Molecular Tagging Velocimetry in Superfluid Helium-4: Progress, Issues, and Future Development
aa r X i v : . [ c ond - m a t . o t h e r] F e b Journal of Low Temperature Physics manuscript No. (will be inserted by the editor)
Molecular Tagging Velocimetry in Superfluid Helium-4:Progress, Issues, and Future Development
Wei Guo
Received: date / Accepted: date
Abstract
Helium-4 in the superfluid phase (He II) is a two-fluid system thatexhibits fascinating quantum hydrodynamics with important scientific and en-gineering applications. However, the lack of high-precision flow measurementtools in He II has impeded the progress in understanding and utilizing its hy-drodynamics. In recent years, there have been extensive efforts in developingquantitative flow visualization techniques applicable to He II. In particular, apowerful molecular tagging velocimetry (MTV) technique, based on trackingthin lines of He ∗ excimer molecules created via femtosecond laser-field ioniza-tion in helium, has been developed in our lab. This technique allows unam-biguous measurement of the normal-fluid velocity field in the two-fluid system.Nevertheless, there are two limitations of this technique: 1) only the velocitycomponent perpendicular to the tracer line can be measured; and 2) there isan inherent error in determining the perpendicular velocity. In this paper, wediscuss how these issues can be resolved by advancing the MTV technique.We also discuss two novel schemes for tagging and producing He ∗ tracers. Thefirst method allows the creation of a tagged He ∗ tracer line without the use ofan expensive femtosecond laser. The second method enables full-space velocityfield measurement through tracking small clouds of He ∗ molecules created vianeutron- He absorption reactions in He II.
Keywords
Quantum turbulence · Superfluid helium-4 · Flow visualization · Molecular tagging · He ∗ excimer molecules W. GuoFlorida State UniversityMechanical Engineering DepartmentNational High Magnetic Field laboratory1800 East Paul Dirac DriveTallahhassee, Florida 32310, U.S.A. E-mail: [email protected] Wei Guo
Liquid helium-4 ( He) transits to the superfluid phase (known as He II) belowabout 2.17 K [1]. In He II, two miscible fluid components co-exist: an inviscidsuperfluid (i.e., the condensate) and a viscous normal fluid (i.e., the thermalexcitations). The hydrodynamics of He II is strongly affected by quantumeffects. For instance, the rotational motion of the superfluid component canoccur only with the formation of topological defects in the form of quantizedvortex lines [2]. These vortex lines all have identical cores with a radius ofabout 1 ˚A, and they each carry a single quantum of circulation κ = h/m ,where h is Plancks constant and m is the mass of a He atom. Turbulencein the superfluid therefore takes the form of an irregular tangle of vortex lines(quantum turbulence) [3]. The normal fluid is expected to behave more like aclassical fluid. But a force of mutual friction between the two fluids [4], arisingfrom the scattering of thermal excitations by the vortex lines, can affect theflows in both fluids.The fraction ratio of the two fluid components in He II strongly depends ontemperature. Above 1 K where both fluids are present, this two-fluid systemexhibits fascinating hydrodynamic properties that have important scientificand engineering applications [5]. For instance, He II supports the most effi-cient heat-transfer mechanism (i.e., thermal counterflow) and therefore hasbeen widely utilized for cooling scientific and industrial equipment such assuperconducting magnets, particle colliders, superconducting accelerator cav-ities, and satellites [6,7,8]. It has also been suggested that He II can be usedto generate flows with extremely high Reynolds numbers for model testing oflarge-scale classical turbulence that can hardly be achieved with conventionaltest fluids such as water and air [9,10,11]. However, despite decades of re-search, the full potential of He II has not yet been realized, largely due to thelack of high-fidelity quantitative flow measurement tools.Typical single-point diagnostic tools used for classical fluids, such as pitotpressure tubes and hot-wire anemometers, either have limited spatial resolu-tion or rely on convective heat transfer that does