Electromagnetic Field Equations Research Articles

Simulation and validation of the effective power absorbed by a non-equilibrium plasma flow inside the medium-power inductively coupled plasma wind tunnel

A non-equilibrium magneto-hydrodynamic model coupled with a power absorption model was established to calculate the effective power absorbed by the plasma flow inside a 110 kW medium-power inductively coupled plasma wind tunnel. This magneto-hydrodynamic model takes into account the coupling of Navier–Stokes equations, electromagnetic field equations, five species and eight chemical reactions of nitrogen, and a four-temperature model. Moreover, the power absorption model not only considers the power loss from the power supply system but also the coupling efficiency between plasma and the inductive coils. First, the anode loss of an electronic tube and its oscillator circuit efficiency is calculated, respectively, to obtain the total power loss from a radio frequency power supply system. Second, a transformer circuit model of the inductively coupled plasma (ICP) is established to calculate the coupling efficiency between the coil and plasma. Third, the effective power absorbed by the plasma flow and the pathways of the power losses of a medium-power ICP wind tunnel are obtained and discussed. Finally, the flow-field properties of the plasma flow, which are simulated by solving the Navier–Stokes equations coupled with the power absorption model, are obtained and analyzed. Furthermore, the simulated results are compared with corresponding experimental data, and they agree well with each other. It is found that the power loss of the electron tube oscillator accounts for 40%. It is the most dominant part of the total power loss. The effective power absorbed by a plasma flow is about 33.6% for the 110-kW inductively coupled plasma wind tunnel.

Galilean Bulk-Surface Electrothermodynamics and Applications to Electrochemistry.

In this work, the balance equations of non-equilibrium thermodynamics are coupled to Galilean limit systems of the Maxwell equations, i.e., either to (i) the quasi-electrostatic limit or (ii) the quasi-magnetostatic limit. We explicitly consider a volume Ω, which is divided into Ω+ and Ω- by a possibly moving singular surface S, where a charged reacting mixture of a viscous medium can be present on each geometrical entity (Ω+,S,Ω-). By the restriction to the Galilean limits of the Maxwell equations, we achieve that only subsystems of equations for matter and electromagnetic fields are coupled that share identical transformation properties with respect to observer transformations. Moreover, the application of an entropy principle becomes more straightforward and finally helps estimate the limitations of the more general approach based the full set of Maxwell equations. Constitutive relations are provided based on an entropy principle, and particular care is taken in the analysis of the stress tensor and the momentum balance in the general case of non-constant scalar susceptibility. Finally, we summarise the application of the derived model framework to an electrochemical system with surface reactions.

Theory of Edge Effects and Conductance for Applications in Graphene-Based Nanoantennas

In this paper, we present a theory of edge effects in graphene for its applications to nanoantennas in the THz, infrared, and visible frequency ranges. The novelty of the presented model is reflected in its self-consistency, which is reached due to the formulation in terms of dynamical conductance instead of ordinary surface conductivity. The physical model of edge effects is based on using the concept of the Dirac fermion and the Kubo approach. In contrast with earlier well-known and widely used models, the surface conductance becomes non-homogeneous and non-local. The numerical simulations of the spatial behavior of the surface conductance were performed in a wide range of values, known from the literature, for the graphene ribbon widths and electrochemical potential. It is shown that if the length exceeds 800 nm, our model agrees with the classical Drude conductivity model with a relatively high degree of accuracy. For rather short lengths, the conductance exhibits a new type of spatial oscillations, which are not present in the ordinary conductivity model. These oscillations modify the form of effective boundary conditions and integral equations for electromagnetic field at the surface of graphene-based antenna. The developed theory opens a new way for realizing electrically controlled nanoantennas by changing the electrochemical potential via gate voltage. The obtained results may be applicable for the design of different carbon-based nanodevices in modern quantum technologies.

