Electromagnetic Field Vectors Research Articles

Исследование отражения и прохождения волны через планарный слой кирального метаматериала, расположенного в прямоугольном волноводе с учетом материальной дисперсии

The work analyzes the diffraction of the fundamental wave of a rectangular waveguide on a planar layer of a chiral metamaterial located in a transverse plane. The mathematical model of the metamaterial takes into account its chirality and dispersion of material parameters. To connect the electromagnetic field vectors through the parameters of the chiral layer, two-sided approximate boundary conditions are used. Cross-polarization of the field is taken into account in the work. A system of linear algebraic equations for the reflection and transmission coefficients of the fundamental and cross-polarized waves was obtained in the work. It is shown that at the cutoff frequencies of the fundamental and cross-polarized waves are also excited in the waveguide. It is shown that at different levels of attenuation in the waveguide, situations arise when the degeneracy of resonant frequencies arises and disappears. It has been proven that the reflection and transmission of the fundamental wave at low attenuation values is of a frequency-selective resonant nature.

Conformable modeling of normalization and recursional electromagnetic fields of spacelike magnetic curves

In this paper, we investigate spacelike magnetic curves according to Bishop frame. Firstly, we present conformable derivatives of Lorentz magnetic fields of these magnetic curves. Moreover, we calculate the conformable derivatives of the normalization and recursional electromagnetic vector fields. Finally, we give conformable energies of normalization and recursional electromagnetic fields related to spacelike magnetic curves.

A NUMERICAL METHOD FOR 3D TIME-DEPENDENT MAXWELL’S EQUATIONS IN AXISYMMETRIC SINGULAR DOMAINS WITH ARBITRARY DATA

In this article, we propose to solve the three-dimensional time-dependent Maxwell equations in a singular axisymmetric domain with arbitrary data. Due to the axisymmetric assumption, the singular computational domain boils down to a subset of R2. However, the electromagnetic field and other vector quantities still belong to R3. Taking advantage that the domain is transformed into a two-dimensional one, by doing Fourier analysis in the third dimension, one arrives to a sequence of singular problems set in a 2D domain. The mathematical tools of such problems have been exposed in [4,19]. Here, we derive a variational method from which we propose an original finite element numerical approach to solve the problem. Numerical experiments are also shown to illustrate that the method is able to capture the singular part of the solution. This approach can also be viewed as a generalization of the Singular Complement Method to three-dimensional problem.

Fractional Vector Cross Product in Euclidean 3-Space

In this research a new definition of fractional vector cross product of two vectors in Euclidean 3-space is presented. Using this new definition the formulae for Euclidean norm, fractional triple vector cross product, curl and divergence of fractional vector cross product of an electromagnetic vector field is discussed. In particular cases, all the properties satisfy definition of standard vector cross product for standard orthogonal basis of R3. The new definition has application in radiation characteristic in micro-strip antenna and can be applied in other branches of mathematics and physics.

Supercurrent and electromotive force generations by the Berry connection from many-body wave functions

The velocity field composed of the electromagnetic field vector potential and the Berry connection from many-body wave functions explains supercurrent generation, Faraday’s law for the electromotive force (EMF) generation, and other EMF generations whose origins are not electromagnetism. An example calculation for the EMF from the Berry connection is performed using a model for the cuprate superconductivity.

Characteristics of electromagnetic vector field generated from rock fracturing

Rock fracturing is often accompanied by electromagnetic phenomenon. As a vector field, in addition to the intensity that is widely concerned, the generated electromagnetic field also has obvious directionality. To this end, a set of electromagnetic antennas capable of simultaneous three-axis measurement is used to monitor the electromagnetic vector field generated from rock fracturing based on Brazilian tests. The signal amplitude on each axis can represent the magnitude of actual magnetic flux density component on the three axes. The intensity and directional characteristics of electromagnetic signals received at different positions are studied using vector synthesis. The directionality of electromagnetic radiation measured using a three-axis electromagnetic antenna shows that the direction of the magnetic flux intensity generated by rock fracturing tends to be parallel to the crack surface, and the measured signal intensity is greater in a direction closer to the crack surface.

