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.     

Emission and accretion of electrons by negatively charged dust particles in a plasma

Taking into account the image force on the electron and Debye shielding an expression for the reduction in the work function for a spherical metallic particle in a dusty plasma on account of the negative charge on the surface has been derived. The dependence of the reduction of the work function on the charge on the particle and Debye radius has been tabulated. The effect of this reduction on the thermionic and photoelectric emission and accretion of electrons by the particle has been discussed. As an interesting application of the work, the observed enhancement of the photoelectric emission from individual micron size grains with increasingly negative surface potential has been explained; the grains were selected from samples of dust collected in the Apollo-17 and Luna-24 missions.     

An application of the dust grain charging model to determination of secondary electron spectra

Dust grains – objects of different shapes with a size distribution from micro to nanometers – are generally considered as a part of many space as well as laboratory plasmas. Among various dust charging processes, electron-induced secondary emission plays an important role in plasmas containing a noteworthy portion of high-energy electrons. Since a part of secondary electrons has not the energy high enough to overcome the surface potential barrier, the resulting grain charge is determined not only by the secondary emission yield (related to the grain material and size) but also by the secondary electron spectrum. We have developed a model of secondary electron emission from small dust grains. In the present contribution, we discuss the profile of a secondary emission yield that can be received from the model and the measured equilibrium grain charge, both as functions of an incident electron beam energy. A comparison of these quantities leads to an estimation of secondary electron spectra. We have found that: (1) the energy spectrum of secondary electrons does not change with the energy of primary electrons and (2) the energy spectrum depends on the target material being harder for gold and silver than for glass grains.     

Effect of radiative cooling on collapsing charged grains

The effect of the radiative cooling of electrons on the gravitational collapse of cold dust grains with fluctuating electric charge is investigated. We find that the radiative cooling as well as the charge fluctuations, both, enhance the growth rate of the Jeans instability. However, the Jeans length, which is zero for cold grains and nonradiative plasma, becomes finite in the presence of radiative cooling of electrons and is further enhanced due to charge fluctuations of grains resulting in an increased threshold of the spatial scale for the Jeans instability.     

Dust in Plasma II. Effects of Secondary Electrons: Ionization and Surface Emission

In this second paper, the effect of secondary electrons on the charge and potential of a dust particle immersed in plasma has been studied. The processes of electron‐induced ionization and those of photo‐electron and secondary electron emission from the particle surface as a function of primary electron temperature have been taken into account. Starting from temperatures as low as 6 eV in an Ar plasma, ionization produces an extra ion flux to the dust surface comparable to that of the ion charge exchange effect. For what concerns the surface emission, results show that a transition from negative to positive dust charge/potential takes place, and that the transition regime is characterized by a non‐monotonic behavior of the electric potential around the particle. In the case of photoelectric emission, the dust charge and potential are monotonic decreasing functions of the electron temperature, while in the case of emission induced by primary electrons a minimum charge/potential is reached before they grow towards positive values. In no case multiple dust charge states have been observed due to the presence of the potential well attached to the particle surface. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

稳态装置中的尘埃等离子体状态

介绍了用于研究尘埃等离子体中波的直流放电的尘埃等离子体装置,该装置能产生长约３０ｃｍ,直径约８．４ｃｍ的尘埃等离子体柱。在等离了体中加入尘埃后,朗缪尔探针的饱和电流明显降低。尘埃所带负电量与电机转速成正比,可达到等离子体负电量的４０％。     

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.     

Theoretical analysis for transmission of Gaussian and sine time irradiance of electromagnetic beam in collisional dusty plasmas

A theoretical model of propagation of Gaussian and Sine time irradiance of an electromagnetic beam in collisional dusty plasma has been done in the present analysis. It contains equilibrium of dust charge, particle density, and energy of plasma ingredients having charge neutrality. Ionization of neutral particles, recombination of free electrons with ions, adsorption and emission of electrons from dust grain surface, and binary collisions between plasma components are also considered in this treatment. Time varying behaviour of modified electron temperature and collision frequency has been illustrated numerically as a function of dust densities. Also, the comparative analyses of variation of beam waist parameter with the dimensionless length of transmission for both the Gaussian and Sine time irradiance are involved in this model as a function of distinguishable time width, collision frequencies, and dust densities under the condition that the size of dust nebulous is greater than the electrons mean free path for the adsorption on the dust grain surface. The observed results are significant for the applications in industry and astrophysics.     

The Bohm criterion for a dusty plasma sheath

The formation of the sheath in a dusty plasma is investigated. The Bohm criterion is derived for two different cases: (a) when electrons are in thermodynamic equilibrium and dust grains provide the immobile, stationary background and (b) when both electrons and ions are in thermodynamic equilibrium and dust grains are moving. In the first case, Bohm criterion gets modified due to the fluctuation of the charge on the grain surface. In the second case, the collisional and Coulombic drag play important role in determining the Bohm criterion.     

Effect of dust size distribution and dust charge fluctuation on dust ion-acoustic shock waves in a multi-ion dusty plasma

The effects of dust size distribution and dust charge fluctuation of dust grains on the small but finite amplitude nonlinear dust ion-acoustic shock waves, in an unmagnetized multi-ion dusty plasma which contains negative ions, positive ions and electrons, are studied in this paper. A Burgers equation and its stationary solutions are obtained by using the reductive perturbation method. The analytical and numerical results show that the height with polynomial dust size distribution is larger than that of the monosized dusty plasmas with the same dust grains, but the thickness in the case of different dust grains is smaller than that of the monosized dusty plasmas. Furthermore, the moving speed of the shock waves also depend on different dust size distributions.     

