DIFFRACTION BY A CONDUCTING HALF-PLANE IN AN ANISOTROPIC PLASMA

1964 ◽  
Vol 42 (8) ◽  
pp. 1455-1468 ◽  
Author(s):  
E. V. Jull
Keyword(s):  
Magnetic Field ◽  
Half Plane ◽  
Scattered Field ◽  
Plane Electromagnetic Wave ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Anisotropic Plasma ◽  
Angle Of Incidence ◽  
Dual Integral Equations ◽  
Magnetostatic Field

The diffraction of a plane electromagnetic wave by a perfectly conducting half-plane in an anisotropic plasma is considered. The plasma is characterized by a permittivity tensor and the wave is assumed to propagate in a direction normal to the magnetostatic field and the diffracting edge, but its angle of incidence is otherwise arbitrary. Only the H-polarized wave of the incident field, which has a single magnetic field component parallel to the edge, is affected by the anisotropy and the analysis is restricted accordingly. Representing the scattered field as an angular spectrum of plane waves leads to dual integral equations from which an expression for the scattered field is obtained. The total field is then reduced to Fresnel integrals and its far-field behavior is investigated. Agreement with Seshadri and Rajagopal's result for a wave normally incident on the conductor, which was obtained by using the Wiener–Hopf technique, is found. The differences between isotropic and anisotropic solutions to this problem, which arise from the differing boundary conditions on the tangential magnetic field, are examined.

A method for the exact solution of a class of two-dimensional diffraction problems

1951 ◽  
Vol 205 (1081) ◽  
pp. 286-308 ◽  
Keyword(s):  
Integral Equation ◽  
Plane Wave ◽  
Integral Equations ◽  
Scattered Field ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Diffraction Theory ◽  
General Interest ◽  
Two Dimensional ◽  
Dual Integral Equations

In the last few years Copson, Schwinger and others have obtained exact solutions of a number of diffraction problems by expressing these problems in terms of an integral equation which can be solved by the method of Wiener and Hopf. A simpler approach is given, based on a representation of the scattered field as an angular spectrum of plane waves, such a representation leading directly to a pair of ‘dual’ integral equations, which replaces the single integral equation of Schwinger’s method. The unknown function in each of these dual integral equations is that defining the angular spectrum, and when this function is known the scattered field is presented in the form of a definite integral. As far as the ‘radiation’ field is concerned, this integral is of the type which may be approximately evaluated by the method of steepest descents, though it is necessary to generalize the usual procedure in certain circumstances. The method is appropriate to two-dimensional problems in which a plane wave (of arbitrary polarization) is incident on plane, perfectly conducting structures, and for certain configurations the dual integral equations can be solved by the application of Cauchy’s residue theorem. The technique was originally developed in connexion with the theory of radio propagation over a non-homogeneous earth, but this aspect is not discussed. The three problems considered are those for which the diffracting plates, situated in free space, are, respectively, a half-plane, two parallel half-planes and an infinite set of parallel half-planes; the second of these is illustrated by a numerical example. Several points of general interest in diffraction theory are discussed, including the question of the nature of the singularity at a sharp edge, and it is shown that the solution for an arbitrary (three-dimensional) incident field can be derived from the corresponding solution for a two-dimensional incident plane wave.

DIFFRACTION BY A CONDUCTING HALF-PLANE IN PLASM

1966 ◽  
Vol 44 (6) ◽  
pp. 1207-1212
Author(s):  
Ll. G. Chambers
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Wave ◽  
Half Plane ◽  
Field Component ◽  
Plane Electromagnetic Wave ◽  
Static Field ◽  
Anisotropic Plasma ◽  
Magnetic Field Component ◽  
Permittivity Tensor ◽  
Arbitrary Direction

The problem considered is that of a plane electromagnetic wave approaching from an arbitrary direction a perfectly conducting half-plane in an anisotropic plasma, characterized by a permittivity tensor. The system is such that the wave has a single magnetic field component, which is parallel both to the magneto-static field and the diffracting edge. The work is a simplification of previous work by Jull, involving the use of methods previously developed by the author.

Dynamic Singular Stresses for a Griffith Crack in a Soft Ferromagnetic Elastic Solid Subjected to a Uniform Magnetic Field

1983 ◽  
Vol 50 (1) ◽  
pp. 50-56 ◽  
Author(s):  
Y. Shindo
Keyword(s):  
Magnetic Field ◽  
Integral Equations ◽  
Fourier Transforms ◽  
Dynamic Stress Intensity Factor ◽  
Elastic Solid ◽  
Griffith Crack ◽  
Dual Integral Equations ◽  
Singular Stress ◽  
Magnetostatic Field ◽  
Soft Ferromagnetic

