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.

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.

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.

scholarly journals The incidence of light upon a transparent sphere of dimensions comparable with the wave-length

1910 ◽  
Vol 84 (567) ◽  
pp. 25-46 ◽  
Keyword(s):  
Magnetic Field ◽  
Maxwell's Equations ◽  
Wave Length ◽  
Plane Waves ◽  
Scattered Wave ◽  
Great Distance ◽  
Primary Wave ◽  
Electro Magnetic Field ◽  
The Difference ◽  
Electro Magnetic

In a paper, now nearly thirty years old, I applied Maxwell’s equations of the electro-magnetic field to investigate the disturbance produced by an obstacle upon plane waves of light which travel through a medium otherwise uniform, giving particular attention to the case where the properties of the obstacle differ but little from those of its surroundings. The difference may consist in a variation of K — the specific inductive capacity, or of μ — the magnetic capacity, or of both; but it was shown that the last supposition leads to results inconsistent with observation, and that the evidence favours the view that μ is to be treated as invariable. Denoting electric displacements by f, g, h , the primary wave was taken to be h 0 = e int e ikx , (23) so that the direction of propagation is along x (negatively), and that of vibration parallel to z . ∆ μ being omitted, the electric displacements ( f 1 , g 1 , h 1 ) in the scattered wave, so far as they depend upon the first power of ∆K, have at a great distance the values f 1 , g 1 , h 1 = k 2 KP/4 πr ( αγ / r 2 , βγ / r 2 , – α 2 + β 2 / r 2 ), (35, 37, 38) in which P = ∭ h 0 ∆K -1 e -ikr dx dy dz . (36)

Cerenkov and cyclotron instabilities in a plasma stream

1967 ◽  
Vol 1 (1) ◽  
pp. 1-27 ◽  
Author(s):  
C. F. Knox
Keyword(s):  
Magnetic Field ◽  
Plane Wave ◽  
Cold Plasma ◽  
Numerical Calculations ◽  
Graphical Form ◽  
Plasma Stream ◽  
Wave Growth ◽  
Stationary Medium ◽  
Phase Propagation ◽  
Positive Ion

The model of a stationary medium traversed by a weak plasma stream directed along a magnetic field is investigated. The usual linear treatment is adopted, and the stream is taken to be ‘cold’, with only electron (perturbation) motions considered. The objective is to assess the plane-wave growth associated with both Cerenkov and cyclotron instabilities; in particular, the dependence of the growth on frequency and angle of phase propagation. The main discussion is of the case when the stationary medium is a cold plasma in which both electron and positive ion motions are taken into account. Various expressions for the growth are derived, and numerical calculations are presented in graphical form.

Euler’s differential equation and the identification of the magnetic point‐pole and point‐dipole sources

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1549-1553 ◽  
Author(s):  
J. O. Barongo
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Magnetic Anomalies ◽  
Field Vector ◽  
Magnetic Data ◽  
Dipole Source ◽  
Point Dipole ◽  
Main Subject ◽  
Depth Extent ◽  
Dipole Sources

The concept of point‐pole and point‐dipole in interpretation of magnetic data is often employed in the analysis of magnetic anomalies (or their derivatives) caused by geologic bodies whose geometric shapes approach those of (1) narrow prisms of infinite depth extent aligned, more or less, in the direction of the inducing earth’s magnetic field, and (2) spheres, respectively. The two geologic bodies are assumed to be magnetically polarized in the direction of the Earth’s total magnetic field vector (Figure 1). One problem that perhaps is not realized when interpretations are carried out on such anomalies, especially in regions of high magnetic latitudes (45–90 degrees), is that of being unable to differentiate an anomaly due to a point‐pole from that due to a point‐dipole source. The two anomalies look more or less alike at those latitudes (Figure 2). Hood (1971) presented a graphical procedure of determining depth to the top/center of the point pole/dipole in which he assumed prior knowledge of the anomaly type. While it is essential and mandatory to make an assumption such as this, it is very important to go a step further and carry out a test on the anomaly to check whether the assumption made is correct. The procedure to do this is the main subject of this note. I start off by first using some method that does not involve Euler’s differential equation to determine depth to the top/center of the suspected causative body. Then I employ the determined depth to identify the causative body from the graphical diagram of Hood (1971, Figure 26).

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.

scholarly journals Optimization of the Sensitivity of a Double-Dot Magnetic Detector

Electronics ◽  
2020 ◽  
Vol 9 (7) ◽  
pp. 1134 ◽  
Author(s):  
Massimo Macucci ◽  
Paolo Marconcini ◽  
Stephan Roche
Keyword(s):  
Magnetic Field ◽  
Flicker Noise ◽  
Electron Gas ◽  
High Mobility ◽  
Enhancement Effect ◽  
Dimensional Electron ◽  
Constructive Interference ◽  
Perfect Symmetry ◽  
Dimensional Electron Gas ◽  
Magnetic Detector

We investigate, by means of numerical simulations, the lowest magnetic field level that can be detected with a given relative accuracy with a sensor based on a double-dot device fabricated in a high-mobility two-dimensional electron gas. The double dot consists of a cavity delimited by an input and an output constriction, with a potential barrier exactly in the middle. In conditions of perfect symmetry, a strong conductance enhancement effect appears as a consequence of the constructive interference between symmetric trajectories. When the symmetry is broken, for example by the presence of an applied magnetic field, this enhancement effect is suppressed. We explore the design parameter space and assess the minimum magnetic field value that can be measured with a given accuracy in the presence of flicker noise.

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