Showing papers on "Electromagnetic field published in 1974"

Augmentation of Bone Repair by Inductively Coupled Electromagnetic Fields

Abstract: Pulsing electromagnetic fields of low frequency and strength have been inductively coupled across skin, directly to bone, to enhance the repair of canine osteotomies. The induced voltage field in bone appears to increase the organization and strength of the repair process at 28 days after "fracture."

Electromagnetic Fields Induced Inside Arbitrarily Shaped Biological Bodies

Abstract: A theoretical method has been developed to determine the electromagnetic field induced inside heterogeneous biological bodies of irregular shapes. A tensor integral equation for the electric field inside the body was derived and solved numerically for various biological models.

Perturbation analysis for gravitational and electromagnetic radiation in a Reissner-Nordström geometry

Abstract: We consider the gravitational and electromagnetic fields produced by a charged (or uncharged) test particle moving in a Reissner-Nordstr\"om geometry as perturbations on the background Reissner-Nordstr\"om geometry and its associated electric field, respectively. The gravitational perturbations are expanded in tensor harmonics in the manner of Regge and Wheeler, while the electromagnetic field is expanded in vector harmonics. Following a previously proposed convention, we find that in the Einstein-Maxwell system of equations, electric gravitational multipoles couple only to electric (TM) electromagnetic multipoles and similarly for magnetic multipoles. It is possible to reduce the entire Einstein-Maxwell system for each type of multipole to two second-order Schr\"odinger-type equations.

Multipole expansions and plane wave representations of the electromagnetic field

Abstract: 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.

Electromagnetic fields in curved spaces: A constructive procedure

Abstract: A new procedure for computing electromagnetic fields in curved space-times is presented. With this procedure, the problem is reduced to solving one complex linear scalar wave equation. Many space-times of astrophysical importance may be treated in this manner, including black-hole and neutron-star spaces and cosmological models.

Electromagnetic fields in spatially dispersive media

Abstract: The structure of the electromagnetic field in a spatially dispersive model medium occupying a plane parallel slab is obtained, free of several customary ad hoc assumptions made in other theories. The model medium is characterized by a dielectric response function appropriate to the neighborhood of an isolated-exciton transition frequency. The exact mode expansion for the electromagnetic field in the slab is derived and it is found that, unlike in the case of an unbounded medium, a single plane wave cannot be generated in the slab. An elementary solution (a single mode) is found to consist, in general, of six plane waves (four transverse and two longitudinal ones), coupled by two linear relations. These relations are shown to be equivalent to two nonlocal boundary conditions (of the form encountered in connection with the Ewald-Oseen extinction theorem in molecular optics), which the nonlocal contribution to the induced polarization must satisfy on the faces of the slab. This result resolves a long-standing controversy about the nature of the so-called additional boundary conditions that are generally believed to be required for solving problems of interaction of an electromagnetic field with a spatially dispersive medium. The results are applied to the problem of refraction and reflection on a spatially dispersive model medium occupying a half-space and a generalization of the classic formulas of Fresnel are obtained. The behavior of the reflected and transmitted waves as functions of the angle of incidence and of the frequency are illustrated by several figures. Our results are shown to differ from those obtained by Pekar in a well-known paper. The difference is traced to the nature of the additional boundary conditions postulated by Pekar; they are found to be inconsistent with the additional boundary conditions that we derive as an exact consequence of Maxwell's theory. Comparisons with several other theories, especially with those of Sein and Birman and of Maradudin and Mills are also made.

