Low attenuation of GHz Rayleigh-like surface acoustic waves in ZnO/GaAs systems immersed in liquid helium

Low attenuation of Sezawa modes operating at GHz frequencies in ZnO/GaAs systems immersed in liquid helium has been observed. This unexpected behaviour for Rayleigh-like surface acoustic waves (SAWs) is explained in terms of the calculated depth profiles of their acoustic Poynting vectors. This analysis allows reproduction of the experimental dispersion of the attenuation coefficient. In addition, the high attenuation of the Rayleigh mode is compensated by the strengthening provided by the ZnO layer. The introduction of the ZnO film will enable the operation of SAW-driven single-photon sources in GaAs-based systems with the best thermal stability provided by the liquid helium bath. © 2013 American Institute of Physics.

Particle fluid mechanics in shear flows, acoustic waves, and shock waves

Three different categories of flow problems of a fluid containing small particles are being considered here. They are: (i) a fluid containing small, non-reacting particles (Parts I and II); (ii) a fluid containing reacting particles (Parts III and IV); and (iii) a fluid containing particles of two distinct sizes with collisions between two groups of particles (Part V).

Part I

A numerical solution is obtained for a fluid containing small particles flowing over an infinite disc rotating at a constant angular velocity. It is a boundary layer type flow, and the boundary layer thickness for the mixture is estimated. For large Reynolds number, the solution suggests the boundary layer approximation of a fluid-particle mixture by assuming W = W_p. The error introduced is consistent with the Prandtl’s boundary layer approximation. Outside the boundary layer, the flow field has to satisfy the “inviscid equation” in which the viscous stress terms are absent while the drag force between the particle cloud and the fluid is still important. Increase of particle concentration reduces the boundary layer thickness and the amount of mixture being transported outwardly is reduced. A new parameter, β = 1/Ω τ_v, is introduced which is also proportional to μ. The secondary flow of the particle cloud depends very much on β. For small values of β, the particle cloud velocity attains its maximum value on the surface of the disc, and for infinitely large values of β, both the radial and axial particle velocity components vanish on the surface of the disc.

Part II

The “inviscid” equation for a gas-particle mixture is linearized to describe the flow over a wavy wall. Corresponding to the Prandtl-Glauert equation for pure gas, a fourth order partial differential equation in terms of the velocity potential ϕ is obtained for the mixture. The solution is obtained for the flow over a periodic wavy wall. For equilibrium flows where λ_v and λ_T approach zero and frozen flows in which λ_v and λ_T become infinitely large, the flow problem is basically similar to that obtained by Ackeret for a pure gas. For finite values of λ_v and λ_T, all quantities except v are not in phase with the wavy wall. Thus the drag coefficient C_D is present even in the subsonic case, and similarly, all quantities decay exponentially for supersonic flows. The phase shift and the attenuation factor increase for increasing particle concentration.

Part III

Using the boundary layer approximation, the initial development of the combustion zone between the laminar mixing of two parallel streams of oxidizing agent and small, solid, combustible particles suspended in an inert gas is investigated. For the special case when the two streams are moving at the same speed, a Green’s function exists for the differential equations describing first order gas temperature and oxidizer concentration. Solutions in terms of error functions and exponential integrals are obtained. Reactions occur within a relatively thin region of the order of λ_D. Thus, it seems advantageous in the general study of two-dimensional laminar flame problems to introduce a chemical boundary layer of thickness λ_D within which reactions take place. Outside this chemical boundary layer, the flow field corresponds to the ordinary fluid dynamics without chemical reaction.

Part IV

The shock wave structure in a condensing medium of small liquid droplets suspended in a homogeneous gas-vapor mixture consists of the conventional compressive wave followed by a relaxation region in which the particle cloud and gas mixture attain momentum and thermal equilibrium. Immediately following the compressive wave, the partial pressure corresponding to the vapor concentration in the gas mixture is higher than the vapor pressure of the liquid droplets and condensation sets in. Farther downstream of the shock, evaporation appears when the particle temperature is raised by the hot surrounding gas mixture. The thickness of the condensation region depends very much on the latent heat. For relatively high latent heat, the condensation zone is small compared with Ʌ_D.

For solid particles suspended initially in an inert gas, the relaxation zone immediately following the compression wave consists of a region where the particle temperature is first being raised to its melting point. When the particles are totally melted as the particle temperature is further increased, evaporation of the particles also plays a role.

The equilibrium condition downstream of the shock can be calculated and is independent of the model of the particle-gas mixture interaction.

