Dynamics Of Charged Particles Research Articles

Semi-analytical solving procedure for the dynamics of charged particle in parametrically variable magnetic field

Semi-analytical solving procedure for the dynamics of charged particle in parametrically variable magnetic field

Electron density and temperature of dual-frequency capacitively coupled argon plasma in two-dimensional distribution obtained and studied in experiment

Behaviors of plasma in spatial distributions are vital for understanding physical mechanisms of low pressure capacitively coupled discharges. However, due to the lack of simple and reliable diagnostic techniques, few experimental studies have focused on two-dimensional distributions of plasma. Recently, we have developed a new method for rapid two-dimensional plasma diagnosis. With this method, the dual-frequency capacitively coupled plasma, an important plasma commonly used in etching, is systematically studied. Three circumstances are presented here: In case I, the plasma discharge was driven by a radio-frequency source; in case II, two radio-frequency sources were applied to one electrode; and in case III, such sources were applied to two separate electrodes. Results show that both the emission intensity and electron density in case III are higher than those in case II, and because the absolute value of the DC self-bias voltage is smaller, the structure of axial discharge is more symmetric in case III. For the asymmetrically capacitive discharges (cases I and II), the position of the maximum axial electron density is close to the powered electrode due to the presence of the DC self-bias voltage. As the low-frequency power increases or gas pressure decreases, the position of the maximum axial electron density moves gradually toward the grounded electrode because of the enlarged thickness of the sheath. However, high-frequency power has a limited influence on the position of the maximum axial electron density. The radial distribution of plasma is more uniform when plasma density is relatively low. For a higher plasma density situation, the center-peaked density profile results from the higher power deposition at the electrode center and/or more local charged particle dynamics. In addition, under the same discharge conditions, a lower electrode gap is favorable for the occurrence of the α-γ mode transition.

Integrability of Kerr-Newman spacetime with cloud strings, quintessence and electromagnetic field

The dynamics of charged particles moving around a Kerr-Newman black hole surrounded by cloud strings, quintessence and electromagnetic field is integrable due to the presence of a fourth constant of motion like the Carter constant. The fourth motion constant and the axial symmetry of the spacetime give a chance to the existence of radial effective potentials with stable circular orbits in two-dimensional planes, such as the equatorial plane and other nonequatorial planes. They also give a possibility of the presence of radial effective potentials with stable spherical orbits in the three-dimensional space. The dynamical parameters play important roles in changing the graphs of the effective potentials. In addition, variations of these parameters affect the presence or absence of stable circular orbits, innermost stable circular orbits, stable spherical orbits, and marginally stable spherical orbits. They also affect the radii of the stable circular or spherical orbits. It is numerically shown that the stable circular orbits and innermost stable circular orbits can exist not only in the equatorial plane but also in the nonequatorial planes. Several stable spherical orbits and marginally stable spherical orbits are numerically confirmed too. In particular, there are some stable spherical orbits and marginally stable spherical orbits with vanishing angular momenta which cover the whole range of latitudinal coordinates.

Geometric continuous-stage exponential energy-preserving integrators for charged-particle dynamics in a magnetic field from normal to strong regimes

This paper is concerned with geometric exponential energy-preserving integrators for solving charged-particle dynamics in a magnetic field from normal to strong regimes. We firstly formulate the scheme of the methods for the system in a uniform magnetic field by using the idea of continuous-stage methods, and then discuss its energy-preserving property. Moreover, symmetric conditions and order conditions are analysed. Based on those conditions, we propose two practical symmetric continuous-stage exponential energy-preserving integrators of order up to four. Then we extend the obtained methods to the system in a nonuniform magnetic field and derive their properties including the symmetry, convergence and energy conservation. Numerical experiments demonstrate the efficiency of the proposed methods in comparison with some existing schemes in the literature.

