Diffraction of electromagnetic waves by a half-plane located in a moving cold plasma

Diffraction of plane electromagnetic waves by a conductive half-plane located in a parallel flow of cold plasma is studied. The velocity of the plasma motion and the propagation direction of the incident wave are normal to the half-plane edge. A general solution of the problem is obtained using the Wiener-Hopf-Fok method. The behavior of the field is analyzed far from the half-plane edge and in its vicinity. State University, Saint Petersburg, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 4, pp. 475–494, April, 1998.     

Diffraction of electromagnetic waves by a nonconducting half-plane in a hot plasma

The diffraction of transverse and longitudinal plane waves by a thin nonconducting perfectly rigid half-plane in a hot plasma is examined. The general solution of the problem and asymptotic formulas for the far zone are found. It is shown that they are significantly simplified for frequencies well above the plasma frequency. The behavior of the field near the edge is analyzed.St. Petersburg State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 12, pp. 1503–1511, December, 1994.     

Diffraction of cylindrical waves by an ideally conducting wedge in an anisotropic plasma

The problem of diffraction of cylindrical waves by an ideally conducting wedge in an anisotropic plasma is formulated and solved. The integral equations for the field are reduced to function equations, which are solved with the aid of a special function that is introduced. The properties of this function are studied. The general solution is represented as a double contour integral in the plane of a complex variable. The radiation field and surface waves for a number of special cases are analyzed: a source of cylindrical waves on an edge; at infinity; etc. Diffraction in a half-plane is studied separately.     

On the possible mechanism of the jet noise intensification near a wing

A qualitative model of the mechanism of intensification of jet noise issuing from a nozzle located near a wing is proposed. A two-dimensional model problem on the diffraction of a plane acoustic wave at the edge of a nozzle nozzle located near a half-plane simulating the wing edge is formulated. It is shown that diffraction on the wing edge of Kelvin-Helmholtz instability waves developing from the edge of the nozzle can lead to the significant intensification of the acoustic energy radiated into the far field.     

Rayleigh Waves in a Homogeneous Isotropic Half-Plane with a Periodic Edge

Doklady Physics - The existence of Rayleigh waves propagating along the periodic boundary of a homogeneous isotropic half-plane with an arbitrary edge profile is proved. It is shown that a periodic...     

Acoustic diffraction by a half-plane in a viscous fluid medium

We consider the diffraction of a time-harmonic acoustic plane wave by a rigid half-plane in a viscous fluid medium. The linearized equations of viscous fluid flow and the no-slip condition on the half-plane are used to derive a pair of disjoint Wiener-Hopf equations for the fluid stresses and velocities. The Wiener-Hopf equations are solved in conjunction with a requirement that the stresses are integrable near the edge of the half-plane. Specific wave components of the scattered velocity field are given analytically. A Padé approximation to the Wiener-Hopf kernel function is used to derive numerical results that show the effect of viscosity on the velocity field in the immediate vicinity of the edge of the half-plane.     

TM plane wave scattering and diffraction from a randomly rough half-plane: (part II) An evaluation of the diffraction kernel

In a previous paper (part I), it has been shown that a random wavefield from a randomly rough half-plane for a TM plane wave incidence is written in terms of a Wiener-Hermite expansion with three types of Fourier integrals. This paper studies a concrete representation of the random wavefield by an approximate evaluation of such Fourier integrals, and statistical properties of scattering and diffraction. For a Gaussian roughness spectrum, intensities of the coherent wavefield and the first-order incoherent wavefield are calculated and shown in figures. It is then found that the coherent scattering intensity decreases in the illumination side, but is almost invariant in the shadow side. The incoherent scattering intensity spreads widely in the illumination side, and have ripples at near the grazing angle. Moreover, a major peak at near the antispecular direction, and associated ripples appear in the shadow side. The incoherent scattering intensity increases rapidly at near the random half-plane. These new phenomena for the incoherent scattering are caused by couplings between TM guided waves supported by a slightly random surface and edge diffracted waves excited by a plane wave incidence or by free guided waves on a flat plane without any roughness.     

