System Of Charged Particles Research Articles

Quasi-periodic boundary conditions for hierarchical algorithms used for the calculation of inter-particle electrostatic interactions

In the present work, a simplified way to apply tri-periodic Boundary Conditions (BCs) in hierarchical algorithms has been devised. The application of these BCs is demonstrated using an in-house algorithm that is used for the calculation of electrostatic interactions in a system of charged particles. The proposed quasi-periodic BCs entail a truncation of the infinite periodic domain with a reasonable cut-off error. For a correct representation of the physics, two properties have to be ensured: the convergence of the electrostatic forces and the isotropy of the electric field. The developed algorithm allows for a rather efficient and precise calculation of the former in a tri-periodic computational domain by separating them in short- and long-range parts, which are calculated exactly and approximately, respectively. The approximation error, computational cost and performance of the proposed algorithm are documented and thoroughly analyzed. Then, an application of the method is presented for dry mono-charged (all particles bear equal charge) particle flows where the fundamentals physics of particle-particle electrostatic interactions are investigated via characteristic length and time scales. It is shown that the underlying mechanism of these interactions is the Coulomb collision, a concept that allows to interpret these interactions in a rather intuitive way. In addition, an attempt is made to provide analytical estimations for several statistical quantities via dimensional analysis based on measured simulation data. Finally, the particle-induced electric field is presented and its characteristics are related to particle motion.

Discrete-to-Continuum Convergence of Charged Particles in 1D with Annihilation

We consider a system of charged particles moving on the real line driven by electrostatic interactions. Since we consider charges of both signs, collisions might occur in finite time. Upon collision, some of the colliding particles are effectively removed from the system (annihilation). The two applications we have in mind are vortices and dislocations in metals. In this paper we achieve two goals. First, we develop a rigorous solution concept for the interacting particle system with annihilation. The main innovation here is to provide a careful management of the annihilation of groups of more than two particles, and we show that the definition is consistent by proving existence, uniqueness, and continuous dependence on initial data. The proof relies on a detailed analysis of ODE trajectories close to collision, and a reparametrization of vectors in terms of the moments of their elements. Second, we pass to the many-particle limit (discrete-to-continuum), and recover the expected limiting equation for the particle density. Due to the singular interactions and the annihilation rule, standard proof techniques of discrete-to-continuum limits do not apply. In particular, the framework of measures seems unfit. Instead, we use the one-dimensional feature that both the particle system and the limiting PDE can be characterized in terms of Hamilton–Jacobi equations. While our proof follows a standard limit procedure for such equations, the novelty with respect to existing results lies in allowing for stronger singularities in the particle system by exploiting the freedom of choice in the definition of viscosity solutions.

Investigation of the dynamic structural factor of binary ionic mixtures

The method of moments is used to investigate and analyze the dynamic characteristics of dense systems consisting of ions of two types with different masses and charges, and the number of screening electrons corresponding to the charges of the ions.In this paper, we discuss the characteristics of a binary ionic mixture whose component masses differ by a factor of two. Within the framework of the developed self-consistent method of moments, the dynamic structure factors (DSF) of such a plasma are calculated for various thermodynamic parameters. In this case, the calculation algorithm is based on the use, on the one hand, of the static structural factor of the system, which is determined from the solution of the Ornstein-Zernike equation, and on the other hand, the so-called Nevanlinna parameter function (NPF), which is included in the calculated relations. The calculations were carried out within the framework of the classical system of charged particles interacting according to the Coulomb law. The paper analyzes the data obtained using various methods for calculating the NPF. The results obtained in this work qualitatively and quantitatively agree with the data of theoretical calculations and numerical experiments of the authors of other studies of the dynamic properties of a dense multicomponent plasma.

Dynamical conductivity of warm dense matter from correlation functions with account for interband transitions

Within the generalized linear response theory, the dynamical conductivity of charged particle systems is obtained from equilibrium correlation functions. Using the force–force correlation function approach, interband transitions in addition to phonon interaction and umklapp processes are taken into account for warm dense matter. For solid-density aluminum and copper plasmas, the results are shown for dynamical collision frequency, dynamical conductivity, and opacity as functions of laser frequency accounting for interband absorption. Calculated opacities for aluminum plasmas are compared with results of first-principles density functional theory–molecular dynamic (DFT-MD) simulations and recent experiments. The problem of underestimating the size of opacities by theoretical models in the vicinity of the L edge is discussed.

