Study of the stability of charged particle dynamics in a Penning–Malmberg–Surko trap with a rotating field

The solutions of equations characterizing the dynamics of charged particles in electromagnetic Penning–Malmberg traps with a rotating transverse electric field are presented and analyzed. The equations of motion are transformed in a way that makes it possible to distinguish between the motions of magnetron and cyclotron particles, reduce the system of equations to a stationary one, and conclude that asymptotically Lyapunov stable solutions of these equations are lacking in a certain parameter interval. This allows one to optimize the confinement of charged particles in such traps.     

Dynamics of a charged particle bunch in a penning trap

The Lagrangean equations for gas dynamics of a spherical bunch of charged particles in a Penning trap are solved. The solution describes the pulsation of an inhomogeneous particle bunch whose center behaves as a spatial oscillator in a coordinate system rotating with the Larmor frequency.     

Formation of ordered structures of charged macroparticles in a photoemission trap

The possibility of confining positively charged macroscopic dust particles in a unique photoemission trap was studied. The spatial distributions of the potentials for a cylindrical geometry of a phototrap were obtained (by the particles in a cell method) and the dynamics of the formation of ordered structures of dust particles in the potential field of the trap was studied (by the molecular-dynamics method). The dependence of the number of dust particles confined by a phototrap on the particle energies and sizes and the buffer-gas pressure were obtained.     

TRANSIENT LIFETIME SPECTRUM OF TWO CHARGED PARTICLES IN A PAUL TRAP

The transient properties of laser-cooled two charged particles in a Paul trap are studied numerically. We find the existence of characteristic lifetime of an attractor, which is thought to be an important feature of the transient dynamics of the weakly dissipative system. The theoretical analysis shows that it is caused by pseudo-periodic orbit which is the residual sign of periodic orbit of the focus-saddle bifurcation. Study of dissipative coupled standard maps shows that this is a general conclusion for weakly dissipative system.     

Optimal Convergence Rates of Classical Solutions for Vlasov-Poisson-Boltzmann System

The dynamics of charged dilute particles can be modeled by the two species Vlasov-Poisson-Boltzmann system when the particles interact through collisions in the self-induced electric field. By constructing the compensating function for multi-species particle system, the optimal time decay of global classical solutions to this system near a global Maxwellian is obtained through a refined energy method.     

Coulomb scatter of diamagnetic dust particles in a cusp magnetic trap under microgravity conditions

The effect of a dc electric field on strongly nonideal Coulomb systems consisting of a large number (~10⁴) of charged diamagnetic dust particles in a cusp magnetic trap are carried out aboard the Russian segment of the International Space Station (ISS) within the Coulomb Crystal experiment. Graphite particles of 100–400 μm in size are used in the experiments. Coulomb scatter of a dust cluster and the formation of threadlike chains of dust particles are observed experimentally. The processes observed are simulated by the molecular dynamics (MD) method.     

The Vlasov–Maxwell–Boltzmann System in the Whole Space

The Vlasov–Maxwell–Boltzmann system is one of the most fundamental models to describe the dynamics of dilute charged particles, where particles interact via collisions and through their self-consistent electromagnetic field. We prove existence of global in time classical solutions to the Cauchy problem near Maxwellians.     

Nonstationary self-consistent model for an ensemble in the self-field

The behavior of a nonstationary system of charged particles interacting with the self-field is studied using integrals of motion for nonstationary systems. Numerical solutions are obtained for the sets of equations describing the characteristics of a system of particles. A nonstationary self-consistent quantum system is also analyzed. The proposed model can be useful for investigating the acceleration of charged particles by the self-field.     

Wave-like excitations in the system of a charged long filament interacting with the microparticles in the linear Paul trap

In this paper, we experimentally and numerically studied the wave-like excitations in the system comprised by a charged nylon filament (macroobject) and charged microparticles levitating in a linear quadrupole electrodynamic trap. It has been found out that a filament with sufficient sag forms a rotating standing-like wave, while the particles due to the Coulomb repulsion are localized in its antinodes. Numerical simulation shows that this dynamic collective motion can be excited at high enough voltages on the electrodes, when the energy losses due to air viscosity can be compensated by the energy contribution of the altering electric fields of the trap.     

The Vlasov–Poisson–Boltzmann System Near Vacuum

Global classical solutions with small amplitude are constructed for the Cauchy problem to the Vlasov–Poisson–Boltzmann system, which describes the dynamics of charged particles interacting with their self-consistent electrostatic potential as well as with themselves through collisions. Received: 29 September 2000 / Accepted: 27 November 2000     

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

Journal of Statistical Physics - The Vlasov–Poisson–Boltzmann equation is a classical equation governing the dynamics of charged particles with the electric force being self-imposed. We...     

Spectral and Structural Characteristics for Cluster Systems of Charged Brownian Particles

We report on the results of analytic and numerical investigations of the dynamics for bounded ensembles of charged Brownian particles in the potential field of an electrostatic trap. Simulation has been performed for cluster systems consisting of (approximately up to one thousand) particles with the Coulomb interaction in a wide range of their parameters. The spectral structures and structural characteristics of the systems being simulated have been compared. The dependence of the form of the pair correlation function and the size of cluster systems on the temperature and the number of particles has been analyzed. The relation between the spectral density of displacements of the center of mass and of individual particles and the structural characteristics and nonideality parameter of the ensembles being modeled has been investigated.     

