (RFT): thermal and electrical performance summary at T1 1:7 K Thermometer CFT-F CCT PFT-G GFT-G10 a
s 0.50 0.60 3.68 0.41
i0 lA
sE lsa
1.0 1.0 0.001 1.0
3.48 538 285 000 2.05
Cc 651 pF.
Given are the sensitivity, operating current, and electrical time constant for each thermometer. The electrical capacitance, Cc given at the bottom of the table is that of the current source and voltage signal coaxial cables, and is used to calculate the electrical time constant from the mean operating resistance, the resistance of the thermometer at the bath operating temperature. In general, the thermal time constant is of the order of 10 ns for every thermometer tested. The designations of the thermometers described below are for naming purposes only. Although they may be deduced, the internals of the designations are not signi®cant to the discussion of this paper. The ®rst is CFT-F, a carbon ®lament of the order of 5±7 lm in diameter, such as a single ®lament of a single tow of the kind used to manufacture composites. The second is CCT, a Lake Shore CX-1080-BG Cernoxâ thermometer bare chip. The third is PFT-G, an S-glass ®lament of the order of 5±7 lm in diameter with a 0.1 lm thick polypyrrole thin-®lm coating. The fourth is GFT-G10, the G-10 sheet with the graphite thin-®lm described above and shown in Fig. 3. The calibration plot of GFT-G10 is presented in Fig. 6 for the cooling and warming cases. No shift is apparent between the cases, suggesting that upon reaching low temperatures, graphite retention is sucient to produce a thermo-mechanically stable thin-®lm. As with any other carbon- or graphite-based thermometer, the GFT-G10 thermometer requires calibration each time it is cycled from room temperature to low temperatures.
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Clearly suggested by Table 1, CCT and PFT-G were unacceptable as SSS thermometers because of their high electrical time constants. However, a parallel multi®lament, tow form of PFT-G was tested, but also yielded unacceptable results. The intention was that the multiple ®laments in parallel would reduce the mean operating resistance, and thus the electrical time constant. The operating sensitivity would not be reduced. A scanning electron micrograph (SEM) of this thermometer is shown in Fig. 7. The scale bar at the bottom of the SEM represents 100 lm. The dark section is the tow exposed by a very thin, narrow mask during a silver/gold PVD. The 150 nm silver thin-®lm and 50 nm gold thin-®lm create electrical contacts to the tow, shown at the left and right of the exposed section. The exposed section is the thermometer proper. A low-temperature current source and source follower circuit was built in an attempt to reduce the thermometer mean operating resistance by impedance matching. Although the circuit operated at 4.2 K, it failed to operate at 1.7 K, probably due to the majority carrier freeze-out in the active device of the source follower [7]. This is unfortunate because the thermometer operating sensitivity is exceptionally high compared to the others. CFT-F shows promise as an SSS thermometer since its electrical time constant is comparable to that of GFT-G10. However, when this thermometer was tested, the heater then installed was too thick, giving a thermal time constant of about 10 ls, and the high-speed, high-gain preampli®er was not present. Later consideration suggested that the small active area of this thermometer may result in signi®cant self-heating. Based on preliminary estimates, the superconductor SSS thermometer (to be designated SFT-S) will have a sensitivity at least comparable to that of GFT-G10, but will have an electrical time constant of the order of 100 ns, at least an order of magnitude smaller. This is because, due to its metallic and superconductive characteristics, it will have a lower mean operating resistance. It will have an operating current of the order of 100 lA, however. The nichrome thin-®lm second sound heaters described above have thermal time constants on the order of 10 ns. With nearly constant mean operating resistances of about 50 X from T < 4:2 K to room temperature, their electrical time constants are also on the order of 10 ns. 4. Shock pulses and resonance waves
Fig. 6. A calibration plot for the cooling and warming cases of the second sound thermometer GFT-G10. The operating current is 1.0 lA.
Shown in Fig. 8 are two samples of received SSS pulses obtained by an apparatus similar to that described above. In this case, the SSS channel was just a G-10 tube 203.2 mm long, 25.4 mm in diameter, without side wall ports for SSR heater and thermometer pairs. A
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Fig. 7. Parallel multi®lament, tow form of thermometer PFT-G. The scale bar at the bottom of the SEM represents 100 lm.
