Charged Particle In Electromagnetic Field Research Articles

Speeding-up direct implicit particle-in-cell simulations in bounded plasma by obtaining future electric field through explicitly propulsion of particles

The direct implicit particle-in-cell is a powerful kinetic method for researching plasma characteristics. However, it is time-consuming to obtain the future electromagnetic field in such a method since the field equations contain time-dependent matrix coefficients. In this work, we propose to explicitly push particles and obtain the future electromagnetic field based on the information about the particles in the future. The new method retains the form of implicit particle pusher, but the future field is obtained by solving the traditional explicit equation. Several numerical experiments, including the motion of charged particle in electromagnetic field, plasma sheath, and free diffusion of plasma into vacuum, are implemented to evaluate the performance of the method. The results demonstrate that the proposed method can suppress finite-grid-instability resulting from the coarse spatial resolution in electron Debye length through the strong damping of high-frequency plasma oscillation, while accurately describe low-frequency plasma phenomena, with the price of losing the numerical stability at large time-step. We believe that this work is helpful for people to research the bounded plasma by using particle-in-cell simulations.

Новая схема интегрирования уравнений движения частиц в методе “частиц-в-ячейках” для задач физики плазмы

Представлен новый метод решения релятивистских уравнений движения заряженных частиц в электромагнитных полях, учитывающий условие постоянства их значений на каждом временном шаге. Проведено сравнение точности и эффективности вычислений при решении тестовых задач в дву- и трехмерной постановках на основе нового метода, метода Бориса и его модификаций. В каждом случае рассматривались варианты аналитически и дискретно заданных значений электрического и магнитного полей. At present, the Boris method is mostly common for the numerical solution of problems of the dynamics of charged particles in electromagnetic fields. In recent years, new modifications of the Boris method have appeared that are capable to simplify, refine, or speed up calculations. However, despite the rather large number of publications which consider algorithms for calculating the trajectories of charged particles, new, more accurate and high-performance algorithms are desired. The article presents a detailed analysis of some explicit methods for solving the problem of the motion of charged particles in electromagnetic fields, which differ in how they set the average values of velocities. A new scheme based on an analytical solution, which has not been studied before, is proposed. For the Boris, Vay, Higuera – Cary schemes and the new VD1 scheme, a comparative analysis of the accuracy, convergence and counting time for the relativistic and nonrelativistic cases is carried out. In the nonrelativistic case, the new scheme allows accurate solving of the equations for motion of charged particles, and in the relativistic case, the accuracy of the new scheme remains higher compared to other schemes. As the relativistic factor increases, the accuracy of all considered schemes for calculating the trajectory of particles in an electromagnetic field decreases. For large values of the relativistic parameter, the new scheme is more accurate than the other schemes and retains the second order. In practical calculations, when particles can have different speeds, the scheme automatically adjusts to the given speed of the particle. The presented new scheme for calculating trajectories can be important for solving a wide range of problems in astrophysics and thermonuclear fusion, where high accuracy in determining particle trajectories in inhomogeneous fields for large moments of time is required.

Charged particle motion and radiation in strong electromagnetic fields

The dynamics of charged particles in electromagnetic fields is an essential component of understanding the most extreme environments in our Universe. In electromagnetic fields of sufficient magnitude, radiation emission dominates the particle motion and effects of nonlinear quantum electrodynamics (QED) are crucial, which triggers electron-positron pair cascades and counterintuitive particle-trapping phenomena. As a result of recent progress in laser technology, high-power lasers provide a platform to create and probe such fields in the laboratory. With new large-scale laser facilities on the horizon and the prospect of investigating these hitherto unexplored regimes, we review the basic physical processes of radiation reaction and QED in strong fields, how they are treated theoretically and in simulation, the new collective dynamics they unlock, recent experimental progress and plans, as well as possible applications for high-flux particle and radiation sources.