not exist in He II. Further-more, since the motion of both fluid components can contribute to the sensorresponse, data analysis can become very complicated when the two fluids havedifferent velocity fields. More straightforward velocity measurements can bemade via direct flow visualization [12]. In the past, researchers used micron-sized solidified particles as tracers and developed particle image velocimetry(PIV) and particle tracking velocimetry (PTV) techniques for He II [13,14,15,16,17,18]. These micron-sized tracers can easily get trapped on quantizedvortices due to their large binding energy to the vortex cores [12]. The trappedtracers have yielded very interesting images of the vortex lines [17,18,19,20].Nevertheless, some issues are known to exist. First, these tracer particles areproduced by injecting room temperature gas mixture to liquid helium, whichintroduces a large heat load and hence disturbs the flow to be studied. Second,the particles produced by this method have a wide range of sizes and irregularshapes and are not neutrally buoyant, which lead to complicated tracer behav- itle Suppressed Due to Excessive Length 3 ior. The strong interaction of the tracers with both the viscous normal fluidand the quantized vortices sometimes makes their motion hardly analyzablein practical turbulent flows [21]. Nevertheless, we note that in our recent PTVstudy of thermal counterflow in He II, a new method for separately analyz-ing the particles trapped on vortices and those entrained by the normal fluidapproves to be very useful [22].On the other hand, the feasibility of using He ∗ excimer molecules as trac-ers in He II has been validated through a series of experiments [23,24,25].These molecules can be created easily as a consequence of ionization or excita-tion of ground state helium atoms [27]. They have exceptionally long radiativelifetime in the electron spin triplet state (about 13 s [26]) and form tiny bub-bles in liquid helium (about 6 ˚A in radius [27]). Due to their small size andhence small binding energy on vortex cores [28], trapping of the He ∗ tracersby quantized vortices can occur only below about 0.6 K in the absence of thenormal fluid [29]. At above 1 K where most of the He II based applicationstake place, He ∗ tracers are solely entrained by the normal fluid since the vis-cous drag force dominates other forces. These He ∗ tracers can be imaged via acycling-transition laser-induced fluorescence (LIF) technique that was devel-oped by McKinsey’s group at Yale where the author worked as a postdoctoralresearcher [23,30,31]. More recently, a powerful molecular tagging velocime-try (MTV) technique based on tracking thin lines of He ∗ tracers, created viafemtosecond laser-field ionization in helium, has been developed in our lab[32]. This technique allows for quantitative measurement of the normal-fluidvelocity field in the two-fluid system. The application of the MTV technique tothermal counterflow turbulence in He II has yielded remarkably fruitful results[33,34,35,36,37,38].Nevertheless, there are two obvious limitations of this MTV technique: 1)only the velocity component perpendicular to the tracer line can be measured;and 2) there is an inherent error in determining the perpendicular velocity.In this paper, we will discuss how these issues can be resolved by creatingcomplex tracer-line patterns for advanced MTV measurement. We will alsodiscuss two novel schemes for tagging and producing He ∗ tracers. The firstmethod is an inverse tagging velocimetry scheme without the use of any ex-pensive femtosecond lasers. This method utilizes the vibrational levels of theHe ∗ molecules but with much improved tagging efficiency compared to themethod reported in ref. [23]. The second method is to create small clouds ofHe ∗ molecules via neutron- He absorption reactions in He II. Each small He ∗ cloud can be treated as a single “tracer” such that unambiguous PTV or PIVmeasurements of the normal-fluid velocity field can be performed. ∗ molecular tagging velocimetry: issues and solutions To create a line of He ∗ tracers via laser-field ionization, laser intensity ashigh as 10 W/cm is needed [27]. This high instantaneous laser intensitycan be achieved by focusing a femtosecond laser pulse in helium. In our lab, Wei Guo
