Micro‐Disperse Particles in Plasmas: From Disturbing Side Effects to New Applications

The research effort in the area of dusty plasmas initially aimed at avoiding particle formation and controlling the contamination level in industrial reactors. Nowadays, dusty plasmas have grown into a vast field and new applications of plasma‐processed dust particles are emerging. There is demand for particles with special properties, and for particle‐seeded composite materials. Low‐pressure plasmas offer a unique possibility of confinement, control and fine tailoring of particle properties. The role of plasma technology in treatment and surface modification of powder grains is reviewed and illustrated with examples. The interaction between plasma and injected micro‐disperse powder particles can also be used as a diagnostic tool for the study of plasma surface processes.     

Behaviour of two‐dimensional liquid dusty plasmas under perpendicular magnetic fields

The collective behaviour of two‐dimensional (2D) liquid dusty plasmas under perpendicular magnetic fields is studied using Langevin dynamic simulations. Based on the positions and velocities of the simulated dust particles, the dynamic parameters of intermediate scattering functions and probability distribution functions are calculated. It is found that, under different 2D liquid dusty plasma conditions, the motion of individual dust particles tends to be more super‐diffusive under stronger perpendicular magnetic fields, well consistent with the previous finding using a different diagnostic technique.     

Nonlinear Electrostatic Structures in Collisional Dusty Plasmas

A review of some problems of electrostatic waves in dusty plasmas is presented. It is concluded that in the most models of waves in dusty plasmas, the charge numbers of the ions and dusty grains are supposed to be constant. Besides most of the studies are elated to linear waves in collisionless systems. It is shown that even if the dynamics of dusty grains is not considered in the models, the physical processes causing wave dissipation have to be taken into account. The existing nonlinear models are mostly one‐dimensional ones. It is summarized that in dusty plasmas various types of nonlinear stationary structures may exist, and that these structures differ from the nonlinear structures found in ionospheric plasmas without dust. The nonlinear electrostatic stuctures seem to be observable in ionospheric, solar or interplanetary plasmas.     

Improved Self‐Energy Calculations for Pressure Broadening of Spectral Lines in Dense Plasmas

Pressure broadening of Lyman‐lines of hydrogen‐like lithium (Li²⁺) has been studied using a quantum statistical approach to the line shape in dense plasmas, for details see [1]. In this communication, we concentrate on the electronic self‐energy, which is a basic input to the theory of spectral line profiles. We discuss the effect of strong, i.e. close, collisions which have been neglected so far for Li²⁺ plasmas, but play generally an important role in dense plasmas, as has been shown in [2]. We present a method to calculate an improved electronic self‐energy including strong collisions based on a two‐body T‐matrix and an effective optical potential. The method is tested for level broadening of the ground state of hydrogen (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Linear propagation of dust acoustic modes in the presence of an electron beam

The physical and optical properties of plasmas are depended on dynamics of species in the discharge volume. Then, the presence of an electron beam, as a separate component, in a dusty plasma can modify the plasma structures through altering the discharge parameters. In this report, the linear propagation of acoustic modes in a collisionless dusty plasma contains electrons, ions and charged dust grains is investigated in the presence of an electron beam. Our analysis indicates that the electron beam can modify the dispersion relations of dust acoustic modes which resulted different data transportation in dusty plasmas. The obtained results are also examined for negative and positive charged dust grains with different number densities. The charge of dust grains represents an important role in the dynamics of the low frequency waves. Additionally, our findings reveal that the propagation of acoustic waves in dusty plasmas can be controlled by adjusting the electron number density of the beam and the cathode potential. Lastly, we obtian the destabilizing effects, originated from dust charge fluctuation, by reconsidering the dispersion relations of both dust acoustic modes.     

