Normal Helium Research Articles

Thermal feedback in coaxial superconducting radio frequency cavities

The surface resistance of superconducting radio frequency (SRF) cavities depends on the strength of the applied rf field. This field dependence is caused by a combination of intrinsic losses and the extrinsic thermal feedback (TFB) effect. To test theories of intrinsic field dependence, the extrinsic part must be compensated for when analyzing experimental data from SRF cavity tests. Performing this compensation requires knowing thermal parameters that describe heat flow in the cavity walls. The relevant thermal parameters have been measured in the case of superfluid helium, below 2.177 K, but no detailed measurements have yet been reported for cooling of niobium surfaces in normal fluid helium baths. Because of this, the impact of TFB on the field dependence at temperatures near 4.2 K is unknown. In the present study, we report measurements of normal fluid helium boiling from niobium surfaces and its dependence on the orientation of the boiling surface and bath temperature. These measurements are used to create a finite-element model of heat transfer in cavities from TRIUMF’s coaxial test program. This tool is then used to compensate for TFB when analyzing a range of datasets from this program. Results are presented showing that TFB has a weak impact for the temperatures of 2.0 and 4.2 K, where SRF cavities are usually operated, but it is an important effect at intermediate temperatures. Published by the American Physical Society 2024

Freeze range of a condensing gas propagating in a liquid helium-cooled tube

Understanding air propagation and condensation following a catastrophic vacuum break in particle accelerator beamlines cooled by liquid helium is crucial for maintaining the operational safety of these facilities. Previous experimental investigations on nitrogen gas propagation in both normal liquid helium (He I) and superfluid helium (He II) cooled copper tubes unveiled a nearly exponential deceleration of the gas propagation. A comprehensive theoretical model incorporating gas dynamics, heat transfer, and condensation mechanisms has been developed, which effectively reproduces various key experimental observations. An intriguing phenomenon uncovered in our model simulation is that the gas propagation appears to nearly stop beyond a certain distance from the location where condensation starts. We refer to this distance as the freeze range. In this paper, we present our systematic study of the freeze range at various inlet mass fluxes and tube diameters. We show that the results can be well described by a simple correlation. The underlying physical mechanism that supports this useful correlation is explained. Knowing the freeze range may allow accelerator engineers to develop protocols for controlling frost-layer contamination in the beamline tubes, which is of great practical importance.

Vortices on the Free Surface of a Normal Helium He-I Layer in a Wide Cell

The appearance of a thermogravitational convective flow in the bulk of a layer of normal liquid helium He-I h ≈ 1–3 cm deep in a wide cylindrical cell, which is heated from above in the gravity field in the temperature range Tλ ≤ T ≤ Tm, is accompanied by the excitation of a vortex flow on the free surface of the liquid. Here Tλ = 2.1768 K is the temperature of transition of liquid 4He from the superfluid He-II to the normal He-I state at the saturated vapor pressure, and Tm ≈ 2.183 K is the temperature at which the He-I density passes through a maximum. Bulk convection serves as a source of energy pumped into the vortex system on the surface of He-I. The nonlinear interaction of vortices on the surface with each other and with convective vortex flows in the bulk of the layer leads to the formation of two large-scale vortices (vortex dipole) on the surface of He-I, and their sizes are limited to the diameter of the working cell and several times exceed the layer depth. This behavior corresponds to the transition from the vortex flow mode on “deep water” (vortices on the surface of a three-dimensional liquid layer) to vortices on the surface of “shallow water” (vortices on the surface of a two-dimensional layer) in time. When the layer is heated further above Tm, the convective flows in the bulk decay quickly, but the vortex motion on the surface of a two-dimensional He-I layer is retained. In the absence of energy pumping from the bulk, the total energy of the vortex system on the surface of a shallow water layer decreases in time according to a near-power law because of the nonlinear interaction of large-scale vortices with each other and friction against the cell walls. As a result, during long-term observations, small-scale vortices with sizes comparable to or less than the layer depth again begin to prevail on the surface of He-I, which corresponds to the transition from a two-dimensional to a three-dimensional liquid layer. The energy of the vortex flow on the surface of a deep water layer decreases according to a near-exponential law. Thus, long-term observations of the dynamic phenomena on the free surface of an He-I layer several centimeters deep in a wide temperature range above Tλ allowed us, for the first time, to study the excitation, evolution, and decay of the vortex flows on the surface of a deep or shallow water layer in one experiment.

