Formation of large‐scale structures in four‐component dusty plasmas

A possibility of self‐organization of magnetized four‐component dusty plasmas to double Beltrami (DB) state is explored. It is found that for a specific set of Beltrami parameters, the four‐component dusty plasma self‐organizes to DB state. The DB state characterized by two scale parameters may represent a paramagnetic or diamagnetic field structure. The impact of Beltrami parameters, charge and densities of dust grains on formation of self‐organized structures has also been investigated. This study has potential relevance to the formation of large‐scale structures in astrophysical plasmas.     

Effects of non‐extensive electrons on the sheath of dusty plasmas with variable dust charge

In this study, a detailed investigation of the problem of sheath is presented using the fluid model in a magnetized three‐component dusty plasma system comprising positive ions, dust grains with variable charge and q‐non‐extensive electrons (i.e., the electrons evolve far away from their Maxwellian thermodynamic equilibrium [q = 1]). The effects of q‐non‐extensivity parameter on the plasma sheath parameters are studied numerically. A significant change is observed in the quantities characterizing the sheath with the presence of the super‐extensive electrons (q < 1) and sub‐extensive electrons (q > 1). In addition, based on the orbital motion limited theory, by taking various forces acting on the dust particle into consideration, the dynamics of the dust located within the sheath, that is, the dust grain charging inside the sheath, is examined under different values of q. It is found that the q‐non‐extensivity has affected significantly the dynamics and the charging process of the dust grains in the sheath.     

Dynamic properties of strongly coupled dusty plasmas with particles of finite dimensions

The aim of the present study is to determine the impact the finite size of dust particles has on the static and dynamic characteristics of the dust component of a plasma. Taking into account both the finite dimensions of dust grains and the plasma screening, a model expression is chosen for the interdust interaction potential. The static structure factor of dust particles is evaluated by iteratively solving the reference hypernetted‐chain approximation, which inherently contains the hard sphere model handled within the Percus–Yevick closure. The self‐consistent method of moments is then engaged to relate the static and dynamic structure factors by assuming that the second derivative of the dynamic structure factor with respect to the frequency vanishes at the origin. Thus, an analytical expression for the dynamic structure factor is validated over quite a broad domain of dusty plasma non‐ideality and grains packing fraction. The calculated spectrum of dust‐acoustic waves reveals the appearance of the roton minimum, which becomes less pronounced when the packing fraction of dust particles rises. It is also predicted that the wavenumber position of the roton minimum is de facto independent of the size of dust particles. New analytical expressions for the dust‐acoustic wave spectrum and decrement of damping are proposed and thoroughly checked.     

Interaction of solitary waves in magnetized warm dusty plasmas with dust charging effects

In consideration of adiabatic dust charge variation, the combined effect of the external magnetized field and the dust temperature on head-on collision of the three-dimensional dust acoustic solitary waves is investigated. By using the extended Poincar\'e--Lighthill--Kuo method, the phase shifts and the trajectories of two solitons after the collision are obtained. The effects of the magnitude and the obliqueness of the external magnetic field and the dust temperature on the solitary wave collisions are discussed in detail.     

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.     

The collision frequency of electron-neutral-particle in weakly ionized plasmas with non-Maxwellian velocity distributions

The collision frequencies of electron-neutral-particle in weakly ionized complex plasmas with the non-Maxwellian velocity distributions are studied. The average collision frequencies of electron-neutral-particle in plasmas are accurately derived. We find that these collision frequencies are significantly dependent on the power-law spectral indices of non-Maxwellian distribution functions and so they are generally different from the collision frequencies in plasmas with a Maxwellian velocity distribution, which will affect the transport properties of the charged particles in plasmas. Numerically analyses are made to show the roles of the spectral indices in the average collision frequencies respectively.     

Methodology for the solutions of some reduced Fokker‐Planck equations in high dimensions

In this paper, a new methodology is formulated for solving the reduced Fokker‐Planck (FP) equations in high dimensions based on the idea that the state space of large‐scale nonlinear stochastic dynamic system is split into two subspaces. The FP equation relevant to the nonlinear stochastic dynamic system is then integrated over one of the subspaces. The FP equation for the joint probability density function of the state variables in another subspace is formulated with some techniques. Therefore, the FP equation in high‐dimensional state space is reduced to some FP equations in low‐dimensional state spaces, which are solvable with exponential polynomial closure method. Numerical results are presented and compared with the results from Monte Carlo simulation and those from equivalent linearization to show the effectiveness of the presented solution procedure. It attempts to provide an analytical tool for the probabilistic solutions of the nonlinear stochastic dynamics systems arising from statistical mechanics and other areas of science and engineering.     

