Self-consistent Electromagnetic Field Research Articles

Quantified asymptotic analysis for the relativistic quantum mechanical system with electromagnetic fields

We study the asymptotic analysis of a relativistic quantum mechanical system interacting with self-consistent electromagnetic fields, with a specific focus on the Maxwell–Klein–Gordon (MKG) system. Firstly, we show that the MKG system is globally well-posed under the Coulomb gauge condition, even in the presence of self-interacting potential. Furthermore, to derive the asymptotic analysis, we consider the non-relativistic and semi-classical regime simultaneously, introducing a single scaling parameter that serves to parameterize both the speed of light and the Planck constant. As the scaling parameter approaches zero, we obtain rigorous and quantified estimates on the asymptotic convergence of the electrostatic MKG system toward the classical Euler–Poisson system. Our analytical framework relies on the modulated energy estimate.

Реализация метода частиц на компьютере с графическими ускорителями

The effective variant of particle method algorithm for modeling surface generation, propagation and scattering of electrons in a self-consistent electromagnetic field is presented. An implementation of the algorithm on a hybrid cluster with graphic processor units (GPU) is worked out. Solutions to the problems of synchronization of recording results and data exchange are considered. The implementation is oriented on problems of electron emission and self-consistent electromagnetic field modeling in apparature blocks.

Mathematical modelling of proton migration in Earth mantle

In the study, we address the mathematical problem of proton migration in the Earth’s mantle and suggest a prototype for exploring the Earth’s interior to map the effects of superionic proton conduction. The problem can be mathematically solved by deriving the self-consistent electromagnetic field potential U(x, t) and then reconstructing the distribution function f(x,v,t). Reducing the Vlasov-Maxwell system of equations to non-linear sh-Gordon hyperbolic and transport equations, the propagation of a non-linear wavefront within the domain and transport of the boundary conditions in the form of a non-linear wave are examined. By computing a 3D model and through Fourier-analysis, the spatial and electrical characteristics of potential U(x, t) are investigated. The numerical results are compared to the Fourier transformed quantities of the potential (V) obtained through field observations of the electric potential (Kuznetsov method). The non-stationary solutions for the forced oscillation of two-component system, and therefore, the oscillatory strengths of two types of charged particles can be usefully addressed by the proposed mathematical model. Moreover, the model, along with data analysis of the electric potential observations and probabilistic seismic hazard maps, can be used to develop an advanced seismic risk metric.

The Role of Mesoscale Plasma Sheet Dynamics in Ring Current Formation

During geomagnetically active periods ions are transported from the magnetotail into the inner magnetosphere and accelerated to energies of tens to hundreds of keV. These energetic ions, of mixed composition with the most important species being H+ and O+, become the dominant source of plasma pressure in the inner magnetosphere. Ion transport and acceleration can occur at different spatial and temporal scales ranging from global quasi-steady convection to localized impulsive injection events and may depend on the ion gyroradius. In this study we ascertain the relative importance of mesoscale flow structures and the effects of ion non-adiabaticity on the produced ring current. For this we use: global magnetohydrodynamic (MHD) simulations to generate self-consistent electromagnetic fields under typical driving conditions which exhibit bursty bulk flows (BBFs); and injected test particles, initialized to match the plasma moments of the MHD simulation, and subsequently evolved according to the kinetic equations of motion. We show that the BBFs produced by our simulation reproduce thermodynamic and magnetic statistics from in situ measurements and are numerically robust. Mining the simulation data we create a data set, over a billion points, connecting particle transport to characteristics of the MHD flow. From this we show that mesoscale bubbles, localized depleted entropy regions, and particle gradient drifts are critical for ion transport. Finally we show, using identical particle ensembles with varying mass, that O+ non-adiabaticity creates qualitative differences in energization and spatial distribution while H+ non-adiabaticity has non-negligible implications for loss timescales.

Building Blocks for the Development of a Self-Consistent Electromagnetic Field Theory of Consciousness.