Theory and simulation of electrokinetic fluctuations in electrolyte solutions at the mesoscale

Electrolyte solutions play an important role in energy storage devices, whose performance relies heavily on the electrokinetic processes at sub-micron scales. Although fluctuations and stochastic features become more critical at small scales, the long-range Coulomb interactions pose a particular challenge for both theoretical analysis and simulation of fluid systems with fluctuating hydrodynamic and electrostatic interactions. Here, we present a theoretical framework based on the Landau–Lifshitz theory to derive closed-form expressions for fluctuation correlations in electrolyte solutions, indicating significantly different decorrelation processes of ionic concentration fluctuations from hydrodynamic fluctuations, which provides insights for understanding transport phenomena of coupled fluctuating hydrodynamics and electrokinetics. Furthermore, we simulate fluctuating electrokinetic systems using both molecular dynamics (MD) with explicit ions and mesoscopic charged dissipative particle dynamics (cDPD) with semi-implicit ions, from which we identify that the spatial probability density functions of local charge density follow a gamma distribution at sub-nanometre scale (i.e. $0.3\,{\rm nm}$ ) and converge to a Gaussian distribution above nanometre scales (i.e. $1.55\,{\rm nm}$ ), indicating the existence of a lower limit of length scale for mesoscale models using Gaussian fluctuations. The temporal correlation functions of both hydrodynamic and electrokinetic fluctuations are computed from all-atom MD and mesoscale cDPD simulations, showing good agreement with the theoretical predictions based on the linearized fluctuating hydrodynamics theory.

On the dynamics of charged particles in an incompressible flow: From kinetic-fluid to fluid–fluid models

In this paper, we are interested in the dynamics of charged particles interacting with the incompressible viscous flow. More precisely, we consider the Vlasov–Poisson or Vlasov–Poisson–Fokker–Planck equation coupled with the incompressible Navier–Stokes system through the drag force. For the proposed kinetic-fluid model, we study the asymptotic regime corresponding to strong local alignment and diffusion forces. Under suitable assumptions on well-prepared initial data, we rigorously derive a coupled isothermal/ pressureless Euler–Poisson system and incompressible Navier–Stokes system (EPNS system). For this hydrodynamic limit, we employ the modulated kinetic, internal, interaction energy estimates. We also construct a global-in-time strong solvability for the isothermal/ pressureless EPNS system. In particular, this global-in-time solvability gives the estimates of hydrodynamic limit hold for all times.

Energy-Preserving Continuous-Stage Exponential Runge--Kutta Integrators for Efficiently Solving Hamiltonian Systems

As one of the most important properties, energy preservation is a natural requirement for numerical integrators of Hamiltonian systems. Considering the limited second-order accuracy of the existing exponential average vector filed (or discrete gradient) method, this paper is devoted to developing high-order energy-preserving exponential integrators for general semilinear Hamiltonian systems. To this end, we first formulate and analyze the continuous-stage exponential Runge--Kutta (ERK) method. After deriving the order conditions, energy-preserving conditions, and symmetric conditions for the continuous-stage ERK method, we construct a novel class of fourth-order symmetric energy-preserving continuous-stage ERK methods with a free parameter based on the established conditions and present a convergence theorem for the fixed-point iteration associated with the continuous-stage ERK method. Furthermore, we extend the proposed continuous-stage ERK method to noncanonical Hamiltonian systems and discuss implementation issues in detail. Finally, numerical results from the FPU problem, the charged-particle dynamics, and the Klein--Gordon equation demonstrate the high efficiency, good energy-preserving behavior, and applicability of large time stepsizes of the proposed fourth-order energy-preserving continuous-stage ERK method.