Investigation of Monte Carlo simulations of the electron transport in external magnetic fields using Fano cavity test

PurposeMonte Carlo simulations are crucial for calculating magnetic field correction factors kB for the dosimetry in external magnetic fields. As in Monte Carlo codes the charged particle transport is performed in straight condensed history (CH) steps, the curved trajectories of these particles in the presence of external magnetic fields can only be approximated. In this study, the charged particle transport in presence of a strong magnetic field B→ was investigated using the Fano cavity test. The test was performed in an ionization chamber and a diode detector, showing how the step size restrictions must be adjusted to perform a consistent charged particle transport within all geometrical regions. MethodsMonte Carlo simulations of the charged particle transport in a magnetic field of 1.5 T were performed using the EGSnrc code system including an additional EMF-macro for the transport of charged particle in electro-magnetic fields. Detailed models of an ionization chamber and a diode detector were placed in a water phantom and irradiated with a so called Fano source, which is a monoenergetic, isotropic electron source, where the number of emitted particles is proportional to the local density. ResultsThe results of the Fano cavity test strongly depend on the energy of charged particles and the density within the given geometry. By adjusting the maximal length of the charged particle steps, it was possible to calculate the deposited dose in the investigated regions with high accuracy (<0.1%). The Fano cavity test was performed in all regions of the detailed detector models. Using the default value for the step size in the external magnetic field, the maximal deviation between Monte Carlo based and analytical dose value in the sensitive volume of the ion chamber and diode detector was 8% and 0.1%, respectively. ConclusionsThe Fano cavity test is a crucial validation method for the modeled detectors and the transport algorithms when performing Monte Carlo simulations in a strong external magnetic field. Special care should be given, when calculating dose in volumes of low density. This study has shown that the Fano cavity test is a useful method to adapt particle transport parameters for a given simulation geometry.

New motion algorithm in the particle-in-cell method

The article proposes a new method for solving the equations of motion of charged particles in electromagnetic fields. In the algorithm, the velocity of a charged particle at a time step is computed in accordance with the exact solution of the differential equation. The method has been compared with various known modifications of the Boris method. The comparison was carried out both in terms of the accuracy of the methods and the time of their operation. A new modification of the method uses the fact that the electric and magnetic fields are constant at a time step. It allows one to compute more accurately the trajectory and velocity of a charged particle without significant increasing the complexity of the computations. It has been shown that when choosing a modification of the Boris method to solve a problem, one should pay attention first of all to the accuracy of the solution, since a simpler and faster scheme may not give a gain in time.

Explicit high-order exponential time integrator for discontinuous Galerkin solution of Maxwell's equations

In this paper, exponential propagator (EP) is introduced to the discontinuous Galerkin finite element method (DG-FEM) for solving transient electromagnetic problems. As a kind of explicit time-stepping method, the proposed EP has fourth order accuracy in time and requires only one storage unit for each of the degrees-of-freedom. It provides an attractive alternative to the high-order low-storage explicit Runge-Kutta (LSERK) approach, which is the most popular time-marching scheme currently used in high-fidelity simulation of Maxwell's equations with DG-FEM. When centered numerical flux is utilized, the discretized Maxwell's system in lossless region is symplectic structure-preserving (energy conserving), and thus very suitable for accurately computing the long-time propagation of waves in non-dissipative medium, or simulating the motion of charged particles in electromagnetic fields. Our method can also handle upwind numerical flux at the sacrifice of symplectic-conserving virtue for higher accuracy in spatial discretization and spurious inhibition. A major contribution of this work is that, the application range of this scheme is extended to lossy media such as conductors and particularly unsplit perfectly matched layers in the framework of DG-FEM. This greatly facilitates the treatment of open boundary conditions in scattering and/or radiation problems. Extensive numerical examples, including the analysis of photonic crystals, dielectric coated perfect conducting cylinder, propagation of waves in zero-index materials, and corrugated O-type Cherenkov oscillators etc., are presented to demonstrate its stability, accuracy, and performance. All the numerical experiments show that the presented method is superior to the LSERK scheme when centered numerical flux is adopted.

