Collective Grain Interaction I. New Paradigm for Plasma Crystal Formation

The concept of collective grain interaction in complex plasmas is developed for large non‐linearity in grain screening. It is shown that for the case where the characteristic collective radius exceeds the non‐linear screening radius the collective interactions can fully determine the non‐linear collective attraction well. Based on the physics of collective non‐linear grain attraction a new paradigm for plasma crystal formation is formulated according to which the plasma crystal formation is related with localization of grains in non‐linear collective attraction wells. Nonlinearity in screening is an important feature of new paradigm and takes into account that the grain charges are large in accordance with most experiments where the plasma crystals where observed. The physical consequence of large non‐linearity is the presence of relative large potential well at distances only several times larger then the non‐linear screening radius. The calculated location of the potential well is of the order of the observed inter‐grain distances in plasma crystals and the deepness of the potential well is close to observed temperature of phase transition. The new paradigm considers formation of plasma crystal as result of grain trapping in the collective non‐linear potential well. The grain interactions close to the position of the potential well are in this paradigm relatively weak contrary to previous paradigm relating the plasma crystal formation with strong grain interactions. This new approach opens the possibility for direct calculation of the deepness of the attraction collective well, the critical value of the coupling constant. Results of these calculations show a reasonable agreement with both the observations of crystals in low pressure high‐frequency discharges and in large pressure discharges. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dust Self‐Organized Structures I. Role of Ion Drag and Ion Diffusion on Screened Grains

Self‐organized dust structures are investigated using a Gurevich‐Parker model for non‐linear dust screening. The non‐linear dust drag coefficients and non‐linear diffusion coefficients are calculated numerically as functions of nonlinear parameter for screening, dust density and ion flux drift velocity. Nonlinear ion dust drag inside the structures creates an electric field with potential well for ions at the structure center. The equilibrium dust structures confine both the dust grains and the plasma particles, have a finite size and have inside an enhanced dust and ion densities. The necessary conditions for existence of equilibrium dust structures are found. The equilibrium dust structures are determined by two global parameters related to the external plasma flux and to the power of ionization. The equilibrium exist only in a restricted phase space of these two parameters and depends on the the drag coefficient at the structure center. The equilibrium requirements are found using non‐linear drag coefficient calculated numerically. It is shown that this phase space area can be broad but it is systematically decreasing with an increase of the ionization rate. It is found that equilibrium exists for dust structures with large dust and ion density concentration at the center and that for these structures the ion diffusion is strongly suppressed by ion scattering on non‐linearly screened grains. The results of the theory can be used to interpret the recently observed compact dust structures in micro‐gravity experiments and can provide some recommendations for future micro‐gravity experiments in spherical chambers (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dust Self‐Organized Structures II. Solutions of Master Equations for Small Diffusion

Master equations for spherical dust structures are solved numerically using the asymptotic solutions at the center of the structures for the case of absence of external ionization and small diffusions. The structures are determined by a single parameter, the external plasma flux at the surface of the structure. The equilibrium states that are possible in a limited range of this parameter are investigated numerically. It is demonstrated that in the range of existence of equilibria the structures are changing their shapes and type of distributions inside the structures. For large external fluxes the ion and dust distributions can have peaks inside the structures while for low external fluxes the dust distribution has a single maximum at the structure center. The lower is the external flux supporting the structure the larger is its size. An increase of the external flux decreases the accumulation of dust and ions at the center. The total number of dust confined by the structure is larger for larger size structures. Estimates of dust crystallization inside structures are given. The role of diffusion is calculated by perturbations and is shown to be small in all structure regions except the structure edges. In the perturbation theory we use the exact expressions of the diffusion coefficients calculated previously numerically. The regions with dust density peaks inside the structures have been calculated with two order of magnitude larger precision that allows to resolve the structure parameter dependencies inside the peaks. It is shown that although in peaks the gradients of all parameters are increased the diffusion flux is still small and that the continuity and hydrodynamic approach are applicable within an accuracy about several %‐s (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dust Self‐Organized Structures III. Solutions of Master Equations in Presence of Volume Ionization

