Current Charge Distribution Research Articles

Making electromagnetic wavelets: II. Spheroidal shell antennas

In the companion paper, a coherent charge-current distribution for radiating electromagnetic wavelets was constructed on an oblate spheroidal surface S�. Its main drawback was the necessity of including magnetic along with electric charges, making the sources impossible to realize. Here we show how this difficulty can be overcome by using Hertz potentials to generate a charge-current distribution due solely to bound electric charges. However, this distribution still appears difficult to realize because it consists of multiple surface layers on S�. We show how it can be replaced by a simple volume distribution on a spheroidal shell. Our method generalizes the usual construction of equivalent Huygens sources, based on boundary conditions on an interface between electromagnetic media, by allowing the transition to be gradual without incurring addition complexity.

Statistics of equally weighted random paths on a class of self-similar structures

In the companion paper, a coherent charge-current distribution for radiating electromagnetic wavelets was constructed on an oblate spheroidal surface S_a. Its main drawback was the necessity of including magnetic along with electric charges, making the sources impossible to realize. Here we show how this difficulty can be overcome by using Hertz potentials to generate a charge-current distribution due solely to bound electric charges. However, this distribution still appears difficult to realize because it consists of multiple surface layers on S_a. We show how it can be replaced by a simple volume distribution on a spheroidal shell. Our method generalizes the usual construction of equivalent Huygens sources, based on boundary conditions on an interface between electromagnetic media, by allowing the transition to be gradual without incurring addition complexity.

Modeling and application of plasma charge current in deep penetration laser welding

Plasma charge current distribution during deep penetration CO2 laser welding was analyzed theoretically and experimentally. The laser-induced plasma above the workpiece surface expands up to the nozzle, driven by the particle concentration gradient, forming an electric potential between the workpiece and the nozzle due to the large difference between the diffusion velocities of the ions and the electrons. The plasma-induced current obtained by electrically connecting the nozzle and the workpiece can be increased by adding a negative external voltage. For a fixed set of welding conditions, the plasma charge current increases with the external voltage to a saturation value. The plasma charge current decreases as the nozzle-to-workpiece distance increases. Therefore, closed-loop control of the nozzle-to-workpiece distance for laser welding can be based on the linear relationship between the plasma charge current and the distance. In addition, the amount of plasma above the keyhole can be reduced by a transverse magnetic field, which reduces the attenuation of the incident laser power by the plasma so as to increase the laser welding thermal efficiency.

Energy conservation for point particles undergoing radiation reaction

For smooth solutions to Maxwell's equations sourced by a smooth charge-current distribution ${j}_{a}$ in stationary, asymptotically flat spacetimes, one can prove an energy conservation theorem which asserts the vanishing of the sum of (i) the difference between the final and initial electromagnetic self-energy of the charge distribution, (ii) the net electromagnetic energy radiated to infinity (and/or into a black hole or white hole), and (iii) the total work done by the electromagnetic field on the charge distribution via the Lorentz force. A similar conservation theorem can be proven for linearized gravitational fields off of a stationary, asymptotically flat background, with the second order Einstein tensor playing the role of an effective stress-energy tensor of the linearized field. In this paper, we prove the above theorems for smooth sources and then investigate the extent to which they continue to hold for point particle sources. The ``self-energy'' of point particles is ill defined, but in the electromagnetic case, we can consider situations where, initially and finally, the point charges are stationary and in the same spatial position, so that the self-energy terms should cancel. Under certain assumptions concerning the decay behavior of source-free solutions to Maxwell's equations, we prove the vanishing of the sum of the net energy radiated to infinity and the net work done on the particle by the DeWitt-Brehme radiation reaction force. As a byproduct of this analysis, we provide a definition of the ``renormalized self-energy'' of a stationary point charge in a stationary spacetime. We also obtain a similar conservation theorem for angular momentum in an axisymmetric spacetime. In the gravitational case, we argue that similar conservation results should hold for freely falling point masses whose orbits begin and end at infinity. This provides justification for the use of energy and angular momentum conservation to compute the decay of orbits due to radiation reaction. For completeness, the corresponding conservation theorems for the case of a scalar field are given in an appendix.

Representation of arbitrary charge–current densities by polarization and magnetization fields

It is shown that any electromagnetic charge–current distribution may be expressed in terms of polarization and magnetization fields, plus a static charge density of one sign if the total charge q is nonzero, and that the standard Maxwell equations reduce, in general, to the conventional form used for material media plus a static Gauss law if q≠0. Examples considered include a capacitor, a point charge and an oscillating point electric dipole in arbitrary motion, and lumpy media composed of oscillating point electric dipoles or other particles.