Fig. 8. A plot of SSS pulses from an initial square pulse of 20 W=cm2 power ¯ux density and 150 ls duration, in a He II bath at TB 1:7 K. The pulse propagation speed is 20.5 m/s.
graphite thin-®lm thermometer of the type shown in Fig. 3 was used. Each sample was generated by a square pulse initiated at zero time into a He II bath at TB 1:7 K. Each trace is an average of ®ve repeated measurements. The z values noted next to the pulses are the distances from the heater to the thermometer. Pulse propagation speed is 20.5 m/s, as measured by the leading edge displacement, in agreement with tabulated second sound speeds and second sound theory [8]. The baselines of the two traces correspond to the bath operating temperature at the times the traces were recorded. Measurement artifacts resulting from electrical pick-up by the thermometer from the heater have been minimized by lead superconductive shielding. Also, a copper plate on a circuit board with the same size and shape as the SSS heater was installed beneath the heater,
in series electrically with the heater. The transient magnetic ®eld of the copper plate partially cancels the transient magnetic ®eld of the heater to an acceptable level. Shown in Fig. 9 is a plot of received power vs sweep frequency, revealing SSR peaks. The plot was obtained by closing o the top end of the G-10 tube mentioned above with a G-10 disk to form a cylindrical resonance cavity 42.6 mm long. The SSS heater and thermometer were used as a single SSR heater and thermometer pair. Sinusoidal rather than pulse power was delivered to the heater, and the frequency was linearly swept from a lower to an upper limit, as shown in Fig. 9. This sweep was achieved by driving the voltage control (VCO) input of the pulse generator, which is also a waveform generator, with a triangle waveform from a second waveform generator (Wavetek 182 A). The mean power ¯ux density was 0:55 W=cm2 , not sucient to induce ®lm boiling at the heater. Film boiling would have prevented resonance. The mean power ¯ux density was determined by increasing it until the appearance of clearly detectable SSR peaks. The plot is a power spectrum of the cavity. Each resonance frequency is the double of its corresponding sweep frequency because both, negative and positive halves of the electrical sinusoid delivered to the heater generate just positive thermal power in the He II bath. Each resonance frequency measured is within 1% of that calculated based on the experimental con®guration and second sound theory [8]. The three peaks shown correspond to three sequential normal modes of the cavity. The availability of multiple modes suggests a potential application, discussed below. Quantum turbulence is viewed as a tangle of quantum vortex lines. It is thus characterized by a line density, K m=m3 , that is, quantum vortex line length per unit volume of He II. The relative attenuation of second sound wave amplitude is an indirect measure of this line density, and thus the amount of quantum turbulence
Fig. 9. A plot of SSR peaks within a 42.6 mm long cylindrical cavity, in a He II bath at TB 1:76 K. Each is labeled by fR , its resonance frequency, the double of its corresponding sweep frequency.
D.K. Hilton, S.W. Van Sciver / Cryogenics 41 (2001) 347±353
present in the path of the second sound. The SSR heater and thermometer pairs will monitor for quantum turbulence induced in conjunction with SSS pulse propagation, by the attenuation of select SSR peaks similar to the ones in Fig. 9. Since the SSS channel is open, crosstalk may result between the pairs if the same normal mode frequency is used by each. The potential application mentioned above is to use dierent normal mode frequencies for dierent heater and thermometer pairs to eliminate the cross-talk. Correlating the SSS pulse propagation characteristics with the subsequent SSR wave attenuation behavior over time at the position of every pair is the primary experimental or operational goal. 5. Conclusions SSS pulses and SSR waves were measured using a nichrome thin-®lm heater, and a graphite thin-®lm thermometer, graphite extracted from pencil lead. The thermometer and heater designs are employed in an instrumentation package being developed to generate and detect SSS pulses in a channel of He II while monitoring for induced quantum turbulence at multiple points along the channel. The system will monitor for quantum turbulence by the attenuation of SSR waves. The experiments using this instrumentation package will oer the ®rst opportunity to directly measure the quantum turbulence time and distance evolution in conjunction with SSS pulses. The designs of second sound thermometers and heaters follow similar criteria due to thermal reciprocity. The operating temperature domain is below the lambda point of liquid helium. Compatible active materials are selected such that the sensitivity of the thermometer is maximized whereas the sensitivity of the heater is minimized. The Biot numbers for both are minimized so that transient thermal gradients within them are negligible during operation. This minimization is achieved expediently by making both, the thermometer and the heater thin in the direction of second sound propagation. This minimizes their thermal time constants also.