Surface tension of cavitation bubbles

We have studied homogeneous cavitation in liquid nitrogen and normal liquid helium. We monitor the fluid content in a large number of independent mesopores with an ink-bottle shape, either when the fluid in the pores is quenched to a constant pressure or submitted to a pressure decreasing at a controlled rate. For both fluids, we show that, close enough to their critical point, the cavitation pressure threshold is in good agreement with the Classical Nucleation Theory (CNT). In contrast, at lower temperatures, deviations are observed, consistent with a reduction of the surface tension for bubbles smaller than two nanometers in radius. For nitrogen, we could accurately measure the nucleation rate as a function of the liquid pressure down to the triple point, where the critical bubble radius is about one nanometer. We find that CNT still holds, provided that the curvature dependence of the surface tension is taken into account. Furthermore, we evaluate the first- and second-order corrections in curvature, which are in reasonable agreement with recent calculations for a Lennard-Jones fluid.

Vortices on the Free Surface of a Normal Helium He-I Layer in a Wide Cell

Vortices on the Free Surface of a Normal Helium He-I Layer in a Wide Cell

Vortex Flow on the Surface Generated by the Onset of a Buoyancy-Induced Non-Boussinesq Convection in the Bulk of a Normal Liquid Helium.

The onset of the Rayleigh–Benard convection (RBC) in a heated from above normal He-I layer in a cylindrical vessel in the temperature range Tλ < T ≤ Tm (RBC in non-Oberbeck–Boussinesq approximation) is attended by the emergence of a number of vortices on the free liquid surface. Here, Tλ = 2.1768 K is the temperature of the superfluid He-II–normal He-I phase transition, and the liquid density passes through a well-pronounced maximum at Tm ≈ Tλ + 6 mK. The inner vessel diameter was D = 12.4 cm, and the helium layer thickness was h ≈ 2.5 cm. The mutual interaction of the vortices between each other and their interaction with turbulent structures appeared in the layer volume during the RBC development gave rise to the formation of a vortex dipole (two large-scale vortices) on the surface. Characteristic sizes of the vortices were limited by the vessel diameter. The formation of large-scale vortices with characteristic sizes twice larger than the layer thickness can be attributed to the arising an inverse vortex cascade on the two-dimensional layer surface. Moreover, when the layer temperature exceeds Tm, convective flows in the volume decay. In the absence of the energy pumping from the bulk, the total energy of the vortex system on the surface decreases with time according to a power law.

Weakly Damped Vortex Flow on the Free Surface of a Normal Helium He-I Layer

Weakly Damped Vortex Flow on the Free Surface of a Normal Helium He-I Layer

The turbulent drag force in superfluid 3He−4He mixtures under oscillations of a quartz tuning fork

We have studied the resonance curves of a quartz tuning fork of the fundamental frequency 32 kHz immersed in superfluid 4He and mixtures 3He–4He with 3He concentration of 5 and 15% in the temperature range of 0.35–2.5 K at saturated vapor pressure. Two types of experiments have been carried out, with a tuning fork both not covered by a bulb and coated by a bulb, i.e., in the restricted geometry. In both cases, the velocity-force dependences for the tuning fork showed a linear damping force at low peak velocities and extra drag due to the appearance of vortex lines accompanying the transition to turbulence under increasing peak velocity. These dependencies are mainly determined by the density of the normal helium component. There is a pronounced difference between superfluid 4He and mixtures of 3He in 4He, where 3He impurity particles provide a constant temperature-independent contribution to the normal component of the mixture. The extra contribution to the damping force, so-called “turbulent drag force”, decreases with concentration increase at the same peak velocity of the tuning fork that can be explained by the extension of the range of laminar flow with an increase in the concentration of 3He. We found that the drag coefficient in superfluid 4He and mixtures 3He–4He reaches a plateau at different peak velocities and different exciting forces and explained this fact by different conditions for vortex formation, depending on the different thickness of the near-wall viscous layer. The comparison between the data obtained in restricted and unrestricted geometries shows that there is an excessive dissipation of the tuning fork motion associated with the emission of the first sound wave in unrestricted geometry.

