Nonlinear Electromagnetic Equations Research Articles

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.

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.

Unexpanded nonlinear electromagnetic gyrokinetic equations for magnetized plasmas

Nonlinear electromagnetic gyrokinetic equations have been constructed without expanding the field variables into background and finite but small-amplitude fluctuating components. At the long-wavelength limit, these unexpanded nonlinear gyrokinetic equations recover the well-known drift-kinetic equations. At the expanded limit, they recover the usual nonlinear gyrokinetic equations. These equations can therefore be applied to long-term simulations covering from microscopic to macroscopic spatial scales.

Multi-Physics Modeling and Numerical Analysis of Tubular Linear Switched Reluctance Motors

This paper proposes a multi-physics modeling and numerical analysis of magneto-mechanical and thermal phenomena of a tubular linear switched reluctance motor (TLSRM) representing a linear stepping motor. Algorithms are developed to study the dynamic performances of TLSRM and investigate the temperatures in different parts in the motor due to the heat generation which causes an increase in the temperature of the machine concentrated particularly in the copper coils. The magneto-mechanical model is based on the nonlinear electromagnetic equations solved using the finite elements method (FEM) and the Macro-Element technique while incorporating the Newton–Raphson algorithm for the magnetic nonlinearity treatment. The validity of this model is checked through a comparison between the predicted displacement results for the TLRSM and the experimental values given in literature. The developed thermal model is solved by FEM where the source term is the power density generated in the coils.

Learning solutions to two dimensional electromagnetic equations using LS-SVM

Abstract In this paper, a new approach based on least squares support vector machines (LS-SVM) is proposed for solving the electromagnetic equations. Firstly, the cubic spline function is employed to smooth the discontinuous boundary. LS-SVM is used to solve the modified problem. Secondly, nonlinear electromagnetic equation is solved by LS-SVM. Finally, multimedia electromagnetic equation is solved by LS-SVM. Same as to the artificial neural networks (ANN), the approximate solutions are composed of two parts. The first part is a known function that satisfies the boundary conditions. The second part is the product of two terms. One term is also a known function which vanished on the boundary. The left part is the combination of kernel functions containing regression parameters. The parameters can be obtained by solving a system of equations. The numerical results show that the proposed method in this paper is feasible.

Variational principle for the parallel-symplectic representation of electromagnetic gyrokinetic theory

The nonlinear (full-f) electromagnetic gyrokinetic Vlasov-Maxwell equations are derived in the parallel-symplectic representation from an Eulerian gyrokinetic variational principle. The gyrokinetic Vlasov-Maxwell equations are shown to possess an exact energy conservation law, which is derived by the Noether method from the gyrokinetic variational principle. Here, the gyrocenter Poisson bracket and the gyrocenter Jacobian contain contributions from the perturbed magnetic field. In the full-f formulation of the gyrokinetic Vlasov-Maxwell theory presented here, the gyrocenter parallel-Ampère equation contains a second-order contribution to the gyrocenter current density that is derived from the second-order gyrocenter ponderomotive Hamiltonian.

Electromechanical coupled nonlinear dynamics of euler beam rails for electromagnetic railgun

The electromagnetic field can cause an essential change of the dynamic behavior of the railgun. The evaluation of the dynamics performance of railgun is a mandatory task. Here, a nonlinear electromagnetic force equation of the railgun is given in which the clearance, the thickness and the width of the rail are considered. Based on it, the nonlinear electromechanical coupled dynamics equations of Euler beam rails for the railgun are proposed. Using the equations, the nonlinear free vibration frequency of the railgun is investigated and the effects of the system parameters on the frequency are analyzed. The nonlinear forced responses of the rail to the electromagnetic excitation are investigated as well. The results show that as the nonlinearity of the railgun system is considered, the vibration frequencies of the railgun system increase; as the current in the rail increases, the difference between the natural frequencies and the nonlinear vibration frequencies increases significantly; the nonlinearity of the railgun system is more obvious for smaller distance between the two rails, smaller rail thickness, and smaller stiffness of the elastic foundation; the unstable dynamics state of the rail system occurs when the armature runs to the exit of the railgun. The results are useful for design and application of the railgun system.

Low Dimensional Born-Infeld Equations Coupled with a Collisionless Matter Model

We consider the Born-Infeld nonlinear electromagnetic field equations and study its Cauchy problem in the case that the Vlasov equation is considered as a matter model. In the present paper, the Vlasov equation is considered on the so-called one and one-half dimensional phase space, and in consequence the Born-Infeld equations are reduced to a quasilinear hyperbolic system with two unknowns. A transformation is introduced in order to make the field equations easy to handle, and suitable assumptions are made on initial data so that the nonlinearity of the field is controlled.