The goal of this work is to compile the basic components for the construction of an electromagnetic field theory of consciousness that meets the standards of a fundamental theory. An essential cornerstone of the conceptual framework is the vacuum state of quantum electrodynamics which, contrary to the classical notion of the vacuum, can be viewed as a vibrant ocean of energy, termed zero-point field (ZPF). Being the fundamental substrate mediating the electromagnetic force, the ubiquitous ZPF constitutes the ultimate bedrock of all electromagnetic phenomena. In particular, resonant interaction with the ZPF is critical for understanding rapidly forming, long-range coherent activity patterns that are characteristic of brain dynamics. Assuming that the entire phenomenal color palette is rooted in the vibrational spectrum of the ZPF and that each normal mode of the ZPF is associated with an elementary shade of consciousness, it stands to reason that conscious states are caused by the coupling of the brain to a particular set of normal modes selectively filtered from the full frequency spectrum of the ZPF. From this perspective, the brain is postulated to function as a resonant oscillator that couples to a specific range of ZPF modes, using these modes as a keyboard for the composition of an enormous variety of phenomenal states. Theoretical considerations suggest that the brain-ZPF interface is controlled by altering the concentrations of neurotransmitters, placing the detailed study of the neurotransmitter-ZPF interaction at the center of future research activities.

Computational Investigations on the Four-Stage MA-Class Fast Linear Transformer Driver With Sharing Cavity Shell

The four-stage fast linear transformer driver (FLTD) with sharing cavity shell, gas insulation, and pluggable main bricks is the fundamental building block of the next-generation China Z-pinch driver CZ34. This contribution presents the self-consistent electromagnetic (EM) field distributions of the four-stage FLTD using the field-circuit coupled time-domain finite integration technique. Principles and methods on establishing the 3-D EM numerical model are discussed. The first analysis on equivalent inductances of the 92 main discharging bricks in the induction cavity and bricks’ EM characteristics is implemented. Simulated and experimental results demonstrate good consistency in the electrical performance of the four-stage FLTD with sharing cavity shell. Comparisons between the sharing cavity shell and independent cavity shell structures are performed in terms of load current and voltage and EM field distributions. Thus, applicability of the newly developed sharing cavity configuration is confirmed. The EM-interference (EMI) inside the induction cavity of the two kinds of FLTDs is also expounded and compared for the first time. This article offers a novel viewpoint on the related problems and supports the subsequent research activity and efforts to improve the performance of FLTD and Z-pinch machine.

Construction of Dirac spinors for electron vortex beams in background electromagnetic fields

Exact solutions of the Dirac equation, a system of four partial differential equations, are rare. The vast majority of them are for highly symmetric stationary systems. Moreover, only a handful of solutions for time dependent dynamics exists. Given the growing number of applications of high energy electron beams interacting with a variety of quantum systems in laser fields, novel methods for finding exact solutions to the Dirac equation are called for. We present a method for building up solutions to the Dirac equation employing a recently introduced approach for the description of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. We illustrate the method by developing several stationary as well as non-stationary solutions of the Dirac equation with well defined orbital angular momentum along the electron's propagation direction. The first set of solutions describe free electron beams in terms of Bessel functions as well as stationary solutions for both a homogeneous and an inhomogeneous magnetic field. The second set of solutions are new and involve a plane electromagnetic wave combined with a generally inhomogeneous longitudinal magnetic field. Moreover, the developed technique allows us to derive general physical properties of the dynamics in such field configurations, as well as provides physical predictions on the self-consistent electromagnetic fields induced by the dynamics.

Non-local Quantum Plasmon Resonance in Ultra-small Silver Nanoparticles

Understanding the mechanisms of light–matter interactions in ultra-small plasmonic nanoparticles (USNP) represents a major challenge because of the importance of size dependence and quantum effects. The plasmon resonance in such small metallic nanoparticles (< 5 nm) exhibits substantial deviation from classical theory predictions, with evident frequency shifts to a higher energy. This is due to the quantum nature of the free charge carriers and the dynamic response of metallic nanoparticle to the self-consistent electromagnetic fields. Such phenomena have so far been poorly understood in experiments while classical theory has mostly focused on nanostructures and sidestepped the size dependence. Here we report a quantum mechanical model of the metal permittivity to describe the USNP behaviour and experimental evidence. The proposed non-local quantum model of the permittivity for the propagation of plasmon waves in quantum-confined silver nanoparticles has no size limitations in the UNSP range.

