Dynamics Of Charged Particles Research Articles

Dynamics of a particle around AdS Schwarzschild black hole environed by quintessence

The field of point particle dynamics is correlated with the particle dynamics around a black hole, and one can initiate the investigation of a more complex motion of extended bodies or celestial bodies. In this article, we study the dynamics of neutral and charged particles around the AdS Schwarzschild black hole surrounded by quintessence. At the foot of Noether symmetries and the conservation laws of the proposed spacetime, we discuss the effect of the cosmological constant, angular momentum, quintessence parameter, and magnetic field on the dynamics of neutral and charged particles in the form of the effective potential, effective force, and escape velocity. Finally, we investigate the orbit stability of spacetime with the help of the Lyapunov exponent.

Dynamics of the particle around de Sitter–Schwarzschild black hole surrounded by quintessence

The study of particle dynamics in the vicinity of a black hole environed by dark energy and magnetic field has attracted researchers for their importance in astrophysics and cosmology. In this paper, we study the dynamics of neutral and charged particles in the vicinity of de Sitter–Schwarzschild black hole (DS–Sch-BH) surrounded by quintessence. The effect of the DS part is explored by virtue of effective potential, effective force, and escape velocity of the particle (neutral and charged) moving around DS–Sch-BH. Finally, a comparative study is also investigated.

Charged particle dynamics in the surrounding of Schwarzschild anti-de Sitter black hole with topological defect immersed in an external magnetic field

In this paper, geodesic motion of the charged particles in the vicinity of event horizon of Schwarzschild anti-de-Sitter black hole (BH) with topological defects has been investigated. Weakly magnetized environment is considered in the surrounding of BH which only effects the motion of the particles and doesn’t effect the geometry of the BH. Hence, particles are under the influence of gravity and electromagnetic forces. We have explored the effect of magnetic field on the trajectories of the particles and more importantly on the position of the innermost stable circular orbit. It is observed that the trajectories of the particles in the surrounding of BH are chaotic. Escape conditions of the particles under the influence of gravitomagnetic force are also discussed. Moreover, the escape velocity of particles and its different features have been investigated in the presence and absence of magnetic field. Effect of dark energy on the size of event horizon, mass of the BH and stability of the orbits of the particles have also been explored in detail. These studies can be used to estimate the power of relativistic jets originated from the vicinity of BH.

Dynamics of charged particles around a magnetically deformed Schwarzschild black hole

The motion of a charged particle around a deformed Schwarzschild black hole in an external magnetic field is studied. If a magnetic parameter is small, the sign and magnitude of deformation parameter affect the shape of effective potential. The radius of an innermost stable circular orbit on the equatorial plane increases as the magnitude of negative deformation parameter increases, but decreases as a positive deformation parameter increases. When the energy and angular momentum are given appropriately, the magnetic parameter has two critical values, small and large values. For the magnetic parameter smaller than the small value or larger than the large value, the deformation parameter does not have an explicit effect on the dynamics of particles on the non-equatorial plane. The former dynamics is ordered, whereas the latter dynamics is strongly chaotic. If the magnetic parameter runs from the small value to the large one, the negative deformation parameter is helpful to strengthen the extent of chaos with its magnitude increasing. However, chaos is weakened with an increase of the positive deformation parameter.

Dynamics of charged particles in fractal media

We consider the influence of the fractality of a medium on the dynamics of charged particles in the external magnetic field and show a significant increase in the sensitivity to weak effects with the fractality of a medium. The dynamical processes in the nonequilibrium nonconservative medium are analyzed in the framework of the Tsallis nonextensive thermodynamics with the use of Jackson’s derivatives.

Aharonov–Bohm effect for bound states on spin-0 scalar charged particles in a rotating cosmic string space–time with Coulomb potentials

In this paper, we study the relativistic quantum dynamics of spin-0 scalar charged particles with a magnetic quantum flux produced by topological defects in a rotating cosmic string space–time. We solve the Klein–Gordon equation subject to Coulomb-type scalar and vector potentials in the considered framework and obtain the energy eigenvalues and eigenfunctions and analyze the analogue effect to Aharonov–Bohm effect for bound states.

