Interaction of two macroparticles in a nonequilibrium plasma

The interaction of two macroparticles in a nonequilibrium plasma at elevated pressures has been investigated. An asymptotic theory of screening, which leads to a two-exponential dependence of the macroparticle potential on distance with different screening constants, is used to determine the electrostatic energy of the system of charges associated with the two macroparticles. The dependence of the electrostatic energy on interparticle distance has been found to have a minimum, as in an equilibrium plasma. The interaction force between the macroparticles has been determined; it turned out to be asymmetric—for different charges, the forces acting on the first and second macroparticles are not equal. This is the result of an asymmetric charge separation near macroparticles with differing charges and indicates that the interaction force in a nonequilibrium plasma is nonpotential. The forces are equal for identical macroparticles or in an equilibrium plasma and the potential energy of the interaction between the macroparticles has been determined for these cases. Attraction between likely charged particles with different (in magnitude) charges has been found to be possible when they come very close together. Relations to determine the modified coupling parameter for an interaction potential that consists of two exponential terms with different screening constants have been derived.     

Electrostatic interaction of macroparticles in a plasma in the strong screening regime

We have studied the electrostatic interaction of spherical particles in an equilibrium plasma or an electrolyte in the moderate and strong screening regimes when the macroparticle size is comparable with or much larger than the Debye screening radius. We have developed an approximate theory of the electrostatic interaction of macroparticles in the case of constant potentials of their surfaces in the weak or moderate screening regimes. In this theory, the charges of macroparticles with a fixed spacing between them are determined using vacuum capacitive coefficients, which are corrected taking into account the plasma screening effects. The force of interaction with the resultant charges is calculated based on the solution of the problem of interaction in a homogeneous dielectric (vacuum) and is multiplied by the plasma factor. We have also obtained an approximate solution to the problem in the strong screening regime. Comparison with the exact solution has demonstrated high accuracy of the proposed methods of calculation.     

Interaction of a dielectric macroparticle with a point charge in plasma

The electrostatic interaction of a charged spherical dielectric macroparticle with a point charge in a plasma in the presence of an external uniform electric field is considered. The electrostatic force and the torque acting on the macroparticle have been determined, and the form of the interaction potential has been established for a nonuniform distribution of free charge on the macroparticle surface. A simple (for calculations) expression for the interaction potential that describes well the exact potential at all interparticle distances is proposed. The angular velocity of the spinning of dust particles caused by a nonuniform distribution of free charge over their surface has been estimated.     

Nonstationary macroparticle charging in an arc plasma jet

The charging of liquid metal macroparticles in the rarified part of a vacuum arc plasma jet is studied. The sheath in the vicinity of the macroparticle is collisionless and the problem with different Debye length to macroparticle radius ratios is analyzed. Maxwellian velocity distribution functions with different temperatures for the electrons and ions in an arbitrary ratio are allowed in the model. By solving the equation for the electric field together with the equation for ion and electron flux, the charging time and the near electric field of the macroparticles were calculated. The kinetics of the macroparticle charging are controlled by the ion and electron flux to the macroparticle, which depend on the potential distribution in the sheath. The potential falls off slower than 1/r² in the case of the large Debye length to macroparticle radius ratio, and falls off more rapidly than 1/r² in the other case. The charge which accumulates on a macroparticle at distances of about 10 cm from a 100-Å cathode is about 10^-16 C and the charging time is about 10^-5 s. The influence of the plasma drift velocity on the macroparticle charging is small. The model presented here agrees well with an experimental study of macroparticle repulsion from biased substrates     

Electrostatic interaction between two conducting spheres

In the paper we consider the problem of the electrostatic interaction between two charged conducting spheres with arbitrary electrical charges and radiuses. Using the image charges method we determine exact analytical formulas for the force F and for the potential energy W of the interaction between these two spheres as well as for the potential V of the electromagnetic field in an arbitrary point created by them. Our formulas lead to Coulomb’s law for point charges.We theoretically prove the experimentally shown fact that two spheres with the same type (positive or negative) of charges can also attract each other.     