Simulation of the Finite-Difference Time-Domain (FDTD) Method in 2-Dimensional Electromagnetic Wave Propagation in Absorption Media

This research reviewed Maxwell’s equations and Numerical Discretization using the Finite Difference Time Dependent (FDTD) method. First, Maxwell’s equations are introduced in a linear dielectric medium for 1-dimensional and 2-dimensional configurations, which are built based on the polarization between Transverse-Magnetic (TM) and Transverse-Electric (TE). Then, it presented the frequency-dependent absorption boundary conditions for the electromagnetic field equations used in that configuration. In addition, the correlation between the variation of the grid with respect to the x-axis and y-axis, as well as the variation of the dielectric constant of the medium on the propagation of electromagnetic waves, has been studied in this paper. A numerical result provides an excellent accuration and approximation in establishing boundary conditions for wave spacing in adsorbed media at 1-dimensional and 2-dimensional configurations

Maxwell Equations in Homogeneous Spaces with Solvable Groups of Motions

The classification of exact solutions of Maxwell vacuum equations for the case where the electromagnetic fields and metrics of homogeneous spaces are invariant with respect to the motion group G3(VII) was completed. All non-equivalent exact solutions of Maxwell vacuum equations for electromagnetic fields and spaces with such symmetry were obtained. The vectors of the canonical frame of a homogeneous space of type VII according to the Bianchi classification and the electromagnetic field potentials were found.

Stochastic formalism for U(1) gauge fields in axion inflation

We develop the stochastic formalism for U(1) gauge fields that has the Chern-Simons coupling to a rolling pseudo-scalar field during inflation.The Langevin equations for the physical electromagnetic fields are derived and the analytic solutions are studied. Using numerical simulation we demonstrate that the electromagnetic fields averaged over the Hubble scale continuously change their direction and their amplitudes fluctuate around the analytically obtained expectation values.Though the isotropy is spontaneously broken by picking up a particular local Hubble patch, each Hubble patch is understood independent and the isotropy is conserved globally byaveraging all the Hubble patches.

Frequency dependencies of the characteristics of an inductively coupled radiofrequency discharge at reduced pressure

The dependence of parameters of an inductively coupled radiofrequency plasma on the electromagnetic field frequency in range 0.25–40 MHz at reduced pressure (113 Pa) was studied. The study was carried out in a 2D axisymmetric time-dependent setting, implemented in the Comsol multiphysics software package using the Navier–Stokes equations, continuity equation for electron density, electron energy density equation, ion density equation, metastable atom density equation, heat transfer equation, Maxwell and Poisson equations for electromagnetic fields. The distributions of the plasma parameters at the output of the discharge tube in dependence on electromagnetic field frequency were obtained. It was found that the dependences of the electron density, electron temperature, and gas temperature on the field frequency are non-linear. The maximum value of these quantities were achieved at different frequencies depending on the discharge power. A mechanism relating the frequency and power to the shift in the positions of the maxima of these plasma parameters is proposed.

1-D FEM-Based Approach for Extracting Dimension-Independent Material Properties of Mn-Zn Toroidal Ferrite Cores

This article presents a finite element (FE) method (FEM)-based approach for identifying the dimension-independent magnetic and dielectric properties of Mn-Zn toroidal ferrite cores. Two 1-D axisymmetric FE models are used for solving the full-wave electromagnetic field equations in a toroidal ferrite core using either the electric field strength ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {E}$ </tex-math></inline-formula> ) or the magnetic field strength ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {H}$ </tex-math></inline-formula> ) as the variable. Impedance measurements are performed for the toroidal cores over a frequency range of 10 kHz–10 MHz. The FE models and the impedance measurements are combined with a non-linear least-squares algorithm for solving the inverse problem for extracting the dimension-independent values of complex permeability and complex permittivity. The extracted permeability is validated against the datasheet of the measured samples.

