General Electromagnetic Field Research Articles

Higher order volume-preserving schemes for charged particle dynamics

A class of higher order numerical methods for advancing the charged particles in a general electromagnetic field is developed based on processing technique. By taking the volume-preserving methods as the kernel, the processed methods are still volume-preserving, and preserve the conservative quantities for the Lorenz force system. Moreover, this class of numerical methods are explicit and are more efficient compared with other higher order composition methods. Linear stability analysis is given by applying the numerical methods to the test equation. It is shown that the newly constructed higher order methods have the better stability property. This allows the use of larger step sizes in their implementation.

Assessment of Risk of Carrier Waves in the Assisted Reproductive Laboratory

Assisted reproductive technology (ART) laboratories represent the marriage of the most basic of biological activities with the most cutting edge technologies. While this association has worked well, the mixture of biology and technology can create risks to normal embryo development. Recently a significant amount of literature has explored the risks of manmade, electrically induced magnetic fields and carrier waves on reproduction, which some studies have suggested will lower functional gamete numbers in the males and potentially induce genetic issues in embryos. However, little is known about these phenomena within the ART laboratory, a laboratory filled with electronic equipment. The object of the present study was to explore the potential exposure of gametes and early stage embryos to two of the most prevalent fields and waves utilized in manmade technologies seen in the general environment, electromagnetic fields (EMF) and radio frequency waves (RF), and determine the effect varying levels of these energetic forces had on gamete function and embryo development. Results indicated that while extremely high concentrations of EMF (approximately 50-100X of laboratory background) caused negative outcomes in both gametes and embryos, levels consistent will the majority of lab equipment did not appear to impact growth, or function. Further, even extremely high RF appeared to have no impact cellular function. Results suggest few issues with EMF or RF on gamete and embryo function at normal laboratory levels for the relatively short exposure times seen in the ART laboratory.

Volume-preserving algorithms for charged particle dynamics

The paper reports the development of volume-preserving algorithms using the splitting technique for charged particle motion under the Lorentz force. The source-free nature of the Lorentz vector field has been investigated. Based on the volume-preserving property of the dynamics, a class of numerical methods for advancing charged particles in a general electromagnetic field has been constructed by splitting the classical evolution operator. This new class of numerical methods, which includes the Boris algorithm as a special case, conserves phase space volume, and globally bounds the numerical errors of energy, momentum, and other adiabatic invariants up to the order of the method over a very long simulation time. These algorithms can be computed explicitly, and thus are effective for the long-term simulation of the multi-scale dynamics of plasmas.

Exact Plane-Wave Expansion With Directional Spectrum: Application to Transmitting and Receiving Antennas

A new exact plane-wave expansion is presented for general time-harmonic electromagnetic fields radiated by an arbitrary finite source region in three dimensions. The plane-wave expansion employs a directional spectrum that is proportional to the far-field pattern of the source. The directionality is achieved through an exact representation that involves a beam parameter, which determines the sharpness of the spectrum. When the beam parameter is set to zero, the new expansion becomes identical to the plane-wave expansion employed in the fast multipole method. The expansion is exact for observations points all the way up to the source region and includes evanescent waves. An antenna- antenna transmission formula follows straightforwardly. Numerical examples demonstrate that the new plane-wave expansion requires fewer plane waves than previously derived plane-wave expansions.

An applied electro-magneto-elastic thin plate theory

The physical variational principle (PVP) in a static magneto-elastic field without source current is discussed first, and then, the PVP in a general electromagnetic field is derived. It is especially useful in the plate vibration problem. Using the PVP and the pseudo total stress principle, the electro-magneto-elastic thin plate bending theory in first order and a Mindlin-type plate bending theory for a moderate thickness plate are easily obtained. This method significantly simplifies the derivation of the governing equations of the thin and moderate plates with nonlinear electromagnetic behavior. The Maxwell stress is naturally included in the governing equation. Using the governing equation of a thin plate, the analyses of the stability and vibration of a plate in an external homogeneous magnetic field are discussed.