The problem of the diffraction of normally incident longitudinal waves on a Griffith crack located in an infinite soft ferromagnetic elastic solid is considered. It is assumed that the solid is a homogeneous and isotropic one and is permeated by a uniform magnetostatic field normal to the crack surfaces. Fourier transforms are used to reduce the problem to two simultaneous dual integral equations. The solution to the integral equations is expressed in terms of a Fredholm integral equation of the second kind having the kernel that is a finite integral. The dynamic singular stress field near the crack tip is obtained and the influence of the magnetic field on the dynamic stress intensity factor is shown graphically in detail. Approximate analytical expressions valid at low frequencies are also obtained and the range of validity of these expressions is examined.

scholarly journals The oblique reflexion of very long wireless waves from the ionosphere

1947 ◽  
Vol 189 (1016) ◽  
pp. 130-147 ◽  
Keyword(s):  
Magnetic Field ◽  
Experimental Data ◽  
Theoretical Basis ◽  
Plane Waves ◽  
Angle Of Incidence ◽  
Vertical Magnetic Field ◽  
Radio Waves ◽  
Contour Integrals ◽  
General Terms ◽  
Made In

An attempt is made in the paper to provide a satisfactory theoretical basis for a future discussion of the experimental data on the propagation of very long radio waves (18,800 m.) given by Best, Ratcliffe & Wilkes, and Budden, Ratcliffe & Wilkes. The reflexion of very long plane waves incident obliquely on a horizontally stratified ionized medium with a vertical magnetic field is first considered in general terms, and it is shown that the medium can be divided into a transition region and a reflecting region. If the ionization in the reflecting region increases linearly with height it is shown that propagation is governed by the following equations: ∂ 2 L / ∂ζ 2 + (α + ζ) L + β M = 0, ∂ 2 M / ∂ζ 2 + (α - ζ) M + β L = 0, where α and β are constants depending on the angle of incidence. Under the conditions of the experiments β is small, and a solution, in terms of contour integrals, valid in this case is obtained.

Radio propagation over a flat Earth across a boundary separating two different media

1953 ◽  
Vol 246 (905) ◽  
pp. 1-55 ◽  
Keyword(s):  
Plane Wave ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Dipole Source ◽  
Radio Waves ◽  
Dual Integral Equations ◽  
Plane Wave Incident ◽  
General Complex ◽  
Infinite Conductivity ◽  
New Feature

A theoretical investigation is given of the phenomena arising when vertically polarized radio waves are propagated across a boundary between two homogeneous sections of the earth’s surface which have different complex permittivities. The problem is treated in a two-dimensional form, but the results, when suitably interpreted, are valid for a dipole source. The earth’s surface is assumed to be flat. In the first part of the paper one section of the earth is taken to have infinite conductivity and is represented by an infinitely thin, perfectly conducting half-plane lying in the surface of an otherwise homogeneous earth. The resulting boundary-value problem is initially solved for a plane wave incident at an arbitrary angle; the scattered field due to surface currents induced in the perfectly conducting sheet is expressed as an angular spectrum of plane waves, and this formulation leads to dual integral equations which are treated rigorously by the methods of contour integration. The solution for a line-source is then derived by integration of the plane-wave solutions over an appropriate range of angles of incidence, and is reduced to a form in which the new feature is an integral of the type missing text where a and b are in general complex within a certain range of argument.

DIFFRACTION OF A PLANE ELECTROMAGNETIC WAVE BY AN INFINITE SET OF PARALLEL METALLIC PLATES IN AN ANISOTROPIC PLASMA

1967 ◽  
Vol 45 (5) ◽  
pp. 1911-1923 ◽  
Author(s):  
C. P. Wu
Keyword(s):  
Electromagnetic Wave ◽  
Plane Electromagnetic Wave ◽  
Angle Of Incidence ◽  
Parallel Plates ◽  
Rapid Variation ◽  
Magnetostatic Field ◽  
Transmission Coefficients ◽  
Phase Functions ◽  
Infinite Set ◽  
Metallic Plates

The diffraction of a plane electromagnetic wave by an infinite set of parallel metallic plates is considered. The plates are assumed to be vanishingly thin and infinitely conducting, and are immersed in a cold plasma which is rendered anisotropic by an external magnetostatic field parallel to the edges of the plates. An exact solution is obtained by using the Wiener–Hopf technique for the case in which the fields have no variation in the direction of the external static magnetic field.It is found that, because of the anisotropy of the medium, the reflection becomes nonvanishing for the TM mode incident normally at the interface between the parallel plates and the free plasma regions. Also, the reflection coefficient is no longer an even or odd function of the angle of incidence. When the degree of anisotropy is relatively small, the results practically reduce to those in an isotropic dielectric, except that the phase functions of the reflection and transmission coefficients would experience a rapid variation for small incident angles. Some numerical examples showing the effects of anisotropy are given.

