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.     

Spatiotemporal evolution of vortex dust structures in a track plasma

Results are presented from experimental studies of the behavior of dust grains in a track plasma produced by an accelerated proton beam. Dynamic dust structures in such a plasma are obtained for the first time, and their spatiotemporal evolution is thoroughly investigated. The structures develop from a dust spiral, which abruptly transforms with increasing dust density into a differentially rotating dust cloud across which dust-sound waves (including spiral waves generated by the dense central core) propagate. As time elapses, the dust cloud loses its fragments and gradually vanishes. At constant experimental conditions, the lifetime of the structures attains a few minutes.     

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.     

Plasma parameters and existence conditions of monolayer dust structures in the electrode sheath of an RF discharge

The plasma parameters in the electrode sheath of an RF discharge were studied experimentally under the conditions of dust monolayer levitation. A new method is proposed for determining the plasma parameters, such as the average electric field, ion density, and ion velocity. The screening parameter and the dust grain charge are estimated. The criteria of stable levitation of a dust monolayer are considered. The obtained results are compared with the available theoretical and numerical data, as well as with the results obtained using other diagnostic methods.     

Nonlinear screening of dust grains and structurization of dusty plasma: II. formation and stability of dust structures

The second part of the review on dust structures (the first part was published in Plasma Phys. Rep. 39, 515 (2013)) is devoted to experimental and theoretical studies on the stability of structures and their formation from the initially uniform dusty plasma components. The applicability limits of theoretical results and the role played by nonlinearity in the screening of dust grains are considered. The importance of nonlinearity is demonstrated by using numerous laboratory observations of planar clusters and volumetric dust structures. The simplest compact agglomerates of dust grains in the form of stable planar clusters are discussed. The universal character of instability resulting in the structurization of an initially uniform dusty plasma is shown. The fundamental correlations described in the first part of the review, supplemented with effects of dust inertia and dust friction by the neutral gas, are use to analyze structurization instability. The history of the development of theoretical ideas on the physics of the cluster formation for different types of interaction between dust grains is described.     

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.     

Nonlinear Wave Structures and Plasma−Dust Effects in the Earth’s Atmosphere

The interaction of charged dust grains with nonlinear vortical structures in the Earth’s atmosphere is analyzed. Certain aspects of the atmosphere?ionosphere interaction, in particular, mechanisms for the appearance of dust grains at ionospheric altitudes, are discussed. It is shown that, at certain altitudes, there are regions in the wavenumber space in which conditions leading to the excitation of acoustic?gravity waves are satisfied. The interaction of nonlinear acoustic?gravity waves with dust grains of meteoric origin at ionospheric altitudes, which leads to the mixing and redistribution of dust grains over the region where vortices exist, is investigated. The possibility of formation of vertical and horizontal dust flows in dusty ionospheric plasma as a result of modulational instability is analyzed. The dynamics of dust grains in dust devils frequently arising in the atmosphere above well-heated surfaces is modeled. The vortical structure of such a dust devil is characterized by a reduced pressure in the center, which facilitates the lifting of small dust grains from the surface. The formulated model is used to calculate the trajectories of dust grains in dust devils with allowance for the influence of the electric field generated in the vortex by colliding dust grains. The calculations show that dust devils play an important role in the transport of dust grains.     

Generation of infrasonic waves by low-frequency dust acoustic perturbations in the Earth’s lower ionosphere

It is shown that, during Perseid, Geminid, Orionid, and Leonid meteor showers, the excitation of low-frequency dust acoustic perturbations by modulational instability in the Earth’s ionosphere can lead to the generation of infrasonic waves. The processes accompanying the propagation of these waves are considered, and the possibility of observing the waves from the Earth’s surface is discussed, as well as the possible onset of acoustic gravitational vortex structures in the region of dust acoustic perturbations. The generation of such structures during Perseid, Geminid, Orionid, and Leonid meteor showers can show up as an increase in the intensity of green nightglow by an amount on the order of 10% and can be attributed to the formation of nonlinear (vortex) structures at altitudes of 110–120 km.     