Investigation of properties of superfluid He4 turbulence using a hot-wire signal

We report hot-wire measurements performed in two very different, co- and counter-rotating flows, in normal and superfluid helium at 1.6 K, 2 K, and 2.3 K. As recently reported, the power spectrum of the hot-wire signal in superfluid flows exhibits a significant bump at high frequency (Diribarne et al. [1]). We confirm that the bump frequency does not depend significantly on the temperature and further extend the previous analysis of the velocity dependence of the bump, over more than one decade of velocity. The main result is that the bump frequency depends on the turbulence intensity of the flow, and that using the turbulent Reynolds number rather than the velocity as a control parameter collapses results from both co- and counter-rotating flows. The vortex shedding model previously proposed, in its current form, does not account for this observation. This suggests that the physical origin of the bump is related to the small scale turbulence properties of the flow. We finally propose some qualitative physical mechanism by which the smallest structures of the flow, at intervortex distance, could affect the heat flux of the hot-wire.

Heat and mass transfer during a sudden loss of vacuum in a liquid helium cooled tube - Part III: Heat deposition in He II

A sudden loss of vacuum can be catastrophic for superconducting particle accelerators. In such an event, air leaks into the liquid-helium-cooled accelerator beamline tube and condenses on its inner surface, causing rapid boiling of the helium and dangerous pressure build-up. Understanding the coupled heat and mass transfer processes is important for the design of the beamline cryogenic system. Our past experimental study on nitrogen gas propagating in a copper tube cooled by normal liquid helium (He I) has revealed a nearly exponential slowing down of the gas front. A theoretical model that accounts for the interplay of the gas dynamics and the condensation was developed, which successfully reproduced various key observations. However, since many accelerator beamlines are actually cooled by superfluid helium (He II) in which the heat transfer is via a non-classical thermal counterflow mode, we need to extend our work to the He II cooled tube. This paper reports our systematic measurements using He II and the numerical simulations based on a modified model that accounts for the He II heat-transfer characteristics. By tuning the He II peak heat-flux parameter in our model, we have reproduced the observed gas dynamics in all experimental runs. The fine-tuned model is then utilized to reliably evaluate the heat deposition in He II. This work not only advances our understanding of condensing gas dynamics but also has practical implications to the design codes for beamline safety.

Multiscale energy budget of inertially driven turbulence in normal and superfluid helium

In this paper we present a novel hydrodynamic experiment using liquid $^4$He. The flow is forced inertially by a canonical oscillating grid using either its normal (He~I) or superfluid (He~II) phase, generating a statistically stationary turbulence. We characterise the turbulent properties of the flow using 2D Lagrangian Particle tracking on hollow glass micro-spheres. As expected for tracer particles, the Vorono\"{i} tessellation on particle positions does not show a significant departure from a random Poisson process neither in He~I nor He~II phase. Particles' positions are tracked with high temporal resolution, allowing to resolve velocity fluctuations at integral and inertial scales while properly assessing the noise contribution. Additionally, we differentiate the particles' positions (by convolution with Gaussian kernels) in order to access small scale quantities like acceleration. Using these measured quantities and the formalism of classical Homogeneous Isotropic Turbulence (HIT) to perform an energy budget across scales we extract the energy injection rate at the large scale, the energy flux cascading through inertial scales, down to small scales at which it is dissipated. We found that in such inertially driven turbulence, regardless of the normal or superfluid state of the fluid, estimates of energy at the different scales are compatible with each other and consistent with oscillating grid turbulence results reported for normal fluids in the literature. The largest discrepancy shows up at small scales where the signal to noise ratio is harder to control and where the 2D measurement is contaminated by the 3D nature of the flow. This motivates to focus future experimental projects towards small scales, low noise and 3D measurements.

Nuclear quantum effects in thermal conductivity from centroid molecular dynamics.

