Electromagnetic Field Equations Research Articles

Propagation of light through an amplifying honeycomb photonic lattice

We consider light propagation through a ballistic amplifying photonic honeycomb lattice below the lasing threshold. Two sublattices of the system are formed by the wave-guides with different complex dielectric permittivities, which results in the non-Hermitian Dirac equation for electromagnetic field. We reveal that there exists a critical length of the amplifying region for which the photonic lattice exhibits an amplifier to generator transition. The transmission and reflection probabilities at the normal angle of incidence are strongly enhanced at a critical length of the system. We also comment on the sensitivity of amplification to the direction of incident light and the thickness of the amplifying region.

Thermodynamic properties of novel black hole solutions in the Einstein\u2013Born\u2013Infeld-dilaton gravity theory

The exact solutions of coupled scalar, electromagnetic and gravitational field equations have been obtained in the framework of Einstein-dilaton gravity theory which is coupled to the Born–Infeld nonlinear electrodynamics. The solutions show that Einstein–Born–Infeld-dilaton gravity theory admits three novel classes of nonlinearly charged black hole solutions with the non-flat and non-AdS asymptotic behavior. Some of the solutions, in addition to the naked singularity, extreme and two-horizon black holes, produce one- and multi-horizon black holes too. The electric charge, mass and other thermodynamic quantities of the black holes have been calculated and it has been proved that they satisfy the standard form of the thermodynamical first law. The black hole local stability has been investigated by use of the canonical ensemble method. Noting the black hole heat capacity the points of type-one and type-two phase transitions and the locally stable black holes have been identified exactly. By use of the thermodynamic geometry, and noting the divergent points of the thermodynamic metric proposed by HEPM, it has been shown that the results of this method are consistent with those of canonical ensemble method. 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. By calculating the Gibbs free energies, we characterized the ranges of horizon radii in which the black holes remain globally stable or prefer the radiation phase.

Effects of the working parameters on the flow-field numerical results for a medium-power ICP wind tunnel

Numerical simulations of subsonic and supersonic nonequilibrium air inductively coupled plasmas (ICPs) were carried out inside a medium-power 100-kW ICP wind tunnel (ICPWT), which is widely used to study the thermal protection system and the blackout phenomenon of reentry vehicles in the aerospace field. A thermochemical nonequilibrium magneto-hydrodynamic numerical model, which takes into account the coupling of Navier–Stokes equations, electromagnetic-field equations, the four-temperature model, and the 32 chemical reactions of air, was constructed and applied. Basic flow characteristics of the inductive plasma, such as the hot plasma flame beneath the inductive coil, the subsonic-supersonic transition in the conical nozzle, and the vortexes in the torch and in the vacuum chamber, were reproduced successfully. Additionally, the effects of different working parameters (e.g., number of coil turns, mass-flow rate, working pressure, and radius of the discharge tube) of the ICPWT on its flow-field properties were numerically investigated. The numerical results demonstrated that atomic N and O are the most dominant chemical components at the coil center. Five turns of the inductive coil is optimal for this medium-power ICPWT.

Nonlinear Waves and Coherent Structures in Laser Induced Plasmas and Polarized Vacuum

Starting from the Vlasov–Maxwell equations describing the dynamics of various species in a free quasi-neutral plasma, an exact relativistic hydrodynamic closure for a special type of water-bag distributions satisfying the Vlasov equation has been derived.It has been shown that the set of equations for the macroscopic hydrodynamic variables coupled to the wave equations for the self-consistent electromagnetic field is equivalent to the Vlasov–Maxwell system. In the case of magnetized quasi-neutral plasma, the hydrodynamic substitution has been used to derive the hydrodynamic equations for the plasma density and current velocity, coupled to the wave equations for the self-consistent electromagnetic fields. Based on the method of multiple scales, a system comprising a vector nonlinear Schrodinger equation for the transverse envelopes of the self-consistent plasma wakefield, coupled to a scalar nonlinear Schrodinger equation for the electron current velocity envelope for free plasma, has been derived. In the case of magnetized plasma, it has been shown that the whistler wave envelopes of the three basic modes satisfy a system of three coupled nonlinear Schrodinger equations. Numerical examples for typical plasma parameters have been presented, which demonstrate the relevance of the results thus obtained to the so-called shock laser-plasma acceleration. In addition, it has been shown that in the case of magnetized plasma, the whistler waves facilitate the transverse confinement considerably. The effect of the nonlinear corrections to the electric displacement vector and the intensity of the magnetic field in nonlinear electrodynamics of Heisenberg-Euler type has been studied. It has been shown that the slowly varying wave envelope in free polarized vacuum satisfies a nonlinear wave equation. In the case, where an external constant magnetic field is applied, the single nonlinear wave equation should be replaced by a system of two coupled nonlinear equations for the two independent wave polarizations. In both cases a novel effect of reduction of the speed of light can be observed, which is due to the vacuum polarization.