Self-Organization of Charged Particles in an Electric Field

Self-organization in small systems of particles with simple dynamic laws has been simulated. The purpose of this work was to investigate self-organization in small systems of charged particles under the influence of an electric field where we could follow individual particles. There are positively and negatively charged particles. The intention is to look for pattern formation as the system evolves. Three electric fields and the particle-to-particle interactions were utilized to provide the forces. The three electric fields were a constant field, a ramp field, and an oscillatory field. The final system states for various electric fields are presented. For the two kinds of particles simulated, like particles have a repulsive force, while unlike particles have an attractive force. Initially, the particles are randomly distributed in a two dimensional square bounded region, and then allowed to dynamically interact for a number of iterations. Using the inverse square law force, modified at short distances, most cases resulted in equilibrium with the particles of opposite polarity paired up. Since this was a state of equilibrium no more movement occurred. The results of the experiments are presented in graphical format. The main conclusions are that this model can be used to study small dynamic systems, and that the presence of an external electric field does not significantly modify the final configuration but hastens the development of the equilibrium state.

Energy exchange in two-fraction systems of charged dust particles

A study of the processes of redistribution of stochastic kinetic energy between two fractions of dust particles with different sizes and temperatures, as well as its redistribution by degrees of freedom, is presented for conditions close to the conditions of experiments in gas-discharge plasma. The numerical simulation was carried out for two-layer ensembles and bulk clouds of charged particles in the gravity field, and for two-dimensional structures formed in the external electric fields under the influence of forces proportional to the square of dust radius. The influence of high temperatures on the energy balance in the analyzed systems is considered. A semiempirical approximation is proposed, which well describes the energy exchange in all considered cases.

Processes of Energy Exchange in Layered Systems of Non-Identical Charged Particles

Processes of Energy Exchange in Layered Systems of Non-Identical Charged Particles

Origin of the anisotropic Coulomb interaction potential for a two-dimensional system of charged particles with anisotropic mass

There have been several studies that have considered an anisotropic Coulomb interaction potential of a specific form to model anisotropic quantum Hall states of two-dimensional systems of electrons in a perpendicular constant magnetic field. The motivation and justification behind such a choice is tacitly implied without providing too many details. This work explains the physical reasons that lead to an anisotropic Coulomb interaction potential of such a form for the case of a two-dimensional system of charged particles with anisotropic effective band mass.

Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics

Explicit structure-preserving geometric particle-in-cell (PIC) algorithm in curvilinear orthogonal coordinate systems is developed. The work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion research. The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms, discrete exterior calculus, and explicit non-canonical symplectic integration. In addition to the truncated infinitely dimensional symplectic structure, the algorithm preserves exactly many important physical symmetries and conservation laws, such as local energy conservation, gauge symmetry and the corresponding local charge conservation. As a result, the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics. The algorithm has been implemented in the SymPIC code, which is designed for high-efficiency massively-parallel PIC simulations in modern clusters. The code has been applied to carry out whole-device 6D kinetic simulation studies of tokamak physics. A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor. The state also admits a steady-state sub-sonic ion flow in the range of 10 km s−1, agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is simulated. It is shown that high-n ballooning modes have larger growth rates than low-n global modes, and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2% level by the E × B flow generated by the instability. These results are consistent with early and recent electromagnetic gyrokinetic simulations.

The Magnetic Hooke-Newton Transmutation in Momentum Space

The magnetic Hooke-Newton transmutation, which emerges from the transformation design of the quadratic conformal mapping for the system of charged particles moving in the uniform magnetic field, is investigated in the momentum space. It is shown that there are two ways to turn the linear interaction force of the system into the inverse square interaction. The first one, which involves simply applying the mapping to the system, has the spectrum with the Landau levels of even angular momentum quantum number. The second one considers the geometric structure of the mapping as an effective potential which leads us to the transmuted Coulomb system with the novel quantum spectrum. The wave functions of momentum for the bound and scattering states of the transmutation system are given. It is also shown that the effective potential due to the geometric structure can be generalized to a general 2D surface, and the Schrödinger equation of a particle moving on the surface while under the action of the potential can be solved by the form-invariant Schrödinger equation of the free particle. The solution of a particle moving on the hyperbolic surface under the potential is given with the conclusion. The presentation manifests the transformation design of the quantum state, depending mainly on the geometric structure of the representation space, not on the action of the specific potential field. This characteristic makes it possible for us to use the geometric structure of different representation spaces to explore some novel behaviors of quantum particles.