Dust ion‐acoustic solitons collision in weakly relativistic plasmas with superthermality‐distributed electrons and positrons: Higher‐order phase shifts

The higher‐order (H‐O) phase shift of dust ion‐acoustic solitons (DIASs) in a weakly relativistic plasma is examined considering the influence of both superthermality‐distributed electrons and positrons. Employing the extended Poincaré–Lighthill–Kuo method (EPLKM), the Korteweg–de Vries equations (KdVEs) and the deviation in trajectories of DIASs (i.e., phase shifts) are obtained after the collision. For obtaining H‐O phase shifts of DIASs, the fifth‐order dispersion terms are added into KdVEs. The effects of the relativistic factor for a weakly relativistic regime and the superthermality of both electrons and positrons on the H‐O phase shifts are discussed. Numerical analysis gives rise to important highlights on the excitation and the collision of DIASs in astrophysical situations such as a pulsar magnetosphere.     

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.     

Effect of non‐extensivity parameter q on the damping rate of dust ion acoustic waves in non‐extensive dusty plasma

Kinetic theory has been applied to study the damping characteristics of dust ion acoustic waves (DIAWs) in a dusty plasma comprising q‐non‐extensive distributed electrons and ions, while the dust particles are considered extensive following the Maxwellian velocity distribution function. It is found that the results of the three‐dimensional velocity distribution function are more accurate compared to the results of the one‐dimensional velocity distribution function. The numerical solution of the dispersion relation is carried out to study the effect of the non‐extensivity parameter q on the dispersion, the damping rate, and the range of the values of the normalized wavenumber ( k λ_D) for which the DIAWs are weakly damped. It is found that the change in the value of the electron non‐extensivity parameter q_e has a minor effect on the dispersion, the damping rate, and the range of the values of the normalized wavenumber ( k λ_D) for which the DIAWs are weakly damped, while on the other hand, ion non‐extensivity parameter q_i has a strong effect on these arguments. The effect of other parameters, such as the ratio of electron to ion number density and ratio of electron to ion temperature, on the damping characteristics of DIAWs is also highlighted.     

Stability criteria of Rayleigh ‐ Taylor modes in magnetized plasmas

The Rayleigh ‐ Taylor (RT) instability is investigated analytically in an inhomogeneous plasma in an external magnetic field. For the case of two distinct fluid layers separated by a sharp boundary and for a fluid of a continuously varying density, RT dispersion relations have been obtained and analyzed. Stability criteria of the excited modes are disscussed with respect to the mode propagation relative to the applied magnetic field. The magnetic field is found to act as a stabilizer up to a threshold value that can be determined from the dispersion relation.     

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)     

Theoretical model for the effect of dust grains on self‐filamentation of a gaussian electromagnetic beam in a fully ionized plasma

A theoretical model for the effect of dust grains on the self‐filamentation of a Gaussian electromagnetic beam propagating in a fully ionized plasma has been developed by employing the energy balance of the plasma constituents, perturbed electron and ion concentrations, and temperature. In this model, neutral atom ionization, re‐integration and accumulation of electrons and ions, photoelectric emission of electrons from the surface of dust grains, as well as elastic and charging collisions have also been considered. The effective dielectric constant in the presence of dust grains has been constructed. The effect of temporal growth of dust grains on various plasma parameters for different values of the dust density has been explored. The variation of the beam width with the normalized channel of propagation has been observed for distinct dust densities and dust charge states. It is observed that the non‐linearity induced by the effective dielectric constant in the presence of dust grains increases the self‐filamentation of the beam, thus enhancing the effective critical power with the dust density. Some of the outcomes of our approach are in line with experimental observations. These outcomes may be useful for explaining space and laboratory plasma experiments as well as for future studies in complex plasmas.     

Floating double probe in non‐Maxwellian plasmas: Determination of the electron density and mean electron energy

A theoretical study of the floating double probe based on the Druyvesteyn theory is developed in the case of non‐Maxwellian electron energy distribution functions (EEDFs). It is used to calculate the EEDF in the electron energy range larger than –e(V_f ? V_p) from the I–V double probe characteristics. V_f and V_p are the floating and plasma potential, respectively. The analytical distribution function corresponding to the best fit of EEDF in the energy range larger than e(V_f ? V_p) allows the determination of the total electron density (n_e) and the mean electron energy (<?_e>). The method is detailed and tested in the case of a theoretical Maxwell–Boltzmann distribution function. It is applied for experiments that are performed in expanding microwave plasmas sustained in argon. Analytical EEDFs determined by this method are compared with those measured by means of single probes under the same experimental conditions. A good agreement is observed between single and double probe measurements. Results obtained under different experimental conditions are used to define the best conditions to obtain reliable results by means of the double probe technique.     

