Pure 4He Research Articles

Cavitation generated by vibrating quartz tuning fork in concentrated 3He–4He mixture

The state of the problem of cavitation in superfluid helium and the content of previous works on this topic are analyzed. The transition between turbulent flow and cavitation under oscillations of a quartz tuning fork in a normal and superfluid isotopic mixture containing 15% of 3He in the temperature range of 0.5–3 K is studied experimentally. The temperature dependences of the critical velocity for the cavitation onset and the critical transition excitation force are obtained. We compare the results of our measurements with the data obtained by other groups. The results of measurements with tuning forks in restricted and unrestricted geometries suggest that the presence of acoustic emission facilitates the conditions for the onset of cavitation and indirectly confirms the role of vortex lines. A comparison of the temperature dependences of the critical velocity of cavitation onset in pure 4He and a concentrated 3He–4He mixture did not give an unambiguous answer to the reason for the sharp increase of this velocity, at the transition to the superfluid state, and the contributions of both thermal effects and the 3He impurities to the velocity increase.

Sound-like Oscillations in the Polar Phase of Superfluid 3He in a Nematic Aerogel

The acoustic spectrum of the polar phase of superfluid 3He in nematic aerogel has been studied. An equation determining the dispersion of sound oscillations of the system has been derived. Solutions of the system have been obtained for low-frequency oscillations, whose propagation velocity is much lower than the speed of first sound in pure 3He, for directions along and across the anisotropy axis of the aerogel. In the same approximation, a solution for purely shear oscillations of the system has been found under special boundary conditions corresponding to an incompressible liquid surrounding the system. The temperature dependence of the found frequencies has been compared with the existing experimental data.

The critical velocity of transition to turbulence in 3He–4He liquid solutions

The transition between laminar and turbulent flows around a quartz tuning fork vibrating with frequency ω in superfluid 4He and concentrated solutions (5 and 15% 3He in 4He) in the temperature range 0.3–2.3 K has been studied. The temperature dependences of the amplitude of the critical transition velocity vcr are obtained. The relationship vcr ∼ √(ηω/ρ) is shown to be applicable for the description of these dependences in concentrated solutions of 3He in 4He with density ρ and viscosity η, but this formula does not hold for the temperature dependence of vcr in pure 4He over the entire temperature range explored. It is also shown that in contrast to pure 4He temperature has virtually no effect in concentrated 3He–4He solutions on the drag coefficient in both laminar and turbulent regimes. The concentration dependences of the drag coefficient in the laminar regime normalized to the effective cross section of the vibrating body are plotted in the temperature range 0.5–1 K. The calculated dependences show that for low concentrations of a solution with x3 < 1% 3He the normalized drag coefficient weakly depends on the concentration of 3He and can be qualitatively described by the formula λ/S∼ρηω. In the x3 > 1% 3He concentration range, this coefficient increases sharply, and the reason for such a growth is currently not clear. Overall, the results of the study show that an increase in the 3He concentration in the solution enhances its stability with respect to the development of turbulence as the exciting force of a quartz tuning fork increases.

Dissipation mechanisms of tuning fork vibrations in superfluid 3He–4He solutions

The amplitude–frequency characteristics of tuning forks immersed in superfluid 3He–4He solutions were measured in the temperature range of 0.1–2.5 K. The tuning fork resonance frequency and the resonance width were measured as functions of temperature for 5% and 15% concentrations of 3He and, for comparison, for pure 4He. The experimental results for the key dissipation mechanisms, that is, viscous friction and first and second-sound emission of a tuning fork, were analyzed. For separation and evaluation of the contributions of viscous damping and first and second-sound waves, “closed” (in a factory capsule) and “open” (without a capsule) tuning forks were used. The resonance width, which is a measure of dissipation of tuning fork vibrations, was found to be higher in solutions than in pure 4He, and to increase with increasing 3He concentration. It was shown that the existing analytical expression for the contribution of viscous friction provides a good description of the experimental data for 4He only in the hydrodynamic region. For the solutions, the viscosity contribution is consistent with the experiment only at high temperatures (above 1.4 K). For the “open” tuning fork, the contribution of the first-sound is consistent with the calculation results only for 4He, whereas for the solutions, the calculated values are underestimated compared to the experiment. The possible contribution of the second-sound to the dissipation of the tuning fork vibrations in solutions was estimated using experiments with the “closed” tuning fork. This contribution was found to vary non-monotonically with a maximum at temperatures of ≈ 0.6–0.8 K. The ratio of the tuning fork energy loss due to the thermal diffusion wave versus the loss due to the radiation flux of the second-sound wave in superfluid solutions was calculated using literature data with an accuracy of 10–3–10–4.