Dust‐ion‐acoustic solitary waves in a magnetized dusty pair‐ion plasma with Cairns‐Gurevich electrons and opposite polarity dust particles

The nonlinear dust‐ion‐acoustic (DIA) solitary structures have been studied in a dusty plasma, including the Cairns‐Gurevich distribution for electrons, both negative and positive ions, and immobile opposite polarity dust grains. The external magnetic field directed along the z‐axis is considered. By using the standard reductive perturbation technique and the hydrodynamics model for the ion fluid, the modified Zakharov–Kuznetsov equation was derived for small but finite amplitude waves and was provided the solitary wave solution for the parameters relevant. Using the appropriate independent variable, we could find the modified Korteweg–de Vries equation. By plotting some figures, we have discussed and emphasized how the different plasma values, such as the trapping parameter, the positive (or negative) dust number density, the non‐thermal electron parameter, and the ion cyclotron frequency, can influence the solitary wave structures. In addition, using the bifurcation theory of planar dynamical systems, we have extracted the centre and saddle points and illustrated the phase portrait of such a system for some particular plasma parameters. Finally, we have graphically investigated the behaviour of the solitary energy wave by changing the plasma values as well as by calculating the instability criterion; we have also discussed the growth rate of the solitary waves. The results could be useful for studying the physical mechanism of nonlinear propagation of DIA solitary waves in laboratory and space plasmas where non‐thermal electrons, pair‐ions, and dust particles can exist.     

Classical Molecular Dynamics Model for Coupled Two‐Component Plasmas – Ionization Balance and Time Considerations

The dynamic properties of ion‐electron two‐component plasmas (TCP) are studied by using classical molecular dynamics (MD) simulations. There is a variety of time dependent and structural results that MD is able to provide in complement to other methods, e.g., useful micro‐field sequences can be generated. The method deals with some specific difficulties: the mass ratio between ions and electrons enforces very small time‐steps appropriate to follow electrons motion while, ions must move significantly in order to build, self consistently, their spatial structure. This results in expensive simulations. Electron trajectories are trapped and de‐trapped with multiple electron collisions around ions resulting in the occurrence of quasi metastable bound electron states. An analysis of micro‐fields at neutral in a hydrogen plasma reveals the need to consider a complete hierarchy of time scales extended typically over 7 order of magnitude, i.e., from a time‐step: ～10^‐19s, to a time required to obtain statistical averages, ～10^‐11s. In order to extend the MD capabilities in representing real coupled plasmas a classical ionization/recombination process has been implemented allowing to follow the evolution of plasmas involving several ion stages and model the ionization balance. Here again TCP simulations deal with extended time‐scale providing information about relaxation of non equilibrium plasma states (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structural Characteristics and Equation of State of the Complex Plasmas

In this paper weakly and strongly non‐ideal plasmas are considered. In both cases the equations of state for hydrogen and dusty plasmas were studied on the basis of effective potentials. In the first case the thermodynamic properties for hydrogen plasmas were studied by the method of effective potentials taking into account quantummechanical diffraction, symmetry and screening effects. For strongly non‐ideal plasma or dusty plasma the equations of state were considered using radial distribution functions and effective interaction potential, which describes interactions of charged dust grains with dipole moments. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magneto‐Modulational Instability in Relativistic Plasmas

The behavior of magnetic fields generated by high frequency transverse plasmons in relativistic plasmas can be described by a set of nonlinear coupling equations, which has considered the nonlinear wave–wave, wave– particle interactions and the relativistic effects of electrons. Modulational instability of the spontaneous magnetic fields is investigated on the basis of the nonlinear coupling equations. Analytical and numerical results indicate the self‐generated magnetic fields are modulationally unstable and will be localized in a narrow region. The characteristic scale and maximum growth rate of the magnetic fields depend on the average Lorentz factor of electrons and the energy density of transverse plasmons. The relativistic effects of electrons will enhance the self‐focusing of magnetic fields (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear Behavior of Electromagnetic Waves in Ultra‐Relativistic Electron‐Positron Plasmas

