A.T.A.M. de Waele

Quantum Magnetoconductance of a Nondegenerate Two-Dimensional Electron Gas

Magnetoconductance measurements are reported for the low-density, two-dimensional classical electron gas formed on the surface of liquid helium. At strong magnetic fields, large deviations from the classical parabolic behaviour are observed. These deviations are described with a quantum-transport theory of scattering within broadened Landau levels.

Numerical simulation of pulse-tube refrigerators

A new numerical model has been developed for simulating oscillating gas ??ow and heat transfer in the tube section of a pulse-tube refrigerator. Pulse-tube refrigerators are among the newest types of cryocoolers. They work by the cyclic compression and expansion of gas, usually helium. Introduced in 1963, pulse-tube refrigerators typically reached temperatures of about 120 K. By the end of the 1990s temperatures below 2 K had been reached. The practical use of pulse-tube cryocoolers is still at an early stage. However, they are beginning to replace the older types of cryocoolers in a wide variety of applications: military, aerospace and medical industries. Advantages such as simplicity, low cost and reliability, combined with high performance, have resulted in an extensive study of pulse tubes in recent years. The ??rst and second laws of thermodynamics have been major tools to investigate pulse-tube refrigerators theoretically. However, a clearer understanding of the ??uid dynamical properties is necessary if one wishes to make quantitative improvements in pulse tube performance. In this study we concentrate solely on the tube section of the pulse-tube refrigerator to identify undesired effects that occur in the tube and reduce the ef??ciency of the coolers. The developed mathematical model is based on the conservation of mass, momentum and energy, and the equation of state. The conservation equations for compressible viscous unsteady ??ow are written in differential form using primitive variables. One-dimensional and two-dimensional cylindrical axisymmetrical cases are considered. According to dimensional analysis, the tube conveys a low-Mach-number compressible ??ow. Therefore, we expanded all relevant variables in terms of powers of M2, a parameter related to the Mach number. This asymptotic consideration reveals several key features of pulse tube ??ow. Two physically distinct roles of pressure are to be distinguished: one as thermodynamic variable and one as hydrodynamic variable. The thermodynamical pressure appears in the energy equation and in the equation of state. It is spatially uniform, thus a function of time only, and is responsible for the global compression and expansion. The hydrodynamical pressure appears in the momentum equations and is induced by inertia and viscous forces. The acoustic pressure does not play a role in pulse tubes. Due to the non-linearity of the resulting system of equations, general analytical solutions are not available. Therefore numerical modelling has been applied. For the numerical solution of the resulting system of equations ??nite difference methods are used. The energy equation for the temperature is a convection-diffusion equation, mostly of a convective nature. It is solved with state-of-the-art ??ux-limiter schemes in an attempt to preserve the steep temperature gradients in a pulse tube. When large gradients are present, either internally or adjacent to a boundary, more accurate solutions can be obtained by grid re??nement. Re??ning a grid throughout the entire computational domain can be expensive, particularly in multi-dimensions. Instead of applying non-uniform locally re??ned grids, we use several uniform grids with different mesh sizes that cover different parts of the domain. One coarse grid covers the entire domain. The mesh size of this global grid is chosen according to the smoothness of the solution outside the high-activity regions. Besides the global grid, ??ne local grids are used which are also uniform. They cover only parts of the domain and contain the high-activity regions. The mesh size of each of these grids follows the activity of the solution. The solution is approximated on the composite grid which is the union of the uniform subgrids. This re??nement strategy is known as local uniform grid re??nement (LUGR). To deal with the problem of pressure-velocity coupling in the ??ow computation, we employ a pressure correction method. It is specially designed for low-Mach-number compressible ??ows. Combining the continuity equation and the energy equation, we derive an expansion equation or velocity divergence constraint. Our pressure correction scheme is based on this expansion equation and not on the continuity equation, which is different from the common approach in the simulation of compressible ??ows. The simulation tool, based on the proposed model, is constructed and tested on classic problems with known analytical solutions. Finally, the model was applied to a typical pulse-tube refrigerator. Results of one-dimensional and two-dimensional axisymmetrical simulations are presented and interpreted. The proposed model is more accurate and versatile than the widely used harmonic analysis and computationally less expensive than a full three-dimensional simulation with commercially available codes. It can be used for practical simulations, for calculating optimal values of the real system design parameters and for investigating different physical effects in the pulse tube.