T=1.85 K; P=SVP in He II ~55 µ m ω lens: f=75 cm (b)(a) ω R Z He fs-laserbeam905 nmimaging beamLens
20 mm (c) u ( r ) r Fig. 1 (a) Schematic diagram showing the optical setup for creating and imaging He ∗ molecular tracer lines in helium. (b) A typical tracer image in He II upon its creation.(c)Schematic showing how the local velocity can be calculated. The dashed line indicatesthe tracer line initial location. a regenerative amplifier laser system (wavelength λ : 780 nm, duration: 35fs, pulse energy: up to 4 mJ) has been utilized for this purpose. As shownschematically in Fig. 1 (a), we focus the fs-laser beam using a lens with afocal length f and pass the beam through an optical cryostat that containsHe II at regulated pressures and temperatures. Anti-reflection coated windowsare used to minimize laser heating. For an ideal Gaussian beam with a beamradius ω at the focal plane, one can define a Rayleigh range Z R = πω /λ ,over which the laser intensity drops by 50% due to beam spreading. The He ∗ tracers are expected to be produced essentially within the Rayleigh range. Inour experiment, a fs-laser pulse energy of about 60 µ J is sufficient to create athin line of He ∗ tracers. We then send in several pulses from a 1-kHz imaginglaser at 905 nm to drive the tracers to produce fluorescent light for line imaging.Fig. 1 (b) shows a typical fluorescence image of the He ∗ tracer line taken rightafter its creation in He II. The width of the tracer line is about 2 ω and itslength is about 2 Z R as expected.To extract velocity information, we allow an initially straight tracer line tomove with the fluid by a drift time △ t . The deformed tracer line is then dividedinto small segments so that the center of each segment can be determined bya Gaussian fit of its intensity profile. When the drift time is small, the velocitycomponent u ( r ) perpendicular to the tracer line can be calculated as the ver-tical displacement of the line segment at r divided by △ t . Valuable flow fieldinformation, such as the streamwise velocity profile and transverse velocitycorrelations, can be extracted from u ( r ). This method has been adopted invarious MTV experiments in classical fluids [39,40], and it has also allowed usto obtain valuable insights in He II thermal counterflow [33,34,35,36,37,38]. itle Suppressed Due to Excessive Length 5 (a) x u t ∆ m y ∆ y y u t ∆ = ∆ xy Base lineDrifted line t t ∆ t ∆ (b) fs pulse Image-1 Image-2 ( ), / , 1, 2 my i m i u y t i = ∆ ∆ = PO P ′ θ Fig. 2 (a) Schematic diagram showing the inherent error in determining the velocity compo-nent perpendicular to the tracer line. (b) Schematic diagram of the double-exposure methodfor correcting the inherent error.
Nevertheless, some limitations have been identified. First, by tracking asingle tracer line, we can only determine the velocity component perpendicularto the tracer line, from which only the transverse velocity correlation at theline location can be extracted. In turbulence research, it is desirable to havethe capability of mapping out the complete velocity field. Second, even forthe velocity component perpendicular to the tracer lines, it is known thatthere is an inherent error involved in the measurement which can become non-negligible when the flow parallel to the tracer line is sufficiently strong [41].The first issue can be easily understood. To see the second issue more clearly,let us consider the schematic shown in Fig. 2 (a). An initially straight tracerline created parallel to the x -axis (i.e., the red solid horizontal line) deformsas it drifts with the fluid by a drift time △ t . If one is to measure the verticalvelocity u y at point O , our existing MTV method will yield a measured velocity u ( m ) y that is given by u ( m ) y = △ y m / △ t , where △ y m is the apparent verticaldisplacement of point O . However, when there is a finite horizontal flow, thefluid particle originally located at point O will move to point P instead P ′ .Therefore, the actual vertical velocity at point O should be u y = △ y/ △ t . Theerror in the vertical velocity △ u y = u y − u ( m ) y is thus given by △ u y = △ y − △ y m △ t = u x △ t · tan θ △ t = u x · (cid:18) ∂u y ∂x (cid:19) · △ t. (1)One sees clearly that the error in the measured vertical velocity is proportionalto both the drift time △ t and the horizontal velocity u x . For a given drift timein an experiment, this error is negligible only if the horizontal flow is small.To fix this issue, Hammer et al . proposed a multi-time-delay approach [41].Here, we shall discuss a simplified double-exposure version. As illustrated inFig. 2 (b), following the creation of a tracer line, we may send two imagingpulse trains at drift times of △ t and △ t , respectively. The camera will besynchronized with these two imaging pulse trains to capture two correspondingimages of the tracer lines. For any given point O on the base line, we can now Wei Guo