Phase of a Microscopic Electromagnetic Field and Its Measurement

Abstract: A novel approach to the quantum mechanical description of phase properties of a one-mode low-intensity radiation field is presented. The procedure is based upon the correspondence between Glauber states and classical waves of fixed phase ϕ and amplitude a, and, in contrast to the conventional quantum mechanical phase concepts, allows to make contact between certain operators ℰm corresponding to the classical quantities exp {imφ} (m = ± 1, ± 2, …) and realistic measurements. In the observation, a large amplification of the microscopic field by means of a linear quantum amplifier plays a decisive role. Since the amplified field is a macroscopic one, the measurement of phase is not problematic, and hence, in particular, average values «exp {imϕ}» can be determined experimentally. The main result of our analysis is that the mean values «exp {imϕ}» are equal to the quantum mechanical expectation values for the operators ℰm with respect to the field before amplification. To obtain this result it became necessary to calculate Glauber's P function for the amplified field in case of an arbitrary state for the initial field.

On a Generalization of the Power-Zienau-Woolley Transformation in Quantum Electrodynamics and Atomic Field Equations

Abstract: A canonical transformation is performed on the conventional Hamiltonian for the electromagnetic radiation field and an assemblage of neutral molecules in interaction. The new Hamiltonian has interaction energies expressed in terms of the electromagnetic fields alone and these energies have direct physical significance. The terms linear in e are the multipole interactions, both electric and magnetic, and the term quadratic in e is a generalization of the elementary diamagnetic energy shift. The intermolecular Coulomb energies have cancelled with transverse polarization fields in the new Hamiltonian, although the intramolecular Coulomb potentials are left unaffected. The equations of motion that follow from the new Hamiltonian are deduced. They are the so-called atomic-field equations for the Maxwell fields and Schrodinger equation for an electron wave in a transverse electromagnetic field. The former are the microscopic analogues of Maxwell’s equations in a medium (not restricted to dipole polarization fields) and the latter are dependent on the field strengths alone (not explicit functions of the vector potential).

Motion of charged particles in homogeneous electromagnetic fields

Abstract: An invariant geometrical description of the world lines of charged particles in arbitrary homogeneous electromagnetic fields is presented. This is accomplished through the combined use of the Frenet‐Serret equations and the Lorentz equation. The results apply to flat as well as Riemannian space‐time. The intrinsic scalars associated with these curves (i.e., their curvatures and first and second torsions) are found to be constants of the motion when they are well defined. Moreover, they form simple relationships with the field invariants as well as with the energy and momentum densities of the rest frame fields. When they are evaluated in the instantaneous rest frame of the particle, the Frenet vectors lend themselves to simple physical interpretation. It is shown that one cannot distinguish in an intrinsic geometrical manner between the curves of positive and negative charges. The same is true for positive and negative magnetic monopoles if they exist. In such a case, however, one would be able to distinguish intrinsically between ordinary and magnetic charges. The effect of duality rotations of the field tensor on the Frenet scalars is studied. A physical realization of the Frenet frame is obtained by considering the classical description of spin precession. Finally the Frenet formalism is applied to timelike Killing trajectories. These are shown to closely resemble the world lines of charged particles in homogeneous electromagnetic fields.

Application of electromagnetic particle simulation to the generation of electromagnetic radiation

Abstract: A three velocity and one‐space dimensional nonrelativistic electromagnetic particle simulation code employing the fast Fourier transform algorithm is described and used to simulate the amplification of electromagnetic radiation by an electron beam passed over a rippled static magnetic field. In the beam frame the rippled magnetic field looks like an intense electromagnetic pump and thus a parametric instability can be produced. In one case, it was observed that 30% of the beam energy was converted to electromagnetic radiation.

A Nonperturbing Temperature Sensor for Measurements in Electromagnetic Fields

Abstract: An electro-optical temperature measuring device which neither perturbs electromagnetic fields nor causes hot spots has been developed for use in monitoring temperature in biological systems during microwave irradiation.

Efficient Numerical Computation of the Frequency Response of Cables Illuminated by an Electromagnetic Field (Short Papers)

Abstract: Computationally efficient numerical methods for determining the frequency response of uniform transmission lines consisting of a large number of mutually coupled conductors in homogeneous and inhomogeneous media, and illuminated by an electromagnetic (EM) field are presented.