Taking an electron-magnon duality shortcut from electron to magnon transport

The quasiparticles in insulating magnets are the charge-neutral magnons, whose magnetic moments couple to electromagnetic fields. For collinear easy-axis magnets, this coupling can be mapped elegantly onto the scenario of charged particles in electromagnetic fields. From this mapping we obtain equations of motion for magnon wave packets equal to those of electron wave packets in metals. Thus, well-established electronic transport phenomena can be carried over to magnons: this duality shortcut facilitates the discussion of magnon transport. We identify the magnon versions of normal and anomalous Hall, Nernst, Ettingshausen, and Righi-Leduc effects. They are discussed for selected types of easy-axis magnets: ferromagnets, antiferromagnets, and ferrimagnets. Besides a magnon Wiedemann-Franz law and the magnon counterpart of the negative magnetoresistance of electrons in Weyl semimetals, we predict that certain low-symmetry ferrimagnets exhibit a nonlinear version of the anomalous magnon Hall-effect family.

Coherent and Semiclassical States of a Charged Particle in Electromagnetic Fields

In the present article we extend our study (BJP 45 (2015) 369) of generalized coherent states (GCS) of a one-dimensional particle considering such important physical system as a 3-dimensional charged particle in electric and magnetic fields. Constructing GCS in many-dimensional case, we meet nontrivial technical complications that make the consideration nontrivial and instructive. The GCS of a system under consideration are constructed. We study properties of these GCS such as completeness relations, minimization of uncertainty relations and so on. We point out which family of the obtained GCS of a charged particle in magnetic field is related with the CS constructed first by Malkin and Man'ko. We obtain conditions under which some of the GCS can be considered as semiclassical states.

Influence of thermal fluctuations on dynamics of charged particles in electromagnetic fields

The numerical study of dynamics of the charged particles in the confined cloud located in a constant electromagnetic field is presented. Calculations are performed for ions with various masses in a wide range of system parameters. For the first time, an influence of thermal fluctuations of particles on their motion in an electromagnetic field is considered. Analytical estimations for the analysis of this effect are proposed.

A fast numerical integrator for relativistic charged particle tracking

In this paper, we report on a fast second-order numerical integrator to solve the Lorentz force equations of a relativistic charged particle in electromagnetic fields. This numerical integrator shows less numerical error than the popular Boris algorithm in tracking the relativistic particle subject to electric and magnetic space-charge fields and requires less number of operations than another recently proposed relativistic integrator.

A family of new explicit, revertible, volume-preserving numerical schemes for the system of Lorentz force

The Lorentz system underlies the fundamental rules for the motion of charged particle in electromagnetic field, which is proved volume-preserving. In this paper, we construct a family of new revertible numerical schemes for general autonomous systems, which in particular, are explicit and volume-preserving for Lorentz systems. These new schemes can prevent the extra numerical errors caused by mismatched initial half-step values in the Boris-like algorithm. Numerical experiments demonstrate the superiorities of our second-order methods in long-term simulations and energy preservation over the Boris algorithm and a higher order Runge-Kutta method (RK3). We also apply these new methods to the guiding center system and find that they behave much better than RK3.

On progressive blast envelope evolution of charged particles in electromagnetic fields

In this paper, we investigate the explosion of a set of charged particles in an electromagnetic field and the progressive time-evolution of the blast envelope. It is shown that the initial spherical blast envelope evolves into the shape of an ellipsoid whose longitudinal axis is aligned with the magnetic field. Specifically, the individual particles rotate around the longitudinal axis, and rotate in decaying orbits until they become stationary, leaving a stationary overall ellipsoidal configuration of particles. In order to investigate this system, a direct multiparticle model is constructed, which balances the detonation energy released from the initial blast pulse with the subsequent particle-system kinetic energy and then computes the trajectories of the discrete interacting material under the influence of the electromagnetic field and drag from any surrounding medium. Under certain simplifying assumptions, the model can be solved for analytically, which provides a guide to identifying the key parameters that control the evolving blast envelope. Three dimensional examples are provided to illustrate the framework/method.