Transmission of electromagnetic waves through a nonlinear over-dense plasma slab

A study on the transmission of the electromagnetic waves from a structure consisting of an over-dense plasma layer with nonlinear effects is undertaken. The applied nonlinearity is presented due to the series expansion of the polarization in the medium. The nonlinear plasma layer is supposed to be placed between two linear dielectric layers. The transparency conditions are investigated for the p-polarized obliquely incident waves. It is shown that the formation of the surface waves can eventuate to the transmission of the incident waves. This fact has already be seen in the case of the linear over-dense plasma, but, here, it is examined in the presence of the nonlinear effects. To determine the propitious conditions for the surface wave excitation, the exact solutions of the electromagnetic field equations are used in all regions. The transmission, the reflection, and the dissipation rates of the electromagnetic waves from the entire structure are obtained, and the effects of the main parameters on them are discussed.

An evaluation method for direct piezoelectric coefficients of thin films using both-ends-hinge-supported unimoprh beams

We have developed a new method for measuring the direct piezoelectric effect of piezoelectric thin films, consisting of both-ends-hinge-supported unimorph beams (BUBs). This method can determine the precise direct transverse piezoelectric coefficient e31,f of arbitrary piezoelectric films by measuring the displacement and the output voltage between the electrodes of the BUBs. We formulated the e31,f values based on the flexure basic formula, and a constitutive equation of electromagnetic field for the BUBs, including measuring systems such as oscilloscopes, which have an arbitrary input impedance. In this study, we were able to obtain a piezoelectric coefficient of a lead zirconate titanate (PZT) thin film on a Si substrate of e31,f = 4.7 Cm−2, regardless of the input impedance of the measurement instrument. Using this method, we then measured the temperature characteristics of e31,f for the PZT thin film. We clearly observed the increase of e31,f , and the relative dielectric constant, with an increase in temperature. We obtained a temperature gradient for of a = 0.01 Cm−2K−1, a value which is in good agreement with previous research. We also measured the time dependences of the e31,f after polling piezoelecric films. The e31,f value decreased over time, and we were able to obtain a logarithmic time gradient for normalized e31,f of p = −0.01, a value consistent with the results of previous studies.

Stability Analysis of Charged Rotating Black Ring

We study the electromagnetic field equation along with the WKB approximation. The boson tunneling phenomenon from charged rotating black ring (CRBR) is analyzed. It is examined that reserve radiation consistent with CRBR can be computed in general by neglecting back reaction and self-gravitational of the radiated boson particle. The calculated temperature depends upon quantum gravity and CRBR geometry. We also examine the corrected tunneling rate/probability of boson particles by assuming charge as well as energy conservation laws and the quantum gravity. Furthermore, we study the graphical behavior of the temperature and check the stability and instability of CRBR.