Kill painting of hypoxic tumors with multiple ion beams

We report on a novel method for simultaneous biological optimization of treatment plans for hypoxic tumors using multiple ion species. Our previously introduced kill painting approach, where the overall cell killing is optimized on biologically heterogeneous targets, was expanded with the capability of handling different ion beams simultaneously. The current version (MIBO) of the research treatment planning system TRiP98 has now been augmented to handle 3D (voxel-by-voxel) target oxygenation data. We present a case of idealized geometries where this method can identify optimal combinations leading to an improved peak-to-entrance effective dose ratio. This is achieved by the redistribution of particle fluences, when the heavier ions are preferentially forwarded to hypoxic target areas, while the lighter ions deliver the remaining dose to its normoxic regions. Finally, we present an in silico skull base chordoma patient case study with a combination of 4He and 16O beams, demonstrating specific indications for its potential clinical application. In this particular case, the mean dose, received by the brainstem, was reduced by 3%–5% and by 10%–12% as compared to the pure 4He and 16O plans, respectively. The new method allows a full biological optimization of different ion beams, exploiting the capabilities of actively scanned ion beams of modern particle therapy centers. The possible experimental verification of the present approach at ion beam facilities disposing of fast ion switch is presented and discussed.

Effects of 4He Film on Quartz Tuning Forks in 3He at Ultra-low Temperatures

In pure superfluid 3He–B at ultra-low temperatures, the quartz tuning fork oscillator response is expected to saturate when the dissipation caused by the superfluid medium becomes substantially smaller than the internal dissipation of the oscillator. However, even with a small amount of 4He covering the surfaces, we have observed saturation already at significantly higher temperatures than anticipated, where we have other indicators to prove that the 3He liquid is still cooling. We found that this anomalous behavior has a rather strong pressure dependence, and it practically disappears above the crystallization pressure of 4He. We also observed a maximum in the fork resonance frequency at temperatures where the transition in quasiparticle flow from the hydrodynamic to the ballistic regime is expected. We suggest that such anomalous features derive from the superfluid 4He film on the oscillator surface.

Kinetic energy and momentum distribution of isotopic liquid helium mixtures.

The momentum distribution and atomic kinetic energy of the two isotopes of helium in a liquid mixture at temperature T = 2 K are computed by quantum Monte Carlo simulations. Quantum statistics is fully included for 4He, whereas 3He atoms are treated as distinguishable. Comparison of theoretical estimates with a collection of the most recent experimental measurements shows reasonable agreement for the energetics of 4He and pure 3He. On the other hand, a significant discrepancy (already observed in previous studies) is reported between computed and measured values of the 3He kinetic energy in the mixture, especially in the limit of low 3He concentration. We assess quantitatively the importance of Fermi statistics and find it to be negligible for a 3He concentration ≲20%. Our results for the momentum distribution lend support to what was already hypothesized by other authors, namely, that the discrepancy is likely due to underestimation of the 3He kinetic energy contribution associated with the tail of the experimentally measured momentum distribution.

