Electromagnetic Field Equations Research Articles

Symmetry and invariance

The concept of invariance relates to both the intrinsic symmetries of physical systems and the symmetry of the set of equivalent reference frames used to observe them. Standard algebraic expressions for electrostatic potentials and crystal-field effective operators display both types of invariance. The concept of a reference frame is generalized to that of an ‘observing system’, which can, for example, be the basis states of a quantum system. This idea is related to Racah’s mathematical machinery for evaluating the matrix elements of many-electron 4f open-shell states in lanthanide ions. It is argued, on the basis of computational flexibility and ease of interpretation, that all equations that represent physical processes be expressible in terms of invariants of the set of observing systems. This ‘Principle of Invariance’ is then applied to special relativity, leading to a simple geometrical interpretation of Maxwell’s electromagnetic field equations. The close relationship between Dirac’s relativistic wave equation and Maxwell’s equations is then exposed. This leads to the concept of an inner structure of space-time and the reinterpretation of particle spin. Finally, it is shown that the use of invariants in relativity theory identifies a set of observing systems with a higher symmetry than that of Minkowski space-time.

The coherent generation of the photon pairs by a stream of excited atoms passing through the cavity

The problem of the coherent generation of the entanglement photon pairs by an ensemble of the two-level atoms passing through the cavity is studied. The dependence of the generation rate of the photon pairs as a function of the coherent states of the atomic stream is established. Considering that the flying time of the atoms passing through the cavity is less than decay time, a new method of the elimination of atomic variables from the system is proposed. The master equation for multimode cavity electromagnetic field is obtained. Using the Fokker–Planck equations, the steady state solution of this master equation is studied. The quantum properties of the multimode electromagnetic field are analyzed, using the non-diagonal P representation for su(1,1) symmetry.

Modeling and Numerical Simulation of a Brushless Permanent-Magnet DC Motor in Dynamic Conditions by Time-Stepping Technique

A method of modeling and numerical simulation of a brushless permanent-magnet dc motor using time-stepping finite-element technique is presented. In the proposed model, the electromagnetic field equations, the stator circuit equation, and the motion equation are solved simultaneously at each time step; thus, the eddy-current effect, the saturation effect, the rotor movement, and the nonsinusoidal quantities can all be taken into account directly in the system of equations. Dynamic conditions of the motor at starting, step voltage variation, and load torque changes are investigated using the proposed dynamic model.

The optical near-field speckles and their first order statistics on the basis of the integral equations of electromagnetic field

From Helmholtz equation of the harmonic electromagnetic waves, the integral equations of the light field at the medium boundaries are obtained by use of the Green's theorem and are discretized into linear equation set with the values of the light field and its derivative as the unknowns. On solving the linear equation set, we realize the rigorous computations of the light fields at the boundaries. Then the intensities of the light waves scattered by the random self-affine fractal surfaces in the optical near-field are calculated, and the propagation characteristics, the evolutions of the contrast and the intensity probability density function of the near-field speckles are studied in detail. The near-field speckles are much different from the conventional speckles in the diffraction regions and in the imaging systems. There are obvious local fluctuations in the intensity distributions of the near-field speckles and such fluctuations disappear after propagating a distance of one wavelength from the medium surfaces. For the random surfaces with smaller lateral correlation lengths, the speckle contrasts approach the saturation values and the speckle fields approach Gaussian distribution within the near-field, while for the random surfaces with larger lateral correlation lengths, such evolutions become comparatively slow.

On a quaternionic Maxwell equation for the time-dependent electromagnetic field in a chiral medium

Maxwell's equations for the time-dependent electromagnetic field in a homogeneous chiral medium are reduced to a single quaternionic equation. Its fundamental solution satisfying the causality principle is obtained which allows us to solve the time-dependent chiral Maxwell system with sources.