We show that the centroid molecular dynamics (CMD) method provides a realistic way to calculate the thermal diffusivity a = λ/ρcV of a quantum mechanical liquid such as para-hydrogen. Once a has been calculated, the thermal conductivity can be obtained from λ = ρcVa, where ρ is the density of the liquid and cV is the constant-volume heat capacity. The use of this formula requires an accurate quantum mechanical heat capacity cV, which can be obtained from a path integral molecular dynamics simulation. The thermal diffusivity can be calculated either from the decay of the equilibrium density fluctuations in the liquid or by using the Green-Kubo relation to calculate the CMD approximation to λ and then dividing this by the corresponding approximation to ρcV. We show that both approaches give the same results for liquid para-hydrogen and that these results are in good agreement with the experimental measurements of the thermal conductivity over a wide temperature range. In particular, they correctly predict a decrease in the thermal conductivity at low temperatures-an effect that stems from the decrease in the quantum mechanical heat capacity and has eluded previous para-hydrogen simulations. We also show that the method gives equally good agreement with the experimental measurements for the thermal conductivity of normal liquid helium.

The interaction between injected charges and a vortex flow in normal and superfluid helium near Τλ

The interaction between injected negative charges and vortex motion formed by standing waves with the frequency ω/2π = 49.88 Hz on the surface of normal and superfluid helium has been experimentally studied. It has been found that the vorticity generation results in the redistribution of the current at segments of a collector. A change in the trajectory of the motion of charges from a source to a receiving collector is caused by their interaction with the vortex flow of the normal component.

Design optimization of the 2 K heat exchanger for the superfluid helium cryogenic systems at KEK

At KEK, the superfluid helium cryogenic systems employ laminated-finned type 2 K heat exchangers (2 K HX). Their purpose is to sub-cool normal liquid helium (He I or LHe) from 4.4 K to 2.2 K or above, using the sensible heat carrying capacity of 2.0 K gaseous helium (GHe). This would help in reducing vapor flash losses during the Joule-Thomson (JT) expansion, hence improving the production rate of 2.0 K saturated superfluid helium (He II). Another equally important factor that affects the production of He II is the GHe pressure drop through the 2 K HX. Higher GHe pressure drop compels the GHe pumping system to operate at lower inlet pressures, reducing the flow rates that can be pumped out, hence reducing the He II production. The performance of a 2 K HX is characterized by a factor known as effectiveness and should be > 83.7% to produce ~ 2.2 K LHe, at the outlet of the 2 K HX and before the JT valve. In this paper, a numerical model has been developed to determine the performance parameters (effectiveness and GHe pressure drop) of the current 2 K HX design and is verified experimentally using a heat exchanger test stand. Furthermore, a parametric study is conducted to improve the performance of the current 2 K HX design, which was also validated experimentally. The improved 2 K HXs will be studied in conjunction with the GHe pumping system to determine the optimal 2 K HX design that maximizes the He II production from the cryogenic systems. The optimized 2 K HX design in this study improved the He II production rate by 7%.

O2 − ion mobility in dense Ne gas: The free volume model

We report data of the O2- ion mobility in neon gas over broad density and temperature ranges along with its theoretical description in terms of the thermodynamic, free volume model that has successfully been adopted for the interpretation of electron and ion mobility in superfluid and normal helium. The free volume model, which is aimed at computing the free volume accessible for the ion motion, along with the Millikan- Cunningham slip factor correction, is able to describe the ion mobility in the crossover region connecting the dilute gas regime described by the classical Kinetic Theory to the high density region ruled by the laws of hydrodynamic transport.

HECAL: A cryostat for calibration of hot wires

The Laboratory SBT (“Systemes à Basse Température”) has studied Fundamental Turbulence at High Reynolds Numbers for many years. Different experiments were performed, which allowed to study high Reynolds Number flows, and also to compare these (normal helium) turbulent flows with superfluid flows driven under the same conditions. First section describes the interest of hot wire anemometry to characterize the turbulent flows. Hot wires were used already in Hejet, and more recently in SHREK. However, the hot wires should be calibrated, which is not always possible in situ. Therefore, we built a facility dedicated to the test and calibration of hot wires. This original facility is described in second section; instead of having a fixed hot wire in an incoming flow, which is the usual situation for hot wire calibration devices, the hot wire to calibrate is installed on a support part, which can be rotated in a fluid at rest. In order to calibrate the hot wires in the same velocity domain as in the SHREK and Hejet experiments, the support of the hot wire can reach velocities of a few meters per second. The first results obtained with Hecal are presented in third section. Fourth section describes the future work to be performed in the CEA facilities.

Effect of mass flow rate on gas propagation after vacuum break in a liquid helium cooled tube.