Kinetic processes in solid helium involving impurities and vacancies (Review)

A brief review is given of the kinetic behavior of impurities and vacancies in solid helium, which Andreev and Lifshitz predicted should be delocalized and converted into unique quasiparticles. Primary attention is devoted to the unusual diffusion processes in solid 3He-4He solutions as they undergo phase separation. Because mechanical stresses develop in the crystal during separation, the diffusive flow is substantially reduced and the effective diffusion coefficient becomes smaller than the coherent quantum diffusion coefficient. During the inverse transition from a separated mixture into the homogeneous state, anomalously rapid mass transfer is observed which can be explained qualitatively in terms of a model in which 3He inclusions are dissolved in three stages. Experimental data on the kinetics of phase separation are compared with a diffusive description of the process that takes into account the difference between diffusion processes outside and inside a nucleus of the new phase. Good agreement is obtained between a theoretical calculation and the experimental data. A homogeneous nucleation model is used to estimate the concentration of nuclei. For the first time, the coefficient of mass diffusion is estimated over the entire range of the concentration of the solutions. The behavior of delocalized vacancies in 4He and 3He solid solutions is studied near the separation temperature. The observed features of the pressure in this kind of system during repeated temperature cycling are explained by the formation of pure 4He vacancy clusters. Although the crystal itself has no strict periodicity owing to the random separation of 3He and 4He atoms at the lattice sites, a periodic structure is realized within a cluster and vacancies become delocalized.

Studies of kinetic processes in a concentrated 3He-4He solution using an oscillating tuning fork

The dissipative processes causing the damping of quartz tuning fork vibrations in a solution of 15% 3He in 4He, are studied in a temperature range of 0.5–2.3 K. The resonance curves of the tuning forks are measured in the laminar flow region of the liquid, and their width is determined by the width of the dissipative processes. We examined tuning forks with a resonance frequency of 32 kHz, located inside a flask (“enclosed”) and tuning forks without a flask (“unenclosed”). The results of the experiment are compared to existing theories. It was found that a significant contribution to the damping of tuning fork oscillations for a solution, as opposed to pure 4He, is from the second sound radiation, the contribution of which exceeds the input of viscous dissipation at low temperatures. The radiation of the first sound does not contribute to the damping of the oscillations of the “enclosed” fork due to the small size of the cell versus the wavelength. In the case of the “unenclosed” fork, the damping is determined by three processes: viscous dissipation and radiation of the first and second sounds.

Design and performance of a cryogenic apparatus for magnetically trapping ultracold neutrons

The cryogenic design and performance of an apparatus used to magnetically confine ultracold neutrons (UCN) is presented. The apparatus is part of an effort to measure the beta-decay lifetime of the free neutron and is comprised of a high-current superconducting magnetic trap that surrounds ∼21l of isotopically pure 4He cooled to approximately 250mK. A 0.89nm neutron beam can enter the apparatus from one end of the magnetic trap and a light collection system allows visible light generated within the helium by decays to be transported to detectors at room temperature. Two cryocoolers are incorporated to reduce liquid helium consumption.

Kinetic mix mechanisms in shock-driven inertial confinement fusion implosions

Shock-driven implosions of thin-shell capsules, or “exploding pushers,” generate low-density, high-temperature plasmas in which hydrodynamic instability growth is negligible and kinetic effects can play an important role. Data from implosions of thin deuterated-plastic shells with hydroequivalent D3He gas fills ranging from pure deuterium to pure 3He [H. G. Rinderknecht et al., Phys. Rev. Lett. 112, 135001 (2014)] were obtained to evaluate non-hydrodynamic fuel-shell mix mechanisms. Simulations of the experiments including reduced ion kinetic models support ion diffusion as an explanation for these data. Several additional kinetic mechanisms are investigated and compared to the data to determine which are important in the experiments. Shock acceleration of shell deuterons is estimated to introduce mix less than or comparable to the amount required to explain the data. Beam-target mechanisms are found to produce yields at most an order of magnitude less than the observations.