The shapes of dust self‐organized structures in presence of volume ionization is investigated. Master Equations for small diffusions and presence of an external ionization describing spherical dust structures are solved numerically using asymptotic solutions at the center of the structures. The structures are determined by two parameters, the external plasma flux at the surface of the structures and the power of volume ionizations. It is shown that the range of possible equilibrium states is reduced with an increase of the ionization power. This reduction is due mainly to an increase of the minimum possible value of ion density at the center of the structure for which the equilibrium is possible (an increase of minimum possible external flux). It is found that for certain large ionization power the equilibrium structure without void at the center cannot exist. The critical value of ionization power is found numerically. In the range of ionization power where the equilibria is possible the distribution of the parameters inside the structures are investigated by solving the Master Equations in the limits of small and large ionization power (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Note on Scattering of Electromagnetic Waves by Nonlinearly Screened Dust Grains in Plasmas

Although most experiments in complex plasmas correspond to non‐linear grain screening, the theoretical models of non‐linear screening have not been checked experimentally. Scattering of electromagnetic waves on a single nonlinearly screened dust grain in plasmas can serve as one of effective methods for investigation of non‐linear screening. In present paper we have developed a theory for electromagnetic wave scattering that includes both the effect of coherency of scattering for long wave range and the loss of coherency with a decrease of the wave length. It is valid for arbitrary non‐linearity in screening and demonstrates that the loss of coherency occurs for wave length less then the characteristic screening length for non‐linear screening being usually substantially larger than the linear Debye screening length. The effect is illustrated numerically using the most popular model of non‐linear screening. The dependence of the cross‐section of scattering on parameter of non‐linearity in screening is calculated numerically. The loss of coherency in scattering by a single grain can serve as effective diagnostic for checking the theoretical models of non‐linear screening. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Collective Grain Interactions for Constant Ionization Source

The dust screening and dust attraction in plasmas is considered for the constant ionization source. Both limits of linear and nonlinear screening are considered. It is shown that the non‐linear screening changes substantially the collective dust screening and collective dust attraction. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Longitudinal Dust Lattice Shock Wave in a Strongly Coupled Complex Dusty Plasma

The effect of hydrodynamical damping that arises due to the irreversible processes within the system have been studied on 1D nonlinear longitudinal dust lattice wave (LDLW) in homogeneous strongly coupled complex (dusty) plasma. Analytical investigation shows that the nonlinear wave is governed by Korteweg‐de Vries Burgers' equation. This hydrodynamical damping induced dissipative effect is responsible for the Burgers' term that causes the generation of shock wave in dusty plasma crystal. Numerical investigation on the basis of the glow‐discharge plasma parameters reveal that LDLW exhibits both oscillatory and monotonic shock. The shock is compressive in nature and its strength decreases (increases) with the increase of the shielding parameter κ (characteristic length L). The effects of dust‐neutral collision are also discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Collective Grain Interactions II. Non‐linear Collective Drag Force

It is found that the collective effects operating at large distances from the grain surface can produce substantial scattering of the ion flux and create an additional collective drag force dominant for large grain densities. The consideration is restricted to large grain charges β = Z_de ²a /T_iλ_Di ? 1 and T_i /T_e ? 1 (–eZ_d being the grain charge in units of electron charge, a being the grain size, λ_Di being the ion Debye radius and T_e,i being electron and ion temperatures, respectively). For present dusty plasma experiments β ≈ 10–50, the large charges of grains are screened non‐linearly and the ion scattering creates non‐linear drag force. The present investigation considers effects of scattering by collective grain fields at large distances from the grains. It is found that the physical reason of the importance of collective drag force, calculated in this paper, is related to presence of weakly screened collective field of grains outside the non‐linear screening distance depending on grain densities. The amplitude of this collective fields of the grains is determined by non‐linear screening at non‐linear screening radius. It is shown that for dust densities of present experiments the collective drag force related to this scattering can be of the order of the non‐linear drag force caused by scattering inside the non‐linear screening radius or even larger. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multidimensional Instability of Dust‐Acoustic Solitary Waves in a Magnetized Hot Dusty Plasma with Superthermal Electrons and Ions

Multidimensional instability of dust‐acoustic solitary wave (DASW) in magnetized dusty plasma with superthermal electrons and ions and micron size hot dust particles is investigated. The Zakharov‐Kuznetsov (ZK) equation, describing the small but finite amplitude DASW, was derived using the reductive perturbation method and its solitary answers was introduced. Effects of electrons and ions superthermality as well as the external magnetic field on the nature of DASW are discussed in detail. Dispersion relation, threshold condition, and growth rate of multidimensional instability of DASW were derived using small‐k (long wavelength plane wave) perturbation expansion method. We found that the direction and strength of external magnetic field extremely affect the growth rate and instability criterion. Results show that growth rate of instability decreases with increasing the number of superthermal electrons and increases with increasing the number of superthermal ions. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

高频感应等离子体流动模型与微型电推进器流场特性分析

微型射频离子推力器具有结构简单、 工作寿命长、 推力动态范围大、 性能调节响应灵敏等特点,是国际微电推进领域的研究热点之一.射频离子推力器电离室内的感性耦合放电等离子体特性和推力器的性能密切相关.为此,文章建立了低气压、小尺寸微型射频离子推力器电离室内感性耦合等离子体流体模型,开展了电磁场、流场、化学反应浓度场的多物理...     

