Visualization of quantum turbulence with excimer molecules Group members: Prof. Daniel N. McKinsey Speaker : Dr. Wei Guo Physics department, Yale University New Haven, CT Dr. Sidney. B. Cahn Dr. David J. Wright Dr. James A. Nikkel Dr. Wade G. Rellergert

Collaborators: Prof. William F. Vinen School of Physics and Astronomy University of Birmingham Birmingham B15 2TT, UK Prof. Gary G. Ihas Department of Physics University of Florida Gainesville, FL 32611, USA Prof. Andrei Golov School of Physics and Astronomy University of Manchester Manchester, M60 1QD, UK

 Application Outline  Introduction Basic properties of excimer molecules  Future projects Imaging molecules: Laser-induced fluorescence Studies on thermal counterflow  Molecule tagging technique  Cloud tracking technique Above 1K: study of structure functions in turbulence Below 1K: imaging individual vortex lines  Evidence of normal-fluid turbulence at large heat flux  Laminar – turbulent transition at small heat flux  Summary

singlet state lifetime: ~1ns triplet state lifetime: ~13s [1]  in spin singlet state and in triplet state can radiatively decay to the dissociative ground state emitting a ~16eV photon. in LHe4: Introduction Basic properties [1] D. N. McKinsey et al., Phys. Rev. A 59, 200 (1999).

 Along the track of high energy particles moving through LHe4 [1].  Generation of excimers ß particles: ~ 1.7 triplet molecules/μm α particles: ~ triplet molecules/μm  Electrical discharge from a sharp needle in LHe4. Metastable molecules are produced as a result of ionization/excitation in LHe4: Compton scattering of gamma rays, neutrons, … He2 molecules can be introduced into LHe4 very easily in controllable ways. (low heat load at low T ! )  Laser field-ionization using a femtosecond laser pulse. [1] J. S. Adams, Ph.D. thesis, Brown University, 2001.

 molecules form little bubbles in LHe. ( R~6Å ) small effective mass and size in LHe4 => does not disturb fluid !  Molecule bubbles can be trapped on vortex lines at low T. Molecules are similar in size to, trapping energy on vortices (~20K).  imaging vortices at low T !  Molecules are neutral particles. no forces other than the interaction with fluid, no space charge effect.  molecules as tracers:  Helium molecules do not aggregate.  Above 1K, molecules trace the normal-fluid component only Two helium molecules decay (Penning ionization) when they meet together. Viscous relaxation time (roughly): ~ 1.5K  Vortex interaction is negligible !

For imaging molecules in the triplet ground state a(0). Imaging molecules: Laser-induced fluorescence (1) Cycling Transitions [2] W.G. Rellergert, Ph.D Thesis, Yale Univ. (2008). molecule detection scheme [1,2] [1] W.G. Rellergert et al., Phys. Rev. Lett, 100 (2008).  Low background imaging and High cycling efficiency ( a few tens of cycles per second [2] ).  A 905 nm pulsed laser is used to drive a cycling transition. (500 Hz, )  Fiber lasers at 1073 nm and 1099 nm are used to prevent molecules from being stuck in higher vibrational levels of the state.  Laser light can be filtered.

(T~2K, tip current ~ -100 pA)  Tracing the normal-fluid flow Wei Guo, et al., J. Low Temp. Phys., 158 (2009) * A normal-fluid jet is formed due to the pulling of the moving electron bubbles. * Molecules entrained in the jet allow us to see the whole process of jet impingement. * Allow laboratory simulation of atmospheric microbursts.

Imaging molecules: Laser-induced fluorescence One may drive the a(0)  c(0) multiple times to achieve high tagging fraction. (2) Pump-probe imaging For imaging molecules in the long-lived a(1) level. a(1) tagging detection scheme [1,2] [1] W.G. Rellergert, Ph.D Thesis, Yale Univ. (2008). [2] W. Guo, et al., Phys. Rev. Lett., 102 (2009)  Pump laser at 910nm drives molecules from a(0)  c(0). 4% of the them fall back to a(1) and are tagged.  Probe laser at 925nm drives molecules from a(1)  d to produce the fluorescent light.