Mobility of 2D Electrons on Pure 4He and on 3He–4He Dilute Solution

The mobility of 2D electrons on pure 4He and on 0.5 % solution of 3He in 4He was investigated for different electron densities in the temperature range 0.12 to 1.3 K. The electrons in the same electron density show the same transition temperature from liquid state to Wigner crystal state in both pure 4He and in the solution. In the high temperature range where the gas-scattering is dominant, the electrons show a smaller mobility in the solution than in the pure 4He due to the electron collision with 3He gas atoms which have a higher vapor pressure. In the middle temperature range where the ripplon-scattering is dominant, the mobility in the solution is smaller than in 4He. This is explained by a smaller surface tension caused by 3He atoms collected at the surface. In the low temperature range where electrons are in the Wigner crystal state, the mobility gradually increases with decreasing temperature in the solution, while it stays almost constant in the pure 4He. The mobility increase is more pronounced in the low electron density. The results are qualitatively in agreement with the existing theory which includes the bulk 3He quasiparticle reflection from surface dimples and the effect of the surface layer of 3He atoms.

Metastability exchange optical pumping of 3He gas up to hundreds of millibars at 4.7 Tesla

Metastability exchange optical pumping (MEOP) is experimentally investigated in 3He at 4.7 T, at room temperature and for gas pressures ranging from 1 to 267 mbar. The 23S-23P transition at 1083 nm is used for optical pumping and for detection of the laser-induced orientation of 3He atoms in the rf discharge plasma. The collisional broadening rate is measured (12.0 ± 0.4 MHz mbar−1 FHWM) and taken into account for accurate absorption-based measurements of both nuclear polarization in the ground state and atom number density in the metastable 23S state. The results lay the ground for a comprehensive assessment of the efficiency of MEOP, by comparison with achievements at lower field (1 mT–2 T) over an extended range of operating conditions. Stronger hyperfine decoupling in the optically pumped 23S state is observed to systematically lead to slower build-up of 3He orientation in the ground state, as expected. The nuclear polarizations obtained at 4.7 T still decrease at high pressure but in a less dramatic way than observed at 2 T in the same sealed glass cells. To date, thanks to the linear increase in gas density, they correspond to the highest nuclear magnetizations achieved by MEOP in pure 3He gas. The improved efficiency puts less demanding requirements for compression stages in polarized gas production systems and makes high-field MEOP particularly attractive for magnetic resonance imaging of the lungs, for instance.

Structural evolution of ferromagnetic 3He multilayers adsorbed on exfoliated graphite

On the basis of our theoretical results describing two-dimensional spin-1/2 Heisenberg model in an external magnetic field we analyze and interpret known from literature experimental data on magnetization of pure 3He monolayers on graphite at ferromagnetic coverages. We clarify the experimentally observed temperature dependences for 2D 3He magnetization under magnetic fields of different magnitude. The cluster size effect in the temperature dependence of the magnetization is studied. We interpret the spin exchange variation in 2D multilayered 3He system during successive promotion of the second, third and fourth layers over first paramagnetic layer strongly coupled with graphite substrate.

Pressure Dependence of the Longitudinal Resonance Frequency of 3He Superfluid Phases in Aerogel

Pulsed NMR measurements have been performed on superfluid 3He within a 98% porosity aerogel over a pressure range of 8 to 26 bar. The aerogel sample is homogeneous and isotropic as indicated by in situ optical birefringence and, on similarly prepared samples, using SAXS characterization [1]. Two different superfluid phases are observed at low temperature. The two phases are identified as the same as the A and B-phases in pure 3He, from tip angle measurement and the NMR equations of Leggett [2]. The pressure and temperature dependence of the longitudinal resonance frequency of each phase is reported in this article.

QCM Study on 2D Vortex in Superfluid 4He and 3He-4He Mixture Films

Two-dimensional (2D) 4He fluid films show the Kosterlitz-Thouless (KT) transition where pairing and unpairing of the thermally excited 2D vortices play an important role. However, in the superfluid submonolayer, the vortex parameters (the diffusion constant D, the core diameter a0) have been incompletely estimated for various conditions. Here, we undertake QCM measurements for pure 4He films (on gold and H2 substrates) and 3He-4He mixture films (on gold substrate) and accurately determine the parameter D/a20 by the high frequency dependence of the superfluid onset from 20 to 180 MHz. By the comparison of the results of pure 4He film on gold and H2 substrates, the vortex diffusion in our study has the largest value D ∼ ℏ/m in the quantum limit. The core diameter a0 is estimated to be the same magnitude as the de Broglie wavelength at TKT between 0.1 and 0.9 K In terms of 3He-4He mixture films, we observe no effect of 3He on the vortex parameters up to the 3He coverage of 15.1 μmol/m2.

