Arbitrary Current Source Research Articles

Wait's complex-image principle generalized to arbitrary sources

The well-known simple and remarkably accurate approximate low-frequency (LF) complex-image method introduced in 1969 by J. R. Wait to compute the effect of the ground to the field of a divergenceless horizontal current (vertical magnetic current) is generalized to arbitrary current sources through the exact image formulation. The images of a vertical dipole, a horizontal current segment, and an oscillating point charge are first reduced to simplified but asymptotically exact forms and, subsequently, in terms of delta and step-functions to approximate image expressions that also include Wait's image. The novel part of the image is tested numerically through a geophysical example.

The calculation of the electromagnetic field created by an arbitrary current distribution placed in the proximity of a multi-layer conductive cylinder; application to thickness determination for metallic coatings on wires

This work is dedicated to the calculation of the electromagnetic field created by an arbitrary current source in the proximity of a cylinder consisting of a certain number of concentric layers made of materials with various electrical conductivities and magnetic permeabilities, using the method of the transfer matrix. The general results obtained are then particularized for the case of an eddy current transducer with a rotating magnetic field, having its reception part of a special construction. The inversion method used to determine the thickness of the protective coatings on a conductive cylinder is presented.

On the fields of a torus and the role of the vector potential

A toroidal current distribution has nonvanishing exterior vector potential A, but zero exterior field B=∇×A=0. This property, together with the absence of fringing fields as in a cylindrical solenoid, makes it convenient for studies involving the vector potential in a field-free region, such as the Aharonov–Bohm effect, or the effect of A in a Josephson junction. We present an immediate general result of magnetostatics, and use it to easily compute A for a torus, to visualize the static vector potential for any current distribution, and to show how one can construct a current distribution to produce any desired A. When the torus current I varies in time, nonzero quasistatic fields E(t) and B(t) are produced (E∼ωI/r3 and B∼ω2I/r2). Radiation is also produced, with the radiation pattern of an electric dipole. The torus provides a counterexample to the common erroneous notion that if all multipole moments of a current distribution vanish then quasistatic fields and radiation must also vanish. We then formulate Maxwell’s equations in a way that obviates the role of gauge transformations. This ‘‘gauge irrelevant’’ form clarifies the relation of potentials to current sources, isolating the role of the transverse part of A. The general result from magnetostatics is extended to time-varying sources, revealing a seldom recognized symmetry of Maxwell’s equations, and showing how one can visualize A for an arbitrary time-dependent current source.

Radiation patterns of electric dipole antenna in the presence of a biisotropic sphere

Analytic expressions of the dyadic Green's function of an arbitrary electric current source embedded in a general biisotropic sphere are presented at first, and the radiation characteristics of an electric dipole antenna placed on the surface of a biisotropic sphere lens are examined. The effects of the electric-and the magnetic-coefficients (ξ e and ξ m ) of biisotropic medium on the radiation patterns of electric dipole antenna are investigated in detail.

An unified theory of electromagnetic missiles generated by an arbitrary plane current source

AbstractIn this article a generalized study of electromagnetic (EM) missiles has been presented. An EM missile source condition has been derived from an arbitrary plane current distribution, and our analysis shows that an arbitrary plane current distribution of finite size has the ability to launch an EM missile, i.e., to realize slow decrease of energy, on any axis perpendicular to the source plane so long as the axis has an intersection point with the source region. This important result reveals that the EM missiles are very much like light beams which do not diverge. © 1992 John Wiley & Sons, Inc.

Electromagnetic interactions with an anisotropic slab

An exact theory is developed for fields due to currents in the presence of an anisotropic slab. The anisotropy is of a type expected of a composite reinforced with unidirectional fiber and is described by a diagonal matrix in Maxwell's equations. A Green's matrix is defined with exact and explicitly computed solutions to Maxwell's equations for point currents. The Green's matrix reduces to quadrature the problems, in frequency and time domains, of computing the field produced inside and outside a slab by arbitrary current sources. Steady-state AC current sheets and loops are considered, and numerical results are presented. >

Comments on "Potentials produced by arbitrary current sources in an infinite- and finite-length circular conducting cylinder".

Recently in this TRANSACTIONS, a paper was published1, dealing with the electric potential problem in a circular conducting cylinder. The authors criticize the approach to the same problem as proposed by Okada in 1956. Obviously, an important motive for preparing the paper was the existence of contradictory results from different solution methods found in literature. We want to rehabilitate Okada's paper. We will point to the small error in Okada's paper. Correction of this error removes the confusing difference with other methods.

Potentials produced by arbitrary current sources in an infinite- and finite-length circular conducting cylinder.

In electrophysiology, the analytical expression of the potentials at the outer surface of a cylinder, caused by an embedded current source distribution, is useful in studies where measured potentials have to be related to unknown generators. The solutions found in the literature for different types of current sources are unfortunately contradictory. This paper rederives the solution to the general case of an arbitrary monopolar or dipolar current source and discloses where and how an error arose in earlier work. The problems encountered during the numerical implementation of the new equations are extensively discussed.

Transmission parameter representation of non‐uniform transmission line Green's functions

AbstractThe Green's function G(x, x') of a non‐uniform transmission line is formulated exactly in terms of partial transmission matrix parameters associated with different segments of the line. Exact differential expressions relate the transmission parameters to each other, and it is shown that G(x, x') can be expressed entirely in terms of a single transmission parameter B(x, x') and its derivatives. The voltage response V(x) on any doubly‐terminated line with arbitrary current source density along the line is given. A new perturbation technique, based on a Volterra integral equation, is developed which determines V(x) in terms of known functions and arbitrary perturbing immittances on the line.

