Theory Of Surface Waves Research Articles

Kinetic Theory of Surface Waves in a Plasma Slab

Propagation of surface waves on the interface between a vacuum (or a dielectric) and plasmas has drawn much attention because of interest in bounded plasmas and their various technological applications [1,2]. Especially, waves propagating in plasma slabs are important because the actual plasmas in laboratory are finite and space plasmas often take slab structures. Solving Vlasov equation for a finite plasma requires a kinematic boundary condition on the distribution function on the boundary. This condition is often taken to be the specular reflection condition. The kinetic dispersion relation of semiinfinite plasmas under the specular reflection boundary condition is well-known [3], but investigations of kinetic modes of surface waves propagating in slabs are rather few. Earlier authors [4, 5] worked out slab dispersion relations under the specular reflection conditions by expanding the electric fields in Fourier cosine series and integrating the Vlasov equation along the unperturbed orbit. Here, we use the ordinary Fourier transform method by suitably extending the plasma electric field out of the plasma region. The dispersion relation thus obtained is very compact and is only slightly different from that of semi-infinite plasma. The advantage of our method over that of Refs. 4 and 5 is immediately apparent: first, we use the conventional method of finding the normal modes via the Fourier transform while the earlier authors introduced unperturbed orbits to integrate the Vlasov equation. Secondly, our dispersion relation is obtained in a closed form, but the dispersion relation in Ref. 4 is written in a Fourier cosine series which require numeri-

Fragmentation behavior during molten material and coolant interactions

A safe design for a fast breeder reactor (FBR) requires post-accident heat removal (PAHR) for any potential core disruptive accident (CDA). It is important to ensure that the molten core material solidifies in the sodium coolant in the reactor vessel even if all of the core material has melted. In the present experiment, molten material was injected into water to experimentally obtain the information on the molten material jet entering the coolant and its fragmentation. Visual information was obtained with a high-speed video camera, showing that fragmentation behavior on the side of the jet was different from that on the jet front, and that the injection nozzle diameter significantly influenced the jet breakup length, while the molten jet temperature and the coolant temperature did not influence the jet breakup length. Comparison of the diameters of fragments of the solidified molten material thus obtained with fragmentation theory shows that the median fragment diameter is between the critical Weber number theory and the most-unstable wavelength of the instability theory of surface waves at a gas liquid interface. The quench behavior of the molten jet in coolant was calculated for FBR conditions by using the model that reflects actual fragmentation behavior. It was clarified that the mass of molten material in the coolant pool is related to the fragment diameter under FBR conditions.

An integral representation of the surface-impedance tensor for incompressible elastic materials

A fundamental result in anisotropic elasticity and surface-wave theory is the integral representation for the surface-impedance tensor first derived by Barnett and Lothe in 1973. However, this representation is only valid for compressible materials but not valid for incompressible materials. In this paper the corresponding integral representation for the surface-impedance tensor valid for incompressible materials is derived and is used to establish the uniqueness of surface-wave speed and to obtain an expression for the tensor Green's function for the infinite space.

Comment on “Kinetic theory of surface waves in plasma jets” [Phys. Plasmas 9, 701 (2002)

It is shown that the dispersion relation of electromagnetic surface waves propagating on the interface between a vacuum and drifting Maxwellian plasmas derived in recent work [Phys. Plasmas 9, 701 (2002)] is incorrect. Correct electromagnetic and electrostatic dispersion relations are obtained.