Characteristics of an atmospheric‐pressure radio frequency‐driven Ar/H2 plasma discharge with copper wire in tube

This paper investigates a plasma discharge driven by a 13.56 MHz radio frequency (RF) power supply at atmospheric pressure, in which a copper wire is inserted in the discharge tube for the deposition of Cu films. The results show that the jet plasma formation originates from the discharge between the copper wire and induction coil because of its electrostatic field. The axial distribution of the plasma parameters in the RF plasma jet, namely the gas temperature, excitation temperature, and electron number density, is determined by diatomic molecule OH fitting, Boltzmann slope, and H_β Stark broadening, respectively. The discharge current significantly declines when a small amount of hydrogen is added to the argon as the plasma‐forming gas, and the gas temperature of discharge plasma increases considerably.     

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)     

Dynamic Collision Frequency in Kelbg‐Pseudopotential‐Modelled Plasmas and the Method of Moments with Local Constraints

The dense plasma dynamic collision frequency is modeled by the first two terms of its asymptotic expansion at high frequencies and its values at a few interpolation points on the real axis. This makes the dynamic collision frequency a non‐rational function whose extension onto the upper half‐plane of the complex frequency is holomorphic with a non‐negative imaginary part and with a continuous extension to the real axis. The validity of the suggested analytic form of the latter is tested against the simulation data, where the Kelbg effective potential was used. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Use of micro‐Raman spectrometry coupled with scanning electron microscopy to determine the chemical form of uranium compounds in micrometer‐size particles

In the frame of nuclear safeguards, knowledge of the chemical form (stoichiometry) of the uranium compounds present in the micrometric particulate material sampled by wiping surfaces in an inspected nuclear facility may point out the industrial process implemented in the installation. Micro‐Raman spectroscopy (MRS) coupled with scanning electron microscopy (SEM) has been used for the first time to analyze micrometer‐size particles of various uranium oxides [UO₂, U₃O₈, UO₃, and UO₄ · 4(H₂O)] deposited on carbon disks. Uranium particles are detected by means of SEM, and Raman analysis is then directly carried out inside the SEM measurement chamber without moving the carbon disk from SEM to MRS. When particles are deposited on appropriate carbon disks (sticky carbon tapes), despite a loss of signal‐to‐noise ratio of about an order of magnitude with regard to the stand‐alone MRS, all uranium oxides are successfully identified in particles by in‐SEM Raman analysis, obtaining similar characteristic bands as the ones obtained with the stand‐alone MRS. Moreover, with the SEM–MRS coupling, particles as small as 1 µm can be analyzed, whereas, without the SEM–MRS coupling, only particles larger than ~5 µm are efficiently analyzed, after localization inside the SEM, transfer of the sample holder into the MRS, and relocation of the particles inside the MRS. Copyright © 2013 John Wiley & Sons, Ltd.     

DFT study the interaction of β‐cyclodextrin with benzyl azide and phenyl acetylene in synthesis of 1,2,3‐triazoles

The phenyl acetylene and benzyl azide cycloaddition reaction in water in the presence of β‐cyclodextrin (β‐CD) as a phase transfer catalyst (PTC) can get a better yield in a shorter time. The interaction between β‐CD and phenyl acetylene or benzyl azide plays an important role in this reaction. This paper studies the complexes of β‐CD with phenyl acetylene and benzyl azide using density functional theory (DFT) method. In order to find out the orientations of guests in the cavity of β‐CD, binding energy and deformation energy are investigated, and the calculated results are confirmed by ¹H nuclear magnetic resonance (¹HNMR). The data from single point energy indicate that the inclusion complexes can improve the solubilities of phenyl acetylene and benzyl azide in water. The ¹³C and ¹⁵N spectra show that the most obvious variation concentrates on C₆ and C₈ of phenyl acetylene and N₁₅ of benzyl azide in complexes. Mulliken charge and frontier orbital are employed for revealing the charge distribution. The effect of β‐CD is discussed in terms of the calculated parameters. Copyright © 2014 John Wiley & Sons, Ltd.