Effects of magnetic nanoparticle diffusion on microwave ablation treatment: A numerical approach

Microwave ablation (MWA) is a targeted process that kills malignant cells by heating a tumor region without damaging the surrounding tissue. The microwave heating of tumors can be improved by the injection of magnetic nanoparticles (MNPs). The effectiveness of this technique, evaluated by the dimensions of the ablation zone, is related to the MNPs’ concentration and the MWA input power and frequency. This work investigates how MNP dissipation affects the temperature profile of solid tumors undergoing MWA. The influences of the injection site, diffusion duration, and the size of the particles are investigated. The temperature profile is numerically estimated by solving coupled electromagnetic field and bio-heat transfer equation using the finite element method. Results demonstrate that the injection process has an essential role in temperature distribution, and that the assumption of uniform drug distribution in the tumor is not a prerequisite. Although increasing the diffusion time decreases the maximum temperature difference from 76.7 °C to 62.6 °C, the radius of the ablation zone increases 1.4 times, because MNPs seeping throughout the tumor increase heat penetration. Results also demonstrate that, compared to 20 nm nanoparticles, 10 nm ones increase the area of ablation by 30%, due to their better diffusion in the tumor. This investigation concludes that diffusion of MNPs in a tumor can improve MWA efficiency.

Computational Analysis of a Pulsed Power Source- Based Electromagnetic Manufacturing Process

Electromagnetic manufacturing (EMMa) methods are being developed as an auxiliary to conventional manufacturing processes as it offers many potential advantages. Numerical methods are being employed to predict the plastic deformation of the workpiece. A multiphysics coupled study of transient electromagnetic, thermal, and mechanical fields is imperative to predict the dynamic deformation of the workpiece during the manufacturing process. The challenging feature of solving a multiphysics problem is the high degree of coupling between the partial differential equations involved. This article describes a fast and efficient method for analyzing a coupled transient electromagnetic and mechanical problem during the process of EMMa process. A 3-D model has been considered for the formulation of electromagnetic and mechanical field equations. The coupling is usually done using finite elements methods (FEMs) which is computationally demanding for solving Electromagnetic fields. Use of FEM for solving an EM problem requires extra fine meshing of the workpiece in order to capture the skin effect and it also needs to mesh the surrounding air domain which is of no interest. This article describes an analytical framework for computing the electromagnetic pressure distribution on the workpiece, and the results have been compared with those obtained using FEM techniques. The mechanical problem is solved using commercial available FEM tools. The effects of deformation in the geometry of the workpiece and its velocity are considered which provide more accurate results.

Discrete phase space, relativistic quantum electrodynamics, and a non-singular Coulomb potential

This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent relativistic quantum electrodynamics, the corresponding Feynman diagrams and [Formula: see text]-matrix elements are derived. In the special case of electron–electron scattering (Møller scattering), the explicit second-order element [Formula: see text] is deduced. Moreover, assuming the slow motions for two external electrons, the approximation of [Formula: see text] yields a divergence-free Coulomb potential.

Two-dimensional comprehensive mathematical model for electroslag remelting process with pipe electrode

Taking the electroslag remelting with pipe electrode (ESR-PE) and electroslag remelting with solid electrode (ESR-SE) as the research objects, a two-dimensional steady-state mathematical model of coupled electromagnetic field equation, energy equation, and flow equation was established. The distribution of its current density, Joule heat, flow field, and temperature field was compared and the difference of their molten metal pool was analyzed. The results show that compared with those of ESR-SE, current density distribution and Joule heating area of ESR-PE are mainly concentrated in the inner and outer wall areas of the electrode tip, while the Joule heat generated in the central area of the slag pool is less. In the ESR-PE, the slag flows from the outside of the electrode to the hollow area of the electrode, which makes the temperature distribution in the slag pool is more uniform. Affected by the Joule heating area and flow field, the heat of ESR-SE is concentrated below the electrode in the slag pool area and it transfers from the center to the periphery. However, in the ESR-PE, the heat is concentrated near the inner and outer walls of the electrode tip, and the heat is transferred from the periphery to the center of the slag pool. The molten metal pool depth of ESR-SE is 0.1188 m and that of ESR-PE is 0.0962 m. Compared with that of ESR-SE, the molten metal pool of ESR-PE is shallower and flatter.

Numerical simulation of knotted solutions for Maxwell equations.

In this work, we use the finite differences in time domain (FDTD) numerical method to compute and assess the validity of Hopf solutions, or hopfions, for the electromagnetic field equations. In these solutions, field lines form closed loops characterized by different knot topologies which are preserved during their time evolution. Hopfions have been studied extensively in the past from an analytical perspective but never, to the best of our knowledge, from a numerical approach. The implementation and validation of this technique eases the study of more complex cases of this phenomena; e.g., how these fields could interact with materials (e.g., anisotropic or nonlinear), their coupling with other physical systems (e.g., plasmas), and also opens the path on their artificial generation by different means (e.g., antenna arrays or lasers).