Non-monotonic size effects on the structure and thermodynamics of Coulomb clusters in three-dimensional harmonic traps

Finite-size effects on the static and thermodynamical properties of small three-dimensional clusters of identical charged particles confined by an harmonic trap are investigated using global optimization and numerical simulations. The relative stabilities of clusters containing up to 100 particles are estimated from the second energy derivatives, as well as from the energy gap between the two lowest-energy structures at a given size. We also provide a lower bound for the number of permutationally independent minima, as a function of size, up to n=75. Molecular dynamics and exchange Monte Carlo simulations are performed to get insight into the finite temperature behaviour of these clusters. By focusing on specific sizes, we illustrate the interplay between the stable structures, the possible competition between different isomers, and the melting point. In particular, we find that the orientational melting phenomenon known in two-dimensional clusters has an equivalent form in some three-dimensional clusters. The vibrational spectra, computed for all sizes up to 100, shows an increasing number of low-frequency modes, but comparing to hydrodynamical theory reveals strong correlation effects. Finally, we investigate the effects of the trap anisotropy on the general shape of Coulomb clusters, and on the melting point of a selected case.     

Storage of an electron plasma in a sextupole radial antihydrogen trap

This work reports for the first time experimental data obtained with electrons stored in a Penning–Malmberg trap surrounded by a sextupole radial magnetic field. This trap geometry is one of the candidates for trapping antihydrogen atoms in the place where they are produced starting from cold antiprotons and positrons or positronium. The measurements show that electron plasmas with parameters matching the range used for positrons and electrons in the antihydrogen experiments (number of particles ranging from few 10⁶ up to several 10⁷ and densities of the order of 10⁸–10⁹ cm⁻³, radius of the order of 1–2 mm) can be transported with 100% efficiency in a trap region that simultaneously confines completely the charged particles and the neutral antihydrogen in the radial plane. Inside this trap plasma storage times of the order of several tens of seconds up to some hundreds of seconds are measured. The plasma storage times are consistent with those needed for antihydrogen production; however the increase of the plasma temperature due to the expansion is not negligible; the consequences of this effect on the antihydrogen trapping are outlined.     

Structure and Spectrum of Binary Classic Systems Confined in a Parabolic Trap

The static and dynamic properties of the two-dimensional classic system of two-species interacting charged particles in a parabolic trap are studied. The ground state energy and configuration for different kinds of binary systems are obtained by Monte Carlo simulation and Newton optimization. The spectrum and normal modes vectors can be gained by diagonalizing the dynamical matrix of the system. It is found that the total particle number, particle number and mass-to-charge ratio of each species are decisive factors for the system structure and spectrum. The three intrinsic normal modes of single species Coulomb clusters are inherent, concluded from our numerical simulations and analytical results.     

Quantitative theory of channeling particle diffusion in transverse energy in the presence of nuclear scattering and direct evaluation of dechanneling length

A refined equation for channeling particle diffusion in transverse energy taking into consideration large-angle scattering by nuclei is suggested. This equation is reduced to the Sturm–Liouville problem, allowing one to reveal both the origin and the limitations of the dechanneling length notion. The values of the latter are evaluated for both positively and negatively charged particles of various energies. New features of the dechanneling dynamics of positively charged particles are also revealed. First, it is demonstrated that the dechanneling length notion is completely inapplicable for their nuclear dechanneling process. Second, the effective electron dechanneling length of positively charged particle varies more than twice converging to a constant asymptotic value only at the depth exceeding the latter.     

Modulated phases and slow dynamics in attractive colloids

A system with a short-range attraction and a competing long-range screened repulsion is studied by using the self-consistent Hartree approximation and a replica approach. It is shown that by varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar and a glassy phase. These results, which are confirmed by molecular dynamic simulations on a system of particles interacting via a DLVO potential, provide novel insights in the role of modulated phases in the slow dynamics of charged colloids in polymeric solutions.     

Closed-form solution of mid-potential between two parallel charged plates with more extensive application

Efficient calculation of the electrostatic interactions including repulsive force between charged molecules in a biomolecule system or charged particles in a colloidal system is necessary for the molecular scale or particle scale mechanical analyses of these systems. The electrostatic repulsive force depends on the mid-plane potential between two charged particles. Previous analytical solutions of the mid-plane potential, including those based on simplified assumptions and modern mathematic methods, are reviewed. It is shown that none of these solutions applies to wide ranges of interparticle distance from 0 to 10 and surface potential from 1 to 10. Three previous analytical solutions are chosen to develop a semi-analytical solution which is proven to have more extensive applications. Furthermore, an empirical closed-form expression of mid-plane potential is proposed based on plenty of numerical solutions. This empirical solution has extensive applications, as well as high computational efficiency.     

Expansion dynamics of a two-component quasi-one-dimensional Bose–Einstein condensate: Phase diagram,self-similar solutions,and dispersive shock waves

We investigate the expansion dynamics of a Bose–Einstein condensate that consists of two components and is initially confined in a quasi-one-dimensional trap. We classify the possible initial states of the two-component condensate by taking into account the nonuniformity of the distributions of its components and construct the corresponding phase diagram in the plane of nonlinear interaction constants. The differential equations that describe the condensate evolution are derived by assuming that the condensate density and velocity depend on the spatial coordinate quadratically and linearly, respectively, which reproduces the initial equilibrium distribution of the condensate in the trap in the Thomas–Fermi approximation. We have obtained self-similar solutions of these differential equations for several important special cases and write out asymptotic formulas describing the condensate motion on long time scales, when the condensate density becomes so low that the interaction between atoms may be neglected. The problem on the dynamics of immiscible components with the formation of dispersive shock waves is considered. We compare the numerical solutions of the Gross–Pitaevskii equations with their approximate analytical solutions and numerically study the situations where the analytical method being used admits no exact solutions.