Effect of external magnetic field and friction force on the dynamic properties of a system of charged particles

The paper describes the algorithm of the method of molecular (Langevin) dynamics, the modeled system and the main parameters characterizing the system. The presented mathematical model is built for a magnetically active dusty plasma taking into account the influence of the friction force due to the presence of the environment (buffer plasma). To solve the equation of motion of dust particles, a modified numerical Verlet scheme obtained by the authors of the work was used. The mathematical model is built for a two-dimensional system, the particles of which interact using the Yukawa potential. A detailed analysis of the autocorrelation functions of velocities and their Fourier transforms of dust particles for different values ​​of the parameters of the magnetic field, coupling and friction is carried out. It was found that an increase in friction causes a decrease in the dominant peak at a fixed value of the magnetic field parameter. This peak corresponds to the combined effect of the magnetic field and strong correlations in the system; the complete disappearance of the peak corresponding to cyclotron oscillations was found when the friction force is not taking into account. It is shown that, with low friction, an increase in the magnetic field leads to a monotonic increase in the amplitude of the dominant peak and with a large value of friction, in contrast to its decrease, which is explained by us that the decay of ultrasonic waves in the medium increases with increasing frequency, however, a more detailed description of this effect may be a topic for further research. Key words: molecular dynamic method, Verlet algorithm velocity autocorrelation functions, external magnetic field, friction force

A new algorithm for electrostatic interactions in Monte Carlo simulations of charged particles

To minimise systematic errors in Monte Carlo simulations of charged particles, long range electrostatic interactions have to be calculated accurately and efficiently. Standard approaches, such as Ewald summation or the naive application of the classical Fast Multipole Method, result in a cost per Metropolis-Hastings step which grows in proportion to some positive power of the number of particles N in the system. This prohibitively large cost prevents accurate simulations of systems with a sizeable number of particles. Currently, large systems are often simulated by truncating the Coulomb potential which introduces uncontrollable systematic errors. In this paper we present a new multilevel method which reduces the computational complexity to O(log⁡(N)) per Metropolis-Hastings step, while maintaining errors which are comparable to direct Ewald summation. We show that compared to related previous work, our approach reduces the overall cost by better balancing time spent in the proposal- and acceptance- stages of each Metropolis-Hastings step. By simulating large systems with up to N=105 particles we demonstrate that our implementation is competitive with state-of-the-art MC packages and allows the simulation of very large systems of charged particles with accurate electrostatics.

Redistribution of the Stochastic Kinetic Energy in Bilayer Systems of Nonidentical Charged Particles

Conditions of energy exchange in bilayer ensembles including two separated fractions of nonidentical particles with different sizes, charges, and temperatures have been studied. Processes of the redistribution of the stochastic energy between different fractions of particles with different temperatures in such systems have been numerically analyzed. The redistribution of the stochastic energy over the degrees of freedom has been considered.

Cyclically parallelized treecode for fast computations of electrostatic interactions on molecular surfaces

We study the parallelization of a flexible order Cartesian treecode algorithm for evaluating electrostatic potentials of charged particle systems in which N particles are located on the molecular surfaces of biomolecules such as proteins. When the well-separated condition is satisfied, the treecode algorithm uses a far-field Taylor expansion to compute O(NlogN) particle–cluster interactions to replace the O(N2) particle–particle interactions. The algorithm is implemented using the Message Passing Interface (MPI) standard by creating identical tree structures in the memory of each task for concurrent computing. We design a cyclic order scheme to uniformly distribute spatially-closed target particles to all available tasks, which significantly improves parallel load balancing. We also investigate the parallel efficiency subject to treecode parameters such as Taylor expansion order p, maximum particles per leaf N0, and maximum acceptance criterion θ. This cyclically parallelized treecode can solve interactions among up to tens of millions of particles. However, if the problem size exceeds the memory limit of each task, a scalable domain decomposition (DD) parallelized treecode using an orthogonal recursive bisection (ORB) tree can be used instead In addition to efficiently computing the N-body problem of charged particles, our approach can potentially accelerate GMRES iterations for solving the boundary integral Poisson–Boltzmann equation.