Calculation of the Parameters of a Two-Winding Transformer without a Magnetic Circuit

A technique for calculating the parameters of a transformer without a magnetic circuit with two cylindrical coaxial multilayer windings of the same length has been developed. Such parameters as inductance, resistance, capacitance, and temperature of windings are determined, which are used to calculate periodic voltages and currents in the steady-state power supply mode of the active load, when the primary winding of the transformer is connected to the voltage inverter. The formulas for calculating the transformer parameters, voltages, and currents, which are obtained based on the equations of electromagnetic fields and electric circuits, are programmed using the Mathcad software. The method’s reliability is confirmed by a satisfactory agreement between the calculated and the experimental values of the transformer parameters, as well as by similar calculated and experimental values of periodic voltage on the resistive load. The results obtained testify to the possibility of the efficient use of transformers without magnetic circuit with high coupling coefficient at sufficiently high frequencies, when the quality factors of the windings are high, the surface effect in the conductors of the windings is negligible and the undesirable shunting effect of parasitic capacitances in the windings is still insignificant.

Solution of the Hamilton – Jacobi Equations in an Electromagnetic Field Using Separation of Variables Method – Staeckel Boundary Conditions

This manuscript aims to resolve the Hamilton-Jacobi equations in an electromagnetic field by two methods. The first uses the separation of variables technique with Staeckel boundary conditions, whereas the second uses the Newtonian formalism to solve the same example. Our results demonstrate that the Hamilton-Jacobi variables can be completely detached by using separation of variables technique with Staeckel boundary conditions that correspond to other results using Newtonian formalism.

Simplified Modeling of Charged Gas Particles Coupled With EM Field Using Monte Carlo and Finite Volume Methods

A simplified numerical model to simulate plasma occurring in a magnetron sputtering device is presented. Motions and collisions of charged gas particles are modeled by the direct simulation Monte Carlo (DSMC) method on an adaptive Cartesian mesh structure. An electromagnetic (EM) field equation is solved by the finite volume method, a discretization method. The potential of the EM field influences the charged gas particles calculated by DSMC through a simplified form of non-Sibson interpolation scheme developed in this article. The DSMC, EM field solver, and interpolation module are validated separately, and integrated calculations are applied to a test scenario in a magnetron sputtering experiment. Although simulation is performed without plasma calculation, the erosion rates obtained from the simulation agreed well with experimental data, with less than 10% difference. The proposed model is expected to be used in real plasma applications, especially for calculations of erosion and deposition rates without rigorous plasma calculation.

Optical modulation of repaired damage site on fused silica produced by CO2 laser rapid ablation mitigation**Project supported by the National Natural Science Foundation of China (Grant Nos. 51775147 and 51705105), the Science Challenge Project of China (Grant No. TZ2016006-0503-01), the Young Elite Scientists Sponsorship Program by CAST (Grant No. 2018QNRC001), the China Postdoctoral Science Foundation funded project (Grant Nos. 2018T110288

CO2 laser rapid ablation mitigation (RAM) of fused silica has been used in high-power laser systems owing to its advantages of high efficiency, and ease of implementing batch and automated repairing. In order to study the effect of repaired morphology of RAM on laser modulation and to improve laser damage threshold of optics, an finite element method (FEM) mathematical model of 351 nm laser irradiating fused silica optics is developed based on Maxwell electromagnetic field equations, to explore the 3D near-field light intensity distribution inside optics with repaired site on its surface. The influences of the cone angle and the size of the repaired site on incident laser modulation are studied as well. The results have shown that for the repaired site with a cone angle of 73.3°, the light intensity distribution has obvious three-dimensional characteristics. The relative light intensity on z-section has a circularly distribution, and the radius of the annular intensification zone increases with the decrease of z. While the distribution of maximum relative light intensity on y-section is parabolical with the increase of y. As the cone angle of the repaired site decreases, the effect of the repaired surface on light modulation becomes stronger, leading to a weak resistance to laser damage. Moreover, the large size repaired site would also reduce the laser damage threshold. Therefore, a repaired site with a larger cone angle and smaller size is preferred in practical CO2 laser repairing of surface damage. This work will provide theoretical guidance for the design of repaired surface topography, as well as the improvement of RAM process.