Charged particle dynamics and distribution functions in low pressure dual-frequency capacitively coupled plasmas operated at low frequencies and high voltages

In high aspect ratio (HAR) dielectric plasma etching, dual-frequency capacitively coupled radio-frequency plasmas operated at low pressures of 1 Pa or less are used. Such plasma sources are often driven by a voltage waveform that includes a low-frequency component in the range of hundreds of kHz with a voltage amplitude of 10 kV and more to generate highly energetic vertical ion bombardment at the wafer. In such discharges, the energetic positive ions can overcome the repelling potential created by positive wall charges inside the etch features, which allows high aspect ratios to be reached. In order to increase the plasma density a high-frequency driving component at several 10 MHz is typically applied simultaneously. Under such discharge conditions, the boundary surfaces are bombarded by extremely energetic particles, of which the consequences are poorly understood. We investigate the charged particle dynamics and distribution functions in this strongly non-local regime in argon discharges by particle-in-cell simulations. By including a complex implementation of plasma-surface interactions, electron induced secondary electron emission (δ-electrons) is found to have a strong effect on the ionization dynamics and the plasma density. Due to the high ion energies at the electrodes, very high yields of the ion induced secondary electron emission (γ-electrons) are found. However, unlike in classical capacitive plasmas, these γ-electrons do not cause significant ionization directly, since upon acceleration in the high voltage sheaths, these electrons are too energetic to ionize the neutral gas efficiently. These γ- and δ-electrons as well as electrons created in the plasma bulk and accelerated towards the electrodes to high energies by reversed electric fields during the local sheath collapse are found to induce the emission of a high number of δ-electrons, when they hit boundary surfaces. This regime is understood fundamentally based on the following approach: first, dual-frequency discharges with identical electrode materials are studied at different pressures and high-frequency driving voltages. Second, the effects of using electrodes made of different materials and characterized by different secondary electron emission coefficients are studied. The electron dynamics and charged particle distribution functions at boundary surfaces are determined including discharge asymmetries generated by using different materials at the powered and grounded electrodes.

Relativistic quantum dynamics of a spin-0 massive charged particle in the presence of external fields in a Gödel-type space-time with Coulomb potentials and Aharonov–Bohm effect

In this paper, we investigate the relativistic quantum dynamics of spin-0 massive charged particles in the presence of an external field in a Godel-type space-time with potentials. We derive the radial wave equation of the Klein–Gordon equation with an external uniform magnetic field including a magnetic quantum flux subject to a Coulomb-type scalar and vector potentials in the background of the Som–Raychaudhuri space-time with a cosmic string. We solve this radial wave equation and evaluate the energy eigenvalues and eigenfunctions and analyze a relativistic analogue effect of the Aharonov–Bohm effect for bound states.

Aharonov–Bohm effect for bound states on spin-0 massive charged particles in a Gödel-type space–time with Coulomb potential

In this paper, we investigate the relativistic quantum dynamics of spin-0 massive charged particles in a Gödel-type space–time with electromagnetic interactions. We derive the radial wave equation of the Klein–Gordon equation with an internal magnetic flux field and Coulomb-type potential in the Som–Raychaudhuri space–time with cosmic string. We solve this equation and analyze the analog effect in relation to the Aharonov–Bohm effect for bound states.

Arbitrarily high-order energy-preserving methods for simulating the gyrocenter dynamics of charged particles

Gyrocenter dynamics of charged particles plays a fundamental role in plasma physics. In particular, accuracy and conservation of energy are important features for correctly performing long-time simulations. For this purpose, we here propose arbitrarily high-order energy conserving methods for its simulation. The analysis and the efficient implementation of the methods are fully described, and some numerical tests are reported.

Observation of the Relativistic Reversal of the Ponderomotive Potential.