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The mean operating resistances are adjusted geometrically such that impedance mismatches with the electronic instrumentation systems in which they are embedded are minimized. Electrical time constants are then minimized where possible. The operating current of the thermometer is optimized to deliver the maximum voltage signal possible without self-heating the thermometer. This operating current and thus the voltage signal can be increased by increasing the area of the thermometer, since self-heating is determined in part by the area. The heater is designed to operate in a selfheating mode, but below its destruction limits, set by the power ¯ux density and duration. Acknowledgements This research is supported by US Department of Energy Grant No. DE-FG02-96ER40751. The authors thank Powell Barber, Andrew Powell, Soren Prestemon, Yehia Eyssa, Robert Goddard, Edward Clark, and James Brooks for their technical support, and Robert Gammon of the University of Maryland for discussions concerning graphite thin-®lms. References [1] Nemirovskii SK, Tsoi AN. Transient thermal and hydrodynamic processes in super¯uid helium. Cryogenics 1989;29:985. [2] Hilton DK, Smith MR, Van Sciver SW. Thin-®lm thermometer and heater design for the detection and generation of second sound shock pulses. Adv Cryo Eng 2000;45B:1025. [3] Turner TN. Using second-sound shock waves to probe the intrinsic critical velocity of liquid helium II. Phys Fluids 1983;26(11):3227. [4] Pellum JR. Investigations of pulsed second sound in liquid helium II. Phys Rev 1949;75(8):1183. [5] Shimazaki T, Iida T, Murakami M. Experimental study of thermal shock wave deformation and decay due to tangled mass of quantized vortices in He II. Adv Cryo Eng 1994;39:1859. [6] Laguna G. Photolithographic fabrication of high frequency second sound detectors. Cryogenics 1976;16(4):241. [7] Lengeler B. Semiconductor devices suitable for use in cryogenic environments. Cryogenics 1974;14(8):439. [8] Keller WE. Helium-3 and helium-4. New York: Plenum Press; 1969.
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Techniques for the detection of second sound shock pulses and induced quantum turbulence in He II D.K. Hilton a,c,*, S.W. Van Sciver b,c a
c
Department of Physics, College of Arts and Sciences, Florida State University, Tallahassee, FL, USA b Mechanical Engineering Department, FAMU-FSU College of Engineering, Tallahassee, FL, USA National High Magnetic Field Laboratory, Florida State University, 1800 E. Paul Dirac Drive, Tallahassee, FL 32310, USA Received 8 January 2001; accepted 15 March 2001
Abstract This paper discusses the design and operation of thin-®lm thermometers and heaters for the detection and generation of second sound shock (SSS) pulses and second sound resonance (SSR) waves. The detection of quantum turbulence at multiple points along a channel is also discussed. An instrumentation package to simultaneously detect SSS pulses and induced quantum turbulence in He II has been developed. This system is able to generate and detect SSS pulses in a channel of He II while monitoring for induced quantum turbulence at multiple points along the channel. The system monitors for quantum turbulence by the attenuation of SSR waves. The experiments using this instrumentation package oer the ®rst opportunity to directly measure the quantum turbulence time and distance evolution of SSS pulses. These experiments have applications in transient heat transfer problems in He II, such as the cooling and stability of superconductors. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Temperature sensors; Thin ®lms; Heat transfer; Fluid dynamics; Super¯uid helium
1. Introduction Transient heat transfer problems in He II, such as the cooling and stability of superconductors, motivate continued research of second sound shock (SSS) pulse propagation. Solutions to such problems would be enhanced by a thorough understanding of the SSS pulse propagation. SSS pulses of sucient amplitude 2 (0:1±100 W=cm ) and short duration (0.01±10 ms) generate wakes of quantum vortex tangles, quantum turbulence, in He II, and are distorted by the quantum turbulence they induce. Nemirovskii and Tsoi presented a review and classi®cation of the existing experimental data [1]. Referring to Fig. 1, the parameter space de®ned by initial power ¯ux density and pulse duration, along with the He II bath temperature, reveals distinct regimes of qualitatively dierent transient heat transfer behaviors in He II, that require
*
Corresponding author. Tel.: +1-850-644-1708; fax: +1-850-6440867. E-mail address: [email protected] (D.K. Hilton).
further physical description. The region centered near 10 W=cm2 and 1 ms has not been extensively explored, and is perhaps the most interesting in that it is the intersection between three major regimes, developing quantum vorticity, fully developed vorticity, and ®lm boiling. The instrument package described in this paper will explore this region further than in previous experiments. All experiments of the type described here are performed in the lower temperature phase of liquid helium, He II, below the lambda point, Tk 2:176 K, on or near the saturation curve of liquid helium, and above T 1:40 K due to the existing equipment capability. Second sound manifests itself as temperature waves in He II. Consequently, second sound resonance (SSR) waves as well as SSS pulses require fast, compact thermometers and heaters for their detection and generation without distortion. Details requisite for an eective design of a SSS pulse research device have been outlined and veri®ed by experiment in a previous paper [2]. Here this discussion is extended to include the detection and generation of SSR waves. Further, the detection of induced quantum turbulence by the attenuation of SSR waves is also discussed.