Formation of plasma and gaseous toroidal vortices in air

The mechanism for the formation of high-temperature (plasma) vortices and low-temperature vortex rings produced by ejecting pulsed subsonic plasma/gas jets into air was investigated experimentally. A toroidal vortex forms due to the interaction between a pulsed jet with the flow induced by this jet in the ambient medium. By analyzing the experimental data and conservation laws, an equation is derived that allows one to determine the initial propagation velocity of the vortex as a function of the characteristics of the vortex generator and the ambient medium. The results obtained by solving this equation agree well with the experimental data.     

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.     

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.     

Ordered dusty structures in nuclear-track neon and argon plasmas

Ordered dusty structures formed of spherical monodisperse and polydisperse grains are obtained for the first time in a nuclear-track plasma produced by α-particles and fission fragments of ²⁵²Cf nuclei passing through neon or argon. A theoretical model of such a plasma is proposed. Monte Carlo computer simulations based on this model are carried out to explain the formation of such structures.     

Dynamics of plasma−dust structures formed in a trap created in the narrowing of a current channel in a magnetic field

The geometry and dynamics of plasma?dust structures in a longitudinal magnetic field is studied experimentally. The structures are formed in a glow-discharge trap created in the double electric layer produced as a result of discharge narrowing by means of a dielectric insert introduced in the discharge tube. Studies of structures formed in the new type of glow-discharge trap are of interest from the standpoint of future experiments with complex plasmas in superstrong magnetic fields in which the dust component is magnetized. Different types of dielectric inserts were used: conical and plane ones with symmetric and asymmetric apertures. Conditions for the existence of stable dust structures are determined for dust grains of different density and different dispersity. According to the experimental results, the angular velocity of dust rotation is ≥10 s^–1, which is the fastest type of dust motion for all types of discharges in a magnetic field. The rotation is interpreted by analyzing the dynamics of individual dust grains.     

Nonlinear dynamics of drift structures in a magnetized dissipative plasma

A study is made of the nonlinear dynamics of solitary vortex structures in an inhomogeneous magnetized dissipative plasma. A nonlinear transport equation for long-wavelength drift wave structures is derived with allowance for the nonuniformity of the plasma density and temperature equilibria, as well as the magnetic and collisional viscosity of the medium and its friction. The dynamic equation describes two types of nonlinearity: scalar (due to the temperature inhomogeneity) and vector (due to the convectively polarized motion of the particles of the medium). The equation is fourth order in the spatial derivatives, in contrast to the second-order Hasegawa-Mima equations. An analytic steady solution to the nonlinear equation is obtained that describes a new type of solitary dipole vortex. The nonlinear dynamic equation is integrated numerically. A new algorithm and a new finite difference scheme for solving the equation are proposed, and it is proved that the solution so obtained is unique. The equation is used to investigate how the initially steady dipole vortex constructed here behaves unsteadily under the action of the factors just mentioned. Numerical simulations revealed that the role of the vector nonlinearity is twofold: it helps the dispersion or the scalar nonlinearity (depending on their magnitude) to ensure the mutual equilibrium and, thereby, promote self-organization of the vortical structures. It is shown that dispersion breaks the initial dipole vortex into a set of tightly packed, smaller scale, less intense monopole vortices-alternating cyclones and anticyclones. When the dispersion of the evolving initial dipole vortex is weak, the scalar nonlinearity symmetrically breaks a cyclone-anticyclone pair into a cyclone and an anticyclone, which are independent of one another and have essentially the same intensity, shape, and size. The stronger the dispersion, the more anisotropic the process whereby the structures break: the anticyclone is more intense and localized, while the cyclone is less intense and has a larger size. In the course of further evolution, the cyclone persists for a relatively longer time, while the anticyclone breaks into small-scale vortices and dissipation hastens this process. It is found that the relaxation of the vortex by viscous dissipation differs in character from that by the frictional force. The time scale on which the vortex is damped depends strongly on its typical size: larger scale vortices are longer lived structures. It is shown that, as the instability develops, the initial vortex is amplified and the lifetime of the dipole pair components-cyclone and anticyclone-becomes longer. As time elapses, small-scale noise is generated in the system, and the spatial structure of the perturbation potential becomes irregular. The pattern of interaction of solitary vortex structures among themselves and with the medium shows that they can take part in strong drift turbulence and anomalous transport of heat and matter in an inhomogeneous magnetized plasma.     

