Nonlinear interaction of electrostatic surface waves in a semi-infinite plasma. Part 1. Derivation of the coupled mode equations

1981 ◽  
Vol 26 (2) ◽  
pp. 217-230 ◽  
Author(s):  
V. Atanassov ◽  
R. Mateev ◽  
I. Zhelyazkov
Keyword(s):  
Surface Waves ◽  
Nonlinear Interaction ◽  
High Frequency ◽  
Low Frequency ◽  
Density Perturbation ◽  
Coupled Mode ◽  
Hybrid Nature ◽  
Bulk Waves ◽  
Amplitude Attenuation

We have derived a set of coupled mode equations which govern the nonlinear interaction of three high-frequency electrostatic surface waves through a low-frequency density perturbation produced by them. The set is compared with that obtained when a similar problem is solved for bulk waves in an infinite plasma. Some differences are shown to exist caused by the specific features of surface waves such as the amplitude attenuation normal to the interface and their hybrid nature.

Nonlinear interaction of electrostatic surface waves in a semi-infinite plasma. Part 2. Time-dependent solutions to the coupled mode equations

1981 ◽  
Vol 26 (2) ◽  
pp. 231-252 ◽  
Author(s):  
V. Atanassov ◽  
E. Mateev ◽  
I. Zhelyazkov
Keyword(s):  
Surface Waves ◽  
Nonlinear Interaction ◽  
High Frequency ◽  
Low Frequency ◽  
Density Perturbation ◽  
Time Dependent ◽  
Opposite Case ◽  
Coupled Mode ◽  
Wave Resonance ◽  
Parametric Approximation

The coupled mode equations which govern the nonlinear interaction of three electrostatic high-frequency surface waves and a low-frequency density perturbation are analysed considering time-dependent solutions only. We show the existence of a filamentation instability in the static limit for the low-frequency density perturbation. In the opposite case (density perturbation close to the lowfrequency surface wave resonance) we arrive at a decay instability where only surface waves take part. The parametric approximation (growth rate and threshold) as well as the nonlinear evolution of both types of instabilities are studied.

scholarly journals The appearance of boundary layers and drift flows due to high-frequency surface waves

2012 ◽  
Vol 707 ◽  
pp. 482-495 ◽  
Author(s):  
Ofer Manor ◽  
Leslie Y. Yeo ◽  
James R. Friend
Keyword(s):  
Boundary Layer ◽  
Surface Waves ◽  
High Frequency ◽  
Slip Boundary Condition ◽  
Inertial Effects ◽  
Velocity Amplitude ◽  
Slip Boundary ◽  
Long Period ◽  
Bulk Waves ◽  
Schlichting Streaming

AbstractThe classical Schlichting boundary layer theory is extended to account for the excitation of generalized surface waves in the frequency and velocity amplitude range commonly used in microfluidic applications, including Rayleigh and Sezawa surface waves and Lamb, flexural and surface-skimming bulk waves. These waves possess longitudinal and transverse displacements of similar magnitude along the boundary, often spatiotemporally out of phase, giving rise to a periodic flow shown to consist of a superposition of classical Schlichting streaming and uniaxial flow that have no net influence on the flow over a long period of time. Correcting the velocity field for weak but significant inertial effects results in a non-vanishing steady component, a drift flow, itself sensitive to both the amplitude and phase (prograde or retrograde) of the surface acoustic wave propagating along the boundary. We validate the proposed theory with experimental observations of colloidal pattern assembly in microchannels filled with dilute particle suspensions to show the complexity of the boundary layer, and suggest an asymptotic slip boundary condition for bulk flow in microfluidic applications that are actuated by surface waves.

Fundamental properties of surface waves in lossless stratified structures

2010 ◽  
Vol 466 (2120) ◽  
pp. 2447-2469 ◽  
Author(s):  
Guido Valerio ◽  
David R. Jackson ◽  
Alessandro Galli
Keyword(s):  
Surface Waves ◽  
Dispersion Equation ◽  
High Frequency ◽  
Low Frequency ◽  
Layered Structures ◽  
Graphical Solution ◽  
Fundamental Properties ◽  
The Past ◽  
Permittivity And Permeability ◽  
Constitutive Parameters

This paper is focused on dispersive properties of lossless planar layered structures with media having positive constitutive parameters (permittivity and permeability), possibly uniaxially anisotropic. Some of these properties have been derived in the past with reference to specific simple layered structures, and are here established with more general proofs, valid for arbitrary layered structures with positive parameters. As a first step, a simple application of the Smith chart to the relevant dispersion equation is used to prove that evanescent (or plasmonic-type) waves cannot be supported by layers with positive parameters. The main part of the paper is then focused on a generalization of a common graphical solution of the dispersion equation, in order to derive some general properties about the behaviour of the wavenumbers of surface waves as a function of frequency. The wavenumbers normalized with respect to frequency are shown to be always increasing with frequency, and at high frequency they tend to the highest refractive index in the layers. Moreover, two surface waves with the same polarization cannot have the same wavenumber at a given frequency. The low-frequency behaviours are also briefly addressed. The results are derived by means of a suitable application of Foster’s theorem.