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.

Schur Complement and Continuous Spectrum in a Kinetic Plasma Model

The goal of this paper is spectral analysis of an evolutionary semigroup generator describing the dynamics of a rarefied two-component plasma subjected to a self-consistent electromagnetic field. For the problem in question, the spectrum is given in terms of the dispersion relationship and an effective approach to the calculation of the instability index is developed.

Variational schemes and geometric simulations for a hydrodynamic-electrodynamic model of surface plasmon polaritons.

A class of variational schemes for the hydrodynamic-electrodynamic model of lossless free-electron gas in a quasineutral background is developed for high-quality simulations of surface plasmon polaritons. The Lagrangian density of lossless free-electron gas with a self-consistent electromagnetic field is established, and the dynamical equations with the associated constraints are obtained via a variational principle. Based on discrete exterior calculus, the action functional of this system is discretized and minimized to obtain the discrete dynamics. Newton-Raphson iteration and the biconjugate gradient stabilized method are equipped as a hybrid nonlinear-linear algebraic solver. Instead of discretizing the partial differential equations, the variational schemes have better numerical properties in secular simulations, as they preserve the discrete Lagrangian symplectic structure, gauge symmetry, and general energy-momentum density. Two numerical experiments were performed. The numerical results reproduce characteristic dispersion relations of bulk plasmons and surface plasmon polaritons, and the numerical errors of conserved quantities in all experiments are bounded by a small value after long-term simulations.

Eulerian variational formulations and momentum conservation laws for kinetic plasma systems

The Eulerian variational principle for the Vlasov-Poisson-Ampère system of equations in a general coordinate system is presented. The invariance of the action integral under an arbitrary spatial coordinate transformation is used to obtain the momentum conservation law and the symmetric pressure in a more direct way than using the translational and rotational symmetries of the system. Next, the Eulerian variational principle is given for the collisionless drift kinetic equation, where particles' phase-space trajectories in given electromagnetic fields are described by Littlejohn's guiding center equations [R. G. Littlejohn, J. Plasma Phys. 29, 111 (1983)]. Then, it is shown that, in comparison with the conventional moment method, the invariance under a general spatial coordinate transformation yields a more convenient way to obtain the momentum balance as a three-dimensional vector equation in which the symmetric pressure tensor, the Lorentz force, and the magnetization current are properly expressed. Furthermore, the Eulerian formulation is presented for the extended drift kinetic system, for which, in addition to the drift kinetic equations for the distribution functions of all particle species, the quasineutrality condition and Ampère's law to determine the self-consistent electromagnetic fields are given. Again, the momentum conservation law for the extended system is derived from the invariance under the general spatial coordinate transformation. Besides, the momentum balances are investigated for the cases where the collision and/or external source terms are added to the Vlasov and drift kinetic equations.

Why do Electrons with “Anomalous Energies” appear in High-Pressure Gas Discharges?

Experimental studies connected with runaway electron beams generation convincingly shows the existence of electrons with energies above the maximum voltage applied to the discharge gap. Such electrons are also known as electrons with “anomalous energies”. We explain the presence of runaway electrons having so-called “anomalous energies” according to physical kinetics principles, namely, we describe the total ensemble of electrons with the distribution function. Its evolution obeys Boltzmann kinetic equation. The dynamics of self-consistent electromagnetic field is taken into the account by adding complete Maxwell’s equation set to the resulting system of equations. The electrodynamic mechanism of the interaction of electrons with a travelling-wave electric field is analyzed in details. It is responsible for the appearance of electrons with high energies in real discharges.