Method and apparatus to determine spatial distribution of magnitude and phase of electro-magnetic fields especially optical fields

Abstract: A method and apparatus for numerical determination of the distribution of magnitude and phase of a time harmonic electromagnetic, particularly an optical, wave field by using the wavefront of a reference wave as the optical reference surface and by introducing additional information to the recording process such that the field becomes uniquely determined and this is realized by the recording of three interference fringe patterns which belong to variations of the reference field distribution. A reference field is chosen whose spatial distribution is similar to the unknown field whereby fringes are obtained the position of which varies slowly with the recording coordinates. The recorded data are numerically evaluated and this may be done conveniently in a computer. After these measurements are made the reference beam is shifted by an optical element e.g. a prism, gaseous wedge, electro-optical diffraction device placed in the reference optical path and a second set of measurements is made. In this way a reference field whose spatial distribution is not known precisely is introduced but the system is such that the reference spatial distribution information is used and then eliminated from the information finally obtained on the unknown wavefield.

Numerical evaluation of electromagnetic fields due to dipole antennas in the presence of stratified media

Abstract: Two numerical methods are used to evaluate the integrals that express the em fields due to dipole antennas radiating in the presence of a stratified medium. The first method is a direct integration by means of Simpson's rule. The second method is indirect and approximates the kernel of the integral by means of the fast Fourier transform. In contrast to previous analytical methods that applied only to two-layer cases the numerical methods can be used for any arbitrary number of layers with general properties.

Solution of 6-component electromagnetic fields in three space dimensions and time by the t.l.m. method

Abstract: The extension of the transmission-line matrix method to three space dimensions is described. The technique provides a solution to the complete set of Maxwell's equations and, in particular, describes wave propagation in mixed media, with or without losses. The method is illustrated by obtaining results for the resonance frequency and field decay time of rectangular cavities partially filled with dielectric.

A dynamic theory for magnetizable elastic solids with thermal and electrical conduction

Abstract: A general dynamical theory of magnetizable, electrically and thermally conducting media is developed for soft ferromagnetic or paramagnetic materials in external electromagnetic fields. The general equations are linearized by assuming infinitesimal strains, linear constitutive equations and that all field variables may be divided into two parts: a "rigid body state" and a "perturbation state". The former is the same as the one in rigid body electrodynamics, and the latter which accounts for electromagnetic interaction with the deformable continuum is coupled with stress and strain through linearized field equations. The theory is developed for general anisotropy but specialized for materials with uniaxial, or higher, symmetry.

A Numerical Method Based on the Discretization of Maxwell Equations in Integral Form

Abstract: AZrstract-A method is described for the solution of the electromagnetic field inside resonant cavities and waveguides of arbitrary shape, whether homogeneously or inhomogeneously filled. The method, suitably programmed for use with a digital computer, is based on the direct discxetization of the Maxwell equations in integral form. Since the method works with the components of the electromagnetic field, the numerical solution directly gives the distributions of the field in the structure, in addition to the resonant frequencies of cavities or the propagation constants of wavegnides. Some numerical applications of the method are given.

A Numerical Method Based on the Discretization of Maxwell Equations in Integral Form (Short Papers)

Abstract: A method is described for the solution of the electromagnetic field inside resonant cavities and waveguides of arbitrary shape, whether homogeneously or inhomogeneously filled The method, suitably programmed for use with a digital computer, is based on the direct discretization of the Maxwell equations in integral form Since the method works with the components of the electromagnetic field, the numerical solution directly gives the distributions of the field in the structure, in addition to the resonant frequencies of cavities or the propagation constants of waveguides Some numerical applications of the method are given

A unified theory on radiation of a vertical electric dipole above a dissipative earth