A set of nonlinear equations which can self‐consistently describe the behavior of high frequency Electromagnetic (EM) waves in un‐magnetized, ultra‐relativistic electron‐positron (e‐p) plasmas is obtained on the basis of Vlasov‐Maxwell equations. Nonlinear wave‐wave, wave‐particle interactions lead to the coupling of high frequency EM waves with low frequency density perturbations which result from EM waves radiation pressure. The same as that in conventional electron‐ion (e‐i) plasmas, strong EM waves in e‐p plasmas will give rise to density depletion in which itself are trapped. But on the contrary to that in e‐i plasmas, there no longer exists electrostatic acoustic–like wave in e‐p plasmas due to the absence of mass difference. For linear polarized EM waves, a stationary EM soliton with a spiky structure will be formed. The possible relation of the localized field to pulsar radio pulse is discussed (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non‐Ideal Dust Structures in Cryogenic Complex Plasmas

The possibility of the formation of dust structures in cryogenic environment at 4.2‐77 K was proved experimentally in the previous researches of cryogenic complex (dusty) plasma [1–5]. It was revealed from the experiments, among others, that the dust structures with high concentration of dust particles can be formed, in which interparticle distance is comparable with particle size ‐ super dense dusty plasma structures. Such structures had exotic properties such as globular (spherical) form, free boundaries, etc. In the present work new results on the experimental investigations of new phenomenon of spheroidizing ‐ process of the dust structure transition to compact globular shape at cryogenic temperatures ‐ were presented. Possible nature of such phenomenon is discussed (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electric Microfield Distributions in Dense One‐ and Two‐Component Plasmas

The electric microfield distributions have been calculated using an integral‐equation method for one‐component plasmas proposed by Iglesias [1] and the coupling‐parameter integration technique for two‐component plasmas proposed by Ortner et al. [2]. Electric microfield distributions are studied in the frame of the Kelbg pseudopotential model, taking into account quantum‐mechanical effects (diffraction, quantum symmetry effects) and screening effects. The screened pseudopotential is represented in a numerically approximated form. The results are compared with simulation results obtained by other authors. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

修正屏蔽库仑势下二维尘埃等离子体的动力学和结构特性

本文考虑等离子体密度分布变化, 得到了修正屏蔽库仑势的解析解. 数值分析以及分子动力学模拟表明, 在常见实验室参数情况下, 等离子体密度分布变化引起的屏蔽库仑势修正对二维尘埃等离 子体系统的动力学和结构特性影响很小. 在极限参数情况下, 本模型的计算结果表明二维尘埃等离子体系统的扩散能力明显降低, 并且系统组态呈圆形分布. 此外, 本文还研究了实验室常见大小磁场对二维尘埃等离子体系统的影响. 关键词： 修正屏蔽库仑势 二维尘埃等离子体 分子动力学模拟     

Dust-ion-acoustic shock waves due to dust charge fluctuation

A dusty plasma system containing Boltzmann electrons, mobile ions and charge fluctuating stationary dust has been considered. The nonlinear propagation of the dust-ion-acoustic waves in such a dusty plasma has been investigated by employing the reductive perturbation method. It has been shown that the dust charge fluctuation is a source of dissipation and is responsible for the formation of the dust-ion-acoustic shock waves. The basic features of such dust-ion-acoustic shock waves have been identified. The implications of our results in space and laboratory dusty plasmas are discussed.     

