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.     

Effect of the size of macroparticles on their electrostatic interaction in a plasma

The electrostatic interaction of two spherical macroparticles in a plasma has been considered. Primary attention has been focused on investigating the electrostatic interaction at short distances where polarization effects of the surface charge of finite-size macroparticles begin to play a dominant role. The first part of this study is devoted to the interaction of a point charge with a charged conducting sphere in an equilibrium plasma. It has been shown that the presence of a plasma in the system leads to a decrease in the potential barrier when two like-charged macroparticles approach each other and that this decrease proves to be the most significant in the case where the macroparticle radius is comparable to the Debye screening length. The second part of this study is concerned with the interaction of two conducting spheres in the bispherical system of the coordinates under the assumption that the charges of the conducting spheres are constant and under the assumption that the surface potentials of the spheres are constant. The latter case is closer to the physics of electrostatic interaction of two macroparticles in a plasma medium where the electrostatic potential of their surface is determined by the floating potential of the plasma. It has been demonstrated that the interaction potentials in these two cases are substantially different from each other and that, at constant macroparticle charges, the energy of the electrostatic field is an interaction potential, but, in the case of macroparticles with constant surface potentials, which are independent of the interparticle distance, the energy of the electrostatic field is not an interaction potential. In the latter case, account must be taken of the work done by external sources on the macroparticle potentials to maintain them constant. The form of the interaction potential has been established in this case from the analysis of the interaction force in terms of the Maxwell tension tensor. In the third part of this study, the interaction of two macroparticles has been considered in the spherical system of coordinates and analytical expressions for the interaction potentials have been derived for both the case of constant macroparticle charges and the case of constant surface potentials of the macroparticles.     

Dusty plasma induced by solar radiation under microgravitational conditions: An experiment on board the Mir orbiting space station

The dynamics of the formation of ordered structures of macroparticles charged by photoemission under the action of solar radiation under microgravitational conditions without the use of electrostatic traps to confine the particles is studied experimentally and theoretically. The working conditions needed for the formation of structures of charged macroparticles are chosen as a result of a numerical solution of the problem posed, the particle charges and the interparticle interaction parameter are determined, and the characteristic times specifying the dynamics of the formation of an ordered system of macroparticles are calculated. The behavior of an ensemble of macroparticles under the effect of solar radiation is observed experimentally on board the Mir space station. An analysis and comparison of the results of the experimental and theoretical investigations permit drawing a conclusion regarding the possibility of the existences of extended ordered formations of macroparticles charged by photoemission under microgravitational conditions. Zh. éksp. Teor. Fiz. 114, 2004–2021 (December 1998)     

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.     

Space-charge-limited 2D electron flow between two flat electrodes in a strong magnetic field

An approximate analytic solution is constructed for the 2D space-charge-limited emission by a cathode surrounded by nonemitting conducting ledges of width Lambda. An essentially exact solution (via conformal mapping) of the electrostatic problem in vacuum is matched to the solution of a linearized problem in the space charge region whose boundaries are sharp due to the presence of a strong magnetic field. The current density growth in a narrow interval near the edges of the cathode depends strongly on Lambda. We obtain an empirical formula for the total current as a function of Lambda which extends to more general cathode geometries.     

Arrays of Charged (±2π)-Twist Disclinations in Ferroelectric Liquid Crystals

The notion of an electrostatic charge of (±2)-twist disclinations is used to approximate the evaluation of the electrostatic interaction energy among disclinations forming arrays in finite samples of ferroelectric chiral smectic C liquid crystals. Screening effects of free charges in a material surrounding the disclination are taken into account by introducing a phenomenological depolarisation factor.The electrostatic interaction energy is important in chiral smectic C materials with high values of the spontaneous polarisation when screening effects of free charges are small. Then the electrostatic interaction leads to elimination of disclinations from the sample. When there is a high concentration of free charges in the sample (smaller value of depolarisation factor), the electrostatic interaction energy is of the order of the elastic interaction energy of disclinations what influences the equilibrium of disclination arrays in the sample. Two disclination configurations are considered. In the Brunet-Williams configuration the disclinations of opposite topological charge have also the opposite electrostatic charge so their attraction is augmented. This attraction can be balanced by the helical structure in the central part of the sample when the sample thickness is rather high.On the contrary, in the Glogarová-Pavel configuration the disclinations of opposite topological charge have the electrostatic charge of the same sign. The equilibrium in this configuration is either a balance of elastic attraction and electrostatic repulsion if elastic and Coulomb forces are of the same order or it is governed by the value of the anchoring energy when electrostatic interaction prevails over the elastic one.     