0011-2275/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 1 - 2 2 7 5 ( 0 1 ) 0 0 0 9 1 - 1
348
D.K. Hilton, S.W. Van Sciver / Cryogenics 41 (2001) 347±353
Fig. 2. Experimental schematic.
Fig. 1. Transient heat transfer regimes of He II [1].
2. Instrumentation package The focus of the instrument package is the SSS channel, a G-10 channel 178 mm long, with a 19:1 mm 12:7 mm rectangular interior cross-section. To minimize the electrical noise, the exterior lateral surface of the channel is layered in lead sheet, electrically grounded, forming a superconductive shield (Pb, Tc 7:2 K). The smoothness of the channel interior surface is as-received. Reviewing selections by previous researchers, neither the surface smoothness nor the material choice of the channel seems to introduce signi®cant artifacts during SSS pulse propagation [3±5]. The maximum duration pulse that can be investigated is determined by the length of the channel and the speed of second sound, of the order of 20 m/s in He II between 1 and 2 K. Shown in Fig. 2 is the experimental schematic, giving the essential spatial con®guration of the required thermometers and heaters. The bottom end holds the primary SSS heater, consisting of a fused silica (amorphous SiO2 ) substrate, 25:4 mm 19:1 mm, 0.83 mm thick, with both faces
ground and the upper active face polished. Upon the upper face is deposited by physical vapor deposition (PVD) a 16.5 nm thin-®lm of nichrome (80% Ni/20% Cr by weight), a centered 19.1 mm square. Nichrome has a nearly constant resistivity of 1:05 10 4 X cm at T < 4:2 K, and this resistivity does not vary signi®cantly over the range of interest up to room temperature. Electrical power pulse contacts are made to the primary heater at opposite edges through 150 nm thin-®lm strips of pure silver deposited by PVD, each 6.35 mm wide. Two brass plates, each 0.38 mm thick and with a superconducting indium (In) interface, are pressed into position to make cold-weld electrical contacts. Above the SSS heater along the longitudinal axis of the channel is the primary SSS thermometer, consisting of an S-glass ®lament of the order of 5±7 lm in diameter, such as the kind used in composites. Following similar work by Laguna [6], a 100 nm thin-®lm of tin (Sn) on top of a 25 nm thin-®lm of gold (Au) is deposited by PVD on one side of the ®lament. Tin is an elemental, Type-I superconductor (Sn, Tc 3:7 K). The layered thin-®lm system of Aux Sn1 x forms a proximity superconductor with an adjustable critical temperature (2:0 K < Tc < 3:7 K) and corresponding transition width. For x 0:2, Tc 2:1 K for this superconductor in zero magnetic ®eld [6]. Furthermore, the transition curve of this superconductor can be shifted down in temperature by the introduction of a low external magnetic ®eld. For example, a magnetic ®eld, B 0:02
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T corresponds to a critical temperature, Tc 1:7 K according to the results of Laguna [6]. Thus, just above the SSS thermometer, mounted on a G-10 support tube for both is a small solenoid electromagnet. The electromagnet consists of a brass coil form, 11.13 mm in diameter, with four layers of 200 turns each of wire to form a solenoid 20.32 mm long. The wire, 0.102 mm in diameter, is a superconducting niobium±titanium/copper composite. At an operating current, I 3 A, this electromagnet can generate a fringe axial magnetic ®eld, B 0:03 T at a distance of 3.5 mm from the end of the solenoid, where the SSS thermometer is placed. Since the electromagnet is an integral component of the primary SSS thermometer, and Fig. 2 is a schematic, the electromagnet is not shown in this ®gure. Along the side walls, across the narrow span of the SSS channel, are heater and thermometer pairs for the generation and detection of SSR waves. The presence of quantum