Evolution Of Electromagnetic Field Research Articles

Parametric Study of Cavity IEMP Responses in a Cylinder by Coupling Monte Carlo Method and 3-D Electromagnetic Particle-in-Cell Method

Internal electromagnetic pulse generated inside a cavity, known as Cavity IEMP, would disturb or damage sensitive electronic systems inside a spacecraft when illuminated by transient X-rays. To ensure their normal operations, accurate prediction and analysis of Cavity IEMP responses are required. In this article, the physical phenomena involved in three-dimensional (3-D) Cavity IEMP problems are numerically studied, including the interaction process between X-rays and the cavity wall material and the self-consistent process involving the motion of electrons and the evolution of electromagnetic fields. The interaction process is simulated with the Monte Carlo method to obtain the actual emission characteristics of forward electrons emitted into a cavity, including their yields, energy, and angular spectra, while the self-consistent process is simulated with a proposed 3-D electromagnetic particle-in-cell method to solve electromagnetic fields generated inside a cavity, whose driving forces are forward electrons with the calculated emission characteristics. This method fully considers electrons with different energies and directions and their impacts on the generated electromagnetic fields. With such method, the electromagnetic field distribution inside a cylinder exposed to transient X-rays is discovered based on the actual emission characteristics of X-ray-induced forward electrons. Furthermore, as forward electron emission characteristics are determined by properties of X-rays and cavities, the impacts of the blackbody temperature in X-ray energy spectrum, the cylinder wall thickness, and the cylinder wall material on the intensity of generated electric fields are fully explored. Based on the results, several suggestions are given to protect electronic systems in cavities against the electromagnetic coupling from Cavity IEMP. The study would guide radiation hardening design of electronic systems in spacecraft.

Fourth-order accurate numerical modeling of the multi-fluid plasma equations with adaptive mesh refinement

This work develops a multi-fluid plasma modeling capability in extension of a parallel, adaptive, fourth-order, finite-volume method, computational fluid dynamics algorithm. The governing equations of the multi-fluid plasma model are derived from moments of the Boltzmann equation, under the assumption of local thermodynamic equilibrium. Maxwell's equations describe the electromagnetic field evolution and are coupled to the fluid equations of charged species. The present work concentrates on two, charged, collisionless fluids as the first step, although the algorithm is designed to accommodate more fluids, both charged and neutral, and collisions between fluids; the extension to multiple fluids is straightforward. The numerical algorithm featuring parallel, high-order (≥4 for smooth flows), adaptive mesh refinement is expected to help cope with the inherent stiffness of the physics involved. The standard, fourth-order Runge-Kutta scheme is used to evolve the solution in time. The current study is primarily focused on verification and testing of the new, adaptive algorithm; we demonstrate 4th-order accuracy using problems with exact solutions and benchmark our solutions for common plasma simulations against references from literature. Using the 4th-order scheme, our multi-fluid model is shown to provide accurate solutions to plasma problems using half the cell count as traditional, 2nd-order methods. Furthermore, adaptive mesh refinement is successfully applied to three, plasma test problems, providing a significant reduction in mesh size. In subsequent work, an optimized version of our multi-fluid plasma algorithm will be applied to plasma test cases with more practical configurations, with a rigorous assessment of the improvements to computational efficiency afforded by our adaptive, higher-order scheme.

Particle-in-Cell Modeling of Omega Experiments on Ablation of Plasmas

The large electric fields due to charge separation generated by a laser pulse propagating in a plasma can accelerate the electrons to very high energies. The hydrodynamics models that are based on the local thermodynamic equilibrium assuming a Maxwellian distribution of velocities cannot describe the evolution of groups of hot electrons of different energy ranges and kinetic particle-in-cell (PIC) simulations are required. The SMILEI PIC code is used to investigate the generation of hot electrons in plasmas produced by laser pulses in the Omega extended performance (EP) experiments. In 2-D PIC simulation using SMILEI code, a Gaussian-shaped laser pulse of 100-ps duration with the intensity of 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{15}$</tex-math> </inline-formula> W/cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{2}$</tex-math> </inline-formula> and a wavelength of 351 nm impinges onto a plasma with the electron density and temperature profiles. The electromagnetic field, electron, and total energies of a plasma as a function of time are evaluated. The evolution of number density, electromagnetic fields, and energy spectra of electrons is studied. The time evolution of hot electrons in a plasma is investigated. These PIC results provide insights into the contribution and importance of the kinetic effects in the expansion dynamics of ablated plasmas, thereby helping to analyze and explain the Omega experimental data and computational fluid dynamics results.