Electromagnetic field in a conducting medium modeled by the fractional Ohm’s law

Classical telegrapher’s equations for electromagnetic field in a conducting medium, which are the consequence of coupling Maxwell’s equations, charge conservation law and Ohm’s law, are generalized by modeling medium’s conducting properties using two types of fractional Ohm’s laws, that include terms accounting for instantaneous and hereditary contribution of electric field to current density, with the hereditary term expressed either through the fractional integral or derivative. Solving the initial value problem for the above mentioned system of equations, the electromagnetic field vectors are obtained in terms of convolution of Green’s function with the initial spatial distribution of electromagnetic field vector describing the evolution of electromagnetic field. It is shown that the propagating nature of the electromagnetic field is due to distributional nature of Green’s function.

Coherence of Ion Cyclotron Resonance in Damped Ion Cyclotron Waves in Space Plasmas

Abstract Ion cyclotron resonance is one of the fundamental energy-conversion processes through field–particle interaction in collisionless plasmas. However, the key evidence for ion cyclotron resonance (i.e., the coherence between electromagnetic fields and the ion phase-space density) and the resulting damping of ion cyclotron waves (ICWs) has not yet been directly observed. Investigating the high-quality measurements of space plasmas by the Magnetospheric Multiscale (MMS) satellites, we find that both the wave electromagnetic field vectors and the bulk velocity of the disturbed ion velocity distribution rotate around the background magnetic field. Moreover, we find that the absolute gyrophase angle difference between the center of the fluctuations in the ion velocity distribution functions and the wave electric field vectors falls in the range of (0, 90)°, consistent with an ongoing energy conversion from wave fields to particles. By invoking plasma kinetic theory, we demonstrate that the field–particle correlation for the damped ICWs in our theoretical model matches well with our observations. Furthermore, the wave electric field vectors ( δ E wave , ⊥ ′ ), ion current density (δ J i,⊥), and energy transfer rate ( δ J i , ⊥ · δ E wave , ⊥ ′ ) exhibit quasiperiodic oscillations, and the integrated work done by the electromagnetic field on the ions is positive, indicating that ions are mainly energized by the perpendicular component of the electric field via cyclotron resonance. Therefore, our combined analysis of MMS observations and kinetic theory provides direct, thorough, and comprehensive evidence for ICW damping in space plasmas.

Invariance of the Electromagnetic Field Vectors Obtained in Course of the Lorentz Transformation Characteristic for the Relativistic Theory

The invariance of several new component electromagnetic-field vectors with respect to the Lorentz transformation has been demonstrated in the paper. The formalism of the classical relativistic mechanics has been applied in examining both the time-square variable of the field, as well as the square-values of the position coordinates of a moving particle.

Wideband Electromagnetic Field Vector Antenna Array Technique and Direction Finding Algorithm

Wideband (UWB) technology has been widely used in ultra-wideband wireless communication, radar detection and other fields because of its advantages such as wide working frequency band, fast transmission rate and accurate positioning. This paper mainly studies the broadband electromagnetic field vector antenna array technology and direction finding algorithm. In this paper, the structure of a broadband resonant antenna unit is designed. The antenna unit adopts the form of printed antenna, which has both the advantages of planar antenna structure and wider bandwidth. For array antenna amplitude-phase error exists when the ideal direction, of the environment theory analyzes the mutual coupling and antenna array yuan border effect influence on beam shaper MUSIC algorithm, this paper proposes a anti-interference antenna phase characteristic difference of the calibration method of using 3 d electromagnetic simulation software HFSS, the mutual coupling matrix calculation, the amplitude-phase error correction, and has carried on the MATLAB simulation, the simulation results show that the method of direction finding pitching Angle error of less than 1, the direction finding azimuth error is less than 2, can be used for the beidou anti-interference antenna of direction finding.

Transient electromagnetic singularities in random three-dimensional optical fields.

We show that on all generic circular or elliptical paths in a random three-dimensional electromagnetic field, the electric and magnetic field vectors generate a cylinder throughout most of the optical cycle. At some point in the cycle, however, this cylinder transforms into a twisted ribbon with two sequential 180° twists. This ribbon exists for a short time and then unwinds, regenerating the cylinder. We discuss how and why these structures form and what determines their lifetimes.

Magnetic helicity and normal electromagnetic vortex filament flows under the influence of Lorentz force in MHD

In this paper, we attempt to introduce a new approach to determine the magnetic helicity and energy dissipation of the normal electromagnetic vortex filaments in magnetohydrodynamics (MHD). We successfully compute the vector potential and magnetic helicity of Frenet–Serret vectors and associated electromagnetic fields in the existence of the Lorentz force. We further describe a set of differential equations relating the magnetic vector potential of the electromagnetic vector fields and the Godbillon–Vey helicity model. Then, we focus on the time evolution of the normal electromagnetic field lines in MHD to evaluate the evolution of the magnetic helicity and energy dissipation theoretically. As a result, we obtain analytical solutions and numerical simulations of the time evolution equations of both geometric quantities as well as the magnetic and electric field vectors.