Dynamics of charged particles and quasi-periodic oscillations in the vicinity of a distorted, deformed compact object embedded in a uniform magnetic field

ABSTRACT This work presents the dynamic properties of charged test particles influenced by the gravitational and electromagnetic fields. Accordingly in this work, we concentrate on the static and axially symmetric metric containing two quadrupole parameters. One relates to the central object, and another relates to the external distribution of matter. This metric may associate the observable effects to these parameters as dynamical degrees of freedom. The astrophysical motivation for choosing such a field is the possibility to constitute a reasonable model for an actual situation occurring in the objects’ vicinity. To test the role of large-scale magnetic fields in accretion processes, we start by analysing different time-like bound orbits under the influence of the system’s different parameters. This leads to examining their stability concerning radial and/or vertical oscillations. The main focus is to discuss the effect of magnetic field on the oscillation modes’ resonant phenomena using different resonant models for disc-oscillation modes. In the present contribution, we further explore the possibility of relating oscillatory frequencies of charged particles to the frequencies of the high-frequency quasi-periodic oscillations observed in the microquasars GRS 1915+105, XTE 1550-564, and GRO 1655-40 via assuming relevance of resonant phenomena on the radial and vertical oscillations.

Study of self‐organised criticality in a coaxial plasma source with gridded cathode

AbstractMultiple luminous sheath structures develop in the localised plasma formation inside a cylindrical gridded cathode plasma source. These structures gradually expand into the whole vessel and undergo a critical state through self‐organised criticality (SOC) along with pronounced sheath oscillations during the variation of anode potential. The present investigation emphasises the stability properties associated with the oscillations of the sheath potential structures in the cylindrical‐gridded cathode in glow discharge regime through SOC phenomena through non‐linear time series analysis. The non‐linear temporal and spatial analysis of potential structure and dynamics of charged particles are correlated with SOC in cylindrical‐gridded cathode in glow discharge regime through the dynamics of multiple sheath structure formations. The existence of flicker noise and long‐range correlation in the time series suggests the existence of SOC behaviour in the system, the multiple sheath structures evolve through reduction and addition of layers. Cylindrical‐gridded cathode discharge initiation during formations of multiple sheath structures, switching of discharge regimes with anode potential, layer reduction and addition inside the sheath structures through SOC behaviour, renders uniqueness to the present regime of investigation. Self‐organised pattern formations and self‐organised criticality behaviour investigated in the present glow discharge regime using the cylindrical‐gridded cathode source are of prime importance to understand the complex behaviour of plasmas in the field of hollow cathode discharges.

Global model study of plasma parameter variation in helicon plasma source in oxygen discharge

In this work, different plasma parameters, such as electron density, temperature, and negative ion density are measured in both the source and expansion chamber of the Helicon Plasma Source (HeliPS) in a radio frequency (RF) oxygen discharge of 13.56 MHz and are compared with the values obtained numerically using the volume-averaged global model. For this purpose, the global model of RF oxygen discharge suitable for the HeliPS having two chambers (source and expansion) together with the electromagnet in the source chamber and the magnetic cage in the expansion chamber to reduce the radial loss of plasma is developed using the particle and power balance equations. In this model, the radial confinement by the axial field of the electromagnet in the source chamber and the confinement in the expansion chamber by the cusped field of the magnetic cage is incorporated. Studies on the charged particle dynamics by both the model and the experiment show comparable values of the variation of species density and electron temperature with RF power and working pressure as well as with the applied magnetic field of the electromagnet in the source chamber.

Weak Turbulence and Quasilinear Diffusion for Relativistic Wave-Particle Interactions Via a Markov Approach

We derive weak turbulence and quasilinear models for relativistic charged particle dynamics in pitch-angle and energy space, due to interactions with electromagnetic waves propagating (anti-)parallel to a uniform background magnetic field. We use a Markovian approach that starts from the consideration of single particle motion in a prescribed electromagnetic field. This Markovian approach has a number of benefits, including: 1) the evident self-consistent relationship between a more general weak turbulence theory and the standard resonant diffusion quasilinear theory (as is commonly used in e.g. radiation belt and solar wind modeling); 2) the general nature of the Fokker-Planck equation that can be derived without any prior assumptions regarding its form; 3) the clear dependence of the form of the Fokker-Planck equation and the transport coefficients on given specific timescales. The quasilinear diffusion coefficients that we derive are not new in and of themselves, but this concise derivation and discussion of the weak turbulence and quasilinear theories using the Markovian framework is physically very instructive. The results presented herein form fundamental groundwork for future studies that consider phenomena for which some of the assumptions made in this manuscript may be relaxed.