 Molecule tagging technique Mesh electrode DC voltage Fiber lasers 910nm pump 925nm probe (1) Molecules are entrained by the normal-fluid jet. (2) Tagging a small group of molecules and imaging at delayed time allows us to determine the normal-fluid velocity. W. Guo, et al., Phys. Rev. Lett., 102 (2009) Normal- fluid jet T~1.9K

Heater Mesh electrode Molecule cloud 905nm pulses  Cloud tracking technique Voltage pulse Fiber lasers (1) By pulsing a tungsten tip in liquid helium, a small molecule cloud can be created. (2) Tracing the positions of a single molecule cloud in a thermal counterflow, we can determine the normal-fluid velocity. T~1.9K

 Studies on thermal counterflow Application Superfluid becomes turbulent when: It has been suspected that the normal fluid may become turbulent:  No inertial range and new to physics. Questions: (1) The existence of normal-fluid turbulent in counterflow. (2) The structure of the normal-fluid turbulence Normal fluid carries heat and entropy. Superfluid flows in opposite direction to conserve the fluid mass. (1) Multiple quantum turbulence stages: T1 and T2 states. (1) Simulation by Melotte and Barenghi (PRL, 80, 4181 (1998)).

Probe laser Pump laser Channel: length~8cm width~0.5cm Imaging normal-fluid velocity profile * Emitted electrons move horizontally to the copper electrode (~1mm distance). Electron disturbance is small. * Lasers illuminate the channel at 6cm from the source region. Focused laser pulse at 910nm tags a line of molecules which is imaged at delayed time by an expanded probe laser pulse at 925nm. * Deformation of the molecule line shows the velocity profile.

* Fluorescence images taken with the probe laser alone and pump laser alone (sum of 40 camera exposures). The heat flux is 640mW/cm^2. Integrated signal intensity for: (b) probe laser alone at 905nm; (c) pump laser alone at 905nm. * Without turning on the heater, no molecules can be seen even at 60s after the source is on. * As the heater is on, molecules move with the normal fluid. They disperse throughout the channel which allows a line of molecules to be tagged. * Continuous fiber lasers at 1073nm and 1099nm were turned on for 5ms before each pump-probe cycle to clean out the background a(1) molecules. * By seeing the deformation of a tagged molecule line, the velocity profile of the normal fluid can be obtained.

* Fluorescence images showing the motion of a tagged molecule line ( heat flux 640 mW/cm^2). (1) The velocity profile is flat !  First direct visualization of the normal-fluid velocity profile in counterflow! (2) Flows with heat fluxes that ranged from 160 to 1000 mW/cm^2 was studied. These heat fluxes are above the critical heat flux for quantum turbulence. At lower heat flux, molecules decay before they can be imaged. (1) For each pump-probe delay time (drift time), up to 40 images were superimposed and an averaged line profile was obtained (examples shown above in false color).

t = 40 ms, heat flux 640 mW/cm^2 (1) The signal is integrated along x-axis and is plotted as a function of y. The center position and the width of the tagged line can be obtained by fitting the line profile using a Lorentzian function (the red line). (2) At a given heat flux, multiple measurements were made as we varied the drift time. We then plotted the center positions versus drift time and fit to a straight line whose slope gives the corresponding normal-fluid velocity. The obtained normal-fluid velocity as a function of heat flux at 1.95 K. (3) The good agreement between our data and the calculated velocities demonstrates that the fluorescing helium molecules do track the normal fluid well.