Conditions for mechanical Bloch oscillations

Using the theory for surface waves, the propagation of a disturbance in elastic media is studied. An important and sufficient condition for achieving Bloch oscillations is the variation of the depth of the fluid. This variation produces changes in the refraction index and in the wave number of the disturbance in such a way that those changes exhibit discontinuities whose magnitudes are directly associated to the predicted frequency. A dispersion relation, that allows us to obtain the oscillations of the disturbance, is determined and applied. The calculation for stationary waves with such relation shows some indications suggesting oscillations which are a reproduction in the space domain of the Bloch oscillations for electrons under an electric field. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Transport and lifeline structures versus accidental and natural hazard actions

The paper deals with the approaches to the response analysis of large transport and lifeline structures. The background theory for simplified analysis is presented. Seismic inputs represent the cases of explosion impacts and large near field earthquake effects. 3DOF and 6DOF input models are based on surface wave theory and applied for calculations and shaking table experiments. Examples of seismic motion simulations are those obtained during large MASTER shaking table tests in Enel.Hydro-ISMES Seriate, Italy in the framework of EC international projects.

Slow nonlinear waves in magnetic flux tubes

The theory of nonlinear slow body and surface waves is developed. The conventional long-wavelength approximation is lifted. A new kind of nonlinear evolution equations is obtained. Two complementary equations are obtained. One of them is of the highest accuracy. Another one has less accuracy but its analytical solutions are found. Two analytical solutions of a distinct kind are found. It is revealed that both dark and bright solitons are the solutions of the evolutionary equation for slow waves. One of these two solutions is not singular for arbitrary amplitudes. Another one is not singular only when the critical amplitude is exceeded. The canonic form of the new evolutionary equation is presented. As a by-product of the exploration, the equation of the highest accuracy for body waves in the long-wavelength approximation is obtained. The interplay of shocks and solitons in flux tubes is discussed.

Uniqueness of the Surface-Wave Speed: A Proof That Is Independent of the Stroh Formalism

It is well-known in surface-wave theory that the secular equation for the surface-wave speed v can be written as det M = 0 in terms of the surface impedance matrix M. It has recently been shown by the present authors that M satisfies a simple algebraic Riccati equation. It is shown in the present paper that a purely matrix algebraic analysis of this equation suffices to prove that whenever a surface wave exists it is unique.

Response to “Comment on ‘Kinetic theory of surface waves in plasma jets’ ” [Phys. Plasmas 10, 3035 (2003)

It will be shown that when plasma jet velocity is much smaller than light speed the dispersion equation obtained in the earlier work [Phys. Plasmas 9, 701 (2002)] is changed to the dispersion equation obtained earlier.

Oscillons at a plasma surface

The theory for nonlinear electrostatic surface waves on a cold semi-infinite plasma is generalized to include an external driving force. An oscillon solution is found.

Nonlinear surface waves in a symmetrical three-layer structure caused by the generation of excitons and biexcitons in semiconductors

A theory of nonlinear TE-polarized surface waves propagating along the flat interfaces of a symmetric flat three-layer structure with a linear core and nonlinear coatings is developed. The coatings are nonlinear due to the optical exciton-biexciton conversion. The dispersion laws of the propagating waves are found and analyzed.

A new identity for the surface–impedance matrix and its application to the determination of surface-wave speeds

It is well known in surface–wave theory that the secular equation for the surface–wave speedυcan be written as det M = 0 in terms of the surface–impedance matrix M . It is shown in this paper that M satisfies the simple identity ( M - i R ) T - 1 ( M + i R T ) - Q + υ 2 I = 0 in the usual notation in the Stroh formalism. This identity provides an efficient method for calculating the wave speed of surface waves in unstressed or pre–stressed elastic half–spaces. The method is explained and illustrated by examples. It is also shown that the buckling/wrinkling pre–stress for a pre–stressed elastic half–space can be calculated using the same procedure but with pre–stress playing the role of υ .

Transient high-frequency ultrasonic water atomization

An experimental study was performed to improve the understanding of the characteristics of ultrasonic water atomization when excited with waves in the MHz range. In the present experiments, small volumes of water were atomized, observing the temporal evolution of the process. Typical diameters of the resulting droplets are of the order of a few microns. To visualize them, images were acquired with very high magnification. Appropriate lenses were used to enable high resolution at a distance from the flow. Droplet size distributions were also calculated with a Malvern diffractometer. Droplet exit velocity was measured using particle image velocimetry. It was noticeable that, as the remaining liquid mass deposited over the ultrasonic transducer decreased, the atomization characteristics changed, and a second peak of larger droplets appeared in the size distribution function. This phenomenon is related to the change in the curvature of the liquid surface. Although results are not conclusive, it appears that, under the conditions in this study, some observations about droplet formation are better described by cavitation phenomena rather than by the simplified surface wave theory usually invoked to explain these processes.