The secular dynamics of a nonrelativistic charged particle in an electromagnetic wave can be described by the ponderomotive potential. Although ponderomotive electron-laser interactions at relativistic velocities are important for emerging technologies from laser-based particle accelerators to laser-enhanced electron microscopy, the effects of special relativity on the interaction have only been studied theoretically. Here, we use a transmission electron microscope to measure the position-dependent phase shift imparted to a relativistic electron wave function when it traverses a standing laser wave. The kinetic energy of the electrons is varied between 80 and 300keV, and the laser standing wave has a continuous-wave intensity of 175 GW/cm^{2}. In contrast to the nonrelativistic case, we demonstrate that the phase shift depends on both the electron velocity and the wave polarization, confirming the predictions of a quasiclassical theory of the interaction. Remarkably, if the electron's speed is greater than 1/sqrt[2] of the speed of light, the phase shift at the electric field nodes of the wave can exceed that at the antinodes. In this case there exists a polarization such that the phase shifts at the nodes and antinodes are equal, and the electron does not experience Kapitza-Dirac diffraction. Our results thus provide new capabilities for coherent electron beam manipulation.

Explicit Symmetric Exponential Integrators for Charged-Particle Dynamics in a Strong and Constant Magnetic Field

In this paper, we derive and analyze symmetric exponential integrators for charged-particle dynamics in a strong and constant magnetic field. We first present the scheme of exponential integrators and then establish the symmetry conditions for the methods. Explicit symmetric exponential integrators up to order four are constructed on the basis of the symmetry conditions. In order to show the remarkable performances of new symmetric methods in comparison with symmetric Runge–Kutta methods including the 2-stage Gauss method, two numerical experiments are carried out and the numerical results demonstrate the super numerical behavior.

Solving procedure for the dynamics of charged particle in variable (time-dependent) electromagnetic field

In this challenging analytic survey, we present a new approach for solving equations of the dynamics of a charged particle (describing its motion in variable, time-dependent electromagnetic field) which has been applied earlier in various fields of mechanics for solving equations of hydrodynamics, Euler–Poisson equations of rigid body rotation and even in celestial mechanics (solution of equations of small body’s motion in the CR3BP problem near librations points): a new type of the solving procedure is implemented in all of these equations as well as in case of solving momentum equation for the aforementioned dynamics of a charged particle, determined by Lorentz force in non-relativistic case. Meanwhile, in each case the system of momentum equations has been successfully solved analytically. The main result of the current research should be formulated as follows: the analytic algorithm is pointed out for solving momentum equation, which has been reduced to the analytical solution of three nonlinear ODEs with respect to the components of velocity of the particle. Moreover, absolutely new partial analytical solutions have been obtained for the special cases of magnetic field (with zero electric field’s components). In addition to this, we conclude that system of Lorentz momentum equations for dynamics of a charged particle has not the analytical presentation of solution in case of nonzero, time-dependent electric field.

The role of the cosmological constant in dynamics of the particle in the Schwarzschild black hole

The behavior of the dynamics of neutral and charged particles in the presence of the cosmological constant in the Schwarzschild black hole(SWBH) is presented in this article. Noether symmetries and the corresponding conservation laws are found. It is observed that the Schwarzschild metric, with non-zero cosmological constants, affects the dynamics of the particle. It is also found that for a positive value of the cosmological constant we can define a short interval in which the cosmological constant lies. This is considered a necessary ingredient for the expansion of the Universe.

Charged particle dynamics near an X-point of a non-symmetric magnetic field with closed field lines

Understanding particle drifts in a non-symmetric magnetic field is of primary interest in designing optimized stellarators in order to minimize the neoclassical radial loss of particles. Quasisymmetry and omnigeneity, two distinct properties proposed to ensure radial localization of collisionless trapped particles in stellarators, have been explored almost exclusively for magnetic fields with nested flux surfaces. In this work, we examine radial particle confinement when all field lines are closed. We then study charged particle dynamics in the special case of a non-symmetric vacuum magnetic field with closed field lines obtained recently by Weitzner & Sengupta (Phys. Plasmas, vol. 27, 2020, 022509). These magnetic fields can be used to construct magnetohydrodynamic equilibria for low pressure. Expanding in the amplitude of the non-symmetric fields, we explicitly evaluate the omnigeneity and quasisymmetry constraints. We show that the magnetic field is omnigeneous in the sense that the drift surfaces coincide with the pressure surfaces. However, it is not quasisymmetric according to the standard definitions.