Neutron reflection from the surface of a liquid 4He-3He mixture

We have used neutron reflection from the liquid surface at ultra-low temperatures to study the surface properties of liquid helium. We measured neutron scattering from the free surfaces of commercially pure 4He (0.3 ppm of 3He impurities) and of a 3He-4He mixture with a 3He concentration of 0.5% for temperatures in the range from 340mK to 2.2K We compare the reflected neutron intensity for different temperatures and we fit a model that describes the collected data. The data are described well by a diffusive 3He layer of a few hundred Angstrom thickness on the bulk 4He liquid surface. Even at high temperatures (∼2K) there is an increased concentration of 3He atoms near the liquid surface. The distribution does not change very much with temperature. At low temperatures the neutron absorption increases significantly, which might be an indication of the formation of Andreev states. However, the shapes of the curves do not change very much which seems to suggest that the layer formed by the 3He atoms in Andreev states is very thin ∼ 10Å. The experimental method, based on neutron reflectometry, opens up new opportunities for the study of the surfaces and interfaces of quantum fluids and solids.

Mutual interactions between objects oscillating in isotopically pure superfluid 4He in the T → 0 limit

We report the results of experiments to explore interactions between physically separated oscillating objects in isotopically pure superfluid 4He at T ∼ 10 mK. The investigations focused mainly on 32 kHz quartz tuning forks, but also consider a nearby 1 kHz oscillating grid. The low-drive linewidth (LDL) and resonant frequency fd of a detector fork were monitored while the maximum velocity of a transmitter fork, separated from the detector by a few mm, was varied over a wide range. Clear evidence was found for mutual interactions between the two forks, and for the influence of the grid on the forks. Monitoring the detector's LDL and fd provides evidence for a generator critical velocity in the range 0.3<υc1<1.0 cm/s for onset of the detector responses, in addition to a second critical velocity υc2∼13 cm/s probably corresponding to the production of quantum turbulence at the generator. The results are discussed, but are not yet fully understood.

Magnetization of 3He layers in ferromagnetic regime: Cluster size effects

Abstract Magnetization of pure 3He monolayers on graphite and solid 3He on 4He-preplated graphite in the ferromagnetic regime is investigated theoretically within a two-dimensional spin-1/2 Heisenberg model in an external magnetic field. We develop an analytical approach based on a second-order two-time Green function formalism which describes the thermodynamic functions for finite as well as for infinite spin systems in the whole temperature range at arbitrary fields h. In particular, the present theory provides a proper description of the magnetization in the intermediate temperature region h T J at h well below the exchange J, that is in the region where the measurements for solid 3He monolayers are usually made. It is known from the experiment that only a part of 3He atoms is involved into ferromagnetic exchange. The ferromagnetic spins form clusters whose size is a function of coverage. The coverage dependences of the exchange constant, saturation magnetization, and average cluster size are found and analyzed. Nonmonotonic variation of the exchange constant with coverage is discussed. The effect of the cluster size on the temperature dependence of the magnetization is studied. To clarify how the cluster shape and boundary conditions affect magnetic properties of nanoclusters we calculate numerically the magnetization of small magnetic systems using the exact diagonalization method.

Mg impurity in helium droplets

Within the diffusion Monte Carlo approach, we have determined the structure of isotopically pure and mixed helium droplets doped with one magnesium atom. For pure (4)He clusters, our results confirm those of Mella et al. [J. Chem. Phys. 123, 054328 (2005)] that the impurity experiences a transition from a surface to a bulk location as the number of helium atoms in the droplet increases. Contrarily, for pure (3)He clusters Mg resides in the bulk of the droplet due to the smaller surface tension of this isotope. Results for mixed droplets are presented. We have also obtained the absorption spectrum of Mg around the 3s3p (1)P(1) ← 3s(2) (1)S(0) transition.