* In a classical homogeneous turbulent flow, two fluid elements will separate faster and the rate of separation is largely governed by the turbulent eddies with size comparable to the separation.  Relative diffusion in turbulence (t)(t) * For particles undergo Brownian motion in static fluid, the mean square separation between them grows linearly in time: There remains the question of whether the flow of the normal fluid is turbulent. Two effects can cause a flattening of the normal-fluid velocity profile: turbulence, and non-linear mutual friction acting on a laminar normal-fluid flow. Better evidence comes from the observed broadening of the line of molecules with increasing time. * For a classical turbulence with a Kolmogorov energy spectrum: when the separation is the inertial range and for time larger than the turn over time of the relevant eddies. Brownian motion  

 The expansion of a tagged molecule line was studied at a heat flux of 277 mW/cm^2. * The square of the mean width of the tagged line is plotted as a function of drift time. * The broadening of the molecule line occurs too rapidly for it to be explained by ordinary diffusion at the experimental temperature (1.95 K). Confirmed that the normal-fluid flow is turbulent ! Wei Guo, et al., Phys. Rev. Lett., 105, (2010). * The data is fit using a power law in time. The best fit value of the power index is 4 + / Is there a laminar flow state of the normal fluid in thermal counterflow? See commentary by Carlo Barenghi, Physics, 3, 60 (2010).

Cluster tracking experiment * A pair of tungsten needles were placed along the central axis of a square glass channel (2mmx2mm). * A high negative voltage pulse is applied to the cathode to create a small cloud of helium molecules. (~0.5mm to 0.8mm in diameter) * Imaging the cloud as it drifts with the normal fluid allows us to measure the normal-fluid velocity in thermal counterflow.

* Fluorescence images showing the motion of a molecule cloud (1) The measured normal-fluid velocity VS heat flux agrees with the two-fluid model except below a transition heat flux at about 50 mW/cm^2. (2) Below the transition heat flux, both fluids are in a laminar flow state. A cluster moving along the central of the channel should have a velocity roughly twice as large as the mean velocity due to the Poiseuille velocity profile of the normal fluid. ( heat flux 119 mW/cm^2).

Future projects (1) Above 1K: studying structure functions in turbulence Beam waist FWHM ~ 45 microns, L~ 1 cm * A focused femtosecond laser pulse can create a thin line of molecules via laser field ionization. ( Molecule density~ 10^12/cc ) (A.V. Benderskii, et. al., J. Chem. Phys., 110, 1542 (1999).) * The molecular line is imaged via cycling- transition fluorescence. High quality single-shot images can be taken. 60 uJ/ pulse, 80 fs 790 nm  Ongoing collaboration experiment between Yale University, University of Birmingham, and University of Florida.

Images are copied from: R. Miles, et. al., Fluid Dynamics Research, 8, 9-17 (1991). (1) Obtain information on the structure functions (transverse and longitudinal) of the normal fluid turbulence: grid turbulence and counterflow turbulence. (2) The transition from laminar flow to turbulent flow of the normal fluid in thermal counterflow (T1 and T2 states). Goal: study both counterflow and towed grid turbulence

(2) Imaging quantized vortices at low T * At low T, an excimer molecule may dissipate its kinetic energy via inducing Kelvin waves as it passes by a vortex line. Molecule trapping on vortex line can occur if this energy dissipation is efficient. (need simulation!) * Molecules that are not trapped will quickly diffuse and quench on the walls. Clear 3-D images of vortex lines may be obtained. Tangle of quantized vortices are decorated by seeded helium molecules. LIF of the molecules enables a direct 3-D visualization of quantum turbulence. * Dressing of vortices with He 2 molecules should allow imaging of vortex dynamics, interaction, and decay of quantum turbulence at low temperatures.

(1) trapping cross-section of excimers on vortex lines at low T * Two things are needed: (2) Excitation spectrum of excimers at low T. (unpublished simulation results.)  Spectrum study will be conducted at Yale in the future.  A collaborative experiment is currently being conducted in Andrei Golov’s lab at University of Manchester.

The end ! Summary (1) Laser-fluorescence techniques for imaging metastable helium molecules have been developed at Yale. Helium molecule tracers are useful in studying the normal-fluid flow above 1K. (2) We studied thermal counterflow in a glass channel by observing the motion of tagged lines of molecules. Our results support the existence of normal-fluid turbulence in counterflow. (3) On going experiment on imaging thin line of molecules created via laser-field ionization will allow us to determine the structure functions of normal-fluid turbulence in both thermal counterflow and towed grid turbulence. (4) At low temperatures, imaging trapped molecules on vortex lines will allow studies of vortex dynamics and decay of quantum turbulence at.