Dynamics of Charged Particles Around Weakly Magnetized Loop Quantum Gravity Black Hole

Dynamics of Charged Particles Around Weakly Magnetized Loop Quantum Gravity Black Hole

OuroborosBEM: a fast multi-GPU microscopic Monte Carlo simulation for gaseous detectors and charged particle dynamics

The design of gaseous detectors for accelerator, particle and nuclear physics requires simulations relying on multi-physics aspects. In fact, these simulations deal with the dynamics of a large number of charged particles interacting in a gaseous medium immersed in the electric field generated by a more or less complex assembly of electrodes and dielectric materials. We report here on a homemade software, called ouroborosbem, able to tackle the different features involved in such simulations. After solving the electrostatic problem for which a solver based on the boundary element method (BEM) has been implemented, particles are tracked and will microscopically interact with the gas medium. Dynamical effects have been included such as the electron-ion recombination process, the charging-up of the dielectric materials and other space charge effects that might alter the detector performances. These were made possible thanks to the nVidia CUDA language specifically optimised to run on Graphical Processor Units (GPUs) to minimize the computing times. Comparisons of the results obtained for parallel plate avalanche counters and GEM detectors to literature data on swarm parameters fully validate the performances of ouroborosbem. Moreover, we were able to precisely reproduce the measured gains of single and double GEM detectors as a function of the applied voltage.

Dynamics of charged particles in the magnetized $$\gamma $$ spacetime

Dynamics of charged particles in the magnetized $$\gamma $$ spacetime

Construction of a Second-order Six-dimensional Hamiltonian-conserving Scheme

Abstract Research has analytically shown that the energy-conserving implicit nonsymplectic scheme of Bacchini, Ripperda, Chen, and Sironi provides a first-order accuracy to numerical solutions of a six-dimensional conservative Hamiltonian system. Because of this, a new second-order energy-conserving implicit scheme is proposed. Numerical simulations of a galactic model hosting a BL Lacertae object and magnetized rotating black hole background support these analytical results. The new method with appropriate time steps is used to explore the effects of varying the parameters on the presence of chaos in the two physical models. Chaos easily occurs in the galactic model as the mass of the nucleus, the internal perturbation parameter, and the anisotropy of the potential of the elliptical galaxy increase. The dynamics of charged particles around the magnetized Kerr spacetime is easily chaotic for larger energies of the particles, smaller initial angular momenta of the particles, and stronger magnetic fields. The chaotic properties are not necessarily weakened when the black-hole spin increases. The new method can be used for any six-dimensional Hamiltonian problems, including globally hyperbolic spacetimes with readily available (3 + 1) split coordinates.

A unified framework for the study of high-order energy-preserving integrators for solving Poisson systems

As is known, a system of differential equations possessing a first integral can be written in a non-canonical Hamiltonian system that often leads to a Poisson system under moderate conditions. Therefore, energy-preserving numerical integrators for such systems have become a subject of intensive investigation. In this paper, we design and analyse two classes of energy-preserving functionally-fitted integrators of arbitrary order for Poisson systems with highly oscillatory solutions using a new framework. We also show that both the order and the stage order of the proposed integrators may be affected by the used quadrature formula in practice. Furthermore, the existence and uniqueness of energy-preserving functionally-fitted integrators, their implementation issues, and the conservation of Casimir functions are investigated in detail. Finally, numerical experiments are carried out with the fourth-order and sixth-order energy-preserving integrators proposed in this paper, including the Lotka-Volterra system and the charged-particle dynamics in a strong magnetic field, and the numerical results demonstrate the remarkable accuracy and efficiency of our high-order energy-preserving integrators compared with the other energy-preserving methods in the literature.