Optical magnetic helicity with binormal electromagnetic vortex filament flows in MHD

In this paper, we construct new efficient insight into the understanding of the configurations of the binormal electromagneto-vortex formation and their consequences in the energy dissipation and magnetic helicity in magnetohydrodynamics (MHD). Firstly, we introduce new formulations of the magnetic helicity of the Lorentz force of the Serret–Frenet frame vectors and associated electromagnetic vector fields of the binormal electromagnetic field lines E − B. Then, we investigate the Godbillon–Vey helicity model. We also compute the time evolution of the binormal electromagnetic field lines of the Frenet–Serret vectors and associated geometric quantities in MHD. Then, we determine a set of partial differential equation systems describing the Hall effect, which establishes the time evolution relation between the binormal electromagnetic field lines and magnetic vector potential in MHD. Finally, for a better comprehension of the time evolution of the binormal electromagnetic field lines, we consider the traveling wave transformation and the Riccati differential equation system to evaluate the evolution of the magnetic helicity and energy dissipation based on the calculation of the theoretical models.

Relativity: photon

For the case of interaction of polarized light with an analyzer (a polarizing device), an experimental scheme based on the Feynman idea of path integrals is proposed. Real and virtual photons are considered in the context of the Lenz rule (in terms of constructive and destructive induction). The Planck formula for the photon energy in the format of a verbal description is considered. The complexity of identifying the wave description of the photon with the ideas of the Ancient Greeks about elementary particles is shown. From the point of view of chronogeometry, it is shown that the stationary observer does not exist at the point of intersection of the cone of the past and the future, but in the time interval separating these regions. It is proposed to consider the fluctuations of the physical vacuum as a relic of the process of permanent inflation according to Linde. Based on the assumption of the self-measurement of the Universe, the quantum Zeno effect, and Hawking’s idea of the Universe being a quantum object with the Nth sum of Feynman stories, it is assumed that the history of the Universe is deterministic. From the perspective of the orthogonality of the electromagnetic field vectors E and B, the Heisenberg equation of the form Δp × Δx = ħ/2 is considered. A thought experiment is considered showing the complexity in describing the interaction of a photon with an electron of an atom from the point of view of the classical interaction of an electromagnetic wave with an antenna device. It is proposed to consider the absorption of a photon by an electron as its inertial collapse on an atom.

Magnetic helicity and electromagnetic vortex filament flows under the influence of Lorentz force in MHD

This paper is intended to present a useful insight into the comprehension of the configurations of electromagneto-vortex formation and their implications in the magnetic helicity and energy dissipation in magnetohydrodynamics (MHD). We introduce the formulations of magnetic helicity of the Lorentz force of the Serret–Frenet frame vectors and associated electromagnetic vector fields E − B firstly. Then, we investigate the Godbillon–Vey helicity model and figure out the intrinsic geometric characterizations of the electromagnetic vector fields and magnetic vector potential under the influence of vanishing magnetic helicity. We also compute the time evolution of the electromagnetic field lines of the Frenet–Serret vectors and associated geometric quantities in MHD. Then, we determine a set of partial differential equation systems describing the Hall effect, which establishes the time evolution relation between the electromagnetic field lines and magnetic vector potential in MHD. Finally, for a better comprehension of the time evolution of the electromagnetic field lines, we improve an appropriate approach to evaluate the evolution of the magnetic helicity and energy dissipation based on calculations on theoretical models.

Retarded resonance Casimir\u2013Polder interaction of a uniformly rotating two-atom system

We consider a two-atom system uniformly moving through a circular ring at an ultra-relativistic speed and weakly interacting with the common quantum fields. Two kinds of fields are introduced here: a massive free scalar field and electromagnetic (EM) vector fields. The vacuum fluctuations of the quantum fields give rise to the resonance Casimir–Polder interaction (RCPI) in the system. Using the quantum master equation formalism, we calculate the second-order energy shift of the entangled states of the system. We find two major aspects of RCPI in a circular trajectory. The first one is the presence of the centripetal acceleration, which gives rise to non-thermality in the system, and secondly, due to the interaction with the above fields, the energy shift for RCPI is retarded in comparison with the massless scalar field. The retardation effect can die out by decreasing the centripetal acceleration and increasing the Zeeman frequency of the atoms. We also show that this phenomenon can be observed via the polarization transfer technique. The coherence time for the polarization transfer is calculated, which is different for the different fields.