Time-dependent plane wave and multipole expansions of the electromagnetic field

A new and conceptually simple derivation is presented of the time-dependent multipole expansion of the electromagnetic field radiated by a time-varying, localized, volume charge-current distribution. The analysis is based on a new time-dependent plane wave representation of the electromagnetic field (i.e., an “angular spectrum expansion” in the time domain), also derived in the paper. Expressions are given for the time-dependent plane wave spectra in terms of a fourfold Radon transform representation of the transverse current distribution. Two alternative expressions for the time-dependent multipole moments are derived; the first gives them in terms of the spectral amplitude vectors of the corresponding time-dependent plane wave representation while the second gives them in terms of a weighted radial-temporal average of the current distribution. Thus the analysis also sheds light on the relationship between the time-dependent plane wave and multipole expansions in their common domains of validity.

Is the pulsar emission produced by superluminally moving charged patterns?

AbstractThere are no physical principles disallowing the existence of extended sources of the electromagnetic field which move faster than light in empty space (Bolotovskii and Ginzburg 1972). Charge-current distributions whose patterns rotate around a fixed axis rigidly, and so have a phase speed that is greater than the speed of light in vacuo outside the light cylinder, emit radiation—different from both Cherenkov and synchrotron radiation—which has the following characteristics:1.It arises almost exclusively from the vicinity of those points within the source which, at the emission time, approach the observer with the speed of light and with zero acceleration.2.It consists of the superposition of a (continuous) set of narrow radiation beams whose flux densities fall off with the radial distance R from the source like R–1 (rather than R–2), and so it is intrinsically coherent.3.It has a power-law spectrum with no exponential cut-off, at high harmonics of the rotation frequency, whose index lies between –1 and –3 if the longitudinal distribution of the source density is pulse-like.4.It consists of two concurrent elliptically polarized signals whose position angles are predominantly orthogonal and simultaneously vary in direction in the course of each rotation.I suggest that this radiation, here referred to as Schott radiation (cf. Schott 1912), may in fact be that received from pulsars.

Electromagnetic fields in an expanding universe

The asymptotic form of the electromagnetic field due to a bounded distribution of charge current in an open, expanding Friedmann–Lemaître–Robertson–Walker universe is studied. The technique used is to first describe a mechanism for passing from a solution of Maxwell’s vacuum field equations on Minkowskian space-time to a solution of Maxwell’s field equations in a region free of charge current on the cosmological background. This is tested on the field of an accelerating point charge and then applied to the rigorous treatment of the asymptotic electromagnetic field of a bounded charge-current distribution in Minkowskian space-time given by Goldberg and Kerr [J. Math. Phys. 5, 172 (1964)]. A ‘‘peeling expansion’’ of the electromagnetic field in the expanding universe is obtained in inverse powers of a parameter that is proportional to the area distance along the generators of future null cones with vertices on the world line of a fundamental observer. The algebraic character of the two leading coefficients in the expansion is the same as that of the two leading coefficients in the Goldberg–Kerr expansion in Minkowskian space-time. In addition, bounds can be calculated, at any instant in the history of a fundamental observer, on all the coefficients in the peeling expansion, as a consequence of the evaluation of such bounds by Goldberg and Kerr in the case treated by them.

Microstrip Dispersion Including Anisotropic Substrates

A perturbation-iteration solution based on potential theory is developed for determining the effective dielectric constant, characteristic impedance, and current-charge distribution on a microstrip transmission line with isotropic and anisotropic substrates. The numerical implementation of the theory is described and is suitable for use on a personal computer. Computed data for several common substrate materials are included.

A speed-of-light barrier in classical electrodynamics

Moving patterns created by changes in the distributions of macroscopic charges and currents act as sources of the electromagnetic field that have no inertia and so travel with an arbitrary velocity. It is shown that the retarded potential arising from such sources---though finite when the source moves either slower or faster than light---is divergent, at certain points within the source, when the source moves on a curved path with a speed equal to that of light. Independently of the speed-of-light barrier set up by the requirements of relativistic mechanics, therefore, it appears that there is a barrier stemming from the relativistic restrictions inherent in electrodynamics itself which forbids the accelerated motion of any localized charge-current distribution, whether with or without inertia, at the speed of light.

A bulk-selvedge coupling theory for multipole surface plasmons

A bulk-selvedge coupling theory is developed for the calculation of multipole surface plasmon dispersion relations, and charge-current distributions, at optical and near-UV frequencies.

On the question of the existence of nonradiating primary planar sources of finite extent

It is known that certain oscillating three-dimensional charge-current distributions do not radiate. In this paper we show that no monochromatic, well-behaved, two-dimensional scalar source distribution that is localized within a finite area may be nonradiating. We also generalize this result to fluctuating, stationary planar source distributions of any arbitrary state of coherence.