Electromagnetic field radiated by lightning to tall towers: Treatment of the discontinuity at the return stroke wave front

Recently, engineering return stroke models were extended to take into account the presence of an elevated strike object, which was modeled as an ideal uniform transmission line. We show in this paper that the current distribution associated with these extended models exhibits a discontinuity at the return stroke wave front, which cannot be considered to be physically plausible. This discontinuity arises from the fact that the current injected into the tower from its top is reflected back and forth at its ends and portions of it are transmitted into the channel; these transmitted pulses, which are supposed to travel at the speed of light, catch up with the return stroke wave front traveling at a lower speed, and no current is allowed to flow in the leader region above the front. This discontinuity needs to be carefully treated when calculating the radiated electromagnetic field through an additional term in the electromagnetic field equations, the so‐called “turn‐on” term. We additionally derive a general analytical formula describing the turn‐on term associated with this discontinuity for various engineering models. We present simulation results illustrating the effect of the turn‐on term on the radiated electric and magnetic fields for an elevated strike object of height h = 168 m, corresponding to the Peissenberg tower in Germany. Finally, possible modifications to engineering models are suggested in order to eliminate this discontinuity.

Influence of a Kerr-Like Medium and the Detuning Parameter on the Statistical Aspects of the Intensity-Dependent-Coupling Hamiltonian

We study the interaction between a one-mode electromagnetic field and a two-level atom in the presence of a Kerr-like medium when the atom is prepared initially in the momentum eigenstate. The wave function is calculated by using the Schrodinger equation for a coherent electromagnetic field and an atom in the excited state. The effects of the Kerr-like medium and the detuning parameters on the statistical aspects of the intensity-dependent-coupling Hamiltonian such as, atomic momentum increment, momentum diffusion, the radiation force, and the field entropy are calculated. We investigate the effect of the detuning, Kerr-like medium and photon number operator on the field entropy.

ON SAMPLING-BIORTHOGONAL TIME-DOMAIN SCHEME BASED ON DAUBECHIES COMPACTLY SUPPORTED WAVELETS

The multi-resolution time domain (MRTD) technique for electromagnetic field equations was proposed by Krumpholz, Katehi et al., using Battle-Lemarie wavelets. The basis principle behind the MRTD is the wavelet-Galerkin time domain (WGTD) approach. Despite its effectiveness in space discretization, the complexity ofthe MRTD makes it unpopular. Recently, the WGTD was significantly simplified by Cheong et al. based on the approximate sampling property ofthe shifted versions ofthe Daubechies compactly supported wavelets. In this paper, we provide a rigorous analysis ofthe MRTD, employing positive sampling functions and their biorthogonal dual. We call our approach as the sampling biorthogonal time-domain (SBTD) technique. The introduced sampling and dual functions are both originated from Daubechies scaling functions of order 2 (referred as to D2), and form a biorthonormal system. This biorthonormal system has exact interpolation properties and demonstrates superiority over the FDTD in terms ofmemory and speed. Numerical examples and comparisons with the traditional FDTD results are provided.

NUMERICAL SIMULATION OF MICROWAVE HEATING ON CHEMICAL REACTION IN DILUTE SOLUTION

currently, microwaves are widely used in chemical industry to accelerate chemical reactions. Some research results have shown that microwave heating can significantly accelerate the reaction. However, there is a need to develop efficient methods to improve the design of microwave applicator in chemistry. In this paper, a numerical model was presented to study the microwave heating on saponification reaction in test tube, where the reactant was considered as a mixture of dilute solution. The coupled electromagnetic field equations, reaction equation (RE) and heat transport equation (HTE) were solved by using finite difference time domain (FDTD) method. To overcome the difficulty of long time calculation with FDTD, two types of techniques were employed. To verify the methods, the temperature rising in the test tube and transmitted power through the transversal electromagnetic (TEM) cell were measured and compared with the computational results. Good agreement can be seen between the measured and calculated results.

