Showing papers on "Maxwell's equations published in 1971"

Solutions of the Coupled Einstein-Maxwell Equations Representing the Fields of Spinning Sources

Abstract: A wide class of exact solutions of the stationary Einstein-Maxwell equations characterized by a flat "background" three-space is obtained. The solutions can be interpreted as the external gravitational and electromagnetic fields of one or more spinning sources with unit specific charge in stationary configuration.

Superheavy elements and an upper limit to the electric field strength.

Abstract: An upper limit to the electric field strength, such as that of the nonlinear electrodynamics of Born and Infeld, leads to dramatic differences in the energy eigenvalues and wave functions of atomic electrons bound to superheavy nuclei. For example, the $1{s}_{\frac{1}{2}}$ energy level joins the lower continuum at $Z=215$ instead of $Z=174$, the value obtained when Maxwell's equations are used to determine the electric field.

Balloon measurement of vertical and horizontal atmospheric electric fields

Abstract: Vertical and horizontal atmospheric electric fields measurements at balloon altitudes, considering magnetospheric processes effect and potential differences

The Darwin Model as a Tool for Electromagnetic Plasma Simulation

Abstract: The Darwin model of electromagnetic interaction is presented as a self‐consistent theory, and is shown to be an excellent approximation to the Maxwell theory for slow electromagnetic waves.

Dynamic structure of vortices in superconductors.

Abstract: The Maxwell equations couple the current and charge j and p to the vector and scalar potentials A and cp. In order to obtain a two-dimensional solution, we previously ignored the boundaries at the sample surfaces and the magnetic field generated by the average transport current j,. Near Hc2 we found the total current to first order in v and IAI2 to consist ofthree parts: the constantj0 the equilibrium supercurrentj. translating with velocity v perpendicular to j,, and a backflow current jb. This backflow current arises when A. is not equal to the screening length ( = ~/J12 introduced for 1/1. Plots of the streamlines of jb for two different directions of j, relative to the Abrikosov lattice are shown in Figs. 1 and 2. Our study of the low-field Iimit revealed similar features. The purpose of the present note is to complete the three-dimensional solution of the moving vortices.

Effects of finite length in solid-rotor induction machines

Abstract: The author presents an analytical solution of Maxwell's equations for the fields in a finite-length, solid-rotor induction motor in which the rotor is not fitted with conducting endrings. It has been assumed as a boundary condition that zero flux enters the ends of the rotor; this is borne out by tests on a typical machine. The solutions for the field distributions are approximate only, but the approximations are good over a wide range of slip. A major advantage of the solutions is that they are expressed in closed, rather than series, form. It is shown that the field distributions and the equivalent-circuit impedances may be considerably different from those obtained by ignoring finite-length effects. Some simple criteria are derived to assess the importance of finite-length effects on machine impedances. The analysis is carried out ignoring rotor saturation and slotting.

An E Vector Variational Formulation of the Maxwell Equations for Cylindrical Waveguide Problems

Abstract: A vector variational formulation of the Maxwell equations applicable to cylindrical waveguide problems is developed in terms of the electric E field. This three-component vector formulation allows an approximate solution of loaded waveguide structures which cannot be described in terms of a single-field component or potential function. The three-component formulation is more economical than corresponding six-component formulations for a given order of approximation because the solution matrices which result are reduced in size (/spl sim/1/2) and contain fewer zero elements. The E-field variational integral is expanded in terms of the field components for inhomogeneously loaded parallel-plate and rectangular waveguide geometries to illustrate a computer-assisted vector variational solution procedure.