turbulence attenuates the SSR waves. Thus, the SSR waves, once established between each heater and thermometer pair, will continuously monitor at this position for quantum turbulence induced in conjunction with the SSS pulses being propagated. Six port pairs are provided along the channel, spaced 25.4 mm apart above the SSS heater. Three heater and thermometer pairs are installed for any given experiment, with the other ports closed o with blank G-10 plugs. Each side wall SSR heater consists of a fused silica (amorphous SiO2 ) disk substrate, 12.37 mm in diameter, 0.83 mm thick, with both faces ground and the interior active face polished. Upon the interior face is deposited by PVD a 34.7 nm thin-®lm of nichrome (80% Ni/20% Cr by weight). Two gold-plated needles 9.63 mm apart center-to-center at opposite edges with indium interfaces are pressed into position to make electrical contacts. Each side wall heater is assembled into a self-contained G-10 port plug machined for the purpose. Each side wall thermometer is also assembled into a similar G-10 port plug. The active interior face of the plug, 12.60 mm in diameter, is abraded in every direction of its surface with medium grit (240 grit) sandpaper to insure retention of a graphite thin-®lm that is the SSR thermometer. The abrasion cuts micro-channels into the surface, forming parallel, temperature-sensitive graphite resistors in the direction of the abrasion, when the graphite is later applied. Thus, the direction of abrasion in part determines the ®nal mean resistance of the thermometer, which in turn determines the electrical time constant [2]. The source of the graphite is a particular brand of pencil lead (Pentel, 0.5 mm, hardness B). The ®nal mean operating resistance and sensitivity of the thermometer is strongly dependent on the graphite source and hardness, graphite being a semi-metal whose resistivity is strongly dependent on its doping and impurity [2]. After surface treatment of the active interior face of the G-10 port plug, the graphite thin-®lm is
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formed also by abrasion. Electrical contact is secured at opposite edges of the thin-®lm using two gold-plated needles 9.63 mm apart center-to-center, and a twocomponent, electrically conductive, silver-®lled epoxy, Epo-Tek H20E. Shown in Fig. 3 is a thermometer of the same type, used in previous, related second sound experiments [2]. The two gold-plated needles are 3.43 mm apart center-to-center in the ®gure. The experiments are initiated, monitored, and documented by a Macintosh computer running LabVIEW software. Shown in Fig. 4 is a ¯ow chart of the electronic apparatus that enables the transfer of SSS pulses along the channel. The computer initiates a square voltage pulse from the pulse generator (HP 8116 A), which is immediately converted to a power pulse by the highspeed power ampli®er (NF 4015). This power is transferred by RG-58/U coax cable and 24 A.W.G. stranded copper wire twisted pair to the SSS heater. The resulting voltage signal from the SSS thermometer is transferred by Lake Shore SC and RG-178 B/U coax cable to a high-speed, high-gain preampli®er. The preampli®er is comprised of three high-precision operational ampli®er stages (PMI OP 27 EP), each set to a gain of about 10, and each with a gain-bandwidth product of about 5 MHz. This gain-bandwidth was chosen to allow the signal to pass without signi®cant distortion and without excessive noise. The digitizing oscilloscope (TDS 744 A)
Fig. 3. Second sound thermometer GFT-G10 consisting of a graphite thin-®lm deposited onto G-10 by abrasion [2]. The two gold-plated needles are 3.43 mm apart center-to-center.
Fig. 4. SSS pulse electronic apparatus ¯ow chart [2].
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Fig. 5. SSR wave electronic apparatus ¯ow chart.