Vacuum polarization and color charge shielding in the external source problem of QCD2 with massless quarks

An approximate treatment of vacuum polarization in the external source problem of two-dimensional QCD with massless quarks is proposed. The static response to a static external source is determined with and without vacuum polarization. In the former case and if the gauge group is SU(2), a static solution is obtained only if the external source is essentially abelian. Complete shielding of the external charge sets in with the screening length equal to the inverse of the Schwinger mass. This shielding is enforced for special, self-screening external charges.     

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.     

Effect of dust particles on the properties of low-temperature plasmas

Parameters of a low-temperature plasma containing dust particles are calculated numerically with the help of a self-consistent solution of the balance equation for production and recombination of electrons and ions, combined with the molecular dynamics method for direct simulation of processes in the vicinity of macroparticles. The relation between the charges of macroparticles and the neutral gas pressure, as well as the dependence of the low-temperature plasma parameters on the volume concentration of dust particles, is analyzed. It is shown that the plasma characteristics and composition may change noticeably relative to the case unperturbed by dust even for comparatively low concentration of dust particles.     

Variational theory for a single polyelectrolyte chain

Variational methods are applied to a single polyelectrolyte chain. The polymer is modeled as a Gaussian chain with screened electrostatic repulsion between all monomers. As a variational Hamiltonian, the most general Gaussian kernel, including the possibility of a classical or mean polymer path, is employed. The resulting self-consistent equations are systematically solved both for large and small monomer-monomer separations along the chain. In the absence of screening, the polymer is stretched on average. It is described by a straight classical path with Gaussian fluctuations around it. If the electrostatic repulsion is screened, the polymer is isotropically swollen for large separations, and for small separations the polymer correlation function is calculated as an analytic expansion in terms of the monomer-monomer separation along the chain. The electrostatic persistence length and the electrostatic blobsize are inferred from the crossover between distinct scaling ranges. We perform a global analysis of the scaling behavior as a function of the screening length and electrostatic interaction strength , where is the Bjerrum length and A is the distance of charges along the polymer chain. We find three different scaling regimes. i) A Gaussian-persistent regime with Gaussian behavior at small, persistent behavior at intermediate, and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and only for intermediate values of the screening length. The electrostatic persistence length is defined as the crossover length between the persistent and the asymptotically swollen behavior and is given by and thus disagrees with previous (restricted) variational treatments which predict a linear dependence on the screening length .ii) A Gaussian regime with Gaussian behavior at small and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and/or strong screening, and the electrostatic repulsion between monomers only leads to subfluent corrections to Gaussian scaling at small separations. The concept of a persistence length is without meaning in this regime. iii) A persistent regime , where the chain resembles a stretched rod on intermediate and small scales. Here the persistence length is given by the original Odijk prediction, , if the overstretching of the chain is avoided. We also investigate the effects of a finite polymer length and of an additional excluded-volume interaction, which modify the resultant scaling behavior. Applications to experiments and computer simulations are discussed. Received 24 December 1997     

Effect of thermophoretic forces on the formation of ordered structures of macroparticles in a thermal plasma

The thermophoretic interaction of macroparticles and its effect on the formation of ordered structures of macroparticles in plasma was studied. It was shown that coexistence of regions with a chaotic arrangement of particles and regions of ordered structures is typical of a thermal plasma with strong interaction of the macroparticles. Computer simulation of a system of strongly interacting macroparticles, taking account of the thermophoretic interaction of the particles, was performed. The results showed that the thermophoretic attractive forces explain the form of the spatial nonuniformity associated with the grouping of particles in small domains. The experimentally obtained correlation function was very close to the correlation function obtained in the computer simulation. Zh. éksp. Teor. Fiz. 116, 1601–1615 (November 1999)     

Debye-Hückel theory for interfacial geometries

The Debye-Hückel theory for bulk electrolyte solutions is generalized to planar interfacial geometries, including screening effects due to mobile salt ions which are confined to the interface and solutions with in general different salt concentrations and dielectric constants on the two sides of the interface. We calculate the general Debye-Hückel interaction between fixed test charges, and analyze a number of relevant special cases as applicable to charged colloids and charged polymers. Salty interfaces, which are experimentally realized by monolayers or bilayers made of cationic and anionic surfactants or lipids, exert a strong attraction on charged particles of either sign at large separations from the interface; at short distances image-charge repulsion sets in. Likewise, the effective interactions between charged particles are strongly modified in the neighborhood of such a salty interface. On the other hand, charged particles which are immersed in a salt solution are repelled from the air (or a substrate) interface, and the interaction between two charges decays algebraically close to such an interface. These general results have experimentally measurable consequences for the adsorption of charged colloids or charged polymers at monolayers, solid substrates, and interfaces.     