The Completeness of Classical Electromagnetic Theory

The core of classical electromagnetic field theory is Maxwell electromagnetic field equations. Each of its formulas is supported by experimental facts, and its mathematical logic is rigorous and self-consistent, which has been tested for a long time in application.Therefore, its correctness is beyond doubt. In this paper, on the premise of affirming the great significance and important contribution of Maxwell equations(ME), the possible problems and solutions are discussed. Since ME and its derived wave equation (MWE) are vectorized partial differential equations, it is difficult to solve them strictly. In this paper, the solutions of vectorized ME and vectorized MWE are discussed in depth, and the necessity of Hansen function analysis is illustrated before the concrete calculation of engineering structures. Another method is to use vector partial differential operator theory to derive the standard basic equations expressed by state functions, and change the traditional calculation in Euclid space to the calculation in wave function space. Singularities and singularity are also avoided in the process. This paper argues that the completeness and modernity of traditional electromagnetic theory can only be improved by introducing the concept of particle, because the wave field processed by ME is actually a quantum field of light. The motion equation of electromagnetic field in classical theory is ME. In quantum theory, the field vector is an operator, governed by ME. The photon theory successfully explained the photoelectric effect in a way that ME could not. But in the mainstream theory, the photon rest mass is equal to zero, which blocks the way to add particle concept to ME. In 1936, Proca equations assumed ≠0, and with the support of quantum electrodynamics(QED), ME was improved. In this paper, the Proca equations are approved and the Proca wave equation (PWE) is further derived. In short, it reflects the adherence to the concept of wave-particle duality. The extended Maxwell equations proposed by Chinese scientist recently should be emphasized and discussed in this paper.

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.

Thermodynamics of novel black holes in massive gravity coupled to nonlinear electrodynamics

By introducing a static and spherically symmetric geometry, we have solved the coupled electromagnetic and gravitational field equations in the presence of both, massive gravitons and nonlinear electrodynamics. The exact solutions show that massive gravity theory admits two novel classes of nonlinearly charged asymptotically AdS black holes. The black holes’ electric charge, mass, and other thermodynamic quantities have been calculated. Then, by use of a Smarr-type mass formula, it has been proved that the thermodynamical first law is valid for both the new massive black hole solutions. The black hole local stability has been investigated by use of the canonical ensemble and geometrical methods, separately. Through comparison of the results, we found that they are compatible provided that the HEPM or QII thermodynamic metrics are used. Global stability and Hawking–Page phase transition points have been studied by use of the grand canonical ensemble method and regarding the Gibbs free energy of the black holes.

Analysis of Electromagnetic Characteristics of a Novel Toroidal Acceleration Linear Motor

A high thrust density linear motor, which adopts a novel toroidal structure, applying to load acceleration in confined space is proposed. The basic structure of the toroidal acceleration permanent magnet synchronous linear motor (TA-PMLSM) is depicted, both with its parameters listed. The main characteristics such as air gap magnetic density and electromagnetic thrust are discussed by establishing the electromagnetic field equation in the cylindrical coordinate system. And simulation comparison between the Halbach permanent magnet array and the classical radial one is also made to get a higher density of the magnetic and electromagnetic thrust. Compared with the conventional radial permanent magnet array, results show that the amplitude of back EMF of ring motor under the action of Halbach permanent magnet array has a better sinusoidal, the magnetic density of the air gap increases by 1.3 times, the thrust density increases by 1.42 times, and the main harmonic content of the two referred physical quantity decreases significantly.

Soliton-like solutions of nonlinear scalar and electromagnetic field equations in gravitational theory

In this work, exact analytical static spherical symmetric solutions to the nonlinear interacting electromagnetic and massless scalar field equations have been determined taking into account the proper gravitational field of elementary particles. The obtained results prove that all solutions of the Einstein equation and those of the interacting fields are regular with localized energy density. All non-zero components of the 4-vector potential are solutions to the inverted Painlevé-Gambier XI equation. Moreover, the total energy of interacting fields is limited and the total charge of elementary particles is finite. These solutions obtained are soliton-like and can be used as a model to describe the internal structure of elementary particles.

Seek of Polishing Transmission Efficiency Based on Modeling over Wireless Charging

Among electric vehicle charging technologies, wireless charging technology is undoubtedly a most convenient method, also needless to get refreshed and repaired as wires do. Nevertheless, it has long been a tough issue that the efficiency remains low, which causes great waste and too much heat even add to the possibility of fire emergency. Due to low charging efficiency and non-universal charging equipment, wireless charging equipment for electric vehicles has not been effectively promoted. Based on this, integrated circuit theory and electromagnetic field equation, this paper established electromagnetic coupling wireless charging circuit model, based on this model, the maximum wireless charging power transmission efficiency and the maximum horizontal offset and other issues are studied.