Phase separation in colloidal suspensions induced by a solvent phase transition

A colloidal suspension of macroparticles in a solvent is considered near a solvent first-order phase transition. The solvent phase transition is described by a Ginzburg-Landau model with a one-component order parameter which is coupled to the macroparticles coordinates. Wetting of the macroparticle surface by one of the two coexisting phases can induce phase separation of the colloidal particles. This phase separation is first explained by simple thermodynamic arguments and then confirmed by computer simulation of the Ginzburg-Landau model coupled to the macroparticles. Furthermore a topological diagnosis of the interface between the stable and metastable phase is given near phase separation and possible experimental consequences of the phase separation are discussed.     

Electrostatic interaction between two macroparticles in the Poisson-Boltzmann model

Considering the electrostatic energy of the system of two macroparticles in a plasma in the Poisson-Boltzmann model, Resendes et al. [Phys. Lett. A 239, 181 (1998)], Ivanov [Phys. Lett. A 290, 304 (2001)], Gerasimov and Sinkevich {Teplofiz. Vys. Temp. 37, 853 (1999) [High Temp. 37, 823 (1999)]}, and D’achkov {Teplofiz. Vys. Temp. 43, 331 (2005) [High Temp. 43, 322 (2005)]} conclude that attraction between identically charged macroparticles is possible. In the Poisson-Boltzmann model, the distribution of electrons and ions has the Boltzmann form in a self-consistent field that is determined by the Poisson equation. In this work, on the basis of the analysis of the force between two macroparticles in a plasma by using the Maxwell stress tensor, it has been shown that two macroparticles with the same charge always repulse each other in both isothermal and nonisothermal plasmas. The interaction between macroparticles at distances, where Boltzmann exponentials can be linearized, is completely described by the Debye-Hückel theory. The free energy of the system of two particles has been found. It coincides with the Yukawa potential and has no minimum; therefore, such a system is thermodynamically unstable. Since the interaction energy obtained by integrating the interaction force coincides with the free energy of the electric field, the interaction between two macroparticles in the equilibrium plasma is potential.     

Macroparticle reflection from a biased substrate in a vacuum arcdeposition system

The reflection of macroparticles, generated by a vacuum arc, from a substrate biased negatively with respect to the surrounding plasma is considered. Charging of macroparticle in the near-substrate sheath and its influence on the macroparticle motion were taken into account. It was found that macroparticles can be either reflected or attracted to the substrate depending strongly on the ion current density. The possibility of macroparticle reflection increases with negative bias voltage and saturates at about a few hundred volts     

Time-dependent interaction across two conducting spheres in an applied electrostatic field

Charged particles exist widely in variety of technological areas as well as in nature. Even a weak charge on the particles can significantly influence their electric interaction. We investigated the phenomenon of time-dependent electric interaction between two conducting spheres in an electrostatic field. A mirror-image method was developed to analyze this system, and the fundamental role of the charges on the spheres was studied. We concluded that charges conducted to the lower sphere through the alumina tube used in our system play a main role in determining the time-dependent interaction, whereas the influence from air ions is negligible.     

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.     

Creation of ordered structures in a classical thermal plasma containing macroparticles: Experiment and computer simulation

We have compared experimental measurements of ordered structures in a thermal plasma containing macroparticles of CeO₂ at atmospheric pressure and a temperature around 1700 K with the results of numerical Monte Carlo calculations for the Yukawa model. We describe several distinctive features of the way the experiments were done, including how the ordered macroparticle structures were detected. We discuss a theoretical model of the behavior of an equilibrium system of charged macroparticles in a plasma and the effective interaction potential between them. Good agreement between the experimental and numerical results is noted, and possible reasons for the observed discrepancies are discussed. Zh. éksp. Teor. Fiz. 111, 889–902 (March 1997)     

Characteristics of Macroparticle Emission from a High-Current-Density Multi-Cathode Spot Vacuum Arc

Macroparticle mass transport, size distribution, and spatial distribution were studied in a 6.5-MA/M2 25-ms Cu multi-cathode spot (MCS) vacuum arc. The macroparticle erosion rate was determined to be 105 ?g/C, and together with ionic emission, accounted for most of the cathodic erosion. The number of macroparticles emitted decreased exponentially with macroparticle diameter, with 20-80-?m macroparticles carrying the bulk of the mass transport. Macroparticles are emitted preferentially at an angle of 20° with respect to the cathode surface. In comparison to previous investigations, higher macroparticle erosion rates, a larger proportion of large macroparticles, and a higher emission angle are observed, and the differences are attributed to the large current density used in the present experiment.     