Resonant Interactions between Particles and Normal Modes in a Cylindrical Plasma

Abstract: A plasma configuration with cylindrical symmetry is studied, containing axial and azimuthal magnetic fields and radial electric field, with arbitrary radial variation. The particle motion is parameterized by three exact action invariants: radial action, canonical angular momentum, and canonical axial momentum; in the limit of small gyroradius they are equivalent to magnetic moment, radial guiding‐center position, and parallel velocity. The perturbed Vlasov‐Maxwell equations lead to a set of normal modes, which can interact resonantly with the particles. The quantum rate equations for this interaction, together with the laws for conservation of energy, angular momentum, and axial momentum, lead (in the classical limit) to a Fokker‐Planck equation in action space for the particles, and to an equation of evolution for mode energy. These coupled kinetic equations satisfy an H theorem, which implies a monotonic approach to a canonical distribution: a rigid‐rotor distribution for particles, and a generalized Rayleigh‐Jeans distribution for the modes. This asymptotic state may, however, be unconfined. The quantum transition probability is deduced from a classical calculation of emissivity. Explicit expressions are obtained for the mode growth rate and for the particle diffusion tensor. Finally, the Vlasov conductivity kernel is deduced from the growth rates, by the use of the Kramers‐Kronig relations.

Wavemechanical formulation of plasma dynamics in longitudinal electric fields

Abstract: The macroscopic dynamics of classical many-component plasmas, in which the particles interact by the self-consistent electric field, is formulated in terms of scalar, complex wave equations. The wave equation of each component is shown to be mathematically equivalent to its nonlinear conservations equations for mass, vector momentum, and energy. Thus, the description through wave equations leads to a considerable mathematical simplification compared to the conventional many-fluid hydrodynamics. As an elementary illustration of the wave mechanical formalism, the dispersion of electrostatic waves in an electron plasma is treated.

On the perturbational solution to the dyadic Green's function of Maxwell's equations in anisotropic media

Abstract: The dyadic Green's functions of Maxwell's equations in anisotropic media are found by a perturbation technique. The solutions are in Taylor's series which may be summed in closed form in the case of uniaxial crystal media. When the medium is biaxial or gyrotropic, approximation by partial sum may be used. The approximate solutions give the near fields in elementary functions, Which may be used to solve integral equations arising from scattering and radiation problems.

Energy Constants Associated with the Nonlinear Theory of Electromagnetic Instabilities

Abstract: For configurations relevant to transverse electromagnetic instabilities, two independent energy constants are derived within the framework of the fully nonlinear Vlasov‐Maxwell equations. It is assumed that the spatial variation in equilibrium and perturbed quantities is perpendicular to a uniform external magnetic field B0. The case B0 = 0 is not excluded, and the spatial variations may be one‐or two‐dimensional. The energy constants, which are applicable in both the stable and unstable regimes, exhibit precisely how the energy is partitioned between the fields and the individual components of plasma kinetic energy perpendicular and parallel to the propagation direction. The corresponding constants at the quasilinear level of description are also examined.

Classical effects from a factorized spinor representation of Maxwell's equations

Abstract: It was demonstrated in earlier work that the vector representation of electromagnetic theory can be factorized into a pair of two-component spinor field equations (Sachs & Schwebel, 1962). The latter is a generalization of the usual formalism, in the sense that in addition to predicting all of the effects that are implied by the vector theory, it predicts additional observable effects that are out of the domain of prediction of the Maxwell formalism. The latter extra predictions were derived in previous publications (Sachs & Schwebel, 1961, 1963; Sachs, 1968a, b). In this paper, the spinor formalism is applied to effects that are expected to agree with the predictions of the standard formalism—the Coulomb force between point charges and the measured speed of a charged particle which moves in an electric potential. While there are no vector or tensor variables involved in this formalism, the results are found, as expected, to be in agreement with the conventional representation of electromagnetic theory. The analysis serves the role of demonstrating that in the appropriate limiting case, the factorized spinor formulation of electromagnetism does predict the explicit classical effects that are also predicted by Maxwell's field equations. The paper also presents a derivation of the general form of the solutions of the spinor field equations.

A Computer-Implemented Vector Variational Solution of Loaded Rectangular Waveguides

Abstract: A 6-field component vector variational formulation of the electromagnetic Maxwell equations is applied to dielectrically loaded rectangular waveguides. The stationary property of the variational formulation leads to a symmetric matrix eigenvalue problem, which is then truncated and solved numerically. The entire solution procedure is computer implemented using standard library subroutines. Propagation curves and functional field representations for all the lower order modes of a waveguide structure are generated and loaded waveguide geometries having no closed-form classical solution are characterized.