Optimal Control of the Inhomogeneous Relativistic Maxwell--Newton--Lorentz Equations

This note is concerned with an optimal control problem governed by the relativistic Maxwell--Newton--Lorentz equations, which describe the motion of charged particles in electro-magnetic fields and consists of a hyperbolic PDE system coupled with a nonlinear ODE. An external magnetic field acts as control variable. Additional control constraints are incorporated by introducing a scalar magnetic potential which leads to an additional state equation in the form of a very weak elliptic PDE. Existence and uniqueness for the state equation is shown and the existence of a global optimal control is established. Moreover, first-order necessary optimality conditions in the form of Karush--Kuhn--Tucker conditions are derived. A numerical test illustrates the theoretical findings.

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators.

Motion-induced X-ray and terahertz radiation of electrons captured in laser standing wave

The motions of charged particles in electromagnetic fields composed of two or more laser beams show a variety of forms due to the adjustable properties of electromagnetic fields. In this paper, we consider the periodic laser standing wave field composed of two laser beams with opposite propagating directions. The movement of electrons in the standing wave field shows a periodic behavior, accompanied with the obvious radiation, especially when electrons are captured by the laser standing wave field. This phenomenon has aroused much interest of us. Under the existing experimental conditions, the free electron beam with low energy from an electron gun or the relativistic electron beam generated from laser acceleration can be easily obtained and injected into the periodic standing wave field. In this paper, using the single-electron model and the classical radiation theory of charged particles, we study the motion and radiation processes of low and high energy electrons in the polarized laser standing wave field. The results show that when the direction of incident electrons with low-speed is perpendicular to the direction of the laser standing wave electric field, the one-dimensional nearly periodic motion of electrons evolves into a two-dimensional folded movement by gradually increasing the light intensity of the laser standing wave field, and the strong terahertz radiation at micrometer wavelength is produced. High energy electrons generate the high-frequency radiation with the wavelength at several nanometers when the incident direction of high energy electrons is perpendicular or parallel to the direction of the laser standing wave electric field. In the case of low-energy electron, the motion of electron, frequency and intensity of radiation are affected by the laser intensity. In the case of incident high-energy electrons, the laser intensity affects the intensity of electronic radiation, and the initial electron energy influences radiation frequency. The bigger the incident electrons energy, the higher the frequency of radiation is. #br#We can obtain electron beams with different energies by laser acceleration, and they can be promising small radiation sources for terahertz and X-ray by using the electron beam radiation in a laser standing wave field. These studies also provide a basis for experimental researches and the applications of electron radiation in a laser standing wave field.

Direct calculation of length contraction and clock retardation

For simple electromagnetic models of a rod and a clock, a change of shape of a rod and of the rate of clock when they are set in uniform motion is calculated exactly, employing the correct equation of motion of a charged particle in electromagnetic field and the universal boostability assumption. Thus it is demonstrated that, for the simple system considered, the length contraction and clock retardation can be interpreted as dynamical cause-and-effect phenomena, and not as kinematical effects as usually construed in conventional presentations of Special Relativity. It is argued that the perspective relativistic change of an object (corresponding to observations from two inertial frames), while certainly being an a causal effect, has a dynamical content in the sense that it is tantamount to an actual dynamical change of the object in one frame.

Noether's theorem and the work-energy theorem for a charged particle in an electromagnetic field

Noether's theorem is based on two fundamental ideas. The first is the extremum of the action and the second is the invariance of the action under infinitesimal continuous transformations in space and time. The first gives Hamilton's principle of least action, which results in the Euler–Lagrange equations. The second gives the Rund–Trautman identity for the generators of infinitesimal transformations in space and time. We apply these ideas to a charged particle in an external electromagnetic field. A solution of the Rund–Trautman identity for the generators is obtained by solving generalized Killing equations. The Euler–Lagrange equations and the Rund–Trautman identity are combined to give Noether's theorem for a conserved quantity. When we use the Lagrangian and the generators of infinitesimal transformations for a charged particle in an external electromagnetic field, we obtain the work-energy theorem.