Magnetic line source diffraction by a conductive half-plane in an anisotropic plasma

An integral theory that is associated with the scattered fields is considered for the solution of H-polarized line source diffraction by a conductive half-plane, which is surrounded by an anisotropic plasma. As the anisotropy does not affect an E-polarized incident wave, only one polarization case is considered. The cold plasma medium is characterized by the dielectric tensor. The constant external magnetic field producing the anisotropy in a cold plasma is applied parallel to the edge of the half-plane. The total, scattered, and diffracted waves are derived in terms of the Fresnel functions. Therefore, finite magnitude values at the transition boundaries are obtained. The wave behaviours are investigated numerically for different quantities of the medium.     

The distribution of equilibrium magnetization currents in systems with dimensional quantization in a finite magnetic field

The distribution of equilibrium magnetization currents in two-dimensional bounded systems placed in an external magnetic field is studied. A half-plane, a quantum disk, and a wide quantum ring are considered. The passage from classical to quantizing magnetic fields is investigated. The edge currents near the boundary of the half-plane are shown to experience damped (far from the boundaries) spatial oscillations related to the Fermi electron wavelength. The region occupied by currents was found to narrow with increasing field. Apart from these oscillations, the current contains a component that smoothly changes with distance but oscillationally depends on the position of the Fermi level relative to the Landau levels. The suppression of the oscillations by temperature is studied. The spatial distribution of the current in a circular disk and a ring is shown to significantly depend on the position of the Fermi level.     

Boundary diffraction wave theory of resistive surfaces with edge discontinuities

The line integral of the boundary diffraction wave theory is derived by considering the exact diffracted fields of a resistive half-plane. The line integral is generalized for arbitrary resistive surface with edge discontinuity. The method is applied to the diffraction problem of waves by a convex resistive spherical reflector and the resultant field expressions are investigated numerically.     

Dynamic stress around a cylindrical nano-inhomogeneity with an interface in a half-plane under anti-plane shear waves

Taking into account the size of the nanostructure, the effect of surface/interface stiffness on the dynamic stress around a cylindrical nano-inhomogeneity embedded in an elastic half-plane subjected to anti-plane shear waves is investigated. The boundary condition at the straight edge of the half-plane is traction free, which is satisfied by the image method. The analytical solutions of displacement fields are expressed by employing a wave function expansion method. The addition theorem for a cylindrical wave function is applied to accomplish the superposition of wave fields in the two half-planes. Analyses show that the effect of the interface properties on the dynamic stress is significantly related to the nano-scale distance between the straight edge and the center of the cylindrical nano-inhomogeneity. The frequency and incident angle of incident waves and the shear modulus ratio of the nano-inhomogeneity to matrix also show different effect on the dynamic stress distribution when the inhomogeneity shrinks to nano-scale. Comparison with the existing results is also given.     

Diffraction of electromagnetic waves by a resistive half-plane in magneto-ionic plasma

The interaction of magnetic polarized electromagnetic wave with a resistive half-plane in magneto-ionic plasma is investigated. The method of transition boundary is used for the evaluation of the diffracted wave. The excitation of surface waves is examined in the medium and their diffracted fields are derived by using the diffraction theory for grazing incidence. The uniform field expressions are obtained with the aid of the uniform theory for evanescent waves. The behaviours of the derived scattered waves are studied numerically.     

Scattering of plane-waves by an impedance half-plane at the interface between isorefractive media

The scattering of plane waves by an impedance half-plane located at the interface of two isorefractive media is investigated. The scattered field, in addition to the diffracted and geometrical optics fields, is analyzed numerically and compared to the scattered field of perfectly conducting half-plane. The effect of the isorefractive media on the scattered field is also examined.     

Study of the Radiation Capability of a Perfectly Conducting Half-Plane Excited by a Slot Perpendicular to the Conductor Edge

Radiophysics and Quantum Electronics - We solve the problem of excitation of an infinite, perfectly conducting half-plane by an external field in the slot line, which is perpendicular to the edge...     