A Proof of the Stokes Conjecture in the Theory of Surface Waves*

This article gives a proof of the famous Stokes conjecture that a gravity wave of greatest height on water has a corner with contained angle 2π/3 at its singular point.

Nonlinear magneto-optic measurement of flux propagation dynamics in thin Permalloy films

Time-resolved nonlinear optics are used to study the propagation of magnetic flux pulses in a 250 nm Permalloy film. The flux is generated in the film by coupling it to a coplanar waveguide structure driven with broadband voltage pulses. Flux pulses propagated in the film with a phase velocity of 4.2×105 m/s and a group velocity of 1.5×105 m/s. Both velocities are consistent with the predictions of Damon–Eshbach theory for magnetostatic surface waves with 200–300 μm wavelengths. Within 100 μm of the excitation source, flux pulses decayed monotonically but with no measurable delay.

Kinetic theory of surface waves in plasma jets

The kinetic theory analysis of surface waves propagating along a semi-bounded plasma jet is presented. The frequency spectra and their damping rate are obtained in both the high and low frequency regions. Finally, the penetration of the static field in the plasma jet under the condition that the plasma jet velocity is smaller than the sound velocity is studied.

Asymptotic Ray Theory for Seismic Surface Waves in Laterally Inhomogeneous Media

A recurrence procedure is outlined for constructing asymptotic series for surface wave field in a half-space with weak lateral heterogeneity. Both horizontal variations of the elastic parameters and of the wave field are assumed small on the distances comparable with the wavelength. This is equivalent to the condition that the frequency ω is large. The Surface Wave Asymptotic Ray Theory (SWART) is an analog of the asymptotic ray theory (ART) for body waves. However the case of surface waves presents additional difficulty: the rate of amplitude variation is different in vertical and horizontal directions. In vertical direction it is proportional to the large parameter ω. To overcome this difficulty the transformation ‘equalizing’ vertical and horizontal coordinated is suggested, Z = ωz. In the coordinates x,y,Z the wave field is represented as an asymptotic series in inverse powers of ω. The amplitudes of successive terms of the series are determined from a recurrent system of equations. Attention is paid to similarity and difference of the procedures for constructing the ray series in SWART and ART. Applications of SWART to interpretation of seismological observations are discussed.

Using Laser-Induced Fluorescence in the Study of Surface Wave Turbulence

The turbulent motion of capillary surface waves is studied using laser-induced fluorescence. A blue laser is focused onto the surface of a solution of fluorescein in water contained in a vertically shaken vessel. The movement of the resulting green spot is followed by a position-sensitive detector. The scaling behavior and cross-over phenomenon for the surface-height-frequency spectrum observed provide direct support to the weak turbulence theory of surface waves.

Surface waves in fibre-reinforced anisotropic elastic media

The aim of this paper is to investigate surface waves in anisotropic fibre-reinforced solid elastic media. First, the theory of general surface waves has been derived and applied to study the particular cases of surface waves — Rayleigh, Love and Stoneley types. The wave velocity equations are found to be in agreement with the corresponding classical result when the anisotropic elastic parameters tends to zero. It is important to note that the Rayleigh type of wave velocity in the fibre-reinforced elastic medium increases to a considerable amount in comparison with the Rayleigh wave velocity in isotropic materials.

Theory of nonlinear plasma surface waves

By means of the cold-electron fluid equations, we deduce a new strongly nonlinear surface solitary-wave solution for a semi-infinite plasma.