On the theory of the thermoelectric effect in a superconducting bimetallic loop

The theory of the thermoelectric effect in a bimetallic superconducting contour is discussed, particularly the calculation of the magnetic flux through the contour. In a previous work ¹ we analyzed this problem and criticized Pickett's approach ² to its solution. Pickett disagrees ³ with our criticsm and with the usual expression for the magnetic flux through the contour. In this work we make some additional remarks to elucidate the correctness of this expression. The possible role of spontaneous changes of the so-called frozen-in magnetic flux through the contour is emphasized, these changes being great enough to explain the experimentally observed very large magnetic flux in a hollow superconducting toroid. It is pointed out that the effect of the spontaneous transitions is very sensitive to the circuit geometry and should be much more pronounced in the case of a hollow superconducting cylinder (or toroid) as compared with a contour of the ring type.     

Thermal Instability of Superfluid Phase-Separated 3He-4He Solution Heated From Below

No Heading The phase separation influence on thermal instability of ³He-⁴He superfluid mixtures heated from below is studied in the temperature range of 70 – 550 mK. The experiments are carried out in a cylindrical cell of 2.38 cm in diameter and 4.7 cm in height with the initial concentration of 9.8 %³He. The thermal instability is registered by observing the anomaly in the dependences of temperature and concentration gradients in the cell as a function of heat flux. The instability is shown to occur only in the phase-separated solutions. We explain this behavior by the influence of capillary effects on the interface of the two-phase liquid. The experimental results are analyzed in terms of the critical Rayleigh and Marangoni numbers.PACS numbers: 44.25.+f, 67.30.–q, 67.80.Gb     

Visualising superfluid turbulent counterflow

No Heading An apparatus has been constructed to make superfluid counterflow in ⁴He visible. The counterflow channel is made of glass and has rectangular cross-section of height 0.01 cm, width 2 cm and length 4 cm. One of the 2 cm × 4 cm faces is silvered to allow a laser beam passing through the other face to reflect and thus traverse the fluid layer twice. We analyse the possibility that the turbulence could be made visible on a shadowgraph image projected onto a cooled CCD sensor. The image could arise either from small perturbations in the temperature gradient driving the counterflow caused by the turbulence itself, or by dispersion of a small tracer amount of ³He injected into the normal fluid streamlines. We conclude that the tracer technique shows the greater promise because of the larger scales of the perturbation in the refractive index of the fluid caused by the introduction of the ³He. We describe our technique for injecting small volume 1 ms pulses of ³He into the channel.PACS numbers: 67.40.Vs, 47.37.+q, 67.57.De     

Experimental Determination of Correlations Between Spontaneously Formed Vortices in a Superconductor

We have imaged spontaneously created arrays of vortices (magnetic flux quanta), generated in a superconducting film quenched through its transition temperature at rates around 10⁹ K/s. From these images, we calculated the positional correlation functions for two vortices and for 3 vortices. We compared our results with simulations of the time dependent Ginzburg Landau equation in 2D. The results are consistent with the Kibble-Zurek scenario of spontaneous vortex creation. Effects due to fluctuations of the gauge field on the correlation functions are below our experimental resolution.     

A Summary of Mass Flux Measurements in Solid 4He

Here we provide a summary and brief review of some of the work done with solid ⁴He at the University of Massachusetts Amherst below a sample pressure of 28?bar. The motivation for the work has been to attempt to pass ⁴He atoms through solid ⁴He without directly applying mechanical pressure to the solid itself. The specific technique chosen is limited to pressures near the melting curve and was initially designed to provide a yes/no answer to the question of whether or not it might be possible to observe such a mass flux. The thermo-mechanical effect and direct mass injection have been separately used to create chemical potential differences between two reservoirs of superfluid ⁴He connected to each other through superfluid-filled Vycor rods in series with solid ⁴He, which is in the hcp region of the phase diagram. The thermo-mechanical effect is a more versatile approach. And, in a particular symmetric application it is designed to provide a mass flux with little or no net increase in the density of the solid. Our observations, off but near the melting curve, have included: (1)?the presence of an increasing DC flux of atoms through the solid-filled cell with decreasing temperature below ≈650?mK and no flux above this temperature; (2)?the presence of a flux minimum and flux instability in the vicinity of 75–80?mK, with a flux increase at lower temperatures; (3)?the temperature dependence of the flux above 100?mK and the dependence of the flux on the net driving chemical potential difference provide interesting insights on the possible mechanism that leads to the flux above 100?mK. The most recent data suggest that whatever is responsible for the flux in solid ⁴He, at least for T>100?mK, may be an example of a Bosonic Luttinger liquid.     