Filamentation and collapse of Langmuir waves in a weak magnetic field

1982 ◽  
Vol 28 (1) ◽  
pp. 19-36 ◽  
Author(s):  
P. Rolland ◽  
S. G. Tagare
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Small Angle ◽  
Nonlinear Interaction ◽  
High Frequency ◽  
Weak Magnetic Field ◽  
Low Frequency ◽  
Langmuir Waves ◽  
The Magnetic Field

The filamentation and collapse of Langmuir waves in a weak magnetic field are analysed in two particular cases of low-frequency acoustic perturbations: (i) adiabatic perturbations which correspond to subsonic collapse, and (ii) nonadiabatic perturbations which correspond to supersonic collapse. Here the existence of Langmuir filaments and Langmuir collapse in a weak magnetic field are due to nonlinear interaction of high-frequency Langmuir waves (which make small angle with the external magnetic field) with low-frequency acoustic perturbations along the magnetic field.

Dispersion and energy conservation relations of surface waves in semi-infinite plasma

1981 ◽  
Vol 25 (2) ◽  
pp. 285-307 ◽  
Author(s):  
V. Atanssov
Keyword(s):  
Surface Wave ◽  
Energy Conservation ◽  
Surface Waves ◽  
Low Frequency ◽  
Conservation Equation ◽  
Hydrodynamic Theory ◽  
Energy Conservation Equation ◽  
Surface Wave Propagation ◽  
Electric And Magnetic Fields ◽  
Bulk Waves

The hydrodynamic theory of surface wave propagation in semi-infinite homogeneous isotropic plasma is considered. Explicit linear surface wave solutions are given for the electric and magnetic fields, charge and current densities. These solutions are used to obtain the well-known dispersion relations and, together with the general energy conservation equation, to find appropriate definitions for the energy and the energy flow densities of surface waves. These densities are associated with the dispersion relation and the group velocity by formulae similar to those for bulk waves in infinite plasmas. Both cases of high-frequency (HF) and low-frequency (LF) surface waves are considered.

RADIATION FROM A SOURCE NEAR A PLANE INTERFACE BETWEEN AN ISOTROPIC AND A GYROTROPIC DIELECTRIC

1964 ◽  
Vol 42 (11) ◽  
pp. 2153-2172 ◽  
Author(s):  
S. R. Seshadri ◽  
A. Hessel
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Surface Waves ◽  
High Frequency ◽  
Free Space ◽  
Line Source ◽  
Low Frequency ◽  
Plane Interface ◽  
Magnetic Current ◽  
Asymptotic Evaluation

The radiation from a line source of magnetic current situated in free space near a plane interface between a semi-infinite free space and a semi-infinite gyrotropic dielectric is investigated for the case in which the gyrotropic axis is parallel to the line source. In addition to the space waves, it is found that in general two unidirectional surface waves are excited along the interface. The dispersion relations for the space and the surface waves are thoroughly examined. Both surface waves have different high-frequency cutoff but no low-frequency cutoff. The characteristics of these surface waves are investigated. An asymptotic evaluation of the total electromagnetic field is carried out for a particularly simple choice of the source frequency. For this frequency, the dependence of the efficiency of excitation of the surface waves on the distance of the source from the interface is determined. The radiation patterns are plotted for various values of the static magnetic field and the position of the source.

scholarly journals Experimental studies of surface waves inside a cylindrical container

2011 ◽  
Vol 677 ◽  
pp. 39-62 ◽  
Author(s):  
CUNBIAO LEE ◽  
HUAIWU PENG ◽  
HUIJING YUAN ◽  
JIEZHI WU ◽  
MINGDE ZHOU ◽  
...  
Keyword(s):  
Surface Waves ◽  
High Frequency ◽  
Experimental Studies ◽  
Low Frequency ◽  
Capillary Waves ◽  
Physical Processes ◽  
Vortex Streets ◽  
Circular Capillary ◽  
Particle Imaging ◽  
Azimuthal Waves

We experimentally investigate the dynamics of surface waves excited by oscillations from a cylindrical sidewall. Particle-imaging-velocimetry measurements with fluorescent particles were used to determine the flow patterns near the sidewall of the cylindrical fluid container and to identify the locations of the evolving air–water interfaces. The high-frequency wall oscillations created four jets that originate at the cylindrical sidewall. Four vortex streets shed from the jets propagate from the sidewall to the centre of the container and subsequently excite a low-frequency gravity wave. The interaction between this gravitational surface wave and the high-frequency capillary waves was found to be responsible for creating droplet splash at the water surface. This phenomenon was first described as ‘Long-Xi’ or ‘dragon wash’ in ancient China. The physical processes for generating the droplet ejection, including the circular capillary waves, azimuthal waves, streaming jets and low-frequency gravity waves, are described in this paper.

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