A general-relativistic scalar field theory in the complex Weyl space

Abstract: In this paper Weyl’s gauge postulate is extended to include the mass term in a complex space. A generally covariant equation and an equivalence relation are then introduced that unify the matter, electromagnetic and gravitational fields in this space. These expressions lead directly to the Klein-Gordon equations as well as to more general wave equations including those for pseudoscalar fields. Consideration is then given to the noninvariant terms under the gauge postulate and it is shown that these terms represent measurable quantities in the laboratory space. Einstein’s free-space field equations are then developed within the context of this theory and the Yukawa problem is solved as an application of these equations. In addition to the Yukawa potential, two core potentials are obtained. Finally, Maxwell’s free-space field equations are developed and the central-charge problem is solved as an application of this theory.

An electromagnetic Thirring problem.

Abstract: A neutral rotating mass shell surrounds a concentric stationary electrically charged insulating shell. The dipole-like magnetic field induced by (and proportional to) the rotation of the neutral shell is calculated on the basis of the coupled linearized Einstein-Maxwell field equations of general relativity. This field is apparently at variance with a conjecture made on Machian grounds, for which a possible explanation is suggested. The corresponding induced quadrupolar electric field is calculated for the region within the charged shell, and the potential is given for this field everywhere. Though understandable on mutually inconsistent elementary grounds, we regard this field as a useful example of a solution of linearized general relativity.-

A New Approximation Method for Wave Theories

Abstract: The scalar field due to a bounded source and obeying the wave equation is analyzed. As a result of this, a set of rules is derived for solving a class of ``wave theories,'' including electrodynamics and general relativity, by expanding the field in a power series of c−1 in null‐spherical coordinates. The method is applied for the Maxwell equations to give all the well‐known results without the use of Fourier analysis and Bessel functions.

A new theory of elementary matter. part ii. electromagnetic and inertial manifestations.

Abstract: In accordance with the philosophical approach and its mathematical implications that were derived in Part I of this series (see p. 433), this paper deals explicitly with the manifestations of matter that are concerned with its electromagnetic and inertial properties. It is demonstrated that a logically and mathematically generalized version of electromagnetism emerges from extending the Faraday-Maxwell field approach, so as to fully unify these features of matter with the field description of matter itself. It is then shown how the most general expression of matter (according to the axioms of this theory), in terms of two-component spinor fields in a Riemannian space, leads to a derivation of the inertial properties of matter. The mass field so-derived (1) is a positive-definite of the (global) coordinates--implying that gravitational forces can only be attractive; (2) approaches a discrete spectrum of values as the mutual coupling among the matter components of the closed system becomes arbitrarily weak; (3) predicts mass doublets in this approximation; and (4) approaches zero as the closed system becomes depleted of all other matter (in accordance with the Mach principle). It is also proven, as a consequence of the same field theory, that electromagnetic forces can be attractive or repulsive, depending on certain features of the geometrical fields of the Riemannian space. 1. Electromagnetic Theory In view of the logical implication of the generalized Mach principle regarding the elementarity of the interaction rather than the free particle, there follows an interpretation of the Maxwell field equations that differs from the usual one. The interaction is described here in terms of the coupling of field variables which are associated with the components of a closed material system. Electromagnetic phenomena are expressible in terms of two types of field variables. One set relates to the field intensity that is conventionally associated with the electric and magnetic field variables. The other set relates to the 'source fields' that are conventionally identified with the charge density and its motion. According to the interpretation that is advocated here, Maxwell's equations are not more than a covariant prescription for determining one of these types of electromagnetic field variables in terms of the other. Thus, Maxwell's equations

Excluded possibilities of geometrodynamical analog to electric charge.