Temperature and electric field dependence of hopping transport in ion-implanted Si:As

Abstract The temperature and electric field dependence of the resistivity of thin layers of As-doped, not intentionally compensated, Si with concentrationsjust below that of the metal-insulator transition are reported. The temperature dependence gives evidence for variable range hopping with a coulomb gap in the density of states at the Fermi-level. From the field dependence of the resistivity, a characteristic length of ≈25 nm can be deduced, which is of the order of magnitude of the hopping length.

Single wire configuration of electrons on a suspended helium film

A new technique to create and measure a single wire arrangement of electrons on helium is presented. Experimental results are reported for a 300 μm wide, 12 mm long channel.

Basic analysis on a thermoacoustic engine with gas and liquid

This paper analyzes the basics of a thermoacoustic engine with gas and liquid as working fluids. The governing equations for the engine are deduced from the dynamics of each individual component. From the governing equations, analytical expressions are obtained for oscillation frequency and onset temperature. The relations for the dependence of the displacement amplitude of liquid column, the velocity amplitude at the end of resonant tube, the pressure amplitude gradient and the enthalpy flow in stack, on the pressure amplitude in resonant tube are formulated. The calculation with the deduced formulae shows that an oscillation frequency below 10 Hz can be achieved in the thermoacoustic engine with gas and liquid. Meanwhile, a lower oscillation frequency, as well as a lower onset temperature, requires a larger liquid mass and a lower mean pressure. Experiments, focusing on the oscillation frequency and the onset temperature, have been performed to validate the computation.

Numerical simulation of superfluid turbulence near the critical velocity

Abstract In the framework of the reconnection vortex-tangle model flow properties of He II are studied numerically with respect to the influence of the periodicity of the boundary conditions and the normal component velocity profile.

Negative low-field magnetoresistance of electrons on liquid helium

Abstract A negative low-field magnetoresistance is reported for the nondegenerate two-dimensional electron gas on the surface of bulk liquid helium. The behaviour is observed at temperatures of about 2 K and is interpreted as a manifestation of weak localisation. Preliminary results indicate that the effect becomes larger for lower electron densities, suggesting that electron-electron scattering contributes to the dephasing mechanism.

Electrical transport in as ion-implanted si in the metal-insulator transition range

Abstract Resistance measurements are reported for silicon, ion-implanted with As, for various concentrations within a few percent of the metal insulator transition at temperatures down to 0.1 K. At the lowest temperatures, the temperature dependence of the resistance is dominated by inhomogeneities in the dopant distribution. The observed current dependence of the resistance is discussed.

Specific heat of BiCaSiCuO below 1 K

Abstract The specific heat of BiCaSrCuO has been measured in the temperature range from 0.1 to 1.0 K. The data can be explained as the combined effect of an electronic Schottky anomaly with level splitting of about 1.5 K and another anomaly, presumably of a nuclear origin, with a level splitting less than 0.1 K. There is no convincing evidence for a contribution linear in T.

Helium-3 Pulse Tube Cryocooler

A three-stage pulse tube refrigerator has been developed for the purpose of reaching temperatures as low as 1.5 K using 3He as the working medium. This work is a continuation of the research on a three-stage pulse tube refrigerator started in 1999 at Eindhoven University of Technology; during that effort a minimum average temperature of 1.78 K was achieved. The size of the three-stage refrigerator is small, compared to other sub-4K pulse tube cryocoolers, in order to have a small amount of 3He gas in the system. The regenerator plays an important role in the performance of the refrigerator. The regenerator was designed to be very flexible in order to be able to test different compositions of materials and their influence on the performance of the cooler. In this contribution we report on the progress in the development of the three-stage pulse tube cryocooler. We also describe our future plans, in which we intend to combine the 3He pulse tube refrigerator with a superfluid vortex cooler in order to achieve temperatures below 0.7 K.