Gravitation and Electromagnetism as Geometrical Objects of a Riemann-Cartan Spacetime Structure

In this paper we first show that any coupled system consisting of a gravitational plus a free electromagnetic field can be described geometrically in the sense that both Maxwell equations and Einstein equation having as source term the energy-momentum of the electromagnetic field can be derived from a geometrical Lagrangian proportional to the scalar curvature R of a particular kind of Riemann-Cartan spacetime structure. In our model the gravitational and electromagnetic fields are identified as geometrical objects of the structure.We show moreover that the contorsion tensor of the particular Riemann-Cartan spacetime structure of our theory encodes the same information as the one contained in Chern-Simons term $${{\bf A} \wedge {\it d}{\bf A}}$$ that is proportional to the spin density of the electromagnetic field. Next we show that by adding to the geometrical Lagrangian a term describing the interaction of a electromagnetic current with a general electromagnetic field plus the gravitational field, together with a term describing the matter carrier of the current we get Maxwell equations with source term and Einstein equation having as source term the sum of the energy-momentum tensors of the electromagnetic and matter terms. Finally modeling by dust charged matter the carrier of the electromagnetic current we get the Lorentz force equation. Moreover, we prove that our theory is gauge invariant. We also briefly discuss our reasons for the present enterprise.

Dirac fermions in strong gravitational fields

We discuss the dynamics of the Dirac fermions in the general strong gravitational and electromagnetic fields. We derive the general Hermitian Dirac Hamiltonian and transform it to the Foldy-Wouthuysen representation for the spatially isotropic metric. The quantum operator equations of motion are obtained and the semiclassical limit is analyzed. The comparison of the quantum mechanical and classical equations shows their complete agreement. The helicity dynamics in strong fields is discussed. Squaring the covariant Dirac equation explicitly shows a similarity of the interactions of electromagnetic and gravitational fields with a charged and spinning particle.

Algebraic structure of general electromagnetic fields and energy flow

The algebraic structures of a general electromagnetic field and its energy–momentum tensor in a stationary space–time are analyzed. The explicit form of the reference frame in which the energy of the field appears at rest is obtained in terms of the eigenvectors of the electromagnetic tensor and the existing Killing vector. The case of a stationary electromagnetic field is also studied and a comparison is made with the standard short-wave approximation. The results can be applied to the general case of a structured light beams, in flat or curved spaces. Bessel beams are worked out as example.

A Gauge Invariant Discretization on Simplicial Grids of the Schrödinger Eigenvalue Problem in an Electromagnetic Field

We propose a method to compute approximate eigenpairs of the Schrödinger operator on a bounded domain in the presence of an electromagnetic field. Formulated for simplicial meshes, the method combines techniques from lattice gauge theory and finite elements, retaining the discrete gauge invariance of the former but allowing for noncongruent space elements as in the latter. The error of the method is studied in the framework of Strang's variational crimes, comparing with a standard Galerkin approach. When the meshes are quasi-uniform and satisfy the discrete maximum principle, we prove that for a smooth electromagnetic field the crime is of the order of the mesh width h, for a Coulomb potential it is of order $h|\log h|$, and for a general finite energy electromagnetic field it is of order $h^{1/2}$.

Simple Synthetic Route for SERS-Active Gold Nanoparticles Substrate with Controlled Shape and Organization

We report a simple synthetic route based on electroless deposition (galvanic displacement) and natural lithography to simultaneously control the shape and organization of Au nanoparticles (NPs). We show for the first time the formation of organized extended domains of Au nanoflowers and nanocrowns with single crystalline tips. The dimension and morphology of the desired nanostructures (NSs) can be tuned easily by controlling the deposition conditions at room temperature using saccharin as an organic additive. The exact role of saccharin on the crystal growth process of Au NPs is also discussed. A systematic surface enhancement Raman spectroscopy (SERS) study of large, ordered areas of organized gold nanoflowers using p-mercaptoaniline (pMA) as the probe molecule shows massive and reproducible enhancements of the Raman signal. By comparing the relative enhancement of the different vibrational modes as a function of the morphology, the specific charge-transfer (chemical effect) SERS mechanism can be distinguished from the general electromagnetic field enhancement (physical effect). A wide range of applications can be envisaged for these SERS substrates.

Magnetic Solutions of (2+1)-dimensional Einstein-born-infeld-dilaton Theory

Magnetically charged static solutions for the axially symmetric (2+1)-dimensional Einstein-BornInfeld-dilaton theory were obtained. The results revealed transformations between the magnetic and the electric solutions of the axially symmetric (2+1)-dimensional gravity theories with the dilaton field and the general nonlinear electromagnetic field including the Born-Infeld theory. The magnetic solutions were calculated from the electric solutions by using these transformations.