Comparison of different techniques for the FLUENT $^{\copyright}$ -based treatment of the electromagnetic field in inductively coupled plasma torches

A new technique for using the CFD commercial code FLUENT\(^{\copyright}\) to simulate inductively coupled plasma torches by means of two-dimensional axisymmetric models is presented. The method is based on an external user-defined function (UDF) which fully solves the electromagnetic field equations, letting the FLUENT\(^{\copyright}\) built-in module calculate only the plasma temperature and velocity fields inside the torch region. In this framework, computations have been carried out for LTE, optica lly thin argon plasmas at atmospheric pressure, using extended grid models with either magnetic dipole or vanishing vector potential boundary conditions for the electromagnetic field. It is shown that our newly developed technique is up to 60% faster on each iteration than that using user-defined scalars (UDS) previously proposed in the literature, as the need of solving flow field equations also outside the plasma zone is eliminated. Calculations are also performed using exact integral boundary conditions for the vector potential, as given by the standard electromagnetic field approach, taking into account the effects of both exciting and induced currents. The corresponding results are compared with the approximate ones obtained by employing extended grid models, showing that for small radial dimensions of the electromagnetic field domain, the magnetic dipole boundary conditions give more realistic solutions than those assuming a vanish ing vector potential.

Source function and dyon’s field in Clifford number representation for electrodynamics

Clifford number representation for linear electrodynamics with dyon sources is considered. Source function for the appropriate system of the first order equations for electromagnetic field is obtained. The field of an arbitrary moving point dyon is derived.

Relativistic Poynting Jets from Accretion Disks

A model is derived for relativistic Poynting jets from the inner region of a disk around a rotating black hole that is initially threaded by a dipole-like magnetic field. The model is derived from the special relativistic equation for a force-free electromagnetic field. The "head" of the Poynting jet is found to propagate outward with a velocity that may be relativistic. The Lorentz factor of the head is Γ = [B/(8π)2ρextc2]1/6 if this quantity is much larger than unity. For conditions pertinent to an active galactic nuclei, Γ ≈ 8(10/)1/3(B0/103 G)1/3(next/1 cm-3)-1/6, where B0 is the magnetic field strength close to the black hole, ρext = next is the mass density of the ambient medium into which the jet propagates, = r0/rg > 1, where rg is the gravitational radius of the black hole, and r0 is the radius of the O-point of the initial dipole field. This model offers an explanation for the observed Lorentz factors of ~10 of parsec-scale radio jets measured with very long baseline interferometry.

Three-dimensional effects in the modelling of ICPTs

In this paper, a 3-D numerical study is performed to investigate the effects of the induction coil design and torch geometry on the characteristics of argon discharges in inductively coupled plasma torches working at atmospheric pressure. Simulations are performed by means of the commercial code FLUENT\(^\copyright\) suitably customized to solve the electromagnetic field equations in the frame of an extended grid model. Steady state continuity, momentum and energy equations are solved for optically thin plasmas under the assumption of LTE and laminar flow. Results are presented for different coil geometries includin g conventional helicoidal, double-stage and planar configurations. The physical behaviour of a torch with elliptical cross-section is also analyzed. Additionally, the effects on plasma temperature and velocity fields of reducing the post-coil length in a conventional torch are shown.

Three-dimensional effects in the modelling of ICPTs

In this paper, we numerically investigate the 3-D effects of different flow operating conditions and of complete or simplified treatments of the electromagnetic field on the characteristics of Ar and Ar/N 2 discharges in inductively coupled plasma torches working at atmospheric pressure. Simulations are performed by means of the commercial code FLUENTE suitably customized to solve the electromagnetic field equations in the frame of an extended grid model. Steady state continuity, momentum and energy equations are solved for optically thin plasmas under the assumption of LTE and laminar flow. Results of parameterization on the net amount of power dissipated in the discharge, frequency of the RF generator, flow rate distribution of inlet gases and swirl velocity are presented, showing the impact of these parameters on the fluid dynamic and electromagnetic behaviour of the plasma.