Minimum energy control analysis of the switched reluctance stepper motor considering a nonlinear finite element model

A method of modeling and numerical simulation of a minimum energy control of the switched reluctance motor using time stepping finite element (FE) technique is presented. In proposed model, the nonlinear electromagnetic field equations and the circuit equations are strongly coupled and solved together with motion equation at each time step. The nonlinearity problem is solved employing the Newton–Raphson (NR) procedure. Presented control technique is based on linear–quadratic problem and adopted to the nonlinear finite element model. The optimal control strategy is numerically investigated and compared with commonly used control strategy for the square wave excitation.

Numerical Modeling of the Coupled Electromagnetic and Mechanical Phenomena of Linear Stepping Motors

In this paper, we propose an electromagnetic-mechanical model based on the finite element and Macro-Element (ME) technique to analyse and study the dynamic characteristics of a Tubular Linear Switched Reluctance Stepping Motor (LSRSM). After the resolution of the non-linear electromagnetic equation governing the behaviour of the different materials of the motor using the nodal-based finite element method, this equation is then coupled to the mechanical equation firstly through the magnetic force computed by Maxwell stress tensor, and secondly by the modified flux distribution due to the moving part. Because of the precision required in the mobile part displacement and the very small air gap of stepping motors, the simulation of the movement is assured by the Macro-Element (ME) technique compared to other movement techniques that present many disadvantages. The validity of the developed model is verified through the comparison of the computed displacement of the LSRSM moving part with those given experimentally [2]. The Results shows satisfactory agreement. The obtained dynamic characteristics, particularly the starting magnetic force, are obtained by considering two values of the supplying currents.

Investigation of the dynamics of electromagnetic valves by a coupled magneto‐mechanical algorithm including contact mechanics

PurposeThe fast and flexible development of fast switching electromagnetic valves as used in modern gasoline engine demands the availability of efficient and accurate simulation tools. The purpose of this paper is to provide an enhanced computational scheme of these actuators including all relevant physical effects of magneto‐mechanical systems and including contact mechanics.Design/methodology/approachThe finite element (FE) method is applied to efficiently solve the arising coupled system of partial differential equations describing magneto‐mechanical systems. The algorithm for contact mechanics is based on the cross‐constraint method using an energy‐ and momentum‐conserving time‐discretisation scheme. Although solving separately for the electromagnetic and mechanical system, a strong coupling is ensured within each time step by an iterative process with stopping criterion.FindingsThe numerical simulations of the full switching cycle of an electromagnetic direct injection valve, including the bouncing during the closing state, are just feasible with an enhanced and robust mechanical contact algorithm. Furthermore, the solution of the nonlinear electromagnetic and mechanical equations needs a Newton scheme with a line search scheme for the relaxation of the step size.Originality/valueThe paper provides a numerical simulation scheme based on the FE method, which includes all relevant physical effects in magneto‐mechanical systems, and which is robust even for long‐term contact periods with multitude re‐opening phases.

Exact energy conservation laws for full and truncated nonlinear gyrokinetic equations

The exact global energy conservation laws for the full and truncated versions of the nonlinear electromagnetic gyrokinetic equations in general magnetic geometry are presented. In each version, the relation between polarization and magnetization effects in the gyrokinetic Poisson and Ampère equations and the quadratic ponderomotive gyrocenter Hamiltonian is emphasized.

ANALYSIS OF NONLINEAR MAGNETOELASTIC DYNAMICS AND STABILITY OF CONDUCTIVE CYLINDRICAL SHELLS

The nonlinear magnetoelastic vibration equations and electromagnetic field equations of a conductive thin cylindrical shell in magnetic fields are derived. The nonlinear principal resonances and dynamic stabilities of the cylindrical shell simply supported in a transverse magnetic field are investigated. Approximate analytical solution and bifurcation equations of the system with principal resonances are obtained by using the method of multiple scales. The stabilities and singularities of the steady-state solutions are analyzed and the stability criterion is given. The transition sets and bifurcation figures of unfolding parameters are also obtained. The variations of the resonance amplitudes with respect to the detuning parameter, the magnetic induction intensity, and the amplitude of excitations are presented. The corresponding phase trajectories in moving phase planes are given. The stabilities of solutions, characteristics of singular points, and bifurcation are analyzed. The impacts of electromagnetic and mechanical parameters on dynamic behaviors are discussed in detail.

Cylindrical electromagnetic waves in a nonlinear nondispersive medium: Exact solutions of the Maxwell equations

The excitation and propagation of cylindrical electromagnetic waves in a nonlinear nondispersive medium are analyzed. It is assumed that the medium lacks a center of symmetry and that the dependence of the electric displacement on the electric field can be approximated by an exponential function. For this case, a method for integrating the system of the Maxwell equations is proposed. Exact solutions to a set of nonlinear electromagnetic field equations are obtained by this method. It is shown that nonlinear effects described by these solutions can become apparent under experimental conditions.