Part V

For a gas containing particles of two distinct sizes and satisfying certain conditions, momentum transfer due to collisions between the two groups of particles can be taken into consideration using the classical elastic spherical ball model. Both in the relatively simple problem of normal shock wave and the perturbation solutions for the nozzle flow, the transfer of momentum due to collisions which decreases the velocity difference between the two groups of particles is clearly demonstrated. The difference in temperature as compared with the collisionless case is quite negligible.

Surface acoustic waves in liquid helium for enhanced single-electron transport applications

High frequency Rayleigh and Sezawa modes propagating in the ZnO/GaAs system capable of operating immersed in liquid helium have been engineered. In the case of the Rayleigh mode, the strong attenuation produced by the liquid is counteracted by the strengthening of the mode induced by the ZnO. However, in the case of the Sezawa modes, the attenuation is strongly reduced taking advantage of the depth profile of their acoustic Poynting vectors, that extend deeper into the layered system, reducing the energy radiated into the fluid. Thus, both tailored modes will be suitable for acoustically-driven single-electron and single-photon devices in ZnO-coated GaAs-based systems with the best thermal stability provided by the liquid helium bath. © 2012 IEEE.

Ion-acoustic waves in a dust-contaminated plasma

A self-consistent theory of ion-acoustic waves in dusty gas discharge plasmas is presented. The plasma is contaminated by fine dust particles with variable charge. The stationary state of the plasma and the dispersion and damping characteristics of the waves are investigated accounting for ionization, recombination, dust charge relaxation, and dissipation due to electron and ion elastic collisions with neutrals and dusts, as well as charging collisions with the dusts.

Ion-acoustic waves in a complex plasma with negative ions

A wave propagation in a complex dusty plasma with negative ions was considered. The relevant processes such as ionization, electron attachment, diffusion, positive-negative ion recombination, plasma particle collisions, as well as elastic Coulomb and inelastic dust-charging collisions were taken self-consistently. It was found that the equilibrium of the plasma as well as the propagation of ion waves were modified to various degrees by these effects.

Ion-acoustic waves in a complex plasma with negative ions

Negative ions and negatively charged micro- to nano-meter sized dust grains are ubiquitous in astrophysical as well as industrial processing plasmas. The negative ions can appear in electro-negative plasmas as a result of elementary processes such as dissociative or non-dissociative electron attachment to neutrals. They are usually rather small in number, and in general do not affect the overall plasma behavior. On the other hand, since the dust grains are almost always highly negative, even in small numbers they can take up a considerable proportion of the total negative charge in the system. The presence of dusts can affect the characteristics of most collective processes of the plasma since the charge balance in both the steady and dynamic states can be significantly altered. Another situation that often occurs is that the electron number density becomes small because of their absorption by the dust grains or the discharge walls. In this case the negative ions in the plasma can play a very important role. Here, a self-consistent theory of linear waves in complex laboratory plasmas containing dust grains and negative ions is presented. A comprehensive model for such plasmas including source and sink effects associated with the presence of dust grains and negative ions is introduced. The stationary state of the plasma as well as the dispersion and damping characteristics of the waves are investigated. All relevant processes, such as ionization, diffusion, electron attachment, negative-positive ion recombination, dust charge relaxation, and dissipation due to electron and ion elastic collisions with neutrals and dust particles, as well as charging collisions with the dusts, are taken into consideration.

Surface acoustic waves of finite amplitude excited by a monochromatic line source

A technique for obtaining a uniformly valid solution to the problem of nonlinear propagation of surface acoustic waves excited by a monochromatic line source is presented. The method of solution is an extension of the method of strained coordinates wherein both the dependent and independent variables are expanded in perturbation series. A special transformation is proposed for the independent variables so as to make the expansions uniformly valid and also to satisfy all the boundary conditions. This perturbation procedure, carried out to the second order, yields a solution containing a second harmonic surface wave whose amplitude and phase exhibit an oscillatory variation along the direction of propagation. In addition, the solution also contains a second harmonic bulk wave of constant amplitude but varying phase propagating into the medium.

Coupled amplitude theory of nonlinear surface acoustic waves

The nonlinear propagation characteristics of surface acoustic waves on an isotropic elastic solid have been studied in this paper. The solution of the harmonic boundary value problem for Rayleigh waves is obtained as a generalized Fourier series whose coefficients are proportional to the slowly varying amplitudes of the various harmonics. The infinite set of coupled equations for the amplitudes when solved exhibit an oscillatory slow variation signifying a continuous transfer of energy back and forth among the various harmonics. A conservation relation is derived among all the harmonic amplitudes.