The vortex state of an antiferromagnet with uniaxial anisotropy

For the model of an antiferromagnet with easy-axis anisotropy, we have determined the multisoliton state that corresponds to the domain boundary on the surface of which antiferromagnetic vortices of various topological charges are localized. We analyze the pattern of interaction between the vortices. We show that repulsive and attractive forces equivalent to the forces of electrostatic interaction between point charges in a plane act between the vortices with like and unlike topological charges, respectively. However, there is a steady state in this case, since these vortices in the model of a uniaxial antiferromagnet have an infinite effective mass and do not change their relative positions. We give a general solution that describes the vortex structures on the surface of the domain boundary.     

Electrostatic potential of point charges inside dielectric prolate spheroids

The exact solution to an electrostatic problem of finding the electric potential of point charges inside a dielectric prolate spheroid is discussed in this note by using the classical electrostatic theory, where the prolate spheroid is embedded in a dissimilar dielectric medium. Such a problem may find its application in hybrid solvent biomolecular simulations, in which biomolecules and a part of solvent molecules within a dielectric cavity are explicitly modeled while a surrounding dielectric continuum is used to model bulk effects of the solvent beyond the cavity. Numerical experiments have demonstrated the convergence of the proposed series solutions.     

Dust-Lower-Hybrid Surface Waves in Classical and Degenerate Plasmas

The dispersion relation for general dust low frequency electrostatic surface waves propagating on an interface between a magnetized dusty plasma region and a vacuum is derived by using specular reflection boundary conditions both in classical and quantum regimes. The frequency limit ω«ω_ci«ω_ce is considered and the dispersion relation for the Dust-Lower-Hybrid Surface Waves (DLHSW's) is derived for both classical and quantum plasma half-space and analyzed numerically. It is shown that the wave behavior changes as the quantum nature of the problem is considered.     

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)     

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     

Collective effects in doped nematic liquid crystals

We studied the collective elastic interaction in a system of many macroparticles embedded in a nematic liquid crystal. A theoretical approach to the interaction of macroparticles via deformation of the director field [1] is developed. It is found that the director field distortion induced by many particles leads to the screening of the elastic pair interaction potential. This screening strongly depends on the shape of the embedded particles: it exists for anisotropic particles and is absent for spherical ones. Our results are valid for the homeotropic and the planar anchoring on the particle surface and for different Frank constants. We apply our results to cylindrical particles in a nematic liquid crystal. In a system of magnetic cylindrical grains suspended in a nematic liquid crystal, the external magnetic field perpendicular to the grain orientation results in inclining the grains to the director and induces an elastic Yukawa-law attraction between the grains. The appearance of this elastic attraction can explain the cellular texture in magnetically doped liquid crystals in the presence of the magnetic field [2].     

Collective plasma corrections to thermonuclear reaction rates in dense plasmas

General kinetic equations are derived for nuclear reactions in dense plasmas by taking into account first-order collective plasma effects. We show that, apart from the corrections proportional to the product of the charges Z _i and Z _j of two reacting nuclei i and j, new corrections comparable in magnitude and proportional to the squares of the nuclear charges Z _i ² and Z _j ² arise. The Salpeter corrections [1] to the nuclear reaction probabilities due to the plasma screening of the interaction potential are shown to be at least a factor of r/d (r is the nuclear size and d is the Debye screening length) smaller than those assumed previously. These are zero in the approximation where the terms of order r/d are disregarded. The correlation corrections proportional to Z _iZ_j have a different physical meaning than those in [1], can have a different sign, and arise for reactions with zero Salpeter corrections. For the correlation corrections that substitute for the previously used Salpeter corrections, strong correlations are difficult to describe analytically. The interpolation formulas between weak and strong Salpeter screenings previously used in many astrophysical applications are inapplicable, because the interpolation formulas between weak and strong correlations cannot yet be obtained. We found a new type of corrections that are proportional to the squares of the charges of reacting nuclei. These are attributable to a change in the collective electrostatic self-energy of the plasma system during nuclear reactions. Plasma corrections for the hydrogen-cycle nuclear reactions are numerically calculated for the temperature, density, and abundances in the solar interior.