The Stability Analysis of the Relativity Motion of Charged Particles in Electromagnetic Fields and the Possibility to Establish Synchrocyclotron without Radiation Losses

According to the classical theory of electromagnetism, charged particles radiate electromagnetic waves when they are accelerated. However, actual situations are not completely the cases. For example, only when electrical current oscillates, antenna radiates radio waves. If parameters are not proper, no radio waves are produced. Although in both situations, electrons do period accelerating and decelerating motions. When electrons collide with atomic nucleus, braking radiation takes place. But electrons do not radiate when they are accelerated in uniform electric field. In synchrocyclotron, electrons radiate, but in electron induction accelerator, no radio radiations were founded (J. Blewett experiment). In fact, in the common loops of alternate or direct currents, as well as in the current loops made from low temperature supper-conductors, no radiations are found. A more foundational fact is that electrons do not radiate when they move around atomic nucleus and atoms are stable. These facts contradict with classical electromagnetic theory. We have no rational explanation for them at present. It is proved in this paper that the forms of forces can not be arbitrary in the dynamic equations of relativity. Otherwise the motions may become impossible. In order to make the motions possible in electromagnetic field, charged particles have to radiate. It is proved that the longitudinal velocities of charged particles in the uniform magnetic fields would exceed light’s speed in vacuum, and therefore the motions are unstable and charged particles have to radiate. In the center electric fields, the motions of charged particles may be both stable and unstable depending on the actual situations, and they may radiate or not radiate. Therefore, acceleration is not the real season for charged particles to radiate. The real one is the instability of relativity motion. The essence of antenna radiations is proved to be the braking radiation and the braking radiation is the effect of relativity actually. The radiation damping forces should be added in the motion equations of relativity to describe charged particle’s motions in electromagnetic fields when they radiate. The forms of damping forces are deduced. The synchrocyclotron oscillation of electron’s obits at longitudinal direction is obtained automatically. It is proved that if a proper electric force is acted at the direction of velocity, the relativity motion of electron in magnetic field will become stable so that it may not radiate. In this way, we can establish high energy synchrocyclotron without or less synchrony radiation losses.

Acceleration of adiabatic quantum dynamics in electromagnetic fields

We show a method to accelerate quantum adiabatic dynamics of wave functions under electromagnetic field (EMF) by developing the preceding theory [Masuda and Nakamura, Proc. R. Soc. London Ser. A 466, 1135 (2010)]. Treating the orbital dynamics of a charged particle in EMF, we derive the driving field which accelerates quantum adiabatic dynamics in order to obtain the final adiabatic states in any desired short time. The scheme is consolidated by describing a way to overcome possible singularities in both the additional phase and driving potential due to nodes proper to wave functions under EMF. As explicit examples, we exhibit the fast forward of adiabatic squeezing and transport of excited Landau states with nonzero angular momentum, obtaining the result consistent with the transitionless quantum driving applied to the orbital dynamics in EMF.

A computational framework for agglomeration in thermochemically reacting granular flows

A computational framework is developed which couples a series of models, each describing vastly different physical events, in order to characterize particle growth (agglomeration) in thermochemically reacting granular flows. The modelling is purposely simplified to expose the dominant mechanisms which control agglomeration. The overall system is comprised of relatively simple coupled submodels describing impact, heat production, bonding and fragmentation, each of which can be replaced by more elaborate descriptions, if and when they are available. Inverse problems, solved with a genetic algorithm, are then constructed to ascertain system parameters which maximize agglomeration likelihood within a range of admissible data.