Echoes of charged black-bounce spacetimes

In present work, the evolution of scalar field and electromagnetic field under the background of the charged black-bounce spacetimes are investigated, and we obtain an obvious echoes signal which appropriately reports the properties of the charged black-bounce spacetimes and disclose the physical reasons behind such phenomena. Furthermore, by studying the quasinormal ringdown, we analyze the three states of the charged black-bounce spacetimes in detail, our results show that the echoes signal only appears when (|{Q}|le m) and (|{l}|> m+ sqrt{m ^{2}-Q^{2} }) in this spacetime, while when the parameters demand (|{Q}|>m), the echoes signal will be transformed into a quasinormal ringdown of the two-way traversable wormhole, and the charged black-bounce is a regular black hole with normal horizons by requiring (|{Q}|le m) and (|{l}|< m-sqrt{m ^{2}-Q^{2} }).

Application of Herglotz’s variational principle to electromagnetic systems with dissipation

This work applies the contact formalism of classical mechanics and classical field theory, introduced by Herglotz and later developed in the context of contact geometry, to describe electromagnetic systems with dissipation. In particular, we study an electron in a non-perfect conductor and a variation of the cyclotron radiation. In order to apply the contact formalism to a system governed by the Lorentz force, it is necessary to generalize the classical electromagnetic gauge and add a new term in the Lagrangian. We also apply the k-contact theory for classical fields to model the behavior of electromagnetic fields themselves under external damping. In particular, we show how the theory describes the evolution of electromagnetic fields in media under some circumstances. The corresponding Poynting theorem is derived. We discuss its applicability to the Lorentz dipole model and to a highly resistive dielectric.

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.

Electromagnetic Field Evolution in Relativistic Heavy Ion Collision and Its Effect on Flow of Particles

We compute the electromagnetic fields generated in relativistic heavy-ion collisions using the iEBE-VISHNU framework. We calculated the incremental drift velocity from the four possible sources of electric force (coulomb, Lorentz, Faraday, and plasma-based) on the particles created. The effect of this external electromagnetic field on the flow harmonics of particles was investigated, and we found out that the flow harmonics values get suppressed and rouse in a non-uniform fashion throughout the evolution. More precisely, a maximum of close to 3% increase in elliptic flow was observed. We also found mass as the more dominant factor than charges for the change in flow harmonics due to the created electromagnetic field. On top of that, the magnetic field perpendicular to the reaction plane is found to be sizable, while the different radial electric forces were found to cancel out each other. Finally, we found out that the inclusion of electromagnetic field affects the flow of particles by suppressing or raising it in a non-uniform fashion throughout the evolution.

Evolution and Structure of Elementary Physical Particles

This paper is presented in two parts. The first part provides a glimpse of the long-awaited unified theory, which explains the parallel activation of different levels of the universe: intellectual (humans), psychological (animals), biological (vegetation), physical (matter), and cosmological (energies) levels, whereas in the conventional approach, the physical and cosmological levels are grouped into the same category. This paper explains the evolution and structure of elementary physical particles (EPPs) based on the evolution and structure of elementary biological particles (cells). The second part of the paper explains the structure and ingredients of the PPE, which are responsible for the creation of the following four fields, as suggested by the author: visibility, forcibility (magnetism), the fullness field, and the hollowness field. All these fields comprise different unknown cosmological substances. These cosmological fields are present in all physical entities and are responsible for all kinds of physical activations. Finally, the paper explains the evolution of electromagnetic waves, electromagnetic fields, gravitation, and repulsion (repulsive gravitation). The theory is consistent with all previously conducted experiments and systematically unfolds several mysteries, thereby demonstrating the validity of the proposed theory.