Screen Cylindricallens Beamexpander He II camera-1camera-2 acquisition &control systemLaser systemHelium celltracer-linegrid (c) (b) to helium bathx yz Tracer-grid plane φ φ camera-1camera-2 h Orientation of the cameras and tracer-grid plane:Intersection point of the tracer lines (a)
Fig. 3
Schematic diagrams of the optical systems for producing: (a) a tracer-line array and(b) a tracer-line grid. (c) Schematic diagram showing the experimental setup for stereoscopicMTV measurement in helium. calculate two vertical velocities using the two images of the deformed line as u ( m ) y, = △ y m, / △ t and u ( m ) y, == △ y m, / △ t . Note that according to Eq. 1,the actual vertical velocity u y can be evaluated as u y = u ( m ) y, + a · △ t and u y = u ( m ) y, + a · △ t (2)where the parameter a = u x · ( ∂u y /∂x ). From Eq. 2, one can then determinethe values for both u y and a at the point O . Therefore, the inherent errorin measuring u y can be remedied. Note that this method assumes that thevalue of a does not change much between the two image acquisitions. Thisassumption holds when both △ t and △ t are small.In principle, based on the definition of a and the obtained u y ( x ), one canalso calculate the horizontal velocity u x . However, this calculation involves theevaluation of spatial derivative ∂u y /∂x from u y ( x ), which is normally highlynoisy and undesired. A more feasible route to obtain information about othervelocity components is to produce and track complex tracer-line patterns [42]. itle Suppressed Due to Excessive Length 7 Creating multiple tracer lines simultaneously in He II is relatively straightfor-ward using our laser system. The maximum pulse energy of our femtosecondlaser (i.e., 4 mJ) is far greater than necessary for creating a single tracer line(i.e., 60 µ J [32]). Therefore, we can divide the fs-laser beam into multiplebeams to produce multiple tracer lines that form patterns. Fig. 3 (a) showsthe concept how the fs-laser beam can be focused into a thin laser sheet whichcan then be passed through a screen with many parallel thin open slots forproducing an array of tracer lines. Overlapping two such arrays can lead tothe formation of a tracer-line grid as shown in Fig. 3 (b). This method hasalready been adopted by Hu and his colleagues in classical MTV experiments[42].In order to obtain full three dimensional (3D) velocity information, a stereo-scopic imaging system needs to be implemented. Instead of tracking the tracerlines themselves, one may track the motion of the intersection points of atracer-line grid. These intersection points can be treated as individual “trac-ers” whose velocities can be accurately measured and are not be affected bythe typical MTV inherent error. An example stereoscopic MTV setup is shownin Fig. 3 (c). A tracer-line grid can be created using the method as illustratedin Fig. 3 (b). Then, two intensified CCD (ICCD) cameras will be synchronizedto take images of the tracer-line grid at the same time from two directions.In a drift time dt , the apparent displacements of the intersection points ofthe grid-lines (i.e., those solid red dots in Fig. 3) in the imaging planes of thetwo cameras can be recorded (i.e., ( dx , dy ) and ( dx , dy )), from which theactual x , y , z displacements of the intersection points can be computed as: dx = f x ( dx , dy , φ , h , m ; dx , dy , φ , h , m ) dy = f y ( dx , dy , φ , h , m ; dx , dy , φ , h , m ) dz = f z ( dx , dy , φ , h , m ; dx , dy , φ , h , m ) (3)where φ , h , and m are the camera viewing angle, the distance between the im-age and the object plane, and the image magnification factor. The forms of thefunctions f x , f y , and f z are complex but have been discussed in great detail inthe literature [43]. The three velocity components can therefore be calculatedas u x = dx/dt , u y = dy/dt , and u z = dz/dt . This velocity measurement is freefrom any ambiguity associated with the MTV inherent error. ∗ tracers ∗ tracer lines. Such a femtosecondlaser system is very expensive and normally not accessible to many researchgroups who would like to conduct MTV measurements in helium. On theother hand, there are many other ways to produce He ∗ molecules in helium Wei Guo u d + Σ u a + Σ g c + Σ g b Π n m n m n m Probe n m Pre-pumping Pump n m