Long term regularity of the one-fluid Euler–Maxwell system in 3D with vorticity

A basic model for describing plasma dynamics is given by the “one-fluid” Euler–Maxwell system, in which a compressible electron fluid interacts with its own self-consistent electromagnetic field. In this paper we prove long-term regularity of solutions of this system in 3 spatial dimensions, in the case of small initial data with nontrivial vorticity.Our main conclusion is that the time of existence of solutions depends only on the size of the vorticity of the initial data, as long as the initial data is sufficiently close to a constant stationary solution.

Nonlinear waves and coherent structures in quasi-neutral plasmas excited by external electromagnetic radiation

Starting from the Vlasov-Maxwell equations describing the dynamics of various species in a quasi-neutral plasma, an exact relativistic hydrodynamic closure for a special type of water-bag distribution 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 fully equivalent to the Vlasov-Maxwell system. 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, has been derived. Using the method of formal series of Dubois-Violette, a traveling wave solution of the derived set of coupled nonlinear Schrodinger equations in the case of circular wave polarization has been obtained. This solution is represented as a ratio of two formal Volterra series. The terms of these series can be calculated explicitly to every desired order.

Parallel implementation of a relativistic semi-Lagrangian Vlasov–Maxwell solver

We describe the parallel implementation of a semi-Lagrangian relativistic VLasov ElectroMagnetic (VLEM) code for the numerical investigation of the dynamics of charged particle distribution in their self-consistent electromagnetic fields. This paper introduces the numerical solution of the Vlasov–Maxwell system in two spatial dimensions, and two or three momentum dimensions. Accuracy, stability, efficiency properties and the implementation of a new algorithm of charge conservation when solving Maxwell equations are discussed. The performances of the code are tested by studying the evolution of Weibel-type instabilities in the relativistic regime. Application to the coupling between Current Filamentation (CFI) and Two-Stream (TSI) instabilities is presented showing the importance of pair-wise vortex merging scenario in the saturation mechanism.

The Euler–Maxwell System for Electrons: Global Solutions in 2D

A basic model for describing plasma dynamics is given by the Euler-Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. In this paper we consider the "one-fluid" Euler--Maxwell model for electrons, in 2 spatial dimensions, and prove global stability of a constant neutral background.

On the Vlasov--Maxwell System with a Strong Magnetic Field

This paper establishes the long time asymptotic limit of the $2d\times 3d$ Vlasov--Maxwell system with a strong external magnetic field. Hence, a guiding-center approximation is obtained in the two-dimensional case with a self-consistent electromagnetic field given by Poisson type equations. Then, we perform several numerical experiments with high order approximation of the asymptotic model, which provide a solid validation of the method and illustrate the effect of the self-consistent magnetic field on the current density.

Simulation of collisionless ultrarelativistic electron–proton plasma dynamics in a self-consistent electromagnetic field

The evolution of a collisionless electron–proton plasma in the self-consistent approximation is investigated. The plasma is assumed to move initially as a whole in a vacuum with the Lorentz factor. The behavior of the dynamical system is analyzed by applying a three-dimensional model based on the Vlasov–Maxwell equations with allowance for retarded potentials. It is shown that the analysis of the solution to the problem is not valid in the “center-of-mass frame” of the plasmoid (since it cannot be correctly defined for a relativistic plasma interacting via an electromagnetic field) and the transition to a laboratory frame of reference is required. In the course of problem solving, a chaotic electromagnetic field is generated by the plasma particles. As a result, the particle distribution functions in the phase space change substantially and differ from their Maxwell–Juttner form. Computations show that the kinetic energies of the electron and proton components and the energy of the self-consistent electromagnetic field become identical. A tendency to the isotropization of the particle momentum distribution in the direction of the initial plasmoid motion is observed.

Моделирование динамики бесстолкновительной ультрарелятивистской электрон-протонной плазмы в самосогласованном электромагнитном поле

Моделирование динамики бесстолкновительной ультрарелятивистской электрон-протонной плазмы в самосогласованном электромагнитном поле