Single long electron beam detected electromagnetic field evolution in laser produced plasma

惯性约束核聚变研究最近取得可喜成果，美国国家点火装置NIF装置实验上聚变增益达到了输入激光能量的三分之二。但是，这一成果与人们的预期还有较大差距，需要更深入研究激光与等离子体相互作用初期的动力学过程。我们发展了一种新方法,用单发长脉冲电子束团为探针，测量激光等离子体内电磁场在整个等离子体持续时间内的演化过程。实验中，高压静电电子源产生能量0~100keV 连续可调、脉宽10ns的电子束团。1焦耳、532nm、脉宽约4ns的激光脉冲聚焦到银靶上，激发产生等离子体。电子束团穿过激光等离子体，被其中的电磁场调制后成像，单发电子束团时间宽度会覆盖整个等离子体持续时间，通过分析电子束团的调制强度，推得等离子体内电磁场的变化。实验上成功实现了单发电子束团对整个激光等离子体内电场的诊断测量，获得了演化曲线，推算出实验条件下电子束通过路径上平均电场的最大值约为7.74×10^5 V/m。

Echoes of novel black-bounce spacetimes

Gravitational wave echoes can be used as a significant observable to understand the properties of black holes horizon. In addition, echoes would also closely relate to the unique properties of compact objects. In this work we study the evolution of electromagnetic field and scalar field under the background of novel black-bounce spacetimes. Our results show an obvious echoes signal that can characterize the properties of novel black-bounce spacetimes, and a detailed analysis about the characteristics of the echoes signal is given. By studying the quasinormal ringdown of the three states of novel black-bounce spacetimes, including black holes in $0<a<2 M$, the one-way wormhole in $a=2M$ and the traversable wormhole in $a>2 M$, we find that the echoes signal only appears when $a>2M$ in this spacetime, but when the parameter $a$ increases to a threshold, the echoes signal will be transformed into a quasinormal ringdown of the two-way traversable wormhole.

Continuous evolution of electromagnetic field in heavy-ion collisions

In relativistic heavy-ion collisions the electromagnetic field exists before the hot nuclear matter emergence. Requiring the field continuity we compute it in the central rapidity region by taking into account the electromagnetic response of the Quark Gluon Plasma. We show that the electromagnetic field is nearly time-independent from about 1 fm/c after the collision until the freezeout. In particular, its value is about 10% of the initial magnitude of the magnetic field. Our result provides a theoretical basis for the common assumption that the electromagnetic field produced in relativistic heavy-ion collisions varies slowly with time.

Elliptic Flow of Particles under the Influence of Electromagnetic Field Evolution in Relativistic Heavy Ion Collision

The bending of flow of identified particles from the relativistic heavy-ion collision is investigated using the iEBE-VISHNU framework. The Maxwell's equations are applied to compute the incremental drift velocity and the change in the elliptic flow of particles from the four sources of the electric force, which are of coulomb (EC), Lorentz (EL), Faraday (EF) and Plasma-based. We find out that the field evolution arouses flow at lower transverse momentum and suppresses it at higher. Heavier particles get higher initial push, and particles and their anti-particles get crudely the same elliptic flow changes. Moreover, elliptic flow is found to show different percentage increase for different collision energies. To conclude, the present study shows that besides the inclusion of electromagnetic fields, the increase in collision energy affects the elliptic flow of particles in a non-uniform fashion throughout the evolution. Further study by softening many of the crude assumptions we made and keeping the functionality of parameters is needed to establish a better understanding of the electromagnetic field evolution and its effects on the created system.

Monolithic Multigrid Methods for Magnetohydrodynamics

The magnetohydrodynamics equations model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. After discretization and linearization, the resulting system of equations is generally difficult to solve due to the coupling between variables and the heterogeneous coefficients induced by the linearization process. In this paper, we investigate multigrid preconditioners for this system based on specialized relaxation schemes that properly address the system structure and coupling. Three extensions of Vanka relaxation are proposed and applied to problems with up to 170 million degrees of freedom and fluid and magnetic Reynolds numbers up to 400 for stationary problems and up to 20,000 for time-dependent problems.