Worldline instantons, vacuum pair production and Gutzwiller's trace formula**Plenary talk at QFEXT07 (Quantum Fields Under External Conditions), Leipzig, September 2007.

In this talk, I describe a new application of the Gutzwiller trace formula formalism, to give a compact expression for the semiclassical vacuum pair production rate in quantum electrodynamics, for general inhomogeneous electromagnetic background fields. The semiclassical rate is expressed in terms of geometric properties of classical periodic phase space orbits for the associated Euclidean problem of propagation of a charged particle in the inhomogeneous background field, parametrized by the proper time.

On the dragging of light by a rotating medium

When light is passing through a rotating medium the optical polarization is rotated. Recently, it has been reasoned that this rotation applies also to the transmitted image. We examine these two phenomena by extending an analysis of Player (Player 1976 Proc. R. Soc. A 349 , 441–445) to general electromagnetic fields. We find that in this more general case, the wave equation inside the rotating medium has to be amended by a term which is connected to the orbital angular momentum (OAM) of the light. We show that optical spin and OAM account for the rotation of the polarization and the rotation of the transmitted image, respectively.

Relativistic Derivations of the Electric and Magnetic Fields Generated by an Electric Point Charge Moving with Constant Velocity

We propose a simple relativistic derivation of the electric and the magnetic fields generated by an electric point charge moving with constant velocity. Our approach is based on the radar detection of the point space coordinates where the fields are measured. The same equations were previously derived in a relatively complicated way [2] based exclusively on general electromagnetic field equations and without making use of retarded potentials or relativistic equations.

A spacetime description of relativistic media†

A discussion is given of relativistic balance laws that may be used to construct models of material media with spin and electromagnetic properties, interacting with general background electromagnetic fields and gravitation described by non-Riemannian geometries. The general framework offers an approximation scheme for modelling relativistic media by supplementing the balance laws with conditions that convert them into an involutive differential system. †Special symposium in honour of 2003 SES Eringen medalist, Gerard Maugin.

Asymptotic directional structure of radiation for fields of algebraic type D

The directional behavior of dominant components of algebraically special spin-s fields near a spacelike, timelike or null conformal infinity is studied. By extending our previous general investigations, we concentrate on fields which admit a pair of equivalent algebraically special null directions, such as the Petrov type-D gravitational fields or algebraically general electromagnetic fields. We introduce and discuss a canonical choice of the reference tetrad near infinity in all possible situations, and we present the corresponding asymptotic directional structures using the most natural parametrizations.

Pentaquarks—status report

The directional behavior of dominant components of algebraically special spin-s fields near a spacelike, timelike or null conformal infinity is studied. By extending our previous general investigations we concentrate on fields which admit a pair of equivalent algebraically special null directions, such as the Petrov type D gravitational fields or algebraically general electromagnetic fields. We introduce and discuss a canonical choice of the reference tetrad near infinity in all possible situations, and we present the corresponding asymptotic directional structures using the most natural parametrizations.

Gravitational and electromagnetic fields near an anti–de Sitter–like infinity

We analyze asymptotic structure of general gravitational and electromagnetic fields near an anti-de Sitter-like conformal infinity. Dependence of the radiative component of the fields on a null direction along which the infinity is approached is obtained. The directional pattern of outgoing and ingoing radiation, which supplements standard peeling property, is determined by the algebraic (Petrov) type of the fields and also by orientation of principal null directions with respect to the timelike infinity. The dependence on the orientation is a new feature if compared to spacelike infinity.

Gravitational and electromagnetic fields near a de Sitter-like infinity.

We present a characterization of general gravitational and electromagnetic fields near de Sitter-like conformal infinity which supplements the standard peeling behavior. This is based on an explicit evaluation of the dependence of the radiative component of the fields on the null direction from which infinity is approached. It is shown that the directional pattern of radiation has a universal character that is determined by the algebraic (Petrov) type of the spacetime. Specifically, the radiation field vanishes along directions opposite to principal null directions.

Erratum: General relativistic electromagnetic fields of a slowly rotating magnetized neutron star - I. Formulation of the equations

The paper ‘General relativistic electromagnetic fields of a slowly rotating magnetized neutron star — I. Formulation of the equations’ was published in. Immediately following equation (138) and after the sentence ending ‘…where the second expression is the one obtained after using the ansatz (60)–(62).’, the following sentence should be added: ‘It follows from equations (143) and (144) that the zero-order term in equation (138) vanishes, so that the leading contribution is at first order in Ω.’