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.     

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.     

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.     

Effect of ion collisions on the parameters of dust-plasma structures

A study is made of how collisions of ions with gas atoms affect the parameters of an ion flow and the interaction between dust grains, as well as their interaction with the flow. The ion velocity distribution in a gas discharge is analyzed with allowance for both resonant charge exchange of the ions with parent gas atoms and polarizing collisions. The interaction forces between a dust grain and an ion flow and among the grains due to the charge exchange of ions with gas atoms near the grain are examined.     

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.     

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.     

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).     

Formation of vortex dust structures in inhomogeneous gas-discharge plasmas

A generalized analytical model of instabilities in a dusty plasma with a nonzero grain charge gradient in a field of nonelectrostatic forces is considered. A review is given of different experimental observations of the dust self-oscillations that occur in the plasmas of an rf capacitive discharge and a dc glow discharge and whose appearance can be explained in terms of the proposed model. It is shown that the change in the grain charge gives rise to dynamic dust structures in laboratory gas-discharge plasmas. Attention is focused on the analysis of the onset of vortex motion of the dust grains.     

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.     

One-dimensional nonlinear self-organized structures in dusty plasmas

Dusty plasmas, which are open systems, can form stable one-dimensional self-organized structures. Absorption of plasma by dust particles results in the plasma flux from the plasma regions where the dust is absent. It is found that, in a one-dimensional dust layer, this flux is completely determined by the number of dust particles per unit area of the layer surface. This number determines all of the other parameters of the steady-state dust structure; in particular, it determines the spatial distributions of the dust density, dust charge, electron and ion densities, and ion drift velocity. In these structures, a force and electrostatic balance is established that ensures the necessary conditions for confining the dust and plasma particles in the structure. The equilibrium structures exist only for subthermal ion flow velocities. This criterion determines the maximum possible number of dust particles per unit area in the steady-state structure. The structures have a universal thickness, and the dust density changes sharply at the edge of the structure. The structures with a size either less than or larger than the ion mean free path with respect to ion-neutral collisions, quasi-neutral and charged structures, and soliton-and anti-soliton-like structures are investigated. Laboratory experiments and observations in extraterrestrial plasma formation are discussed in relation to dust structures.     

Study of the process of dust grain discharging in the afterglow of an RF discharge

The process of decay of dust structures formed of polydisperse grains injected into an RF discharge is investigated. The dust grain velocities after switching-off of the discharge are measured. The number density, dimensions, and residual charges of dust grains are estimated from the balance of forces acting on the grains after discharge is switched off.     

Helical structures in complex plasma I: Noncollective interaction

The conditions for the formation and stability of helical quasi-crystals in a complex plasma containing dust grains of equal size are investigated. A study is made of both the confinement of such helical structures in a direction transverse to the cylinder axis by means of an external parabolic potential well and the possibility of their self-confinement. Computer simulations of the helical dust structures were carried for two cases: for a structure of infinite length along the symmetry axis (or a closed structure in toroidal geometry) and for a structure of finite length. The dust grains were assumed to interact through a potential that is a superposition of the non-Debye nonlinear screened potential and the nonscreened noncollective attractive potential (the Lesage effect). Molecular dynamics simulations showed that, in the presence of dissipation, any initial random distribution of the dust grains interacting through such a potential in cylindrical geometry evolves to an equilibrium helical structure. When the external control parameter was varied smoothly, the pitch angle of the helix was observed to bifurcate (i.e., to undergo sharp jumps). The structure of the helix was also observed to bifurcate when the external parameter was varied: a helix changed into two interwoven helices, which then changed into three interwoven helices, etc. The smaller the confinement parameter (and, accordingly, the larger the radius of the helical structures) and the stronger the attractive forces between the grains, the larger the number of bifurcations. The results of analytical calculations of the parameters of the equilibrium structures and of their energies are in complete agreement with numerical results. It is also shown that noncollective attraction between dust grains makes it probable that helical structures will exists when the external confinement parameter is zero or even when it is negative. Bifurcations in such systems may provide the possibility of creating new types of memory elements.     

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.     