Quasipositive links and electromagnetism

For every link L we construct a complex algebraic plane curve that intersects S3 transversally in a link L˜ that contains L as a sublink. This construction proves that every link L is the sublink of a quasipositive link that is a satellite of the Hopf link. The explicit construction of the corresponding complex polynomial f:C2→C can be used to give upper bounds on its degree and to create arbitrarily knotted null lines in electromagnetic fields, sometimes referred to as vortex knots. Furthermore, these null lines are topologically stable for all time. We also show that the time evolution of electromagnetic fields as given by Bateman's construction and a choice of time-dependent stereographic projection can be understood as a continuous family of contactomorphisms with knotted field lines of the electric and magnetic fields corresponding to Legendrian knots.

Constraint-Preserving Hybrid Finite Element Methods for Maxwell’s Equations

Maxwell’s equations describe the evolution of electromagnetic fields, together with constraints on the divergence of the magnetic and electric flux densities. These constraints correspond to fundamental physical laws: the nonexistence of magnetic monopoles and the conservation of charge, respectively. However, one or both of these constraints may be violated when one applies a finite element method to discretize in space. This is a well-known and long-standing problem in computational electromagnetics. We use domain decomposition to construct a family of primal hybrid finite element methods for Maxwell’s equations, where the Lagrange multipliers are shown to correspond to a numerical trace of the magnetic field and a numerical flux of the electric flux density. Expressing the charge conservation constraint in terms of this numerical flux, we show that both constraints are strongly preserved. As a special case, these methods include a hybridized version of Nédélec’s method, implying that it preserves the constraints more strongly than previously recognized. These constraint-preserving properties are illustrated using numerical experiments in both the time domain and frequency domain. In 2-D, we also observe a superconvergence phenomenon, where hybrid post-processing yields an improved estimate of the magnetic field.

Field-Circuit Coupled Analysis of a Series-Augmented Electromagnetic Railgun

A field-circuit coupled algorithm was developed to model the circuit behaviors and electromagnetic-field details of electromagnetic railguns. The railgun launcher was described by a 3-D transient eddy current field model with the electric current as the exciting source. The launcher was also treated as an RL series load of an external circuit composed of capacitor-based pulse forming networks. The variable resistance and inductance of the launcher were calculated by the electromagnetic field results, and the field-circuit coupling was achieved by matching the current, resistance, and inductance in both the external circuit and the launcher. The algorithm was partly verified by experiments of a two-turn series-augmented railgun system. The full dynamic numerical results, such as the current and voltage histories, transient load characteristics, and time evolution of electromagnetic field, provided a deep insight on the launching process of the augmented railgun.

Material equations in electrodynamics of medium consisting of two-level emitters

The process of self-ordering in the famous Dicke model was studied in the framework of eliminating the boson variables. But the reduced description method enables us to obtain also the picture of electromagnetic field evolution provided field amplitudes and correlation functions are included into the number of reduced description parameters. In the Dicke Hamiltonian structure the interaction term includes the operators of emitter dipole moments or dipole moment density (polarization) since a spatial system is under consideration. Thus operator evolution equations are based on using such operators and their derivatives. The chain of evolution equations for averaged field amplitudes and binary correlation functions are obtained with using the statistical operator calculated in a perturbation theory in quasispin-photon interaction assumed to be small. The problem of chain decoupling does not arise since at any step we have a closed set of equations. The sets should be solved on the basis of material equations for current density and their generalizations for more complicated correlation functions. The way to constructing such equations and estimating the material parameters which are necessary for the numerical modeling of the development of correlations is discussed in the paper.

