Dust grain charges in a nuclear-track plasma and the formation of dynamic vortex dust structures

Results are presented from Monte Carlo calculations of the electric charge of dust grains in a plasma produced during the slowing down of the radioactive decay products of californium nuclei in neon. The dust grain charging is explained for the first time as being due to the drift of electrons and ions in an external electric field. It is shown that the charges of the grains depend on their coordinates and strongly fluctuate with time. The time-averaged grain charges agree with the experimental data obtained on ordered liquidlike dust structures in a nuclear-track plasma. The time-averaged dust grain charges are used to carry out computer modeling of the formation of dynamic vortex structures observed in experiments. Evidence is obtained of the fact that the electrostatic forces experienced by the dust grains are potential in character.     

Numerical simulations of ion and electron transport in a low-temperature dusty plasma

Charged particle transport and kinetic processes in a low-temperature dusty plasma are numerically simulated. Dust grains are represented as spheres with a given radius. The self-consistent electric field in the plasma surrounding a charged dust grain is calculated taking into account the perturbations of plasma quasineutrality near the grains. It is shown that applying an external electric field leads to a rearrangement of the plasma space charge and a break of the spherical symmetry of the electron and ion density distributions around the grain. The mutual influence of two identical charged dust grains is considered, and the energy of the electrostatic interaction between the grains is calculated. It is shown that this energy has a minimum at a certain finite distance between the grains.     

Self-organization of dust grains in proton beam plasma

The results of investigations of dust grain behavior in plasma formed by a proton beam in inert gases (He, Ar, Kr) are demonstrated. Stable ordered dust structures, namely “a plasma-dust crystal” formed of dust grains 1.0, 3.0, and 4.8 μm in diameter are obtained in the proton beam range for the first time. The mathematical model which allows for numerical simulation of crystal formation from dust grains formed by proton beam plasma is developed.     

Self-consistent quasineutral dust structures

Distributions of the dusty plasma parameters (electron, ion, and dust densities; dust grain charge; and ion drift velocity) in quasineutral dust structures whose dimensions are much greater than the mean free path of the ions in their interactions with neutral particles are calculated numerically under conditions such that ionization sources are located outside the structures. Planar, cylindrical, and spherical structures are investigated. It is shown that static equilibrium structures are governed by a single (basic) parameter: the electrostatic potential drop between the center of the structure and its boundary. It is found that the maximum value of the basic parameter (in energy units) does not exceed the electron temperature. The basic parameter also determines the total number of dust grains in the structure and the power of external ionization sources that are necessary to sustain this structure. The fact that the basic parameter varies within a limited range allows one to consider all the possible structures with a given dimensionality (planar, cylindrical, and spherical).     

Processes accompanying the charging of dust grains in the ionospheric plasma

The influence of the neutral component of the dusty ionospheric plasma on the process of dust grain charging is analyzed. Microscopic ion fluxes onto a dust grain are calculated with allowance for the interaction with the neutral components of the ionospheric plasma for both negatively and positively charged dust grains. For the latter case, which takes place in the presence of intense UV or X-ray solar radiation, the electron heating caused by the photoelectric effect is also investigated. It is found that the efficiency of electron heating depends on the density of neutral particles. The altitudes at which these effects appreciably influence the charging of different types of nano- and microscale dust grains are determined. It is shown that these effects should be taken into account in describing noctilucent clouds, polar mesosphere summer echoes, and physical phenomena involving grains of meteoric origin.     