Cosmological Evolution of a Scalar-Charged Degenerate Cosmological Plasma with Higgs Scalar Fields

A mathematical model of the cosmological evolution of statistical systems of scalarly charged particles with Higgs scalar interaction is formulated and investigated. Examples are given of numerical modeling of such systems, revealing their very remarkable properties, in particular, the formation of paired bursts of cosmological acceleration.

On the evolution of classic charged particles

In this work, we obtain a closed system of equations for the non-probabilistic microscopic distribution functions of charged point particles moving in the electromagnetic field generated by them. The laws of change of both the total energy of a system of charged point particles and its momentum are also derived. All calculations have been performed in the covariant form. The resulting equations describe an irreversible evolution.

Probability-free relativistic kinetic theory of classical systems of charged particles

In the complete system of equations of evolution of the classical system of charges and the electromagnetic field generated by them, the field variables are excluded. An exact closed relativistic non-Hamiltonian system of nonlocal kinetic equations, that describes the evolution of a system of charges in terms of their microscopic distribution functions, is obtained. The solutions of this system of equations are non-invariant with respect to time reversal, and also have the property of hereditarity.

CsI calorimeter for the J-PARC KOTO experiment

An electromagnetic calorimeter made of undoped CsI crystals is used in the J-PARC KOTO experiment to search for new physics beyond the standard model with the KL→π0νν̄ decay. The calorimeter is designed to operate in vacuum of 0.1 Pa and in a high-rate environment where the counting rate due to KL decays is O(100) kHz. A special method to calibrate the calorimeter during the data taking without using a tracking system for charged particles is reported. The energy, position, and timing resolutions of the calorimeter were evaluated in several beam tests, and the resolutions satisfy the required performance. The energy resolution with the total energy E is 0.66⊕1.81∕E[GeV]% in the inner region of the calorimeter.

Dynamic Effects of Laser Action on Quasi-Two-Dimensional Dusty Plasma Systems of Charged Particles.

We present the results of an experimental study of the behavior of a colloidal plasma system formed by copper-coated and uncoated polymer particles under the action of laser irradiation. A comparative study of particle velocity distribution profiles depending on the power of the pushing laser was conducted. In the case of uncoated melamine-formaldehyde (MF) particles, we observed the well-known action of light pressure, causing shear stress in the colloidal plasma structure and leading to the occurrence of a laminar flow within the affected area. For the copper-coated MF particles, we revealed some additional patterns of behavior for the dust particles, i.e., kinetic temperature growth due to laser radiation absorption by the copper coating, as well as the appearance of chaotic particle motion. We believe that this happens due to the existence of defects in the coating, causing asymmetric heating of the particles, which in turn leads to chaotic deviations of the photophoretic force pushing the particles in different directions.

Model for Investigating the Physical Properties of a System of Charged Particles Taking into Account the External Magnetic Field and Friction Force

In the present work, a numerical modified Verlet scheme (MVS) is obtained. This scheme is intended to solve the equations of motion of charged particles immersed in an external stationary environment and a uniform magnetic field, for example, charged particles of a condensed substance in a buffer plasma (dusty plasma). The influence of the environment on the particle dynamics is described by the friction force. The particle dynamics are also affected by interparticle interaction and an external uniform magnetic field. To obtain the Verlet scheme (VS), the coordinates and velocities of the particles are decomposed into a Taylor series, taking into account the Lorentz force and the friction force. All Taylor series expansion terms that give the same order of accuracy are taken into account. In the obtained numerical scheme, the time step of modeling does not depend on the magnitude of the magnetic field but is determined only by the internal physical properties of the system under consideration, which is important when modeling an ensemble of charged particles taking electromagnetic fields into account. The paper solves a test problem for which particle trajectories obtained based on the conventional and modified VS for different values, both the friction parameter and the magnetic field parameter, are compared. Based on the analysis of the dependence of the maximum relative deviation of the coordinate on the time step, the time step is independent of the magnetic field in the Taylor expansion scheme, while in the inverse VS it is dependent.