Second gradient electrodynamics: A non-singular relativistic field theory

In this paper, we give the covariant formulation of second gradient electrodynamics, which is a generalized electrodynamics of second order including derivatives of higher order. The relativistic form of the field equations, the energy–momentum tensor and the Lorentz force density are presented. For a point charge, the generalized Liénard–Wiechert potentials and the corresponding electromagnetic field strength tensor are given as retarded integral expressions. Explicit formulas for the electromagnetic potential vector and electromagnetic field strength tensor of a uniformly moving point charge are found without any singularity and discontinuity. In addition, a world-line integral expression for the self-force of a charged point particle is given. The relativistic equation of motion of a charged particle coupled with electromagnetic fields in second gradient electrodynamics is derived, which is an integro-differential equation with nonlocality in time. For a uniformly accelerated charge, explicit formulas of the self-force and the electromagnetic mass, being non-singular, are given. Moreover, the wave propagation and the dispersion relations in the vacuum of second gradient electrodynamics are analyzed. Three modes of waves were found: one non-dispersive wave as in Maxwell electrodynamics, and two dispersive waves similar to the wave propagation in a collisionless plasma.

A Tutorial on the Classical Theories of Electromagnetic Scattering and Diffraction

AbstractStarting with Maxwell’s equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector electromagnetic fields. The famous Sommerfeld solution to the problem of diffraction from a perfectly conducting half-plane is elaborated. Far-field scattering of plane waves from obstacles is treated in some detail, and the well-known optical cross-section theorem, which relates the scattering cross-section of an obstacle to its forward scattering amplitude, is derived. Also examined is the case of scattering from mild inhomogeneities within an otherwise homogeneous medium, where, in the first Born approximation, a fairly simple formula is found to relate the far-field scattering amplitude to the host medium’s optical properties. The related problem of neutron scattering from ferromagnetic materials is treated in the final section of the paper.

Electromagnetic wave absorbing performance of 3D printed wave-shape copper solid cementitious element

Electromagnetic wave (EMW) pollution impairs the performance of equipment, facilities, information security, and human health. Ordinary, plain cementitious composite has limited EMW-reflecting capacity. To correct this, a macrostructure EMW absorbing element has been developed to reduce EMW pollution. As conventional casting of macrostructures is not cost-effective and lacks quality because of the demand for special formwork, 3D printing technology offers greater design flexibility, higher efficiency, and improved mechanical properties. Moreover, the surface texture of 3D-printed material exhibits natural corrugation to enhance EMW reflection further. In this study, novel wave-shaped EMW absorbing elements were fabricated using 3D cementitious printing technology. The EMW absorbing performance was analyzed by the naval research laboratory (NRL) system in the range of 1 GHz–18 GHz. Significant improvement of reflectivity was observed, especially in the low-frequency range. The optimum configuration was identified through effectiveness evaluation to be a K3 sample with 45 mm of heave height and 2/3 tan(θ), exhibiting a minimum reflectivity −43.7 dB, mean reflectivity −25 dB, and an absorbing bandwidth of 18 GHz. The experimental reflectivity was also simulated by the finite element method, which agrees with the experimental results. The synthetic vector electromagnetic field distribution was also studied to explore space impedance characteristics. Moreover, the finite element method attempted to correct drawbacks in experiments, including multiple direction reflection measurement and wave-number interruption. Based on simulation calibration, the influence of wave-shaped parameters (heave height and tangent value) upon EMW absorbing capacity was induced accurately.

Polarization effects in Kerr black hole shadow due to the coupling between photon and bumblebee field

We present firstly the equation of motion for the photon coupled to a special bumblebee vector field in a Kerr black hole spacetime and find that the propagation of light depends on its polarization due to the birefringence phenomenon. The dependence of black hole shadow on the light's polarization is dominated by the rotation of black hole. In the non-rotating case, we find that the black hole shadow is independent of the polarization of light. However, the status is changed in the rotating case, in which the black hole shadow depends on the light's polarization and the coupling between bumblebee vector field and electromagnetic field. These features of black hole shadow casted by polarized lights could help us to understand the bumblebee vector field with Lorentz symmetry breaking and its interaction with electromagnetic field.