Nonlinear screening of dust grains and structurization of dusty plasma

A review of theoretical ideas on the physics of structurization instability of a homogeneous dusty plasma, i.e., the formation of zones with elevated and depressed density of dust grains and their arrangement into different structures observed in laboratory plasma under microgravity conditions, is presented. Theoretical models of compact dust structures that can form in the nonlinear stage of structurization instability, as well as models of a system of voids (both surrounding a compact structure and formed in the center of the structure), are discussed. Two types of structures with very different dimensions are possible, namely, those smaller or larger than the characteristic mean free path of ions in the plasma flow. Both of them are characterized by relatively regular distributions of dust grains; however, the first ones usually require external confinement, while the structures of the second type can be self-sustained (which is of particular interest). In this review, they are called dust clusters and self-organized dust structures, respectively. Both types of the structures are characterized by new physical processes that take place only in the presence of the dust component. The role of nonlinearities in the screening of highly charged dust grains that are often observed in modern laboratory experiments turns out to be great, but these nonlinearities have not received adequate study as of yet. Although structurization takes place upon both linear and nonlinear screening, it can be substantially different under laboratory and astrophysical conditions. Studies on the nonlinear screening of large charges in plasma began several decades ago; however, up to now, this effect was usually disregarded when interpreting the processes occurring in laboratory dusty plasma. One of the aims of the present review was to demonstrate the possibility of describing the nonlinear screening of individual grains and take it into account with the help of the basic equations for the equilibrium between plasma components when analyzing equilibrium structures. The effect of plasma screening nonlinearity on both the diffusion processes and the forces of dust drag by plasma fluxes is analyzed. It is shown how self-organized dust structures form in these processes. In the limit of very small dust grain charges, the forces acting on the dusty plasma components and the set of basic equations for stationary dust structures (with allowance for nonlinear screening) take a standard form. New qualitative effects, such as the suppression of diffusion due to ion scattering from dust grains and the formation of structures of different configurations, are described. A detailed comparison with previous results is performed. It is shown that the solution of basic nonlinear equations for dust structures yields new qualitative effects. A number of new effects to be studied in future dusty plasma experiments with the formation of structures in spherical chambers are predicted (it is assumed that diffusion will play a significant role under microgravity conditions). Recent ground-based experiments, as well as experiments carried out onboard the International Space Station, directly confirm the nonlinear character of screening and the significant role played by this nonlinearity in the structurization of dusty plasma. Experiments on the formation of structures consisting of smaller dust grains within structures formed of larger grains are discussed. It is shown that those experiments can be interpreted only using the concept of nonlinear screening.     

Dust ion acoustic solitary structures in the presence of isothermal positrons

The Sagdeev potential technique has been employed to study the dust ion acoustic solitary waves and double layers in an unmagnetized collisionless dusty plasma consisting of negatively charged static dust grains, adiabatic warm ions, isothermally distributed electrons, and positrons. A computational scheme has been developed to draw the qualitatively different compositional parameter spaces or existence domains showing the nature of existence of different solitary structures with respect to any parameter of the present plasma system. The present system supports both positive and negative potential double layers. The negative potential double layer always restricts the occurrence of negative potential solitary waves, i.e., any sequence of negative potential solitary waves having monotonically increasing amplitude converges to a negative potential double layer. However, there exists a parameter regime for which the positive potential double layer is unable to restrict the occurrence of positive potential solitary waves. As a result, in this region of the parameter space, there exist solitary waves after the formation of positive potential double layer, i.e., positive potential supersolitons have been observed.     

Ordered dusty structures in the plasma of an RF electrodeless gas discharge

Results are presented from the experimental studies and numerical simulations of the behavior of dust grains in the plasma of an inductive RF discharge. The experiments were carried out with neon at a pressure of 25–500 Pa and with 1.87-μm melamine formaldehyde grains. The discharge was excited by a ring inductor supplied from a generator operating at a 100-MHz frequency. The effective dust-grain interaction potential used in numerical simulations involved the spatial dependence of the grain charge on the plasma floating potential, grain-interaction anisotropy resulting from the focusing of the drift ion current by the negatively charged grains, and specific features of the shielding of the dust grains by the plasma electrons and ions recombining both in the plasma bulk and on the grain surface. The results of Monte Carlo simulations show that the dust grains form specific filament structures observed experimentally in the plasma of an inductive electrodeless discharge. __________ Translated from Fizika Plazmy, Vol. 26, No. 5, 2000, pp. 445–454. Original Russian Text Copyright ? 2000 by Zobnin, Nefedov, Sinel’shchikov, Sinkevich, Usachev, Filinov, Fortov.     