DIFFRACTION BY AN IMPEDANCE HALF-PLANE IN AN ANISOTROPIC PLASMA

1966 ◽  
Vol 44 (11) ◽  
pp. 2915-2925 ◽  
Author(s):  
R. W. Breithaupt
Keyword(s):  
Boundary Condition ◽  
Surface Waves ◽  
Half Plane ◽  
Incident Wave ◽  
Incident Field ◽  
Anisotropic Plasma ◽  
Permittivity Tensor ◽  
Impedance Boundary Condition ◽  
Magnetostatic Field ◽  
Impedance Boundary

The problem solved previously by Jull (1964) for a perfectly conducting half-plane is extended to the case of an impedance half-plane. As assumed by Jull, the direction of the incident wave is normal to both the magnetostatic field and the diffracting edge. The plasma is characterized by a permittivity tensor; and only the TM incident field is considered, as the anisotropy does not affect an incident TE wave. The impedance boundary condition is found to introduce unidirectional surface waves propagating at some angle into or away from the surface, as well as the usual radiated far fields.

Electromagnetic scattering by a system of two parallel dielectric prolate spheroids

1990 ◽  
Vol 68 (4-5) ◽  
pp. 376-384 ◽  
Author(s):  
M. F. R. Cooray ◽  
I. R. Ciric ◽  
B. P. Sinha
Keyword(s):  
Electromagnetic Wave ◽  
Incident Wave ◽  
Electromagnetic Scattering ◽  
Scattered Field ◽  
Plane Electromagnetic Wave ◽  
Angle Of Incidence ◽  
Algebraic Equations ◽  
Column Matrix ◽  
Prolate Spheroids ◽  
Expansion Coefficients

An exact solution to the problem of scattering of a plane electromagnetic wave by two dielectric prolate spheroids with parallel major axes is obtained by expanding the incident, scattered, and transmitted electric and magnetic fields in terms of an appropriate set of vector spheroidal eigenfunctions. The incident wave is considered to be a monochromatic, uniform plane electromagnetic wave of arbitrary polarization and angle of incidence. The boundary conditions are imposed by expressing the electromagnetic field scattered by one spheroid in terms of the spheroidal coordinates attached to the other, using the translational addition theorems for vector spheroidal wave functions. The column matrix of the total transmitted and scattered field-expansion coefficients is equal to the product of a square matrix, which is independent of the direction and polarization of the incident wave, and the column matrix of the known incident field-expansion coefficients. The solution of the associated set of algebraic equations gives the unknown transmitted and scattered field-expansion coefficients. Even though the problem is formulated in general, the numerical results are presented for the bistatic and backscattering cross sections of two lossless prolate spheroids with various axial ratios and center-to-center distances.

Electromagnetic radiation from a dipole source in a homogeneous magnetoplasma

1983 ◽  
Vol 309 (1509) ◽  
pp. 503-557 ◽  
Keyword(s):  
Magnetic Field ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Great Distance ◽  
Dipole Source ◽  
Constructive Interference ◽  
Limited Frequency ◽  
Source Dipole ◽  
Positive Ion

An electric Hertzian dipole is immersed in a cold homogeneous magnetoplasma and it is required to calculate the electromagnetic field at a moderate or great distance. Known methods of doing this are reviewed and extended. They all, in effect, express the field as an integral representing an angular spectrum of plane waves or of waves with conical wavefronts. The integral is evaluated by the method of steepest descents and extensions of it. Results are then presented of some calculations for various plasmas containing one or more species of positive ion. A study is made of the dependence of the radiated field, and of its Poynting vector, on direction and on frequency, when the source dipole is parallel to the superimposed magnetic field. There are three conditions where signals of large or very large amplitude can occur, namely ( a ) enhancement for directions very close to the direction of the superimposed magnetic field, ( b ) resonance cones, in which the signal is large for directions where the refractive index is very large, and ( c ) Storey cones and reversed Storey cones, which may be thought of as conical caustic surfaces where two rays have moved to coalescence and give constructive interference. These three features occur only in certain limited frequency ranges. The classification of these results is complicated and necessitates discussion of the transition frequencies of the plasma. For a plasma with more than one species of positive ion the phenomenon of crossover occurs, and its effect on the three types of signal enhancement is discussed.

scholarly journals Night-time Sferic Propagation at Frequencies Below 10 KHz

1967 ◽  
Vol 20 (1) ◽  
pp. 101 ◽  
Author(s):  
KJW Lynn ◽  
J Crouchley
Keyword(s):  
Magnetic Field ◽  
Geographic Distribution ◽  
Angle Of Incidence ◽  
European Studies ◽  
Earth’S Magnetic Field ◽  
Night Time ◽  
The West ◽  
Earth's Magnetic Field ◽  
Effective Angle

Results of a study at Brisbane of individual night-time sferics of known origin are described. A propagation attenuation minimum was observed in the 3-6 kHz range. The geographic distribution of sferic types was also examined. Apparent propagation asynunetries were observed, since sferics were detected at greater ranges to the west than to the east at 10 kHz, whilst the number of tweek-sferics arising from the east was about four times that arising from the west. Comparison with European studies suggest that these asymmetries are general. These results are then " interpreted in terms of an ionospheric reflection cgefficient which is a function of the effective angle of incidence of the wave on the ionosphere and of orientation with respect to the Earth's magnetic field within the ionosphere.

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