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Register a new userObservation of Crossover from Ballistic to Diffusion Regime for Excimer Molecules in Superfluid $^4$He
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We have measured the temperature dependence of the time of flight of helium excimer molecules He2* in superfluid 4He and find that the molecules behave ballistically below 100mK and exhibit Brownian motion above 200 mK. In the intermediate temperature range the transport cannot be described by either of the models.
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We develop an analytic theory of strong anisotropy of the energy spectra in the thermally-driven turbulent counterflow of superfluid He-4. The key ingredients of the theory are the three-dimensional differential closure for the vector of the energy flux and the anisotropy of the mutual friction force. We suggest an approximate analytic solution of the resulting energy-rate equation, which is fully supported by the numerical solution. The two-dimensional energy spectrum is strongly confined in the direction of the counterflow velocity. In agreement with the experiment, the energy spectra in the direction orthogonal to the counterflow exhibit two scaling ranges: a near-classical non-universal cascade-dominated range and a universal critical regime at large wavenumbers. The theory predicts the dependence of various details of the spectra and the transition to the universal critical regime on the flow parameters. This article is a part of the theme issue Scaling the turbulence edifice.
There are two commonly discussed forms of quantum turbulence in superfluid $^4$He above 1K: in one there is a random tangle of quantizes vortex lines, existing in the presence of a non-turbulent normal fluid; in the second there is a coupled turbulent motion of the two fluids, often exhibiting quasi-classical characteristics on scales larger than the separation between the quantized vortex lines in the superfluid component. The decay of vortex line density, $L$, in the former case is often described by the equation $dL/dt=-chi_2 (kappa/2pi)L^2$, where $kappa$ is the quantum of circulation, and $chi_2$ is a dimensionless parameter of order unity. The decay of total turbulent energy, $E$, in the second case is often characterized by an effective kinematic viscosity, $ u$, such that $dE/dt=- u kappa^2 L^2$. We present new values of $chi_2$ derived from numerical simulations and from experiment, which we compare with those derived from a theory developed by Vinen and Niemela. We summarise what is presently known about the values of $ u$ from experiment, and we present a brief introductory discussion of the relationship between $chi_2$ and $ u$, leaving a more detailed discussion to a later paper.
Collisions in a beam of unidirectional quantized vortex rings of nearly identical radii $R$ in superfluid $^4$He in the limit of zero temperature (0.05 K) were studied using time-of-flight spectroscopy. Reconnections between two primary rings result in secondary vortex loops of both smaller and larger radii. Discrete steps in the distribution of flight times, due to the limits on the earliest possible arrival times of secondary loops created after either one or two consecutive reconnections, are observed. The density of primary rings was found to be capped at the value $500{rm ,cm}^{-2} R^{-1}$ independent of the injected density. This is due to collisions between rings causing piling-up of many other vortex rings. Both observations are in quantitative agreement with our theory.
We use particle tracking velocimetry to study Eulerian and Lagrangian second-order statistics of superfluid $^4$He grid turbulence. The Eulerian energy spectra at scales larger than the mean distance between quantum vortex lines behave classically with close to Kolmogorov-1941 scaling and are almost isotropic. The Lagrangian second-order structure functions and frequency power spectra, measured at scales comparable with the intervortex distance, demonstrate a sharp transition from nearly-classical behavior to a regime dominated by the motion of quantum vortex lines. Employing the homogeneity of the flow, we verify a set of relations that connect various second-order statistical objects that stress different aspects of turbulent behavior, allowing a multifaceted analysis. We use the two-way bridge relations between Eulerian energy spectra and second-order structure functions to reconstruct the energy spectrum from the known second-order velocity structure function and vice versa. The Lagrangian frequency spectrum reconstructed from the measured Eulerian spectrum using the Eulerian-Lagrangian bridge differs from the measured Lagrangian spectrum in the quasi-classical range which calls for further investigation.
We calculate the effect of a heat current on transporting $^3$He dissolved in superfluid $^4$He at ultralow concentration, as will be utilized in a proposed experimental search for the electric dipole moment of the neutron (nEDM). In this experiment, a phonon wind will generated to drive (partly depolarized) $^3$He down a long pipe. In the regime of $^3$He concentrations $tilde < 10^{-9}$ and temperatures $sim 0.5$ K, the phonons comprising the heat current are kept in a flowing local equilibrium by small angle phonon-phonon scattering, while they transfer momentum to the walls via the $^4$He first viscosity. On the other hand, the phonon wind drives the $^3$He out of local equilibrium via phonon-$^3$He scattering. For temperatures below $0.5$ K, both the phonon and $^3$He mean free paths can reach the centimeter scale, and we calculate the effects on the transport coefficients. We derive the relevant transport coefficients, the phonon thermal conductivity and the $^3$He diffusion constants from the Boltzmann equation. We calculate the effect of scattering from the walls of the pipe and show that it may be characterized by the average distance from points inside the pipe to the walls. The temporal evolution of the spatial distribution of the $^3$He atoms is determined by the time dependent $^3$He diffusion equation, which describes the competition between advection by the phonon wind and $^3$He diffusion. As a consequence of the thermal diffusivity being small compared with the $^3$He diffusivity, the scale height of the final $^3$He distribution is much smaller than that of the temperature gradient. We present exact solutions of the time dependent temperature and $^3$He distributions in terms of a complete set of normal modes.
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