Ion-acoustic solitons in dusty plasma

The dynamics of dust ion-acoustic solitons is analyzed in a wide range of dusty plasma parameters. The cases of both a positive dust grain charge arising due to the photoelectric effect caused by intense electromagnetic radiation and a negative grain charge established in the absence of electromagnetic radiation are considered. The ranges of plasma parameters and Mach numbers in which ??conservative?? (nondissipative) solitons can exist are determined. It is shown that, in dusty plasma with negatively charged dust grains, both compression and rarefaction solitons can propagate, whereas in plasma with positively charged dust grains, only compression solitons can exist. The evolution of soliton-like compression and rarefaction perturbations is studied by numerically solving the hydrodynamic equations for ions and dust grains, as well as the equation for dust grain charging. The main dissipation mechanisms, such as grain charging, ion absorption by dust grains, momentum exchange between ions and dust grains, and ion-neutral collisions are taken into account. It is shown that the amplitudes of soliton-like compression and rarefaction perturbations decrease in the course of their evolution and their velocities (the Mach numbers) decrease monotonically in time. At any instant of time, the shape of an evolving soliton-like perturbation coincides with the shape of a conservative soliton corresponding to the current value of the Mach number. It is shown that, after the interaction between any types of soliton-like perturbations, their velocities and shapes are restored (with a certain phase shift) to those of the corresponding perturbations propagating without interaction; i.e., they are in fact weakly dissipative solitons.     

Formation of quasi-two-dimensional dust structures in an external electric field

Conditions are considered under which quasi-two-dimensional extended structures are formed consisting of charged dust grains that are suspended in a gravitational field by an external electric field. Formulas are derived that describe the relationships between the parameters of the intergrain interaction potential, the number of dust grains, and the gradients of the linear electric field of the device. A criterion is proposed that determines the onset of a new dust layer in a quasi-two-dimensional dust system.     

Analysis of the formation of ordered dust-grain structures in a thermal plasma

The possibility is studied of the formation of ordered dust-grain structures in a low-temperature thermal plasma consisting of electrons, ions, and micron-sized charged dust grains. The range of the required values of the coupling parameter Γ defining the degree to which the plasma is nonideal is calculated using the results of diagnostic measurements carried out in a plasma consisting of combustion products of propane in air with grains of different materials. The results obtained show that the most favorable conditions for the formation of strongly correlated grain structures (for both positively and negatively charged grains) take place at the maximum grain number density and a plasma temperature close to the minimum flame temperature (∼1600 K). In this case, the optimum grain radii lie in the range 4–10 μm and the maximum value of the parameter Γ is less than 200. Since the calculated values of Γ give an upper estimate, liquidlike ordered structures are most likely to form in a thermal plasma. Based on the results of the analysis, it is stated that an increase in the parameter Γ and, accordingly, the formation of plasma-crystal structures in a thermal plasma can only occur for positively charged grains. __________ Translated from Fizika Plazmy, Vol. 26, No. 7, 2000, pp. 626–632. Original Russian Text Copyright ? 2000 by Samarian, Vaulina, Nefedov, Petrov.     

Determination of the pairwise interaction potential between dust grains in plasma

Results are presented from measurements of the pairwise interaction potential between dust grains in plasma. The experiments were carried out with RF capacitive discharges over a wide range of dusty plasma parameters. All the experiments under analysis revealed a repulsive interaction potential that was close in shape to the screened Coulomb potential. The grain charges and the radii at which they were screened are determined.     

Coagulation of dust grains in the plasma of an RF discharge in argon

Results are presented from experimental studies of coagulation of dust grains of different sizes injected into a low-temperature plasma of an RF discharge in argon. A theoretical model describing the formation of dust clusters in a low-temperature plasma is developed and applied to interpret the results of experiments on the coagulation of dust grains having large negative charges. The grain size at which coagulation under the given plasma conditions is possible is estimated using the developed theory. The theoretical results are compared with the experimental data.     

Solitary dust sound waves in a plasma with two-temperature ions and distributed grain size

The propagation of weakly nonlinear dust sound waves in a dusty plasma containing two different-temperature ion species is explored. The nonlinear equations describing both the quadratic and cubic plasma nonlinearities are derived. It is shown that the properties of dust sound waves depend substantially on the grain size distribution. In particular, for solitary dust sound waves with a positive potential to exist in a plasma with distributed grain size, it is necessary that the difference between the temperatures of two ion species be larger than that in the case of equal-size grains.     

Properties of dust-plasma structures formed in a glow discharge above the lower wall of the discharge chamber

The properties are studied of dusty plasma structures formed in a glow discharge in a dust trap above the lower wall of the side branch of the discharge tube, near the turn of the discharge channel. The dust structure is three-dimensional with a characteristic size of up to 3 cm and contains about 30000 dust grains. Depending on the experimental conditions, dust-acoustic, dissipative, and charge-gradient instabilities can develop in such a structure. When using highly polydisperse dust grains of arbitrary shape, the effect of selection of dust grains by the plasma with respect to their mean size and shape was discovered. This effect was studied quantitatively in two gases by using the method of gathering and extraction of the dust grains levitating in the trap. The morphology of the dust structures was determined from the pair correlation functions of the horizontal cross sections containing long-range order peaks and elements of a hexagonal lattice. Stratification of a uniform structure accompanied by convective rotation caused by the grain charge gradient was observed. Applications of the dusty plasma created in this type of device are discussed.