Nonlinear Bloch waves in resonantly doped photonic crystals

We demonstrate the existence of self-consistent Bloch modes in resonant nonlinear photonic crystals with a complex, intensity-dependent, and frequency-dependent dielectric function. Such a dielectric response may arise by "doping" the photonic crystal with resonant quantum dots, atomic impurities, or other two-level light emitters. These exact solutions of the nonlinear electromagnetic wave equation exhibit Bloch periodicity and describe fundamental eigenmodes of an active photonic crystal under incoherent pumping. In a simple model two-dimensional photonic crystal, doped with active two-level atoms, the optical field intensity of these waves shows a laserlike threshold behavior with pumping. This appears to be a universal property of active, nonlinear photonic crystals and photonic band gap materials, arising from multidirectional distributed feedback. We describe an iterative technique for computing the detailed properties of these exact, self-consistent nonlinear waves in strongly scattering photonic crystal architectures with regions of gain and loss.

Kinetic effects on relativistic solitons in plasmas

We present theoretical and numerical studies of nonlinear interactions between a short, intense laser-beam and a plasma containing hot electrons. Such plasmas are frequently observed in fast-ignition experiments where electrons are heated by intense laser beams. Due to the combined effects of relativistic electron mass increase and relativistic ponderomotive force of the intense laser fields, there appear localized laser pulses in association with large amplitude localized positive potentials. The latter can trap and accelerate electrons to ultra-relativistic energies. This is demonstrated by means of computer simulations of the time-dependent nonlinear electromagnetic wave equation, supplemented by the Vlasov and Poisson equations.

A new method for computing nonlinear carrier diffusion in semiconductor optical devices

The solution of carrier diffusion equations typically associated with semiconductor optical devices has been achieved by combining a function expansion scheme, using the Hermite-Gauss functions as the basis set, with the collocation numerical procedure. Results for a wide range of cases obtained by this new scheme compare very favorably with those calculated with other methods. Not only is the present process computationally fast and efficient, but it has the added attraction of providing the basis for conveniently solving also the nonlinear electromagnetic wave equation for the self-consistent modeling of such devices.

Nonlinear electromagnetic gyrokinetic equation for plasmas with large mean flows

A new nonlinear electromagnetic gyrokinetic equation is derived for plasmas with large flow velocities on the order of the ion thermal speed. The gyrokinetic equation derived here retains a collision term and is given in the form which is valid for general magnetic geometries including the slab, cylindrical and toroidal configurations. The source term for the anomalous viscosity arising through the Reynolds stress is identified in the gyrokinetic equation. For the toroidally rotating plasma, particle, energy and momentum balance equations as well as the detailed definitions of the anomalous transport fluxes and the anomalous entropy production are shown. The quasilinear anomalous transport matrix connecting the conjugate pairs of the anomalous fluxes and the forces satisfies the Onsager symmetry.

Interaction of soliton-like beam in a diffusive nonlinear planar waveguide

A laser beam propagating in a medium causes a temperature rise, as a consequence of light absorption. This phenomenon provides a variation of refractive index governed by the heat diffusion in the material. The coupling between the nonlinear electromagnetic wave equation and the heat diffusion equation has been investigated for a weakly absorbing material. In this hypothesis, the possibility of stabilization of propagation through self-focusing in a planar waveguide has been studied. A numerical model of propagation in planar waveguides has been developed. Although stable propagation is not achieved, a quasi-confined propagation on a short distance is obtained. The interaction between quasi-soliton beams with different phase relationship has been investigated.

Nonlinear electromagnetic gyrokinetic equations for rotating axisymmetric plasmas

The influence of sheared equilibrium flows on the confinement properties of tokamak plasmas is a topic of much current interest. A proper theoretical foundation for the systematic kinetic analysis of this important problem has been provided here by presenting the derivation of a set of nonlinear electromagnetic gyrokinetic equations applicable to low-frequency microinstabilities in a rotating axisymmetric plasma. The subsonic rotation velocity considered is in the direction of symmetry, with the angular rotation frequency being a function of the equilibrium magnetic flux surface. In accordance with experimental observations, the rotation profile is chosen to scale with the ion temperature. The results obtained represent the shear flow generalization of the earlier analysis by Frieman and Chen [Phys. Fluids 25, 502 (1982)], where such flows were not taken into account. In order to make it readily applicable to gyrokinetic particle simulations, this set of equations is cast in a phase-space-conserving continuity equation form.