Vacuum break in particle accelerators is a major concern due to risks associated with personnel and extensive equipment damage. Continuing research in our lab focuses on the sudden loss of vacuum in the liquid helium cooled beam-line tubes of superconducting particle accelerators. In our previous research, we studied nitrogen gas propagation in a uniform tube system immersed in both normal helium (He I) and superfluid helium (He II). It was observed that He II has a stronger effect in slowing down the gas propagation compared to He I, but this effect was largely due to the variation of the point where condensation and deposition of the nitrogen gas on the tube inner wall. Here, we discuss our modifications to the tube system that now allow us to accurately control the starting location of gas condensation in both the He I and He II experiments. Systematic studies of gas propagation were conducted using this new tube system by varying the nitrogen mass flow rate at the tube inlet.

Vortices on the Surface of Normal He I Generated by the Rayleigh–Bénard Thermogravitational Convection in the Bulk of a Liquid

It has been experimentally found that the appearance of the Rayleigh–Benard thermogravitational convection in the bulk of a normal helium He-I layer heated from above in an immobile working vessel at temperatures close to the critical temperature Tλ is accompanied by the generation of vortices on the free surface of He-I. The interaction of these vortices between each other and with vertical vortex structures, which are formed in the bulk of the layer in the process of establishment of turbulent Rayleigh–Benard thermogravitational convection, results in the appearance of large-scale vortices (vortex dipole) on the surface. Rayleigh–Benard thermogravitational convection in the bulk of the liquid layer heated above 2.3 K decreases rapidly with the time. In the absence of pumping, in the temperature range 2.6–3.3 K, the maximum energies of large-scale vortices on the surface in the k space decrease with time as Emax ~ t–1.

A method for constrained optimisation of the design of a scanning helium microscope

We describe a method for obtaining the optimal design of a normal incidence Scanning Helium Microscope (SHeM). Scanning helium microscopy is a recently developed technique that uses low energy neutral helium atoms as a probe to image the surface of a sample without causing damage. After estimating the variation of source brightness with nozzle size and pressure, we perform a constrained optimisation to determine the optimal geometry of the instrument (i.e. the geometry that maximises intensity) for a given target resolution. For an instrument using a pinhole to form the helium microprobe, the source and atom optics are separable and Lagrange multipliers are used to obtain an analytic expression for the optimal parameters. For an instrument using a zone plate as the focal element, the whole optical system must be considered and a numerical approach has been applied. Unlike previous numerical methods for optimisation, our approach provides insight into the effect and significance of each instrumental parameter, enabling an intuitive understanding of effect of the SHeM geometry. We show that for an instrument with a working distance of 1 mm, a zone plate with a minimum feature size of 25 nm becomes the advantageous focussing element if the desired beam standard deviation is below about 300 nm.

Progress Toward a Compact Fusion Reactor Using the Sheared-Flow-Stabilized Z-Pinch

The sheared-flow-stabilized (SFS) Z-pinch is a promising confinement concept for the development of a compact fusion reactor. The Z-pinch has been theoretically and experimentally shown to be stable to magnetohydrodynamic modes when sufficient radial shear of the axial flow is present. At the University of Washington, the Fusion Z-pinch Experiment (FuZE) research project examines scaling the SFS Z-pinch toward fusion conditions. The FuZE device produces long-duration, 50-cm-long pinches with measured ion and electron temperatures over 1 keV and number densities greater than cm. Plasma properties are measured with a diagnostic suite that includes magnetic field probes, heterodyne quadrature interferometry, digital holographic interferometry, ion-Doppler spectroscopy, and fast framing photography. Neutrons are produced in the FuZE device when deuterium is injected along with the normal hydrogen or helium fueling species. Neutron generation is diagnosed using plastic scintillator detectors. The neutron production is sustained for 5 to 8 μs, thousands of times longer than the static Z-pinch instability growth time. Measured neutron production is consistent with calculated theoretical values for thermonuclear yield at the observed plasma temperatures and scales with the square of the deuterium concentration. A preliminary reactor concept is designed to incorporate flowing liquid metal walls, which would serve as an electrode, a heat transfer fluid, a radiological shield, and a breeding blanket. Using a liquid metal wall could address several unresolved material and technology issues in existing fusion reactor designs.