Study of charged particles trajectories in free-fall electrostatic separators

The objective of this paper is to develop a mathematical model for computing the millimeter-sized particles trajectories in the free-fall electrostatic separator. The simulation involves the numerical solution of motion equations of the particles subjected to electric and gravitational forces. The air-drag force and the impact of the particles with the electrodes were also considered. The resolution algorithm is implemented as a MATLAB program that uses the results of electric field computation performed with COMSOL software. The model obtained is used to study the factors influencing the quality of the products recovered at the outlet of the separator.     

Some effects of the electrostatic interaction of water drops in the atmosphere

The electric field at the surface of two conducting spherical charged particles and their interaction force are calculated. It is shown that as particles carrying like charge approach each other, the force changes sign and becomes attractive. The case where the charge on each particle varies as the square of its radius is an exception (repulsion at any distance between the particles). Self-similar asymptotic solutions for the interaction force and energy are found for particles of identical size. For a pair of charged water drops falling simultaneously in the atmosphere, a numerical simulation shows that a drop formed by coalescence of the pair may be subject to the Rayleigh instability. Zh. Tekh. Fiz. 69, 12–17 (December 1999)     

On the interaction between charged linear harmonic oscillators

A systematic investigation, including the effect of retardation, is given for the interaction of two one-dimensional harmonic oscillators. The comment of Reinecke and Ruder [1], where a repulsive character for the force over a certain region of separation has been described, is shown to arise because of permanent moments implicit in the model. The calculation of the potential energy is made using quantum electrodynamics with all the intersystem interaction being mediated by photons: the method allows the calculation of the next term in inverse powers ofR.     

On the force of electrostatic interaction between two conducting spheres

A compact solution is obtained to the problem on the force of interaction between two conducting spheres with preset charges on their surfaces in zero external field. The derivation is based on exact solution of the problem of the potential distribution in the bispherical coordinate system. The expression for the force was derived by differentiating the potential energy of interaction between the spheres with respect to the distance between their centers. It is shown using numerical calculations that with decreasing distance between the spheres, the ratio of their charges for which the forces of interaction between the charges are zero tends to the ratio of the charges of contacting spheres. It follows hence that for any ratio of charges of the same polarity, which differs from the ratio of charges of the contacting spheres, there always exists a small distance between the spheres, at which they attract each other.     

On correlations between charged and neutral particles in a cluster model

Correlations between charged and neutral pions at high energies are investigated in the framework of a cluster model in which neutral clusters have a decay distribution determined by isospin conservation and statistical independence. For 〈n₀〉_n? an asymptotic expansion around the mean 〈n_?〉 leading asymptotically to a quadratic form in n_? is derived and compared with data.     

On the absence of breakdown of symmetry for the plane rotator model with long-range random interaction

We study the plane rotator model with hamiltonian $$ - \frac{1}{2}\sum\limits_{x \ne y} {J_{xy} \frac{{\cos (\theta _x - \theta _y )}}{{\left| {\left. {x - y} \right|} \right.^{3 + \in } }}}$$ whereJ _xy for different pair (x, y) are independent symmetric random variables. It is proved that for almost allJ, all the Gibbs statesP(J) are rotation invariant.     

On the interaction between a charged drop and an external acoustic field

An interaction between capillary oscillations of a charged drop and an external acoustic field is investigated under conditions in which nonlinear components of the acoustic pressure on the drop surface may be neglected. It is shown that equations describing the temporal evolution of modes of the capillary waves in this case may be either the Mathieu-Hill equations or ordinary inhomogeneous equations of the second order describing forced oscillations. In both cases, the drop instability (of a parametric or resonance type) may result in its disintegration due to deformation caused by the acoustic field at its own drop charge, subcritical in the sense of the Rayleigh criterion.     