A theoretical study of ion selectivity of zeolites—application to chabazite

As a contribution towards a better theoretical understanding of zeolite properties, the mechanism of ion migration through zeolite lattices has been studied with special reference to ion selectivity in chabazite. We have started from the Cartesian coordinates obtained by combining experimental data and the values for a model having standard bond lengths and angles. Then we have applied the Del Re method (with appropriate parameters for Si and Al⁻) to determine the net charges of the framework atoms. Then we have computed the potential energy profiles for one or more cations crossing the larger cavity of the chabazite unit cell (ca 200 atoms). The interaction energy contains electrostatic terms associated with point-charge interaction and polarization effects.Two different pictures have been analyzed: a totally idealized one, where ion motion takes place in the fully dehydrated zeolite, and a more realistic one, where the ion is seen as a moving aquo complex. In the latter case, the presence of the solvent has been taken into account by introducing a dielectric constant depending on ion size and channel diameter. Whereas no significant differences between ions having the same formal charges have been found in the dehydrated case, polarization effects being too small to bring about a distinct selectivity, the model taking solvation into account does predict the expected selectivity, and agrees well with available experimental results. Equilibrium sites, the corresponding free energies, and energy barriers between them have been used for the discussion.The value of the two models in attempts to understand elementary physico-chemical processes in zeolites is emphasized, with extensive reference to existing literature.     

The dynamics of macroparticles in a direct current glow discharge plasma under microgravitation conditions

The dynamics of large-sized (70-180 μm) spherical bronze particles in a direct current glow discharge plasma was studied experimentally under microgravitation conditions. The temperatures, velocities, pair correlation functions, and self-diffusion coefficients of macroparticles were measured at various discharge currents. The charges of dust particles (on the order of 10⁶ e) corresponded to high surface potentials of about 30–40 V. The experimental data were in close agreement with the simulation data on Yukawa systems with weak screening of dust charges. The influence of macroparticles on equilibrium ionization in a dense dust cloud was considered.     

On interaction of two closely spaced charged conducting spheres

Electrostatic interaction between two charged conducting spheres is analyzed in the case of a small spacing between them, when the polarization effects are significant. It is shown that short-range polarization forces result in the attraction of the like-charged spheres. At a sufficiently small spacing, this attraction replaces repulsive forces acting on like charges.     

On the polarization interaction between two closely spaced conducting spheres in a uniform electrostatic field

An electrostatic interaction between two separate, grounded, uncharged, perfectly conducting spheres of different radii in a uniform electrostatic field is investigated. It is shown that at a small center-to-center distance of the spheres, the force of the polarization interaction between the spheres depends appreciably more weakly on that distance in comparison to the force of the electrostatic interaction of two elementary dipoles as it should be in view of the interaction between two like polarization charges.     

Self-oscillations of macroparticles in the dust plasma of glow discharge

Two types of instabilities emerging in dust-plasma systems with a spatial gradient of the macroparticle charge are considered. It is shown that the change in the macroparticle charge is an effective mechanism for exciting dust self-oscillations in a laboratory plasma. The results of experimental observations and an analysis of the conditions for the development of various self-oscillations of macroparticles in the strata of a dc glow discharge are presented.     

Electrostatic Interaction of Two Conducting Spheroids

Technical Physics - Finite-element method is used to calculate the force of electrostatic interaction of two conducting spheroidal objects with specified surface charges in the absence of external...     

Two identical conducting spheres with same potential in a uniform electric field

Interaction, polarization, and charges or electric field distribution of conducting spheres in applied electric field are in many fields including electrorheological fluids, electrophoresis, and electrical engineering. A system with two equipotential conducting spheres in an applied uniform electric field is analyzed by image method. A new method is put forward to calculate the image charges distribution when using image method, which ensures the validity of image method to analyze equipotential cases. An apparatus is constructed to measure the force experimentally as well. Results show that the distribution of electric field and electric interaction are different with the case not equipotential.