displays the signals, and stores them for later retrieval by the computer [2]. Shown in Fig. 5 is a ¯ow chart of the electronic apparatus that enables the establishment of SSR waves across the channel. Sinusoidal rather than pulse power is delivered to each SSR heater from a dedicated power waveform generator. Each waveform generator is based on an XR-2206 monolithic function generator. The resulting voltage signal from each SSR thermometer is processed by a dedicated analog lock-in ampli®er. Each lock-in ampli®er is based on an MPY 634 precision analog multiplier. The digitizing oscilloscope displays these signals synchronously with the SSS pulse signal, and stores them also for later retrieval by the computer. The present design is capable of generating and detecting SSS pulses with durations between 10 ls and 10 ms approximately, and with initial power ¯ux densities up 2 to about 85 W=cm . 3. Thermometer and heater design A summary of the selection and design of the installed thermometers and heaters is given here. More details are presented in [2]. Second sound thermometers and heaters have similar requirements due to an analog of electromagnetic reciprocity. Their Biot numbers (Bi hL=k) must be less than 0.1 for them to respond at high speed without signi®cant transient internal temperature gradients. Here L in the Biot number de®nition is the active thickness. Active thickness is the thickness in the direction of the thermal power ¯ux, either out of the heater, or into the thermometer. Here the direction of the thermal power ¯ux is the direction of second sound propagation. Also, k is the thermal conductivity of the heater or the thermometer, and in He II, h is the Kapitza conductance. With their Biot numbers less than 0.1, the thermometer and the heater can then be described by lumped parameter ®rst-order ordinary dierential
equations for thermal transport. However, they can also be described by lumped parameter ®rst-order ordinary dierential equations for electrical transport also, because they are embedded in an electronic instrumentation system. How they interact with this system as well as how they behave in the He II bath are both important for their operation. The time constants in both cases must be considered with respect to the required minimum pulse duration or maximum sinusoid frequency to arrive at a correct design for the thermometer and the heater. A thermometer and heater are considered to be correctly designed when they are suciently thin in the direction of the thermal power ¯ux that their thermal time constants are minimized without inducing a signi®cant electrical impedance mismatch. However, in a correct design, the electrical time constant sE RC is comparable to or larger than the thermal time constant sh qVc=hA for the thermometer and the heater, and in fact, may determine the high-speed performance. Here R is the electrical resistance of the thermometer or the heater, and C is the electrical capacitance of the connecting cables. Also, q is the mass density and c is the speci®c heat of the thermometer or the heater, respectively. Also, the heater must have a resistance comparable to the impedance of its power source for maximum power transfer, and an active area small enough to give the required thermal power ¯ux density. Active area is the area of the thermal power ¯ux, either out of the heater, or into the thermometer. The cross-section of the SSS channel is determined by the active area of the SSS heater. The thermometer current must be as high as possible without inducing signi®cant self-heating for the thermometer to deliver the maximum possible voltage signal. A thin thermometer with a large active area experiences less self-heating than one with a small active area, because the self-heating is primarily dependent on the active area with the thickness determined, whereas the thermal time constant is primarily dependent on the characteristic length, active thickness. The thermal time constant and the Biot number of the thermometer or the heater are determined by their active thickness. The thermometer and the heater must be approximately matched in impedance to their respective coaxial cables. The assumed power-law relationship between the bath temperature, T1 , and the mean resistance of the thers mometer, R1 aT1 ; de®nes the meaning of thermometer operating sensitivity, s dlnR=dlnT , with a a proportionality constant. The thermal and electrical performance of a thermometer can thus be speci®ed by its mean operating resistance, sensitivity, Biot number, operating current, electrical time constant, thermal time constant, and the bath operating temperature. In Table 1 is a summary of the thermal and electrical performance of dierent resistive ®lament or ®lm thermometer (RFT) types tested as potential SSS thermometers [2].
D.K. Hilton, S.W. Van Sciver / Cryogenics 41 (2001) 347±353 Table 1 Resistive ®lament/®lm thermometer (RFT): thermal and electrical performance summary at T1 1:7 K Thermometer CFT-F CCT PFT-G GFT-G10 a
s 0.50 0.60 3.68 0.41
i0 lA
sE lsa
1.0 1.0 0.001 1.0
3.48 538 285 000 2.05
Cc 651 pF.
Given are the sensitivity, operating current, and electrical time constant for each thermometer. The electrical capacitance, Cc given at the bottom of the table is that of the current source and voltage signal coaxial cables, and is used to calculate the electrical time constant from the mean operating resistance, the resistance of the thermometer at the bath operating temperature. In general, the thermal time constant is of the order of 10 ns for every thermometer tested. The designations of the thermometers described below are for naming purposes only. Although they may be deduced, the internals of the designations are not signi®cant to the discussion of this paper. The ®rst is CFT-F, a carbon ®lament of the order of 5±7 lm in diameter, such as a single ®lament of a single tow of the kind used to manufacture composites. The second is CCT, a Lake Shore CX-1080-BG Cernoxâ thermometer bare chip. The third is PFT-G, an S-glass ®lament of the order of 5±7 lm in diameter with a 0.1 lm thick polypyrrole thin-®lm coating. The fourth is GFT-G10, the G-10 sheet with the graphite thin-®lm described above and shown in Fig. 3. The calibration plot of GFT-G10 is presented in Fig. 6 for the cooling and warming cases. No shift is apparent between the cases, suggesting that upon reaching low temperatures, graphite retention is sucient to produce a thermo-mechanically stable thin-®lm. As with any other carbon- or graphite-based thermometer, the GFT-G10 thermometer requires calibration each time it is cycled from room temperature to low temperatures.