Abstract: Analytical expressions are derived for the electromagnetic field associated with a vertical electric dipole (VED) above a dissipative earth. The scattered field is shown to consist of a direct contribution from a perfect image source, and a correction due to the finite conductivity of earth which is expressible in terms of an incomplete Hankel function. The resultant expression readily reduces to the well-known asymptotic solutions in both the space-wave and ground-wave regions. Validity of the space-wave expression in the far zone is found to be dependent upon the observation angle as well as the refractive index of earth. In the near field, alternative approximate formulas in closed form are derived from the incomplete Hankel function expression for different elevation angles. These formulas are shown to yield accurate results whenever the distance from the image source is greater than about 0.2λc where λc is the effective wavelength (or skin depth) of earth. For distance smaller than 0.2λc, however, an analytical expression based upon a quasistatic approximation is generally applicable and has been discussed elsewhere.

Electromagnetic Field Penetration into a Spherical Cavity

Abstract: A plane wave is symmetrically incident on a spherical shell with a circular aperture. The fields inside and outside the cavity are expanded in terms of spherical vector wave functions and the modal coefficients are found by application of the least squares method to the boundary conditions. Computed data are obtained and the results exhibited in the form of amplitude curves of the interior and aperture fields as functions of position for a variety of cavity and aperture sizes. Within the cavity it appears that the field variations are primarily determined by the cavity size and that the aperture size serves only to scale them.

A minimum photon “rest mass” — Using Planck's constant and discontinuous electromagnetic waves

Abstract: Reasons for taking1/2h/c 2 in cgs units as an equivalent in grams for the photon “rest mass” are given. Its numerical value of3.68×10 −48 g corresponds to the minimum mass equivalent energy for one half-cycle of an electromagnetic dipole field distribution, which is discontinuous. For the fluid models that are discussed, this field distribution corresponds somewhat to a hydrodynamic toroidal vortex which is stationary—if we use toroidal coordinates and assume that the ring origin has the radial velocity c, that the gauge is defined by the ring origin diameter, and that free space is represented by a two-fluid model (the fluids oppositely charged). There are mappings which can transform such toroidal entities (photons) into spherical ones. The toroidal entities are possible candidates for the role of “hidden variables.”

An Introduction to Electromagnetic Theory

Abstract: Preface Part I. Basic Concepts: 1. Charged particles, force and field 2. Charge and current density 3. Practical units and magnitudes 4. Development of the theory Part II. The Vacuum Field of Charge and Current: Mazwell's Equations: 1. The field of static charge 2. The field of steady current 3. Faraday's law of induction 4. Maxwell's 'displacement' current 5. Maxwell's equations Part III. Electrostatics: 1. Field and potential 2. Energy 3. Potential theory 4. Dielectrics Part IV. The Magnetic Field of Steady and Slowly Varying Currents: 1. Steady currents in a conductor 2. Currents and field 3. Energy 4. Circuits 5. Magnetic media Part V. Electromagnetic Waves: 1. Maxwell's equations 2. Monochromatic plane waves in vacuum 3. Monochromatic plane waves in media 4. Radiation Part VI. The Electromagnetic Properties of Media: 1. Polarization and magnetization 2. Free electron gas 3. Dielectrics 4. Magnetic media Appendix Index.

Electromagnetic Fields Induced Inside of Biological Bodies

Abstract: A theoretical study has been conducted to determine the electromagnetic field induced inside of biological bodies of irregular shapes. A tensor integral equation was derived and solved numerically for various biological models.

Radio frequency resistivity and dielectric constant well logging utilizing phase shift measurement

Abstract: The invention disclosed herein includes methods and apparatus for determining the resistivity and dielectric constant of earth materials in the vicinity of a well borehole. A radio frequency electromagnetic field in the frequency range from 20 to 40 megahertz is generated in a borehole and the total electromagnetic field at two longitudinally spaced locations is detected. Measurements of the relative phase shift in the field between the detector locations and the amplitude of the field at least at one of the detector locations may then be interpreted according to predetermined relationships in terms of the earth formation resistivity and dielectric constant.