Diffraction from a half-plane. A new derivation of the Sommerfeld solution

It is shown that the Sommerfeld solution for the diffraction of a plane wave by a perfectly conducting half-plane can be obtained in an elementary manner by a superposition of anisotropic cylindrical waves.     

Nonuniform elastic stagnant wave in a wedge-shaped plate

An acoustic field near the edge of an elastic wedge-shaped plate is studied. The field is represented in the form of two counterpropagating nonuniform waves. The standing vibration profiles varying with distance to the edge are constructed. A specific acoustic effect arising when the wave moves away from the wedge is revealed. Theoretical results are confirmed by measuring the standing wave amplitudes with a proprietary setup.     

Control over the instability wave in terms of the two-dimensional model of a nozzle edge

The problem of generation of an instability wave leaving the edge of a half-plane that separates an immobile medium from a moving medium is considered. It is assumed that the instability wave is initiated by an acoustic wave arriving from the moving medium. The possibility of suppressing the instability wave by another acoustic wave incident from the nonflowing medium is considered. It is shown that the suppression is always possible by adjusting the amplitude and phase of the control perturbation to the parameters of the instability wave.     

Low-frequency scattering of acoustic waves by a bounded rough surface in a half-plane

The problem of the scattering of harmonic plane waves by a rough half-plane is studied here. The surface roughness is finite. The slope of the irregularity is taken as arbitrary. Two boundary conditions are considered, those of Dirichlet and Neumann. An asymptotic solution is obtained, when the wavelength lambda of the incident wave is much larger than the characteristic length of the roughness iota, by means of the method of matched asymptotic expansions in terms of the small parameter epsilon= 2piiota/lambda. For the Dirichlet problem, the solution of the near and far fields is obtained up to O(epsilon2). The far field solution is given in terms of a coefficient that have a simple explicit expression, which also appears in the corresponding solution to the Neumann problem, already solved. Also the scattering cross section is given by simple formulas to O(epsilon3). It is noted that, for the Dirichlet problem, the leading term is of order epsilon3 which, by contrast, is different from that of the circular cylinder in full space, that is, of order epsilon(-1) (log epsilon)(-2). Some examples display the simplicity of the general results based on conformal mapping, which involve arcs of circle, polygonal lines, surface cracks and the like.     

Scattering and diffraction of a plane wave by a randomly rough half-plane*

Abstract

The scattering and diffraction of a TE (transverse electric) plane wave by a randomly rough half-plane are studied by a combination of three techniques: the Wiener-Hopf technique, the small perturbation method and a probabilistic method based on the shift-invariance of a homogeneous random function. By use of the D^a-Fourier transformation based on the shift-invariance, it is shown that the scattered wave is written by an inverse Fourier transformation of a homogeneous random function with a complex parameter. For a small rough case, such a random function with a complex parameter is expanded in a perturbation series and then the first-order solution is obtained exactly in an integral form. The first-order solution involves two physical processes such that the edge-diffracted wave is scattered by the randomly rough plane and the scattered wave, due to roughness, is diffracted by the half-plane. The solution is transformed into a sum of the Fresnel integrals with complex arguments, an integral along the steepest descent path and a branch-cut integral, which are evaluated numerically. Then, intensities of the coherently scattered wave and incoherent wave are calculated in the region near the edge and illustrated in figures.     

Nonlinear Elastic Waves in a Solid Isotropic Wedge with Defects

The paper presents experimental data for linear and nonlinear elastic waves in an acute-angled wedge made of D16 isotropic polycrystalline alloy with defects. The localization of waves at the edge of the wedge has been studied using laser vibrometry. The velocities of wedge waves have been measured by a pulse method in the frequency range 0.25–1.50 MHz. Measurements have not revealed any dispersion. The second harmonic of the wedge waves has been found. The dependences of the velocity and amplitude of the second harmonic on the amplitude of the first harmonic have been studied. It is noted that nonlinear effects observed in wedge waves may be explained in terms of the Murnaghan classical five-constant theory of elasticity. They are attributed to a defect-induced structural nonlinearity present in the wedge.