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.     

On the Structure and Intensity of Vortex in RF Inductively Coupled Argon Plasma

Numerical simulation of a specific technical RF inductively coupled argon plasma with three coils, discharge current in the range of J_coil = 100–250 A, and generator frequency 3 MHz is presented. The temperature, pressure, and velocity fields are obtained under different discharge currents and different flow rates of central gas. A reversed flow (vortex) is found between the injected cool gas and high-temperature plasma-forming gas. The formation mechanisms of such a vortex and the influence of the discharge current and flow rate of central gas on the vortex structure and intensity are studied. Special attention is paid to investigating two different kinds of vortex flow patterns—Benard and toroidal. A critical flow rate of central gas above which the flow pattern would transform from Benard to toroidal is determined and approximated as a function of the discharge current by theoretical calculations and numerical simulations. The maximum negative velocities along the axis in the vortex zone are also determined under different discharge currents and different flow rates of central gas.     

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.     

Numerical simulations of a high-current plasma lens

The dynamic processes by which an electrostatic plasma lens with a wide-aperture ion beam and electrons produced from the secondary ion-electron emission relaxes to a steady state is investigated for the first time by the particle-in-cell method. The parameters of a two-dimensional mathematical model were chosen to correspond to those of actual plasma lenses used in experimental studies on the focusing of high-current heavy-ion beams at the Institute of Physics of the National Academy of Sciences of Ukraine (Kiev, Ukraine) and the Lawrence Berkeley National Laboratory (Berkeley, USA). It is revealed that the ion background plays a fundamental role in the formation of a high potential relief in the cross section of a plasma lens. It is established that, in the volume of the plasma lens, a stratified electron structure appears that is governed by the nonuniform distribution of the external potential over the fixing electrodes and the insulating magnetic field. The stratification is very pronounced because of the finite sizes of the cylindrical fixing electrodes of the lens. It is shown that the presence of such a structure limits the maximum compression ratio for an ion beam to values that agree with those observed experimentally.     

Transport properties of quasi-two-dimensional dissipative systems with a screened Coulomb potential

Results are presented from numerical investigations of the dynamics of quasi-two-dimensional systems in the form of a monolayer of dust grains interacting by means of a screened Coulomb potential and suspended in the Earth’s gravitational field by an external electric field. The structural and transport characteristics of such a system, including the pair correlation functions and the viscosity and diffusion coefficients, were investigated over a broad parameter range corresponding to the conditions under which dust structures are observed in RF capacitive discharge plasmas. An analysis of the results obtained revealed that there is a specific topological transition typical of systems having a low spatial dimension.     

Complex plasmas IV: Theoretical approaches to complex plasmas and their application

This paper completes a series of reviews devoted to the physics of complex plasmas, in which one of the components (dust) is in a crystalline or liquid state, while the others (electron, ions, and neutral atoms) are in a gaseous state. This review is devoted to the theoretical approaches used to describe complex plasmas so far. The main theoretical developments have been concentrated in the gaseous and weakly nonideal states of complex plasmas. Here, we describe the achievements in the new kinetic and new hydrodynamic approaches to complex plasmas. At present, only generalizations of the van der Waals approach for complex plasmas have been used to describe phase transitions and plasma condensation in complex plasmas. Here, criteria for transitions are described and compared with the existing experimental observations. Theoretical and numerical results for nonlinear structures, such as dust layers, dust voids, dust sheaths, and dust convective vortices, obtained by solving the stationary balance equations, are also discussed and compared with state-of-the-art experiments. At present, experiments in this field are progressing very fast, while theory is not advancing at the same rate of development. To further develop new theoretical models, one can use the elementary physical processes in complex plasmas described in the previous parts of the review. However, the detailed comparison of theory and experiments also needs more detailed experimental diagnostics of the phenomena observed. In the concluding part of our review, the trends in experiment and theory, as well as some existing applications, including industrial, environmental, and astrophysical ones, are described.