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Clearly suggested by Table 1, CCT and PFT-G were unacceptable as SSS thermometers because of their high electrical time constants. However, a parallel multi®lament, tow form of PFT-G was tested, but also yielded unacceptable results. The intention was that the multiple ®laments in parallel would reduce the mean operating resistance, and thus the electrical time constant. The operating sensitivity would not be reduced. A scanning electron micrograph (SEM) of this thermometer is shown in Fig. 7. The scale bar at the bottom of the SEM represents 100 lm. The dark section is the tow exposed by a very thin, narrow mask during a silver/gold PVD. The 150 nm silver thin-®lm and 50 nm gold thin-®lm create electrical contacts to the tow, shown at the left and right of the exposed section. The exposed section is the thermometer proper. A low-temperature current source and source follower circuit was built in an attempt to reduce the thermometer mean operating resistance by impedance matching. Although the circuit operated at 4.2 K, it failed to operate at 1.7 K, probably due to the majority carrier freeze-out in the active device of the source follower [7]. This is unfortunate because the thermometer operating sensitivity is exceptionally high compared to the others. CFT-F shows promise as an SSS thermometer since its electrical time constant is comparable to that of GFT-G10. However, when this thermometer was tested, the heater then installed was too thick, giving a thermal time constant of about 10 ls, and the high-speed, high-gain preampli®er was not present. Later consideration suggested that the small active area of this thermometer may result in signi®cant self-heating. Based on preliminary estimates, the superconductor SSS thermometer (to be designated SFT-S) will have a sensitivity at least comparable to that of GFT-G10, but will have an electrical time constant of the order of 100 ns, at least an order of magnitude smaller. This is because, due to its metallic and superconductive characteristics, it will have a lower mean operating resistance. It will have an operating current of the order of 100 lA, however. The nichrome thin-®lm second sound heaters described above have thermal time constants on the order of 10 ns. With nearly constant mean operating resistances of about 50 X from T < 4:2 K to room temperature, their electrical time constants are also on the order of 10 ns. 4. Shock pulses and resonance waves
Fig. 6. A calibration plot for the cooling and warming cases of the second sound thermometer GFT-G10. The operating current is 1.0 lA.
Shown in Fig. 8 are two samples of received SSS pulses obtained by an apparatus similar to that described above. In this case, the SSS channel was just a G-10 tube 203.2 mm long, 25.4 mm in diameter, without side wall ports for SSR heater and thermometer pairs. A
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Fig. 7. Parallel multi®lament, tow form of thermometer PFT-G. The scale bar at the bottom of the SEM represents 100 lm.
Fig. 8. A plot of SSS pulses from an initial square pulse of 20 W=cm2 power ¯ux density and 150 ls duration, in a He II bath at TB 1:7 K. The pulse propagation speed is 20.5 m/s.
graphite thin-®lm thermometer of the type shown in Fig. 3 was used. Each sample was generated by a square pulse initiated at zero time into a He II bath at TB 1:7 K. Each trace is an average of ®ve repeated measurements. The z values noted next to the pulses are the distances from the heater to the thermometer. Pulse propagation speed is 20.5 m/s, as measured by the leading edge displacement, in agreement with tabulated second sound speeds and second sound theory [8]. The baselines of the two traces correspond to the bath operating temperature at the times the traces were recorded. Measurement artifacts resulting from electrical pick-up by the thermometer from the heater have been minimized by lead superconductive shielding. Also, a copper plate on a circuit board with the same size and shape as the SSS heater was installed beneath the heater,
in series electrically with the heater. The transient magnetic ®eld of the copper plate partially cancels the transient magnetic ®eld of the heater to an acceptable level. Shown in Fig. 9 is a plot of received power vs sweep frequency, revealing SSR peaks. The plot was obtained by closing o the top end of the G-10 tube mentioned above with a G-10 disk to form a cylindrical resonance cavity 42.6 mm long. The SSS heater and thermometer were used as a single SSR heater and thermometer pair. Sinusoidal rather than pulse power was delivered to the heater, and the frequency was linearly swept from a lower to an upper limit, as shown in Fig. 9. This sweep was achieved by driving the voltage control (VCO) input of the pulse generator, which is also a waveform generator, with a triangle waveform from a second waveform generator (Wavetek 182 A). The mean power ¯ux density was 0:55 W=cm2 , not sucient to induce ®lm boiling at the heater. Film boiling would have prevented resonance. The mean power ¯ux density was determined by increasing it until the appearance of clearly detectable SSR peaks. The plot is a power spectrum of the cavity. Each resonance frequency is the double of its corresponding sweep frequency because both, negative and positive halves of the electrical sinusoid delivered to the heater generate just positive thermal power in the He II bath. Each resonance frequency measured is within 1% of that calculated based on the experimental con®guration and second sound theory [8]. The three peaks shown correspond to three sequential normal modes of the cavity. The availability of multiple modes suggests a potential application, discussed below. Quantum turbulence is viewed as a tangle of quantum vortex lines. It is thus characterized by a line density, K m=m3 , that is, quantum vortex line length per unit volume of He II. The relative attenuation of second sound wave amplitude is an indirect measure of this line density, and thus the amount of quantum turbulence
Fig. 9. A plot of SSR peaks within a 42.6 mm long cylindrical cavity, in a He II bath at TB 1:76 K. Each is labeled by fR , its resonance frequency, the double of its corresponding sweep frequency.