Phase Slips and Josephson Weak Links in Superfluid Helium

When superfluid ⁴He flows through a submicron aperture, the velocity is limited by a critical value which marks the onset of quantized vortex creation. The evolution of the vortices causes the quantum phase across the aperture to change by 2π, leading to a detectable drop in flow energy. Recent studies of these phase slip events have provided new insights into the nucleation mechanisms for quantum vortices. By contrast, superfluid ³He passing through a submicron aperture exhibits nonlinear hydrodynamics, characterized by a Josephson-like current phase relation. Recent experiments have revealed a multitude of effects analogous to phenomena observed in superconductors. The experiments also reveal unexpected effects such as bistability, π-states, and novel dissipation mechanisms. PACS numbers: 67.57.-z, 74.50.+r, 67.40.Hf, 67.40. Vs.     

基于辐射传递理论的印刷品光谱反射预测模型

准确预测印刷品的颜色一直是印刷复制中一个十分重要的课题。基于光能的辐射传递理论,通过分析光在油墨层表面及内部传播过程中的散射与吸收等规律,并引入荧光激发函数,对Kubelka-Munk模型预测印刷品时蓝紫波段反射率偏差的问题进行了修正,并建立了新的印刷品光谱反射预测模型。该模型可为计算机光谱配色和高精度仿真印刷系统的开发提供理论基础。     

Self-Organized Heat Transport Near the Superfluid Transition in 4He

Heat transport through a column of superfluid ⁴ He has been observed experimentally to self-organize, resulting in a thermal gradient that exactly matches the gradient in the superfluid transition temperature across the column, leaving the entire sample at a constant distance from the superfluid critical point¹. We describe a new experiment that is designed to accomplish three objectives: 1) search for the upper critical heat flux above which self-organized heat transport can no longer occur, 2) measure the heat capacity of the self-organized heat transport state, and 3) test recent theoretical predictions^2,3 of the microscopic mechanism that is responsible for this self-organization.     

Two-phase pressure drop of R-410A in horizontal smooth minichannels

Convective boiling pressure drop experiments were performed in horizontal minichannels with a binary mixture refrigerant, R-410A. The test section was made of stainless steel tubes with inner diameters of 1.5 mm and 3.0 mm and with lengths of 1500 mm and 3000 mm, respectively. This test section was uniformly heated by applying electric current directly to the tubes. Experiments were performed at inlet saturation temperature of 10 °C, mass flux ranges from 300 to 600 kg m⁻² s⁻¹ and heat flux ranges from 10 to 40 kW m⁻². The current study showed the significant effect of mass flux and tube diameter on pressure drop. The experimental results were compared against 15 two-phase pressure drop prediction methods. The homogeneous model predicted well the experimental pressure drop, generally. A new pressure drop prediction method based on the Lockhart–Martinelli method was developed with 4.02% mean deviation.     

Pressure drop data and prediction method for enhanced external boiling tube bundles with R-134a and R-236fa

The pressure drops of external flow over enhanced tube bundles were experimentally obtained at both adiabatic and diabatic conditions using R-134a and R-236fa as test fluids. The tests were carried out at saturation temperatures of 5 and 15 °C, mass fluxes from 4 to 40 kg m⁻² s⁻¹, heat fluxes from 15 to 70 kW m⁻² and inlet vapour qualities ranging from 10% to 90%. The frictional pressure drop was found to be primarily a function of mass flux and vapour quality. After comparisons were made with prediction methods in literature a new pressure drop prediction method was proposed for adiabatic and diabatic conditions. The proposed method is based on local measurements (4 and 8 tube rows) and flow conditions (evaluated per tube pitch) and the prediction method is well adapted to local incremental implementation for flooded evaporator design.     