95% 910 nm cw laser a(0)
905 nm a(1)
Flow channel (a)
He II flow (b)
Fig. 4 (a) Schematic diagram showing the optical transitions of the inverse tagging method.The levels labeled by 0 and 1 for each electronic state are the vibrational levels of the cor-responding state. (b) Schematic diagram of the experimental setup that utilizes the inversetagging method for imaging a single tagged He ∗ tracer line. without involving a femtosecond laser. For instance, one may use a radioactivesource [31] or apply a high voltage on a sharp tungsten needle to ignite a fieldemission [23,25]. The He ∗ molecules produced by these methods can dispersein the whole fluid. Then, a key question is how to tag or select a group of thedispersed He ∗ molecules at a desired location for imaging so that quantitativevelocity information can be obtained by tracking the tagged molecules. Ref.[23] reported a tagging method that utilizes the long-lived vibrational levelsof the He ∗ triplet ground state a Σ + u . The basic concept is to use a focusednanosecond pump laser pulse at 910 nm to excite a line of He ∗ molecules fromtheir ground state a (0) to the excited electronic state c (0). About 4% of the c (0) molecules non-radiatively decay in a few nanoseconds to the long-livedvibrational level a (1) and are tagged. An expanded nanosecond probe laserat 925 nm can then be used to only drive the tagged a (1) molecules to theexcited d state to induce 640 nm fluorescence via the d to b transition. Thismethod has allowed the first tagging of a He ∗ tracer line in He II thermalcounterflow [25]. Nevertheless, due to the low tagging efficiency (i.e., about4%), many images must be superimposed at a given pump-probe delay timeto achieve a good image quality. Consequently, deformations of individual linesthat contain turbulent velocity field information are completed smoothed out.Here we would like to discuss a new inverse-tagging method that allowsfor high quality imaging of individual tagged tracer lines. The scheme of thismethod is shown in Fig. 4 (a). Instead of tagging the molecules by drivingthem to the a(1) state, a pre-pumping continuous laser at 910 nm can be used itle Suppressed Due to Excessive Length 9 to drive the molecules from the a (0) to the c (0) state. Since the c to a decaytime is only a few tens of nanoseconds, molecules that decay back to a (0) canquickly be re-excited to c (0). Each time the molecules promoted to the c (0)state have about 4% of the chance to decay to the a (1) level. As a consequence,after a few excitation-decay cycles, essentially all the molecules will end up intothe a(1) level. A pump laser pulse at 1073 nm can now be used to excite themolecules from the a(1) level to the c(0) state. From the c(0), about 95% ofthe molecules decay to the a(0) state and are tagged. A probe laser pulse at905 nm can then be used to drive only the tagged a (0) molecules to the d stateto produce the fluorescence. Compared to the old tagging method, this newscheme makes use of the a (0) state to tag the molecules. The tagging efficiencyis now 95% instead of 4%. Furthermore, for the tagged molecules in the a(0)state, multiple 905 nm laser pulses can be used to drive cycling transitionsto enhance the fluorescence strength. Experimentally, one may pass the fluidseeded with the a(0) molecules through a region illuminated by the 910 nmpre-pumping laser so as to convert the a (0) molecules into a (1)s (see Fig. 4(b)). A focused pump laser pulse at 1073 nm tags a line of a(0) moleculeswhich is then imaged by an expanded 905 nm probe laser pulse at a delayedtime. Due to the enhanced tagging and imaging efficiency, it is expected thatthe overall signal-to-noise