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present in the path of the second sound. The SSR heater and thermometer pairs will monitor for quantum turbulence induced in conjunction with SSS pulse propagation, by the attenuation of select SSR peaks similar to the ones in Fig. 9. Since the SSS channel is open, crosstalk may result between the pairs if the same normal mode frequency is used by each. The potential application mentioned above is to use dierent normal mode frequencies for dierent heater and thermometer pairs to eliminate the cross-talk. Correlating the SSS pulse propagation characteristics with the subsequent SSR wave attenuation behavior over time at the position of every pair is the primary experimental or operational goal. 5. Conclusions SSS pulses and SSR waves were measured using a nichrome thin-®lm heater, and a graphite thin-®lm thermometer, graphite extracted from pencil lead. The thermometer and heater designs are employed in an instrumentation package being developed to generate and detect SSS pulses in a channel of He II while monitoring for induced quantum turbulence at multiple points along the channel. The system will monitor for quantum turbulence by the attenuation of SSR waves. The experiments using this instrumentation package will oer the ®rst opportunity to directly measure the quantum turbulence time and distance evolution in conjunction with SSS pulses. The designs of second sound thermometers and heaters follow similar criteria due to thermal reciprocity. The operating temperature domain is below the lambda point of liquid helium. Compatible active materials are selected such that the sensitivity of the thermometer is maximized whereas the sensitivity of the heater is minimized. The Biot numbers for both are minimized so that transient thermal gradients within them are negligible during operation. This minimization is achieved expediently by making both, the thermometer and the heater thin in the direction of second sound propagation. This minimizes their thermal time constants also.
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The mean operating resistances are adjusted geometrically such that impedance mismatches with the electronic instrumentation systems in which they are embedded are minimized. Electrical time constants are then minimized where possible. The operating current of the thermometer is optimized to deliver the maximum voltage signal possible without self-heating the thermometer. This operating current and thus the voltage signal can be increased by increasing the area of the thermometer, since self-heating is determined in part by the area. The heater is designed to operate in a selfheating mode, but below its destruction limits, set by the power ¯ux density and duration. Acknowledgements This research is supported by US Department of Energy Grant No. DE-FG02-96ER40751. The authors thank Powell Barber, Andrew Powell, Soren Prestemon, Yehia Eyssa, Robert Goddard, Edward Clark, and James Brooks for their technical support, and Robert Gammon of the University of Maryland for discussions concerning graphite thin-®lms. References [1] Nemirovskii SK, Tsoi AN. Transient thermal and hydrodynamic processes in super¯uid helium. Cryogenics 1989;29:985. [2] Hilton DK, Smith MR, Van Sciver SW. Thin-®lm thermometer and heater design for the detection and generation of second sound shock pulses. Adv Cryo Eng 2000;45B:1025. [3] Turner TN. Using second-sound shock waves to probe the intrinsic critical velocity of liquid helium II. Phys Fluids 1983;26(11):3227. [4] Pellum JR. Investigations of pulsed second sound in liquid helium II. Phys Rev 1949;75(8):1183. [5] Shimazaki T, Iida T, Murakami M. Experimental study of thermal shock wave deformation and decay due to tangled mass of quantized vortices in He II. Adv Cryo Eng 1994;39:1859. [6] Laguna G. Photolithographic fabrication of high frequency second sound detectors. Cryogenics 1976;16(4):241. [7] Lengeler B. Semiconductor devices suitable for use in cryogenic environments. Cryogenics 1974;14(8):439. [8] Keller WE. Helium-3 and helium-4. New York: Plenum Press; 1969.