Local Well-Posedness of Vlasov–Poisson–Boltzmann Equation with Generalized Diffuse Boundary Condition

The Vlasov-Poisson-Boltzmann equation is a classical equation governing the dynamics of charged particles with the electric force being self-imposed. We consider the system in a convex domain with the Cercignani-Lampis boundary condition. We construct a uniqueness local-in-time solution based on an $L^\infty$-estimate and $W^{1,p}$-estimate. In particular, we develop a new iteration scheme along the characteristic with the Cercignani-Lampis boundary for the $L^\infty$-estimate, and an intrinsic decomposition of boundary integral for $W^{1,p}$-estimate.

A gyrokinetic model for the plasma periphery of tokamak devices

A gyrokinetic model is presented that can properly describe large and small amplitude electromagnetic fluctuations occurring on scale lengths ranging from the electron Larmor radius to the equilibrium perpendicular pressure gradient scale length, and the arbitrarily large deviations from thermal equilibrium that are present in the plasma periphery of tokamak devices. The formulation of the gyrokinetic model is based on a second-order accurate description of the single charged particle dynamics, derived from Lie perturbation theory, where the fast particle gyromotion is decoupled from the slow drifts assuming that the ratio of the ion sound Larmor radius to the perpendicular equilibrium pressure scale length is small. The collective behaviour of the plasma is obtained by a gyrokinetic Boltzmann equation that describes the evolution of the gyroaveraged distribution function. The collisional effects are included by a nonlinear gyrokinetic Dougherty collision operator. The gyrokinetic model is then developed into a set of coupled fluid equations referred to as the gyrokinetic moment hierarchy. To obtain this hierarchy, the gyroaveraged distribution function is expanded onto a Hermite–Laguerre velocity-space polynomial basis. Then, the gyrokinetic equation is projected onto the same basis yielding the spatial and temporal evolution of the Hermite–Laguerre expansion coefficients. A closed set of fluid equations for the lowest-order coefficients is presented. The Hermite–Laguerre projection is performed accurately at arbitrary perpendicular wavenumber values. Finally, the self-consistent evolution of the electromagnetic fields is described by a set of gyrokinetic Maxwell equations derived from a variational principle where the velocity integrals are explicitly evaluated.

A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field

A modification of the standard Boris algorithm, called filtered Boris algorithm, is proposed for the numerical integration of the equations of motion of charged particles in a strong non-uniform magnetic field in the asymptotic scaling known as maximal ordering. With an appropriate choice of filters, second-order error bounds in the position and in the parallel velocity, and first-order error bounds in the normal velocity are obtained with respect to the scaling parameter. This also yields a second-order approximation to the guiding center motion. The proof compares the modulated Fourier expansions of the exact and the numerical solutions. Numerical experiments illustrate the error behaviour of the filtered Boris algorithm.

(py)LIon: A package for simulating trapped ion trajectories

The (py)LIon package is a set of tools to simulate the classical trajectories of ensembles of ions in electrodynamic traps. Molecular dynamics simulations are performed using LAMMPS, an efficient and feature-rich program. (py)LIon has been validated by comparison with the analytic theory describing ion trap dynamics. Notable features include GPU-accelerated force calculations, and treating collections of ions as rigid bodies to enable investigations of the rotational dynamics of large, mesoscopic charged particles. Programme summaryProgram Title: (py)LIonProgram Files doi:http://dx.doi.org/10.17632/ywwd9nnxjh.1Licencing provisions: MITProgramming language: Matlab, PythonSubprograms used: LAMMPSNature of problem: Simulating the dynamics of ions and mesoscopic charged particles confined in an electrodynamic trap using molecular dynamics methodsSolution method: Provide a tested, feature-rich API to configure molecular dynamics calculations in LAMMPSUnusual features: (py)LIon can treat collections of ions as rigid bodies to simulate larger objects confined in electrodynamic traps. GPU acceleration is provided through the LAMMPS ▪ package.

Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field

The differential equations of motion of a charged particle in a strong non-uniform magnetic field have the magnetic moment as an adiabatic invariant. This quantity is nearly conserved over long time scales covering arbitrary negative powers of the small parameter, which is inversely proportional to the strength of the magnetic field. The numerical discretisation is studied for a variational integrator that is an analogue for charged-particle dynamics of the Stormer–Verlet method. This numerical integrator is shown to yield near-conservation of a modified magnetic moment and a modified energy over similarly long times. The proofs for both the continuous and the discretised equations use modulated Fourier expansions with state-dependent frequencies and eigenvectors.