Nonlinear equilibrium spherical dust structures II: Dependence of equilibrium states on volume ionization,number of trapped dust grains,and neutral gas pressure

A study is made of how equilibrium spherical dust structures depend on the volume ionization power, the neutral gas pressure, the number of trapped dust grains, and the ion-to-electron temperature ratio. It is shown that the structures are charged negatively and their charge is determined by the floating potential, which depends on the radius of the structure and on the ion temperature. The structures are charged mainly by absorbing a plasma flux. Conditions are determined under which the polarization fields and charges out-side the structures change sign, indicating the presence of overscreening effects, previously known only for individual dust grains. It is shown that overscreening outside the structures results exclusively from the plasma fluxes that are generated by the structure itself and are required to maintain it in equilibrium.     

Behavior of a dust grain in the double layer of an electric probe in a gas-discharge plasma

Equations for the motion of an individual dust grain in the double layer of a negatively charged cylindrical probe in a glow discharge plasma are derived and solved numerically. The distribution of the electric potential near the probe is determined, and the grain charge is calculated as a function of the distance from the probe for different probe potentials. The trajectories of grains with different initial energies are traced. An analysis of the grain trajectories shows that, at a certain distance from the probe, high-energy grains may be recharged; i.e., the grain charge may change sign. The grains are found to have no direct effect on the probe current in a dusty plasma of a glow discharge.     

Development of a self-consistent model of dust grain charging at elevated pressures using the method of moments

A model of dust grain charging is constructed using the method of moments. The dust grain charging process in a weakly ionized helium plasma produced by a 100-keV electron beam at atmospheric pressure is studied theoretically. In simulations, the beam current density was varied from 1 to 10⁶ μA/cm². It is shown that, in a He plasma, dust grains of radius 5 μm and larger perturb the electron temperature only slightly, although the reduced electric field near the grain reaches 8 Td, the beam current density being 10⁶ μA/cm². It is found that, at distances from the grain that are up to several tens or hundreds of times larger than its radius, the electron and ion densities are lower than their equilibrium values. Conditions are determined under which the charging process may be described by a model with constant electron transport coefficients. The dust grain charge is shown to be weakly affected by secondary electron emission. In a beam-produced helium plasma, the dust grain potential calculated in the drift-diffusion model is shown to be close to that calculated in the orbit motion limited model. It is found that, in the vicinity of a body perturbing the plasma, there may be no quasineutral plasma presheath with an ambipolar diffusion of charged particles. The conditions for the onset of this presheath in a beam-produced plasma are determined. __________ Translated from Fizika Plazmy, Vol. 29, No. 3, 2003, pp. 214–226. Original Russian Text Copyright ? 2003 by Filippov, Dyatko, Pal’, Starostin.     

Nonlinear equilibrium spherical dust structures I: Basic equations and criterion for the existence of self-organized structures

Basic equations for dust structures are formulated that account for the balance of the forces, plasma fluxes, and grain charges with allowance for nonlinearity in the screening of individual grains and possible violation of quasineutrality due to the interaction of collective fields with plasma fluxes. A theory of non-linear drag forces exerted by plasma fluxes on dust grains is developed for moderate drift flux velocities, higher than the mean ion thermal velocity but much lower than the acoustic speed. It is shown that equilibrium dust structures have finite sizes and negative charges and that they can exist only in a certain range of intensities of external fluxes on their surfaces. When there is no additional volume ionization, the size of the structures is determined by the intensity of the external flux. A study is made of a weakly ionized dusty plasma in which the interaction of its components with neutral gas atoms plays a major role. The ion, electron, and dust density distributions, as well as the distributions of the dust grain charges and plasma fluxes, are calculated self-consistently as functions of the distance from the center of a structure.     