Dynamics of charged test particles around quantum-corrected Schwarzschild black holes

We investigate neutral and charged test particles’ motions around quantum-corrected Schwarzschild black holes immersed in an external magnetic field. Taking the innermost stable circular orbits of neutral timelike particles into account, we find that the black holes can mimic different ranges of the Kerr black hole’s spin |a/M| from 0.15 to 0.99. Our analysis of charged test particles’ motions suggests that the values of the angular momentum l and the energy E^{2} are slightly higher than Schwarzschild black holes. The allowed regions of the (l,E^{2}) demonstrate that the critical energy E^{2}_{c} divides the charged test particle’s bounded trajectory into three types. With the help of a Monte Carlo method, we study the charged particles’ probabilities of falling into the black holes and find that the probability density function against l depends on the signs of the particles’ charges. Finally, the epicyclic frequencies of the charged particles are considered with respect to the observed twin peak quasi-periodic oscillations frequencies. Our results might provide hints for distinguishing quantum-corrected Schwarzschild black holes from Schwarzschild ones by using the dynamics of charged test particles around the strong gravitational field.

Dynamics of Charged Particles Moving around Kerr Black Hole with Inductive Charge and External Magnetic Field

We mainly focus on the effects of small changes of parameters on the dynamics of charged particles around Kerr black holes surrounded by an external magnetic field, which can be considered as a tidal environment. The radial motions of charged particles on the equatorial plane are studied via an effective potential. It is found that the particle energies at the local maxima values of the effective potentials increase with an increase in the black hole spin and the particle angular momenta, but decrease with an increase of one of the inductive charge parameter and magnetic field parameter. The radii of stable circular orbits on the equatorial plane also increase, whereas those of the innermost stable circular orbits decrease. On the other hand, the effects of small variations of the parameters on the orbital regular and chaotic dynamics of charged particles on the non-equatorial plane are traced by means of a time-transformed explicit symplectic integrator, Poincaré sections and fast Lyapunov indicators. It is shown that the dynamics sensitivity depends on small variations in the inductive charge parameter, magnetic field parameter, energy, and angular momentum. Chaos occurs easily as each of the inductive charge parameter, magnetic field parameter, and energy increases but is weakened as the angular momentum increases. When the dragging effects of the spacetime increase, the chaotic properties are not always weakened under some circumstances.

Cosmological models based on a statistical system of scalar charged degenerate fermions and an asymmetric Higgs scalar doublet

On the basis of the general relativistic statistical and kinetic theory, a consistent closed cosmological model is formulated. It is based on a statistical system of scalar charged fermions interacting by means of classical and phantom scalar fields. Based on the study of the microscopic dynamics of scalar charged particles, within the framework of the Lagrangian as well as Hamiltonian formalism, a function of the dynamic mass of scalar charged particles was constructed and it was shown that for the consistency of the theory, it is necessary to remove the nonnegativity condition for this function. On the basis of the Lagrangian formalism, equations of gravitational and scalar fields with singular sources are formulated and microscopic conservation laws are obtained. Within the framework of the general relativistic kinetic theory, macroscopic equations of gravitational and scalar fields are formulated and macroscopic conservation laws are obtained. These equations' full correspondence to microscopic equations with singular sources is shown. Further, on the basis of the obtained equations, a cosmological model for a degenerate system of scalarly charged fermions is formulated. An exact solution of the constitutive equations for a degenerate scalar-charged plasma in the cosmological model is obtained, which made it possible to significantly simplify the original system of equations. On the basis of the obtained solution of the constitutive equations, two fundamentally different cosmological models are formulated, one of which has two types of singly scalarly charged fermions, while the second has one kind of fermions charged with two charges of various nature. A qualitative analysis of the obtained 6-dimensional dynamic system for a two-component model is carried out.

Energy-preserving splitting methods for charged-particle dynamics in a normal or strong magnetic field

In this letter, we study energy-preserving (EP) splitting methods for solving charged-particle dynamics in a normal or strong magnetic field. Two novel EP splitting methods are formulated, and their energy-preserving property and accuracy are analysed. A numerical experiment is carried out to demonstrate the error and energy behaviour of the splitting methods.