Raman light scattering,infrared absorption and DSC studies of the phase transition and vibrational and reorientational dynamics of H2O ligands and ClO4– anions in [Ba(H2O)3](ClO4)2

[Ba(H₂O)₃](ClO₄)₂ between 90 and 300 K possesses two solid phases. One phase transition of the first‐order type at: = 211.3 K (on heating) and = 204.6 K (on cooling) was determined by differential scanning calorimetry. The entropy change value (ΔS ≈ 15 Jmol^–1 K^–1), associated with the observed phase transition, indicates a moderate degree of molecular dynamical disorder. Both, vibrational and reorientational motions of H₂O ligands and ClO₄^– anions, in the high‐temperature and low‐temperature phases, were investigated by Fourier transform far‐infrared and middle‐infrared and Raman light scattering spectroscopies. The temperature dependences of the full‐width at half‐maximum values of the bands associated with ρ_w(H₂O) mode, in both infrared (~570 cm^–1) and Raman light scattering (~535 cm^–1) spectra, suggest that the observed phase transition is not associated with a sudden change of a speed of the H₂O reorientational motions. Ligands reorient fast, with correlation time of the order of several picoseconds, with a mean activation energy value E_a = 5.1 kJ mol^–1 in both high and low temperature phases. On the other hand, measurements of temperature dependences of full‐width at half‐maximum values of the infrared band at ~460 cm^–1, associated with δ_d(OClO)E mode, and Raman band at ~1105 cm^–1, associated with ν_as(ClO)F₂ mode, revealed the existence of a fast ClO₄^– reorientation in phase I and in phase II, with the E_a(I) and E_a(II) values equal to 8.0 and 6.5 kJ mol^–1, respectively. These reorientational motions of ClO₄^– are slightly distorted at the T_C. Fourier transform far‐infrared and middle‐infrared spectra with decreasing of temperature indicated characteristic changes at the vicinity of PT at T_C, which suggested lowering of the crystal structure symmetry. All these experimental facts suggest that the discovered phase transition is associated with small change of H₂O ligands and somewhat major change of ClO₄^– anions reorientational dynamics, and with insignificant change of the crystal structure, too. Copyright © 2012 John Wiley & Sons, Ltd.     

A paradigm shift in rate determining step from single electron transfer between phenylsulfinylacetic acids and iron(III) polypyridyl complexes to nucleophilic attack of water to the produced sulfoxide radical cation: a non‐linear Hammett

Mechanism of oxidative decarboxylation of phenylsulfinylacetic acids (PSAAs) by iron(III) polypyridyl complexes in aqueous acetonitrile medium has been investigated spectrophotometrically. An initial intermediate formation between PSAA and [Fe(NN)₃]³⁺ is confirmed from the observed Michaelis–Menten kinetics and fractional order dependence on PSAA. Significant rate retardation with concentration of [Fe(NN)₃]³⁺ is rationalized on the basis of coordination of a water molecule at the carbon atom adjacent to the ring nitrogen of the metal polypyridyl complexes by nucleophilic attack at higher concentrations. Electron‐withdrawing and electron‐releasing substituents in PSAA facilitate the reaction and Hammett correlation gives an upward ‘V’ shaped curve. The apparent upward curvature is rationalized based on the change in the rate determining step from electron transfer to nucleophilic attack, by changing the substituents from electron‐releasing to electron‐withdrawing groups. Electron‐releasing substituents in PSAA accelerate the electron transfer from PSAA to the complex and also stabilize the intermediate through resonance interaction leading to negative reaction constants (ρ). Conversely, electron‐withdrawing groups, while retarding the electron transfer exert an accelerating effect on the nucleophilic attack of H₂O which leading to low magnitude of ρ⁺ compared to high ρ^? values of electron‐releasing groups. Marcus theory is applied, and a fair agreement is seen with the experimental values. Copyright © 2016 John Wiley & Sons, Ltd.