Experimental MeanyValues and Integrated Structure Functions for Neutrino and Antineutrino Scattering at High Energy

We present measurements of for deep-inelastic charged-current distributions with incident neutrino and antineutrino energies ranging from 45 to 205 GeV. The neutrino values show little energy dependence, while the antineutrino data indicate a 10% rise over this energy range. Integrated structure functions obtained from our total-cross-section and results are also discussed.

Hadronic matter current distribution inside a polarized nucleus and a polarized hadron

The concept of nucleonic current density (or velocity profile) inside a polarized nucleus and the concept of hadronic matter current density inside a polarized hadron are introduced. Utilizing the increasing opaqueness of hadrons relative to each other at increasing relative velocities, these current densities can be obtained from a measurement of the R( t) parameter in elastic hadron-nucleus and elastic hadron-hadron scattering. For very high energies, the spin dependence in elastic hadron-hadron scattering will be solely due to this non-vanishing R( t) parameter. Measurements of R( t) and therefore the nucleonic current or hadronic matter current thus provide powerful probes for the structure of polarized nuclei and hadrons. The results can be used to check nuclear theory and models of hadron structure. Estimates of the magnitude of R are given by assuming the proportionality between the hadronic matter density-current distribution and the electric charge-current distribution. This proportionality hypothesis which is heuristic is shown to be dependent on the concept of homogenization and the principle of minimum electromagnetic interactions for the basic constituents of hadrons. In the appendix it is shown that the spin of a Dirac particle does involve motion (currents).

Classical dynamics for charged particles

The requirement that there be zero net electromagnetic energy-momentum flux passing through a spherical surface of radiusr 0 bounding and comoving with a stable charge-current distribution leads to a new classical equation of motion for the center point of the distribution. For any spherically symmetric distribution of chargeq, rest massm, in the nonrelativistic limit the new motion equation reduces to the Abraham-Lorentz equation, with Lorentz external force, for all external fields with wavelengths λ≫r 0, and field strengths ≪|q|/r 0 2 , providedr 0=2q 2/3mc 2. Only retarded fields are used.

Multipole expansions and plane wave representations of the electromagnetic field

A new and conceptually simple derivation is presented of the multipole expansion of an electromagnetic field that is generated by a localized, monochromatic charge-current distribution. The derivation is obtained with the help of a generalized plane wave representation (known also as the angular spectrum representation) of the field. This representation contains both ordinary plane waves, and plane waves that decay exponentially in amplitude as the wave is propagated. The analysis reveals an intimate relationship between the generalized plane wave representation and the multipole expansion of the field and leads to a number of new results. In particular, new expressions are obtained for the electric and magnetic multipole moments in terms of certain components of the spatial Fourier transform of the transverse part of the current distribution. It is shown further that the electromagnetic field at all points outside a sphere that contains the charge-current distribution is completely specified by the radiation pattern (i.e., by the field in the far zone). Explicit formulas are obtained for all the multipole moments in terms of the radiation pattern.

New representations for multipole moments and angular spectrum amplitudes of electromagnetic fields

New results are reported, concerning the relationship between the multipole expansion and the angular spectrum plane-wave expansion of the electromagnetic field generated by a monochromatic localized charge-current distribution. An intimate connection between these two types of expansions is revealed. Based on these results, new source representations are obtained for the multipole moments and for the angular spectrum amplitudes. It is also shown how the field may be determined, at every point outside a sphere that contains the charge current distribution in its interior, from the knowledge of the radiation pattern.

Relativistic treatment of multipole radiation from an extended charge-current distribution: I. Asymptotic properties of the electromagnetic field

The electromagnetic field due to a localized charge-current distribution is expanded in terms of a set of multiple moments defined with respect to a given time-like world line. The behaviour of this expansion in the asymptotic region is studied, leading to the identification of the radiation field. It is shown that the radiation field is a null field.

Relativistic treatment of multipole radiation from an extended charge-current distribution: II. Energy-momentum and angular-momentum radiation rate; radiation reaction

General expressions for the energy-momentum and angular-momentum radiation rate in terms of the multipole moments of a localized charge-current distribution are derived. The argument is essentially based on the observation that the radiative parts of the energy-momentum and the angular-momentum tensor are conserved outside the source. For a charged dipole system which does not accelerate and oscillate too rapidly, the radiation reaction force and torque are exhibited explicitly.

Soft multipole radiation and charge-current distribution in a nucleus

The conditions that a vector field vanish outside a given radius are applied to the emitted radiation. It is shown that the determination of the multipole radiation with polarization allows a determination of the curl and divergence of radiating current.