Abstract: in 1956, J. A. Wheeler and C. W. Misner [I] showed in some detail that the existence of charges in the world need not be associated with sources in the electromagnetic field equations, but rather could be described as a consequence of Maxwell's free field equations (i.e. Ffj,,:~,l =0 and F~'";,--0) in a space with a multiply connected topology [2]. The electric lines of force can be ' tra?ped' in the topological structure of space, with the number of trapped lines of force being directly proportional to the charge associated with that field. To make this idea clearer, let us examine a simple example of a multiply connected, or 'v, ormhole' topology trapping electric lines of force. If the interiors of two solid spheres of equal radius are removed from an ordinary three dimensional Euclidean space, and' the appropriate points On the surfaces of the two spheres are identified, we obtain a "wormhole' in our space. If now we imagine that the t**o spheres had been conducting, one having charge q and the other charge q . and that the resultant electric field were fixed during the above reconstruction of our space, we discover that the resultant electric field everywhere obeys the free field equations. However, for an)'one located outside the cutaway portions of the space, there wouk! be no way of telling that the charges were no longer there. For example, integrating the field over any closed surface surrounding one of the wormhole mouths would tell him that the surface still enclosed a charge q. We have created, in Wheeler's words, 'charge without charge'. Due to the symmetry in Maxwell's equations between E and B, magnetic lines of force could similarly be trapped by the topology, creating magnetic charges, ilowever, these have never been observed in nature [3l. Wc theretore make the natural assumption that magnetic lines of force cannot be trapped in a multiply-connected topology. The above concepts can bc put into a rigorous mathematical form [4]. The electromagnetic tensors/-'*~ and ~,,~,~,f'p" are curl free antisymmetric I~ensors, and as such coffespond to closed differential 2+formsfand *f(i.e

Kinetic theory of electromagnetic waves obliquely incident upon a plasma slab

Abstract: The problem of an electromagnetic wave obliquely incident upon a plasma slab is considered as a boundary-value problem, using a self-consistent solution of the coupled linearized Vlasov and Maxwell equations for the electrons, with the ions treated as a fixed, uniform background. Power reflection, transmission, and absorption coefficients are derived under the assumption that electrons undergo specular reflection at the surfaces of the plasma slab. Although our analysis is valid for arbitrary slab thickness, computational results are presented for slabs which are thin compared to a free-space wavelength. The results show a series of resonances which are attributed to the kinetic behavior of the plasma. The results further show that the resonances are Landau damped as the thermal velocity of the plasma electrons increases. While similar resonances can be predicted from the coupled linearized hydrodynamic Maxwell equations, such a model does not predict Landau damping. The effects of a finite collision frequency are then included via a simple Bhatnager-Gross-Krook collision term. The numerical computations vividly indicate that the resonances undergo severe damping for extremely small ratios of the collision frequency to signal frequency.

A technique for solution of Maxwell's equations in a moving dielectric medium

Abstract: A simple technique is presented for converting a known solution for the electric and magnetic vector fields in a dielectric medium at rest into the corresponding fields in a moving dielectric medium. The technique combines methods presented by Tai [1] with a scaling procedure developed by Clemmow [2]. Tai's work reduces the moving medium problem to the solution of Maxwell's equations in a uniaxial medium, and Clemmow's procedure enables one to convert a known solution in an isotropic medium to the corresponding solution in a uniaxial medium. Thus by first solving for the fields in the medium at rest, then following Clemmow's procedure to obtain the fields in Tai's uniaxial medium, and finally applying Tai's reasoning, one may easily obtain the solution of Maxwell's equations in the moving medium.

Electromagnetic wave tails in the second approximation to the Einstein-Maxwell equations

Abstract: With a finite oscillating linear coherent distribution of electric charge chosen as the source of electromagnetic radiation, it is shown that the outgoing multipole electromagnetic waves of the linear approximation to the Einstein-Maxwell equations produce wave tails in the second approximation which, after the end of the source vibration, constitute incoming multipole waves.

Orthotomic systems of rays in inhomogeneous isotropic media.

Abstract: The behavior of orthotomic systems of rays, rays associated with a system of wavefronts, is analyzed from the point of view of classical geometrical optics. The rays themselves are described in terms of the ray equation derived from Fermat’s principle. A condition for an aggregate of rays to comprise an orthotomic system is found. Some consequences of this condition on the geometric properties of wavefronts are found. The resemblance of some of these to the Maxwell equations is noted.