ratio can be improved by two orders of magnitudecompared to that in the old tagging experiment.3.2 He ∗ cloud tracking velocimetryIn classical fluid dynamics research, quantitative PIV and PTV techniques aremore widely used compared to MTV measurement [44]. Unlike standard MTVwhere the velocity can be measured only at the locations of the tracer lines,PIV can generate a smoothly varying velocity field in the full visualizationspace, and PTV allows the measurement of Lagrangian quantities such as thelocal velocity and its derivatives. In He II, PIV and PTV measurement tech-niques have been developed based on the use of micron-sized tracer particles[13,14,15,16,17,18]. However, the injection of these particles and their inter-actions with both fluid components in He II lead to known inherent issuesas discussed in Sec. 1. Therefore, it is natural to ask whether it is possibleto perform PIV and PTV measurements in He II with smaller tracer parti-cles, such as He ∗ molecules. Unfortunately, the cycling transition laser-drivenfluorescence scheme for detecting He ∗ molecules has not yet been pushed tothe limit for imaging individual He ∗ molecules. Instead of tracking individ-ual He ∗ molecules, a more feasible route is to develop a method to producemany small clouds of He ∗ molecules in He II and then treat each cloud as a“tracer”. Such tracer clouds can be readily imaged for traditional PIV andPTV measurements.To create small clouds of He ∗ molecules in He II, an innovative methodbased on neutron- He absorption reactions was first proposed by the authorat a workshop on quantum turbulence held in Abu Dhabi in 2012 [45]. Then, n + He H H (191 keV) ( k e V ) *2 He n He H H 764 keV + → + + } ~ 80 m µ (a) (b) needlesource m µ Fig. 5 (a) Schematic diagram showing the neutron- He absorption reaction that leads tothe creation of a cloud of about 10 He ∗ molecules. (b) A fluorescence image of a cloud ofabout 10 -10 He ∗ molecules, produced by applying a voltage pulse (30-60 ms) to a sharptungsten needle in He II [23]. this method was discussed in more details later at a neutron workshop at OakRidge National Lab in 2016 [46]. The basic concept is that He atoms thatnaturally exist in He II as impurity particles can absorb neutrons as shownin the reaction schematic in Fig. 5 (a) [47]. The absorption cross-section σ depends on the energy of the incident neutrons and can be quite large forthermal neutrons that have spins aligned with the He atoms (i.e., σ ∼ − cm ) [48,49]. This reaction produces two charged particles, a proton ( H) anda tritium ( H), that move back to back with a total kinetic energy of 764keV [49]. The two particles have sufficient energies to ionize and excite groundstate He atoms along their tracks in He II, which leads to the generationof He ∗ molecules. The total length of the two tracks, evaluated based on theknown energy deposition rate of H and H in helium [49], is about 80 µ m. Wecan also estimate that about 10 He ∗ molecules are produced, considering thefraction of the kinetic energy of H and H that goes to the generation of He ∗ molecules [50,51]. Therefore, every n - He absorption event in He II creates acloud of about 10 He ∗ molecules with a size of about 80 µ m. Imaging theseclouds should be feasible since we have already demonstrated high-qualityfluorescence imaging of tiny clouds of He ∗ molecules created by pulsing atungsten needle in He II (see Fig. 5 (b)) [23]. Due to the very small moleculardiffusion of He ∗ molecules in He II (i.e., ∼ µ m during typical drift time[30]), every cloud can be treated as a single tracer, and a spatial resolution ofa few tens of microns is achievable. Tracking these He ∗ clouds should allow usto map out the full-space velocity field.Experimentally, one can pass a thermal neutron beam with a suitable flux(i.e., ∼ /cm per pulse) through a He II filled sample cell (see Fig. 6). Byadjusting the concentration of the He impurity, one can conveniently tunethe number density of the resulted He ∗ clouds. For instance, with a He con-centration as low as 50 ppm (part per million), which is far smaller than thenumber density of thermal rotons in He II above 1 K, we estimate that about10 clouds will be produced per 1 cm volume of He II, which should be suf- itle Suppressed Due to Excessive Length 11 NeutronbeamLaser He } ~ 80 m µ *2 He cloud:He II filled cell Fig. 6