Propagation of ion-acoustic waves in a multi-component plasma

The authors derive the Korteweg-de Vries equation in a multicomponent plasma that includes any number of positive and negative ions. The solitary wave solutions are also found explicitly for the case of isothermal and non-isothermal electrons.

Nonlinear mode coupling of surface acoustic waves on an isotropic solid

The nonlinear mode coupling between two co-directional quasi-harmonic Rayleigh surface waves on an isotropic solid is analysed using the method of multiple scales. This procedure yields a system of six semi-linear hyperbolic partial differential equations with the same principal part governing the slow variations in the (complex) amplitudes of the two fundamental, the two second harmonic and the two combination frequency waves at the second stage of the perturbation expansion. A numerical solution of these equations for excitation by monochromatic signals at two arbitrary frequencies, indicates that there is a continuous transfer of energy back and forth among the fundamental, second harmonic and combination frequency waves due to mode coupling. The mode coupling tends to be more pronounced as the frequencies of the interacting waves approach each other.

Nonlinear surface acoustic waves on an isotropic solid

A systematic derivation of the approximate coupled amplitude equations governing the propagation of a quasi-monochromatic Rayleigh surface wave on an isotropic solid is presented, starting from the non-linear governing differential equations and the non-linear free-surface boundary conditions, using the method of mulitple scales. An explicit solution of these equations for a signalling problem is obtained in terms of hyperbolic functions. In the case of monochromatic excitation, it is shown that the second harmonic amplitude grows initially at the expense of the fundamental and that the amplitudes of the fundamental and second harmonic remain bounded for all time.

Korteweg-De Vries Equation for Non-Linear Ion-Acoustic Waves in a Plasma with Negative Ions

The theoretical analysis, based on the perturbation technique, of ion-acoustic waves in the vicinity of a Korteweg-de Vries (K-dV) equation derived in a plasma with some negative ions has been made. The investigation shows that the negative ions in plasma with isothermal electrons introduced a critical concentration at which the ion-acoustic wave plays an important role of wave-breaking and forming a precursor while the plasma with non-isothermal electrons has no such singular behaviour of the wave. These two distinct features of ion waves lead to an overall different approach of present study of ion-waves. A distinct feature of non-uniform transition from the nonisothermal case to isothermal case has been shown. Few particular plasma models have been chosen to show the characteristics behaviour of the ion-waves existing in different cases

Korteweg-de Vries equation for the propagation of fast ion-acoustic waves in multi-dimensions

Abstract is not available.

Evolution and decay of cylindrical and spherical nonlinear acoustic waves generated by a sinusoidal source

The present work gives a comprehensive numerical study of the evolution and decay of cylindrical and spherical nonlinear acoustic waves generated by a sinusoidal source. Using pseudospectral and predictor–corrector implicit finite difference methods, we first reproduced the known analytic results of the plane harmonic problem to a high degree of accuracy. The non-planar harmonic problems, for which the amplitude decay is faster than that for the planar case, are then treated. The results are correlated with the known asymptotic results of Scott (1981) and Enflo (1985). The constant in the old-age formula for the cylindrical canonical problem is found to be 1.85 which is rather close to 2, ‘estimated’ analytically by Enflo. The old-age solutions exhibiting strict symmetry about the maximum are recovered; these provide an excellent analytic check on the numerical solutions. The evolution of the waves for different source geometries is depicted graphically.

Coupling of surface acoustic waves propagating in two separated piezoelectric media

The coupling of surface acoustic waves propagating in two separated piezoelectric media is studied using the perturbation theory of Auld. The results of the analysis are applied to two configurations using Bi12GeO20 and CdS crystals. It is found that the loss due to coupling is about 7 dB at 50 MHz in the cases of (111)-cut, [110]-prop. Bi12GeO20 and Y-cut, 60°-X prop. CdS combination. On étudie le couplage des ondes acoustiques de surface se propageant sur deux milieux piezo-eléctriques par la théorie de perturbation de Auld. Les resultats d'analyse sont appliqué's aux deux configurations des cristanx Bi12GeO20 et CdS. On trouve que la perte par couplage est environ de 7 dB a 50 MHz dans le cas de combination de (111)-coupe, [110]-prop. Bi12GeO20 et Y-coupe, 60°-X prop. CdS.