Light quark mass differences and charge symmetry breaking in hyperon-nucleon interaction

Quantum chromodynamics based isovector isoscolar particle mixing arising out of isospin violating quark mass differences has been used to construct a new charge-symmetry breaking Λ-N interaction element. It appears that vector meson exchanges between N and a physical Λ rather than pseudoscalar exchanges provide the largest contribution to explain the binding energy difference between the mirror hyper-nuclei _ΛHe⁴ and _ΛH⁴. Prediction of the model to Λn and Λp scattering lengths have been compared with those obtained from the combined analysis of ΛN scattering and s-shell hyperfragment data. We find satisfactory agreement of our results.     

A miniature charged plate for testing charge accumulation in hard disk drives

A technique for monitoring electrostatic charge accumulation inside a hard disk drive (HDD) is described: a miniature charged plate is built into the top cover of the HDD, connected to a charged plate monitor. Experiments show that the miniature plate technique can be used for detection and measurement of the voltage induced by the charge generated inside the grounded enclosure of a hard drive.     

Polarization's interaction and bound states of like charged particles in plasma

It has been shown that, as a result of the plasma polarization, there appears a minimum of potential energy of interaction of small like charged particles. With a use of the quasi-classical approximation, an existence condition of the bound state of two like unit charges has been obtained. An opportunity of electron pairs formation caused by the plasma polarization in high temperature superconductors is evaluated.     

电解液中带电平板与带电胶体球之间的有效相互作用

用Poisson-Boltzmann方程，计算了在具有单价离子的电解质溶液中均匀地带同号电荷的两无限大平行平板间的有效相互作用，以及用Derjaguin近似研究了边界对带电胶体球的影响.不考虑微离子相互作用时，两带电平板只有排斥作用，而且边界条件(面电荷密度)的改变对它们之间的有效相互作用影响不大.带电平板与带电胶体球之间的相互作用也有类似规律. 关键词： Poisson-Boltzmann方程 Derjaguin近似 双电层 渗透压     

On the energy losses of fast charged particles

The energy losses of fast charged particles colliding with atoms have been considered in the eikonal approximation. It has been shown that the nonperturbative contribution to the effective stopping from the region of the intermediate impact parameters (comparable with the characteristic sizes of the electron shells of the target) not only can be significant as compared to shell corrections to the Bethe-Bloch formula (usually considered in the first order of perturbation theory), but also can provide significant (up to 50%) corrections to this formula.     

Kinetics of charged particles in a high-voltage gas discharge in a nonuniform electrostatic field

A high-voltage gas discharge is of interest as a possible means of generating directed flows of low-temperature plasma in the off-electrode space distinguished by its original features [1–4]. We propose a model for calculating the trajectories of charges particles in a high-voltage gas discharge in nitrogen at a pressure of 0.15 Torr existing in a nonuniform electrostatic field and the strength of this field. Based on the results of our calculations, we supplement and refine the extensive experimental data concerning the investigation of such a discharge published in [1, 2, 5–8]; good agreement between the theory and experiment has been achieved. The discharge burning is initiated and maintained through bulk electron-impact ionization and ion–electron emission. We have determined the sizes of the cathode surface regions responsible for these processes, including the sizes of the axial zone involved in the discharge generation. The main effect determining the kinetics of charged particles consists in a sharp decrease in the strength of the field under consideration outside the interelectrode space, which allows a free motion of charges with specific energies and trajectories to be generated in it. The simulation results confirm that complex electrode systems that allow directed plasma flows to be generated at a discharge current of hundreds or thousands of milliamperes and a voltage on the electrodes of 0.3–1 kV can be implemented in practice [3, 9, 10].     