Dispersion of Dust Acoustic Modes and Perturbations of Plasma Flux Balance

Previous considerations of dust acoustic waves is demonstrated to be inconsistent ‐ the required equilibrium state for perturbations was not defined since balance of plasma fluxes was neglecting. The self‐consistent treatment shows that plasma flux perturbations are accompanying any collective waves propagating in dusty plasmas and can play an important role in wave dispersion, wave damping and can create instabilities. This is illustrated by the derivation of dispersion relation for dust acoustic modes taking into account the plasma flux balances and plasma flux perturbations by waves. The result of this approach shows that the dust acoustic waves with linear dependence of wave frequency on the wave number exist only in restricted range of the wave numbers. Only for wave numbers larger than some critical wave number for low frequency modes the frequency can be have approximately a linear dependence on wave number and can be called as dust acoustic wave but the phase velocity of these waves is different from that which can be obtained neglecting the flux balance and depends on grain charge variations which are determined by the balance of fluxes. The presence of plasma fluxes previously neglected is the main typical feature of dusty plasmas. The dispersion relation in the range of small wave numbers is found to be mainly determined by the change of the plasma fluxes and is quite different from that of dust acoustic type, namely it is found to have the same form as the well known dispersion relation for the gravitational instability. This result proves in general way the existence of the collective grain attractions of negatively charged grains for for large distances between them and for any source of ionization. The attraction of grains found from dispersion relation of the dust acoustic branch coincides with that found previously for pair grain interactions using some models for the ionization source. For the existing experiments the effective Jeans length for such attraction is estimated to be about 8 – 10 times larger than the ion Debye length and the effective gravitational constant for the grain attraction is estimated to be several orders of magnitude larger than the usual gravitational constant. The grain attraction at large inter‐grain distances described by the gravitationlike grain instability is considered as the simplest explanation for observed dust cloud clustering, formation of dust structures including the plasma crystals. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of overlapping Debye spheres on structures of 2D dusty plasmas

In dusty plasmas, overlapping Debye spheres around dust grains could produce an attractive force between them. Its effects on static structures of two-dimensional (2D) dusty plasmas are studied here by using molecular dynamics simulations. Results, in terms of the equilibrium radial distribution function, are compared with those deduced from purely repulsive Debye-Hückel or Yukawa potential for different Coulomb-coupling and screening parameters. The effect of the attractive force is found quite noticeable for usual experimental conditions, and becomes more pronounced for larger screening parameter κ. In particular, it is observed that for large κ the attractive force is dominant, and dust grains tend to aggregate and form patterns with scattering voids.     

Dust ion‐acoustic solitons with trapped q‐non‐extensive electrons,dissipative processes,and streaming ions

The characteristics of dust ion‐acoustic waves (DIAWs) that are excited because of streaming ions and hot q‐non‐extensive electrons obeying a vortex‐like distribution are investigated. By exploiting a pseudo‐potential technique, we have derived an energy integral equation. The presence of non‐extensive q‐distributed hot trapped electrons and a streaming ion beam has been shown to influence soliton structure quite significantly. The evolution of the soliton‐like perturbations in complex plasmas, taking into account the dissipation processes, are also investigated, obtained by numerically solving the modified Schamel, equation whose widths are dependant on electron trapping efficiency β. Our illustrations indicate that compressive DIAWs develop in this plasma. As the plasmas in reality have a relative flow, such an analysis can be used to understand the DIA solitary structures observed in the mesospheric noctilucent clouds.     

Kinetic treatment of acoustic waves in a four‐component dusty plasma

A kinetic formulation is developed to investigate low‐frequency dust ion acoustic waves (DIAWs) and dust acoustic waves (DAWs) as well as numerically for a four‐component, collisionless, unmagnetized dusty plasma, using the linearized Vlasov–Poisson model for species obeying the Maxwellian distribution. In particular, the dynamics of low‐frequency DIAWs is investigated by considering two cases. In the first case, ions and positive dust particles are assumed to be dynamically adiabatic while the negative dust particles are static in the background. In second case, the ions are taken adiabatic, while both positive and negative dust particles are static in the background. For DAWs, the ions are assumed to be isothermal, while both positive and negative dust species are considered adiabatic. Electrons are assumed to be isothermal in all cases. The linear characteristics and Landau damping rates for DIAWs and DAWs are investigated with effects of the dust particle concentrations and different temperature ratios. It is noted that for higher values of positive dust concentration, DIAWs (DAWs) are less (more) damped. It is also observed that the damping rate increases (decreases) as T_i approaches T_e for DIAWs (DAWs). It is worth adding here that the theoretical results presented here are supported by numerical analyses and illustrations. The relevance of the study to laboratory and cosmic plasmas is also pointed out.