Large-scale ab initio simulation of light–matter interaction at the atomic scale in Fugaku

In the field of optical science, it is becoming increasingly important to observe and manipulate matter at the atomic scale using ultrashort pulsed light. For the first time, we have performed the ab initio simulation solving the Maxwell equation for light electromagnetic fields, the time-dependent Kohn-Sham equation for electrons, and the Newton equation for ions in extended systems. In the simulation, the most time-consuming parts were stencil and nonlocal pseudopotential operations on the electron orbitals as well as fast Fourier transforms for the electron density. Code optimization was thoroughly performed on the Fujitsu A64FX processor to achieve the highest performance. A simulation of amorphous SiO2 thin film composed of more than 10,000 atoms was performed using 27,648 nodes of the Fugaku supercomputer. The simulation achieved excellent time-to-solution with the performance close to the maximum possible value in view of the memory bandwidth bound, as well as excellent weak scalability.

Soliton-Like Spherical Symmetric Solutions to the Electromagnetic and Scalar Nonlinear Induction Field Equations in the General Relativity Theory

In this paper, we have used the static spherical symmetric metric. The parameter of the nonlinearity fields is included in the arbitrary function characterizing the interaction between the electromagnetic and scalar fields. Taking into account the own gravitational field of elementary particles, we have obtained exact static spherical symmetric solutions to the electromagnetic and scalar field equations of nonlinear induction. Considering all forms of the solution of Liouville equation, we proved that the metric functions are regular with localized energy density. Moreover, the total energy of the nonlinear induction fields is bounded and the total charge of the elementary particles has a finite value (soliton-like). In the flat space-time, soliton-like solutions exist.

Exact Static Plane Symmetric Soliton-Like Solutions to the Nonlinear Interacting Electromagnetic and Scalar Field Equations in General Relativity

This research work is related to soliton solutions considered as models that can describe the complex configuration of elementary particles from the study of the interactions of their fields. It is interested in the interaction of fields between two different elementary particles by expressing their physical properties. For that, we have obtained, exact static plane symmetric soliton-like solutions to the nonlinear equations of interacting electromagnetic and scalar fields taking into account the own gravitational field of elementary particles using the calibrated invariance function P(I). It has been proved that all solutions of the Einstein, nonlinear electromagnetic and scalar field equations are regular with the localized energy density. Moreover, the total charge of particles is finite and the total energy of the interaction fields is bounded. It have been emphasized the importance to the own gravitational field of elementary particles and the role of the nonlinearity of fields in the determination of these solutions. In flat space-time, soliton-like solutions exist but the total energy of the interaction fields is equal to zero. We have also shown that in the linear case, soliton-like solutions are absent.

A pedagogical review of the vacuum retarded dipole model of pulsar spin down

Abstract Pulsars are rapidly spinning highly magnetised neutron stars. Their spin period is observed to decrease with time. An early analytical model for this process was the vacuum retarded dipole (VRD) by Deutsch (1955, AnAp, 18). This model assumes an idealised star and it finds that the rotational energy is radiated away by the electromagnetic fields. This model has been superseded by more realistic numerical simulations that account for the non-vacuum like surroundings of the neutron star. However, the VRD still provides a reasonable approximation and is a useful limiting case that can provide some qualitative understanding. We provide detailed derivations of the spin down and related electromagnetic field equations of the VRD solution. We also correct typographical errors in the general field equations and boundary conditions used by Deutsch (1955, AnAp, 18).

On the Maximal Lp-Lq Regularity Theorem for the Linearized Electro-Magnetic Field Equations with Interface Conditions

On the Maximal Lp-Lq Regularity Theorem for the Linearized Electro-Magnetic Field Equations with Interface Conditions

Spatio-temporal properties of pulse propagation in a graphene quantum system

In this paper we have theoretically studied the spatial-temporal evolution of electromagnetic light propagation through a four-level graphene quantum system by using density matrix method and perturbation theory. The four-level graphene quantum medium interacted by an elliptical polarized coupling and a weak probe lights, respectively. We present the analytical solution for solving the Maxwell–Bloch equations for graphene and electromagnetic field in space and time domains. Then, we have analyzed the dynamic control of pulse propagation and optical dual switching in such a laser-driven quantum system. Our theoretical findings show that by adjusting the optical parameters such as elliptical angle i.e. phase difference between right-and-left circularly polarized, one can easily control the absorption spectrum and pulse propagation of the probe light in graphene medium. Our results may have potential applications in designing the new quantum devices for usage in quantum information processing.