Focusing of high-energy particles in the electrostatic field of a homogeneously charged sphere and the effective momentum approximation

The impact of the strongly attractive electromagnetic field of heavy nuclei on electrons in quasi-elastic (e, e') scattering is often accounted for by the effective momentum approximation. This method is a plane wave Born approximation which takes the twofold effect of the attractive nucleus on initial- and final-state electrons into account, namely the modification of the electron momentum in the vicinity of the nucleus, and the focusing of electrons towards the nuclear region leading to an enhancement of the corresponding wave function amplitudes. The focusing effect due to the attractive Coulomb field of a homogeneously charged sphere on a classical ensemble of charged particles incident on the field is calculated in the highly relativistic limit and compared to results obtained from exact solutions of the Dirac equation. The result is relevant for the theoretical foundation of the effective momentum approximation and describes the high-energy behavior of the amplitude of continuum Dirac waves in the potential of a homogeneously charged sphere. Our findings indicate that the effective momentum approximation is a useful approximation for the calculation of Coulomb corrections in (e, e') scattering off heavy nuclei for sufficiently high electron energies and momentum transfer.     

Suppression of the radiation limit through autoresonant acceleration of charged particles by an electrostatic field

We consider the autoresonant motion of a charged particle in the field of a transverse electromagnetic wave propagating with the speed of light along a stationary homogeneous magnetic field with allowance for radiative friction. It is shown that the loss of wave-particle synchronism due to radiative friction can be suppressed by an external electrostatic field that is parallel to the magnetic field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 4, pp. 458–463, April, 1996.     

Linear (in oscillation dimensionless amplitude) interaction between the modes of a nonspherical charged drop in an external electrostatic field

The stability of a heavily charged drop in a weak uniform electrostatic field (in which the equilibrium shape of the drop can be represented by a prolate spheroid) is calculated in the fourth order of smallness in the eccentricity of the spheroidal drop and in the first order of smallness in the drop oscillation dimensionless amplitude. It is found that as the order of approximation in eccentricity grows, so does the number of modes interacting with the initially excited mode. In the given order of smallness, the preferred (initially excited) mode is shown to interact with the nearest eight modes. The drop becomes unstable if such is the second mode.     

On the scattering of charged particles in complex current configurations

The scattering of charged particles in the magnetic fields of current sheets with bell-shaped and double-humped current density profiles has been studied analytically and numerically. The particle scattering processes are shown to depend significantly on the structure of the current sheet. Thus, for example, when particles are scattered in double current sheets, a regime under which the compensation of two successive jumps in particle magnetic moments can lead to a quasi-regular type of motion, instead of a chaotic one, can be maintained in the system.     

Drift theory of the resonant interaction of charged particles with wave packets

Averaged equations of motion are obtained for charged particles resonantly interacting with high-frequency wave packets in the case of finite cyclotron radius. It is shown that the mean action of the packet on the particle is not a potential function. Cherenkov resonance of particles with the beats of two wave packets in inhomogeneous plasma is considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 10–13, April, 1982.     

Symmetries of electrostatic interaction between DNA molecules

A model for pair interaction U of DNA molecules generated by the discrete dipole moments of base-pairs and the charges of phosphate groups is studied. A noncommutative group of eighth order ℒ of symmetries that leave U invariant is found. The minima are classified with the use of group ℒ and numerical methods are employed for finding them. The minima may correspond to several cholesteric phases, as well as to phases formed by crosslike conformations of molecules at an angle close to 90°—the “snowflake phase.” The results depend on the effective charge Q of the phosphate group, which can be modified by the polycations or the ions of metals. The snowflake phase could exist for Q above the threshold Q _C. Below Q _C, there could be several cholesteric phases. Close to Q _C, the snowflake phase could change into the cholesteric one at constant distance between adjacent molecules. The text was submitted by the authors in English.     

Passive electrostatic recycling spectrometer of desk-top size for charged particles of low kinetic energy

A passive electrostatic recycling spectrometer for charged particles is described and demonstrated to store electrons with typical kinetic energies of tens of eV. The design of the charged particle optics and the basic operating characteristics of the storage ring are discussed. The storage lifetime achieved is approximately 50 micros, which is target gas pressure limited and corresponds to approximately 200 orbits of the 0.65 m orbital circumference. The storage ring also has controllable energy dispersive elements enabling it to operate as a spectroscopic device.