Rotating solutions of nonideal transverse Chern-Simons magnetohydrodynamics

In order to gain deeper insight into the physics of the novel rotating solution of nonideal transverse magnetohydrodynamics (MHD), presented in one of our recent works, we replace the previously considered Maxwell theory with the ${\cal{CP}}$ violating Maxwell-Chern-Simons (MCS) theory. In this way, dissipationless chiral magnetic (CM) and anomalous Hall (AH) currents appear in the MCS equation of motion, that, together with equations of relativistic hydrodynamics, builds the set of constitutive equations of the nonideal transverse Chern-Simons magnetohydrodynamics (CSMHD). We are, in particular, interested in the effect of these currents on the evolution of electromagnetic fields in a uniformly and longitudinally expanding quark-gluon plasma with chirality imbalance. Combining the constitutive equations of CSMHD under these assumptions, we arrive, as expected, at two distinct rotating and nonrotating solutions for electromagnetic fields. The rotation occurs with increasing rapidity and a constant angular velocity $\omega_{0}$. Remarkably, the relative angle between the electric and magnetic fields, $\delta$, turns out to be given by the coefficient of AH current $\kappa_{E}$ and the electric conductivity of the medium $\sigma$, as $\delta=\tan^{-1}(\kappa_{E}/\sigma)$. Whereas the nonrotating solution implies the AH coefficient to be vanishing, and thus nonrotating electric and magnetic fields to be either parallel or antiparallel, the relative orientation of rotating electric and magnetic fields and the evolution of the CM conductivity $\kappa_{B}$ are strongly affected by nonvanishing $\kappa_{E}$. We explore the effect of positive and negative $\omega_{0}$ on the evolution of the CM current, and show, in particular, that a rotation of electromagnetic fields with negative $\omega_{0}$ implies a sign flip of the CM current in a chiral fluid with nonvanishing AH current.

Conservative finite-difference scheme for the problem of THz pulse interaction with multilevel layer covered by disordered structure based on the density matrix formalism and 1D Maxwell's equation.

On the basis of the Crank-Nicolson method, we develop a conservative finite-difference scheme for investigation of the THz pulse interaction with a multilevel medium, covered by a disordered layered structure, in the framework of the Maxwell-Bloch equations, describing the substance evolution and the electromagnetic field evolution. For this set of the partial differential equations, the conservation laws are derived and proved. We generalize the Bloch invariant with respect to the multilevel medium. The approximation order of the developed finite-difference scheme is investigated and its conservatism property is also proved. To solve the difference equations, which are nonlinear with respect to the electric field strength, we propose an iteration method and its convergence is proved. To increase the computer simulation efficiency, we use the well-known solution of Maxwell’s equations in 1D case as artificial boundary condition. It is approximated using Cabaret scheme with the second order of an accuracy. On the basis of developed finite-difference scheme, we investigate the broadband THz pulse interaction with a medium covered by a disordered structure. This problem is of interest for the substance detection and identification. We show that the disordered structure dramatically induces an appearance of the substance false absorption frequencies. We demonstrate also that the spectrum for the transmitted and reflected pulses becomes broader due to the cascade mechanism of the high energy levels excitation of molecules. It leads to the substance emission at the frequencies, which are far from the frequency range for the incident pulse spectrum. Time-dependent spectral intensities at these frequencies are weakly disturbed by the disordered cover and, hence, they can be used for the substance identification.

Hybrid iterative approach for simulation of radio-frequency fields in plasma

A novel iterative approach for solving discretized linear wave equations in a frequency domain, which combines time evolution with iterative relaxation schemes, is presented. In this hybrid approach, each iteration cycle consists of evolution of electromagnetic (EM) fields in time over a specified number of field periods followed by several iterative relaxations. Provided that there is sufficient dissipation, both the time evolution and the iterative relaxations contribute to the convergence of the EM fields to the solution of the formulated full wave boundary value problem. Time evolution rapidly distributes EM fields, propagating with group velocity, over the simulation domain, while the iterative relaxations smooth the fields, reducing the numerical errors such that iteration cycles converge to a steady state solution, approximating the solution of the formulated problem. This approach is intended for large scale simulations which are beyond the capabilities of direct solvers presently used for solving wave equations in the frequency domain. The technique is demonstrated for solving wave equations on a regular grid using a cold plasma dielectric model with collisions for 2D modeling of EM fields in tokamak in an electron cyclotron frequency range.