Schematic of the experimental setup for producing and imaging He ∗ clouds producedvia n - He absorption reactions in He II. ficient for velocity-field mapping purpose. This method indeed also leads toa very sensitive mechanism for neutron detection. Recently, two collaborativeexperimental projects have been launched on fluorescence detection of n - Heabsorption events in He II. The first project was initiated by Shimizu and col-leagues at Nagoya University in collaboration with some researchers at otherinstitutes in Japan and the author [52]. This project utilizes the neutron fa-cilities at the Japan Proton Accelerator Research Complex (J-PARC), andits first report has been submitted as a proceeding paper to the 2018 Inter-national Conference on Quantum Fluids and Solids (i.e., QFS2018) [53]. Theother project is being conducted at the Oak Ridge National Lab (ORNL) inthe United State and is led by Fitzsimmons in collaboration with his colleaguesat University of Tennessee and ORNL together with the author [54]. Prelimi-nary results obtained in both projects have shown promising evidences for He ∗ cloud production in He II via n - He absorption reactions.
We have briefly reviewed the progresses made in recent years in developingquantitative flow visualization techniques applicable to He II using He ∗ molec-ular tracers. A MTV technique based on tracking a thin line of He ∗ moleculescreated via femtosecond laser-field ionization proves to be remarkably valuable.Nevertheless, two limitations of this method has been identified. These limi-tations are inherent of the single-line tracking scheme. We have discussed thatby creating multiple tracer lines that form a tracer-line grid, one can performstereoscopic MTV measurements that are completely immune from these limi- tations. Furthermore, two novel schemes for tagging He ∗ tracers are discussed.The first method involves an inverse tagging scheme that greatly improves thetagging efficiency. It is expected that this method will allow the tagging andimaging of a He ∗ tracer line without the use of any expensive femtosecondlasers. The second method relies on the creation of small clouds of He ∗ tracersvia n - He absorption reactions in He II. This method enables unambiguousquantitative PTV/PIV measurements of the full-space normal-fluid velocityfield in He II.The quantitative MTV techniques we have discussed are applicable notonly to He II but also to the classical phase of liquid helium (He I) and gaseoushelium. They have the potential to unlock the full power of cryogenic helium.For instance, helium gas is particularly useful in natural thermal convectionresearch. Heat transfer and fluid flow in natural convection are controlled bythe Rayleigh number Ra and the Prandtl number P r [55]. Studying the scalinglaws of the flow parameters at large Ra numbers, where turbulent convectionsets in, is of both theoretical and practical significance [56]. Close to its criticalpoint, gaseous helium can be used to produce convection flows with extremelylarge Ra , and the range of Ra can be tuned by a factor of 10 by simplyadjusting the gas pressure [57,58,59], which makes laboratory study of oceanconvection and atmospheric circulation possible [56]. However, velocity fieldmeasurement in helium gas has not been conducted so far, largely due to thelack of appropriate tools. The development of novel He ∗ based quantitativeMTV techniques may open the door for new avenues of research in this field. Acknowledgements
The author would like to acknowledge the contributions made byprevious and current students in the lab, including J. Gao, A. Marakov, E. Varga, B. Mas-tracci, S. Bao, Y. Zhang, and H. Sanavandi. The author would also like to thank manycolleagues in quantum turbulence and classical fluid dynamics research fields for valuablediscussions. The work has been supported by U.S. Department of Energy under grant No.DE-FG02-96ER40952 and by the National Science Foundation under Grants No. DMR-1807291 and No. CBET-1801780. All the experiments have been conducted at the NationalHigh Magnetic Field Laboratory, which is supported by NSF Grant No. DMR-1644779 andthe state of Florida.
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