Radiation from a source in a cold magnetoactive plasma, re-examined. Application to cyclotron and multipole radiation

An analysis is presented of the radiation emitted by an arbitrary source embedded in a cold, magnetoactive plasma and physically distinct from the latter. The plasma is supposed to be infinite and homogeneous; its dielectric properties are described by a dielectric tensor ε. Expressions for the radiation fields are derived using the technique of Fourier decomposition. An expression for the vector potential is constructed and elaborated as far as possible for an arbitrary current source. The approach differs from that in previous work on technical points, the main one being the sequence in which the various integrations are carried out. The radiation flux is defined on the basis of Poynting’s vector S; a distinction is made between current sources behaving as a given function of time and randomly fluctuating sources. In the latter case an ensemble average is preferred over a time average. A comparison is made with existing treatments in the literature, and a variety of defects is pointed out. The general result for the radiation flux is then specified for cyclotron radiation from a stationary ensemble of electrons and for multipole radiation. Throughout the paper a compact notation is used based on the work of Bremmer.

The Calculation of the Electromagnetic Fields of a Sheet Current Source with Arbitrary Spatial Intensity Distribution over a Layered Half Space--II. The Computer Program and its Application

A general computer program to solve the electromagnetic induction problem for an arbitrary sheet current source over a half space with up to three layers is given. The arbitrary source is constructed from a number of elementary sources by superposition. A description of the program is included. A sample run to illustrate the use of the program is given.

Self-similar solution of distributed linear and nonlinear networks

The method of solution of partial differential equations is introduced and applied to the distributed RGC network. For linear networks convolution integrals, V(x,t) = V_{\delta} \times V_{source} and V(x,t) = V_{\delta'} \times I_{source} are obtained where V_\delta and V_\delta' are, respectively, the responses to the \delta function voltage and current sources found and from the self-similar analysis, and V_source and I_{source} \propto \partial V_{source}/\partial x are arbitrary voltage and current sources. For certain sources, these integrals have been performed and the results will be presented. The technique is also successfully applied to nonlinear networks which are useful in modeling various microelectronic circuit components.

On the Incompleteness of E and H Modes in Wave Guides

It is shown that a field expansion in terms of E and H modes for an arbitrary current source in a wave guide is complete for points outside the source region but does not give the complete field within the source region in general. It is also shown how the expansion may be completed by the addition of an extra term of simple form.

An Arbitrary Current Source in a Homogeneous Anisotropic Plasma

In analogy with the free-space solution of Maxwell's equations, the excitations which are set up in an anisotropic, macroscopically neutral plasma by an arbitrary current can be described by potentials. The equations which the one vector and two scalar potentials must satisfy are first obtained for a relatively general physical situation. Due to the complexity of the mathematics, however, one cannot expect to obtain analytic solutions to this set of coupled equations without first making some realistic simplifications. One particular case that can be solved without an inordinate amount of difficulty is that of the point charge moving with uniform velocity parallel to a strong magnetic field. It is shown that the propagating waves which arise in this situation are electroacoustic in nature but very different from those created by a moving charge in an isotropic plasma.

Fields Produced by a Current Source in a Partly Ionized Gas

A technique is developed for treating each of the waves generated by an arbitrary current source in a partly ionized gas with no steady magnetic field. Starting with Maxwell's equations and three sets of coupled hydrodynamic equations (for the electrons, ions, and neutral molecules), it is shown that one can obtain a separate inhomogeneous wave equation for each type of wave in the plasma, with the source term for the transverse and longitudinal waves dependent, respectively, on the curl and divergence of the current source.

Radiation Processes in Plasmas

The problem of arbitrary test current sources embedded in an infinite spatially homogeneous Vlasov plasma is considered. By computing the rate at which the test sources do work on the plasma, the energy emission into transverse and longitudinal waves is obtained. A variety of radiation problems can be handled by appropriate choice of the current sources. Use of the time varying dipole moment due to encounters between shielded electrons and ions leads to expressions for the bremsstrahlung spectra. If the currents are produced by the interaction of waves with density fluctuations, the scattering and coupling of waves is obtained. By equating the rate of emission of longitudinal or transverse waves to their rate of absorption, expressions for the steady-state energy densities of such waves are obtained.

Electromagnetic radiation generated by a current source in an anisotropic medium

The expressions for the electromagnetic field generated by an arbitrary current source in an anisotropic medium are calculated by the method of Fourier analysis. The radiation emitted by a charged particle moving in a helical orbit of uniform pitch in a magnetoionic medium is evaluated.

Excitation of Waves in a Warm Plasma by a Current Source

The general expression for the electromagnetic field due to an arbitrary monochromatic current source in an unbounded, homogeneous, warm, collisionless plasma in the absence of a magnetostatic field is derived. A hydrodynamic description is used in which ion and electron motion is included. The general results are specialized to the case of an electric dipole source. It is found that the field is generally composed of three parts which, in the radiation region, correspond to the well-known transverse, longitudinal electron, and longitudinal ion waves. The power flow in the radiation region is shown to be largest along the axis of the dipole for low frequencies whereas the maximum occurs perpendicular to the dipole at high frequencies.