Free convection of a heat generating fluid in a hemispherical closed volume

From a theoretical analysis and results of previous studies, a model of the free convection of a heat-generating fluid in a hemispherical closed volume with a completely isothermal boundary is developed. By applying analytical estimates, we establish that at values of modified Rayleigh numbers Ra₁ > 10¹³, the flow in the entire volume is turbulent, which substantially simplifies the problem. Integrated relations for heat emission through the upper and lower parts of the boundary of the hemispherical capacity are obtained as a result. Results of numerical calculations have shown that the majority of heat is removed through the spherical surface downwards. The ratio of the heat flux through the upper horizontal boundary to heat flux through the lower boundary decreases from 0.5 to 0.3 in the range of modified Rayleigh numbers Ra_I from 10⁹ to 10¹⁷.     

From Flux Quantization to Superconducting Quantum Bits

One of the important predictions of the early phenomenological theories of superconductivity such as the London and Ginzburg–Landau (GL) theory is the quantization of magnetic flux in multiply connected superconductors, which is one of the first demonstrations of a quantum effect on a macroscopic scale. In this paper, which is devoted to Vitalij Lazarevich Ginzburg on the occasion of his 90th birthday, we analyze a superconducting cylinder acting as a flux box as well as a superconducting disk acting as a Cooper pair box in the framework of GL theory. We extend this analysis to leaky flux and Cooper pair boxes which are obtained by introducing weak links allowing for the entry and exit of flux quanta and Cooper pairs from the respective boxes at finite rates. Flux and Cooper pair slippage processes by coherent quantum tunneling result in effective two-level quantum systems forming the basis for flux and charge quantum bits presently considered for the solid-state implementation of quantum information processing. We show that the corresponding Hamiltonians describing the leaky flux and Cooper pair box can be transformed into each other by a canonical transformation. PACS numbers: 74.20.De, 74.25.Bt, 74.25.Ha, 74.50.+r     

Half-Integer Flux Quantization in a Superconducting Loop with a Ferromagnetic π-Junction

Superconducting loops containing a π-junction are predicted to show a spontaneous magnetic moment in zero external magnetic field. In order to confirm this longstanding prediction experimentally, we performed magnetization measurements on individual mesoscopic superconducting niobium loops with a ferromagnetic (PdNi) π-junction. The loops are prepared on top of the active area of a micro Hall-sensor based on high mobility GaAs/AlGaAs heterostructures. We observe switching of the loop between different magnetization states at very low-magnetic fields, which is asymmetric for positive and negative sweep direction. This is evidence for a spontaneous current induced by the intrinsic phase shift of the π-junction. In addition, the presence of the spontaneous current at zero applied field is directly revealed by an increase of the magnetic moment with decreasing temperature, which results in a half integer flux quantization in the loop at low temperatures. This work is dedicated to H. von L?hneysen on the occasion of his 60th birthday.     

Hydrogen transport by group 5 metals: Achieving the maximal flux density through a vanadium membrane

Hydrogen transport by 100-μm-thick vanadium and palladium membranes was studied in the pressure range from 1 × 10^?8 to 4.5 × 10^?1 MPa at a temperature of 400°C. Both sides of the vanadium membrane were covered by 2 μm of palladium (Pd-V-Pd) for facilitating the dissociative absorption and associative desorption of H₂ molecules. At low pressures, hydrogen flux densities through vanadium and palladium membranes are nearly the same; at high pressures, the flux through the vanadium membrane becomes 16 times larger than the flux through the palladium membrane and attains a value of 2.4 scc cm^?2 s^?1. This flux of permeating hydrogen is larger than all values ever observed earlier for membranes made of group 5 metals or any other unsupported metal membranes.     