Helical structures in complex plasma II: Collective interaction

The conditions for the formation and stability of quasi-crystal helical structures formed of charged dust grains of equal size in a complex plasma are investigated. A study is made of both the transverse confinement of such structures by means of an external parabolic potential well and the possibility of their self-confinement or confinement by the field of the smaller background grains. It is shown that, in the presence of dissipation, any initial random distribution of dust grains in a cylindrical external potential evolves into an equilibrium helical structure with a constant pitch angle. It is found that, when the external control parameter is smoothly varied, the pitch angle of the helix changes abruptly and the structure of the quasi-crystal undergoes bifurcations, during which the number of interwoven helices changes. The smaller the confinement parameter and the weaker the attractive forces between the grains, the larger the number of bifurcations. In addition, it is found that, because of the attraction (both noncollective and collective) between the dust grains, stable helical structures may exist not only at zero value of the external confinement parameter, but also at a negative one, and that the collective interaction between the grains not only increases the number of bifurcations but also changes their character.     

Heat transfer in dust structures in an RF discharge plasma

Results are presented from experimental studies of heat transfer in liquid-like plasma-dust structures. The experiments were performed with aluminum oxide grains ～3–5 μm in size in an RF discharge plasma. The heat capacity of the dust grains in plasma is measured. The thermal conductivity and thermal diffusivity of liquid-like plasma-dust structures are deduced under the assumption that the observed temperature gradients and the propagation of a thermal perturbation in a dusty plasma are related to heat conduction within the dust component. The measured temperature dependences of the thermal conductivity and thermal diffusivity are in qualitative agreement with the results of numerical simulations performed in the model of a simple single-atom liquid. It is shown that quantitative discrepancy between the experimental and numerical results is related to the energy loss of dust grains in their collisions with the neutral particles of the ambient gas.     

Structure and stability of complex coacervate core micelles with lysozyme

Encapsulation of enzymes by polymers is a promising method to influence their activity and stability. Here, we explore the use of complex coacervate core micelles for encapsulation of enzymes. The core of the micelles consists of negatively charged blocks of the diblock copolymer PAA42PAAm417 and the positively charged homopolymer PDMAEMA150. For encapsulation, part of the positively charged homopolymer was replaced by the positively charged globular protein lysozyme. We have studied the formation, structure, and stability of the resulting micelles for three different mixing ratios of homopolymer and lysozyme: a system predominantly consisting of homopolymer, a system predominantly consisting of lysozyme, and a system where the molar ratio between the two positively charged molecules was almost one. We also studied complexes made of only lysozyme and PAA42PAAm417. Complex formation and the salt-induced disintegration of the complexes were studied using dynamic light-scattering titrations. Small-angle neutron scattering was used to investigate the structures of the cores. We found that micelles predominantly consisting of homopolymer are spherical but that complex coacervate core micelles predominantly consisting of lysozyme are nonspherical. The stability of the micelles containing a larger fraction of lysozyme is lower.     

Nonlinear dust-acoustic structures in space plasmas with superthermal electrons,positrons, and ions

Some features of nonlinear dust-acoustic (DA) structures are investigated in a space plasma consisting of superthermal electrons, positrons, and positive ions in the presence of negatively charged dust grains with finite-temperature by employing a pseudo-potential technique in a hydrodynamic model. For this purpose, it is assumed that the electrons, positrons, and ions obey a kappa-like (κ) distribution in the background of adiabatic dust population. In the linear analysis, it is found that the dispersion relation yield two positive DA branches, i.e., the slow and fast DA waves. The upper branch (fast DA waves) corresponds to the case in which both (negatively charged) dust particles and (positively charged) ion species oscillate in phase with electrons and positrons. On the other hand, the lower branch (slow DA waves) corresponds to the case in which only dust particles oscillate in phase with electrons and positrons, while ion species are in antiphase with them. On the other hand, the fully nonlinear analysis shows that the existence domain of solitons and their characteristics depend strongly on the dust charge, ion charge, dust temperature, and the spectral index κ. It is found that the minimum/maximum Mach number increases as the spectral index κ increases. Also, it is found that only solitons with negative polarity can propagate and that their amplitudes increase as the parameter κ increases. Furthermore, the domain of Mach number shifts to the lower values, when the value of the dust charge Z _d increases. Moreover, it is found that the Mach number increases with an increase in the dust temperature. Our analysis confirms that, in space plasmas with highly charged dusts, the presence of superthermal particles (electrons, positrons, and ions) may facilitate the formation of DA solitary waves. Particularly, in two cases of hydrogen ions H⁺ (Z _i = 1) and doubly ionized Helium atoms He²⁺ (Z _i = 2), the mentioned results are the same. Additionally, the mentioned dusty plasma does not support DA solitons with positive polarity (compressive solitons). Furthermore, our analysis confirms that DA double layers cannot exist in such a system. Moreover, the positron density has not a considerable effect on the behavior of DA solitons in our model.     