A proposed theory of the phenomenon of ball lightning

The paper describes a solution of the electromagnetic field equations representing the basic wave equation in spherical coordinates, characterized by extremely strong electric fields at the center giving rise to a local ionized region of the ambient gas. The solution describes the localized fields as a standing wave of radial direct current (DC) pulses in an electrodeless spherical transmission line forming a floating ‘free space circuit’. The presentation describes a sequence of processes initiated by excitation of the spherical circuit by atmospheric discharges, followed by a parametric type conversion of the prestrike electric energy stored in the charged cloud, via magnetic energy during the strike, to poststrike electric energy stored in the spherical system as the final state. Most of the stored energy is localized outside the ionized region inside which small conduction losses as well as emission of visible light cause decay of the trapped energy so that the phenomenon dies out after some time. The resemblance to the characteristics of ball lightning is immediately apparent. The described energy conversion process is not a singular or rare event but is bound to happen regularly as the aftermath of any atmospheric discharge; otherwise Maxwell’s field equations would be violated. But apparently, only a small fraction of the events give rise to ball lightning, a fact attributed to the demand of additional conditions to be satisfied in order for the ionization to happen. The paper discusses the expected characteristics of the described phenomenon, which are shown to be compatible with the bulk of typical ball lightning observations, with no obvious contradictions. The parametric type conversion process, which appears to be an unavoidable aftermath of atmospheric discharges of any kind, might possibly give rise to a wider group of phenomena than just ball lightning such as the often observed higher altitude atmospheric light phenomena of various kind.

TM mode in inhomogeneous slab waveguide as an exactly solvable oscillator-like Hamiltonian

In all practical waveguides, the index of refraction produced by a diffusion process (e.g. ion exchange) is inhomogeneous. For determining the optical characteristics, the numerical approach is suitable in the general case. In this paper we will obtain a mathematical analogy between a quantum mechanical harmonic oscillator-like Hamiltonian and the Helmholtz equation for TM-mode electromagnetic fields propagating in the slab waveguide. Using this approach, oscillator-like index of refraction profiles for exact solutions of the Helmholtz equation are proposed.

Super-high-frequency heating of a composite material of a periodic structure

In this work there is given the solution of a problem of a laminated composite and of a fibrous one-way directed composite with regular arrangement of fibres. Such structures are the simplest technologic ones and are taken as model objects. In the process of solution there were used the known mathematical methods of heat conductance and electromagnetism [5], [6]. Derivation of Maxwell's averaged equations and the general variated formulation of the problem on a cell for a composite insulator and conductor are given in [7]. Averaging of Maxwell's equations for monochromatic electromagnetic fields is considered in [8]. The general scheme of the solution of the problem of heating of a composite material of periodical structure in a high-frequency electromagnetic field is considered in [9].

NEW METHOD FOR DERIVATION OF LORENTZ TRANSFORMATION

in the modern field of heavy ion atomic physics, determined through Lorentz transformation [W. Greiner 1997]. At high energies one must investigate the relative wave equations. This means equations, which are invariant under Lorenz transformation. The Lorentz transformation is so important, that it needs, to be derived on a more logical basis. Many textbooks and research papers have derived Lorentz transformation by different postulates [Anderson, J.L. 1967][G. Nadean 1962][H.A. Atwater 1974], which are not treated electro-dynamically this paper exhibits a method of finding the Lorentz transformation by exploiting the Maxwell's famous equations of the electromagnetic field equations

Fast analysis of bounces on power/ground planes using even-odd partition

A novel method for analyzing the bounces on structure of parallel power/ground planes by using the even-odd mode partition is presented in this paper. Based on the distributed RLCG circuit model derived from the two dimensional electromagnetic field equations of the power/ground planar structure, this method can speed up the circuit simulation of the bounces on power/ground planes by using even-odd mode partition. Furthermore, the method can be used to evaluate the effects of the terminated decoupling capacitors and the hole structures on power/ground plane. The numerical examples demonstrate that the method has both high efficiency and good precision.

Characteristic Analysis of a Double Squirrel-Cage Induction Motor by Finite Element Method

This paper investigated a method for the analysis of characteristics of 3-phase double squirrel-cage induction motor by using two-dimensional Finite Element Method. Proposed method is that conductance in the double squirrel-cage rotor is converted into the electric circuit, and the circuit equations through the outside rotor bar and the inside one are solved simultaneously with the equations in electromagnetic field by two-dimensional Finite Element Method. The calculated speed-torque and speed-current characteristics of the double squirrel-cage induction motor were good agreement with the measured ones on condition of the range of the slip which generally used.