Pinning of the Vortex System and Magnetostriction of Superconductors

No Heading Hard type-II superconductors usually reveal a large, of the order of 10^–5 or 10^–4, magnetostriction in the external magnetic field of several Tesla. Such a strong magnetostriction can be well understood in the framework of the model of the pinning-induced magnetostriction. Although the assumptions of this model are easy to understand, the solution of the problem for realistic sample shapes is difficult, because the stress induced in the sample volume by the screening currents has non uniform distribution and it may also change the sample shape. The model of pinning-induced magnetostriction is insufficient to explain all magnetostriction results in superconductors. Sometimes, it is necessary to consider also other mechanisms of the magnetostriction. Magnetostriction of superconductors was analyzed theoretically and studied experimentally in a large number of both conventional and high temperature superconductors. In this paper we present a review of the most characteristic results. We also present the phenomenon of giant magnetostriction jumps, which is closely related to the phenomenon of giant flux jumps or thermomagnetic instabilities in type-II superconductors.PACS numbers: 74.25.Qt, 75.80.+q     

Thermal phenomena in the flow of superfluid 3He through a weak link

No Heading We report on experiments performed with a weak link which was the only flow connection between two volumes of ³He. The deflection of a flexible wall between the volumes was measured to monitor the flow through the weak link as well as to measure the pressure difference across it. The temperature of the main volume was changed in steps of approximately 0.2 mK. After these temperature steps a fountain pressure developed and decayed on a time scale of several hundred seconds. This thermomechanical effect was found in normal and in superfluid ³He. We did not observe any influence of the quantum phase difference on the heat conductivity.PACS numbers: 67.57.De, 67.57.Fg, 74.50.+r, 85.25.Cp     

4He atom reflection from rough liquid4He surfaces

When an atom is evaporated from or added to a free liquid surface there is a density perturbation of the surface. We have detected this surface spoiling using a⁴He atomic beam at glancing angles to the surface. With a perfect free liquid surface some of the atoms reflect specularly and some condense. We find that the specular reflection coefficient decreases as the surface is spoiled by another beam of⁴He atoms. The degree of spoiling as measured by the decrease in reflectivity, is initially proportional to the spoiling beam flux, but at higher fluxes the spoiling saturates. A phenomenological model is developed to describe this behaviour.     

Flux flow velocity in superconducting films by measurement of passage time

The velocity of flux tubes in thin superconducting films has been determined by measuring the time for their passing across the film. A legion of flux tubes has been pulsed in on the left side of a film carrying a current large enough to break the pinning. The arrival of the flux tubes on the right side is observed with a pick-up coil. Flow velocities of 3 to 50×10⁴ cm/sec have been observed with current densities up to 10⁵ A/cm².Supported in part by the National Science Foundation, in part by the Cryogenics Center through a grant from the DOD Themis program.     

Ballistic quasiparticle beam experiments in superfluid3He-B

In³He-B at temperatures of the order of 0.1T_c, where the meanfree path of the excitations measures several hundreds of metres, we are able to perform experiments on fully ballistic quasiparticle beams. We describe the first direct production and detection of a quasiparticle beam in superfluid ³ He with the use of a black-body radiator. The radiator may be used as a smoothly controllable continuous source and also as a bolometric detector, sensitive to a quasiparticle energy flux of order 100 fW mm ^–2 .     

SH-SAW Sensor for Superfluid 3He

No Heading We have developed a new technique to study the transverse acoustic properties of superfluid ³He, employing a shear horizontal surface acoustic wave (SH-SAW) sensor. The transverse acoustic impedance can be obtained from the velocity and damping of SH-SAW which acoustically couples with liquid ³He all the interface. Since ultrasonic measurements provide the information about superfluid order-parameter through the excitation of collective modes, the SH-SAW sensor is expected to be a useful tool to study the boundary effect of superfluid ³He. Preliminary measurements were carried out at pressures of 17 and 23 bar, by the pulse transmission method at a frequency of 70 MHz. At 17 bar, imaginary squashing mode was observed as the sharp drop of the imaginary part of acoustic impedance. At 23 bar, the supercooled A-B phase transition was observed, as a jump of the real part of acoustic impedance, which was not observed in the warming process.PACS numbers: 67.57.Jj, 43.58.+z