Potential of a dust grain in a nitrogen plasma with a condensed disperse phase at room and cryogenic temperatures

The first numerical study is presented of the self-consistent potential of a dust grain in a nitrogen plasma with a condensed disperse phase at room and cryogenic temperatures and at high gas pressures for which the electron and ion transport in the plasma can be described in the hydrodynamic approximation. It is shown that the potential of the dust grain is described with good accuracy by the Debye potential, in which case, however, the screening radius turns out to be larger than the electron Debye radius. The difference between the radii is especially large in a plasma with high ionization rates (about 10¹⁶–10¹⁸ cm^?3 s^?1) at room temperature. It is found that, in a certain range of the parameters of a nitrogen dusty plasma, the parameter describing the interaction between the grains exceeds the critical value above which one would expect the formation of plasma-dust structures such as Coulomb crystals. For a plasma at cryogenic temperature (T=77 K), this range is significantly wider.     

Vortex dust structures in the track plasma of a proton beam

Results are presented from experimental and theoretical investigations of the behavior of dust grains in a track plasma produced by a beam of accelerated protons. The dynamic ordered dust structures in a proton-beam-produced plasma are obtained for the first time. The processes leading to the formation of such structures are simulated numerically. The experimentally obtained dynamic vortex dust structures in a track plasma of a proton beam are explained theoretically, and the theoretical model developed to describe such a plasma is verified experimentally. Numerical investigations carried out by the method of Brownian dynamics made it possible to qualitatively explain the characteristic features of the formation of vortex dust structures.     

Influence of grain charge gradients on the dynamics of macroparticles in an electrostatic trap

An analytical model of anomalous heating of charged dust grains (macroparticles) caused by their stochastic motion in a bounded plasma volume is proposed. Analytical expressions allowing one to describe the pumping (heating) of interacting grains with additional stochastic energy due to grain charge gradients are derived. The analytical results are verified by numerical simulation of the problem. It is shown that spatial variations in the charges of dust grains can lead to their anomalous heating in laboratory plasma.     

Electrostatic Solitary Pulses in a Dusty Electronegative Magnetoplasma

The nonlinear characteristics of dust-electron-acoustic (DEA) waves in a dusty electronegative magnetoplasma system consisting of nonextensive hot electrons, inertial cold electrons, positively charged static ions, and negatively charged immobile dust grains has been investigated. In this observation, the well-known reductive perturbation technique is employed to determine different types of nonlinear dynamical equations, namely, magnetized Korteweg–de Vries (KdV), magnetized modified KdV (mKdV), and magnetized Gardner equations. The stationary solitary wave and double layer solution of these three equations, which describe the characteristics of solitary waves and double layers of DEA waves, are obtained and numerically analyzed. It is noticed that various plasma parameters (viz., hot electron nonextensivity, positive ion-to-cold electron number density ratio, dust-to-cold electron number density ratio, etc.) significantly affect the basic properties of DEA solitary waves (DEASWs) and Gardner solitons (GSs). The prodigious results found from this theoretical investigation may be useful for researchers to investigate the nonlinear structures in various space and laboratory plasmas.