Phase transition and geometrical thermodynamics of energy-dependent dilatonic BTZ black holes with power-law electrodynamics

Abstract The coupled scalar, electromagnetic, and gravitational field equations of Einstein–dilaton gravity theory have been solved in a three-dimensional energy-dependent spacetime and in the presence of power-law nonlinear electrodynamics. The scalar potential is written as the linear combination of two exponential functions, and two families of three-dimensional dilatonic black hole solutions have been introduced which indicate the impacts of rainbow functions on the spacetime geometry. Through consideration of curvature scalars, it has been found that the asymptotic behavior of the solutions is neither flat nor anti-de Sitter. It has been illustrated that, with a suitable choice of parameters, the solutions can produce the two-horizon, extreme and naked singularity black holes. By calculating the black hole charge, mass, entropy, temperature, and electric potential, it has been proved that they fulfill the standard form of the first law of black hole thermodynamics. The thermodynamic stability of the black holes has been analyzed by utilizing the canonical and grand canonical ensembles and noting the signature of the black hole heat capacity and Gibbs free energy of the black holes. The points of type-1, type-2, and Hawking–Page phase transitions and the ranges at which the black holes are locally or globally stable have been determined. The geometrical thermodynamics of the black holes has been studied by use of different thermodynamic metrics, and the results of different approaches have been compared.

Nonlinearly charged AdS black hole solutions in three-dimensional massive gravity's rainbow

Two new families of nonlinearly charged and asymptotically anti-de Sitter (AdS) rainbow black holes have been introduced, as the exact solutions to the coupled electromagnetic and gravitational field equations, in massive gravity theory and in the presence of power-law nonlinear electrodynamics. The conserved and thermodynamic quantities such as black hole mass, charge, temperature, entropy and electric potential have been calculated from geometric and thermodynamic approaches. Despite the fact that some of them receive corrections from rainbow functions and nonlinear electrodynamics, it has been proved that they fulfill the first law of black hole thermodynamics. Thermal stability of the black holes has been studied by use of the canonical ensemble and geometrical thermodynamics methods, separately. Regarding the black hole heat capacity and thermodynamic Ricci scalars, the points of type-one and type-two phase transitions and the conditions under which the black holes remain locally stable have been determined. Also, global stability of the novel rainbow black holes has been investigated from the viewpoint of the grand canonical ensemble. Through calculation of Gibbs free energy of the black holes, the points of Hawking-Page phase transition and the size of the black holes which are globally stable or in the radiative phase have been determined.

Quaternionic comparisons of electromagnetism using Lorentz transformations

In this paper, by defining properties of the real and complex quaternion algebras, the electromagnetic field equations including monopoles have been studied in $$\hbox {S}'$$ reference systems, which moves with the velocity u according to the fixed reference system $$\hbox {S}$$. Quaternionic source and wave equalities have been derived in a more compact and elegant manner in $$\hbox {S}'$$ system. Besides, Poynting theorem has been firstly obtained in moving media. Additionally, the comparisons between $$\hbox {S}$$ and $$\hbox {S}'$$ reference systems have been separately done for field, source, potential and wave equations in quaternion basis elements. Furthermore, Poynting theorems have been compared by means of $$\hbox {S}$$ and $$\hbox {S}'$$ systems for the first time.

Alternative formulation of the macroscopic field equations in a linear magneto-dielectric medium: field equations

We derive an alternative formulation of the field equations for macroscopic electromagnetic fields in a linear magneto-dielectric medium as an identity of the Maxwell–Minkowski equations, complementing a variety of other representations including the Ampère, Chu, Lorentz, and Minkowski formulations of continuum electrodynamics. In the new formulation of the macroscopic field equations, the material properties are carried as a renormalization of the temporal and spatial coordinates instead of as independent material constants. The new representation of the field equations raises some interesting physical issues with relativity and boundary conditions.