尘埃等离子体中非线性波的叠加效应及稳定性问题

研究了小的有限振幅的无磁场尘埃等离子体中的非线性波.在一维情况下由Kortewegde Veries(KdV)方程来描述,考虑了二维情况下尘埃等离子体中尘埃颗粒上电荷的变化效应以及双温度离子效应后,尘埃等离子体受到横向高阶扰动后动力学方程由Kadomtsev-Petviashvili(KP)方程来描述.在此基础上,研究了以任意夹角传播的两个及三个孤立子的相互作用问题,考虑非线性效应后振幅相等的双孤立子在相互作用区域内振幅最大值是单个孤立子振幅的4倍,振幅相等的三孤立子在相互作用区域内振幅最大值是单个孤立子振幅的9倍.研究还表明波的传播方向受到横向高阶扰动后是稳定的.     

Numerical study of an electrostatic plasma sheath with non-thermal electrons and charged nanoparticles

Numerical solutions of the multi-fluid equations are used to investigate the effects of non-thermal electrons on the structure of an electrostatic plasma sheath in the presence of nano-sized dust grains. It is assumed that electrons obey the Cairns distribution [Cairns et al. Geophys. Res. Lett. 22, 2709 (1995)], with a parameter α that determines the effect of non-thermal electrons and shows the deviation from the Maxwellian distribution. The results revealed that sheath parameters are strongly modified in the presence of non-thermal electrons and with increasing α the sheath width increases. With the increase in α, the absolute dust charge increases while the dust density is reduced.     

Fluctuations of the charge on a dust grain in a plasma

A dust grain in a plasma acquires an electric charge by collecting electron and ion currents. These currents consist of discrete charges, causing the charge to fluctuate around an equilibrium value 〈Q〉. Electrons and ions are collected at random intervals and in a random sequence, with probabilities that depend on the grain's potential. We developed a model for these probabilities and implemented it in a numerical simulation of the collection of individual ions and electrons, yielding a time series Q(t) for the grain's charge. Electron emission from the grain is not included, although it could be added easily to our method. We obtained the power spectrum and the RMS fluctuation level, as well as the distribution function of the charge. Most of the power in the spectrum lies at frequencies much lower than 1/τ, the inverse charging time. The RMS fractional fluctuation level varies as 0.5 |〈N〉|^-1/2, where 〈N〉=〈Q〉/e is the average number of electron charges on the grain. This inverse square-root scaling means that fluctuations are most important for small grains. We also show that very small grains can experience fluctuations to neutral and positive polarities, even in the absence of electron emission     

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.     

强耦合尘埃等离子体中正电扰动下的尘埃声激波

研究了强耦合尘埃等离子体的尘埃声波的线性色散关系和尘埃声孤波的非线性传播。考虑一个包含电子、离子、正电扰动尘埃颗粒的完全电离的三成分模型等离子体。假定其电子、离子数密度服从玻尔兹曼分布,而大质量的尘埃成分用一组经典流体方程描述,对系统方程进行线性化,得到了尘埃声波的线性色散关系,发现离子的集中参数对色散关系的影响很大。用约化摄动法对系统方程进行展开,得到了描述小振幅孤波的伯格斯方程。基于伯格斯方程研究了尘埃声孤波的基本特性,发现尘埃颗粒的强耦合效应对尘埃声孤波有很大的修正作用。该研究结果有助于理解尘埃空间等离子体中局域波的一些特性。     

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研究了强耦合尘埃等离子体的尘埃声波的线性色散关系和尘埃声孤波的非线性传播。考虑一个包含电子、离子、正电扰动尘埃颗粒的完全电离的三成分模型等离子体。假定其电子、离子数密度服从玻尔兹曼分布,而大质量的尘埃成分用一组经典流体方程描述,对系统方程进行线性化,得到了尘埃声波的线性色散关系,发现离子的集中参数对色散关系的影响很大。用约化摄动法对系统方程进行展开,得到了描述小振幅孤波的伯格斯方程。基于伯格斯方程研究了尘埃声孤波的基本特性,发现尘埃颗粒的强耦合效应对尘埃声孤波有很大的修正作用。该研究结果有助于理解尘埃空间等离子体中局域波的一些特性。     

Nucleation and initial growth of diamond by biased hot filament chemical vapour deposition

6 cm^-2 for non-scratched silicon. The maximum value of the nucleation density was over 10¹¹ cm^-2 on mirror-polished Si(100) at -300 V. The transportation process of the ion flux from the filament to the substrate is discussed in detail for biased substrates. The nucleation enhancement by the positive bias is believed to be a result of the increased impingement of the electrons emitted from the filament to the substrate surface. The studies have shown that electron emission from diamond plays a key role in negative-bias-enhanced nucleation by accelerating the dissociation of molecular hydrogen and hydrocarbon species into various free radicals and causing a plasma to be ignited near the substrate surface. The negative bias pretreatment is also a critical step in growing heteroepitaxial diamond films: the enlargement of the area of diamond clusters in contact with the substrate enhances the orientated growth of the films. Received: 18 October 1996/Accepted: 4 February 1997     

Dust ion-acoustic shock waves due to dust charge fluctuation in a superthermal dusty plasma

The nonlinear propagation of dust ion-acoustic (DIA) shock waves is studied in a charge varying dusty plasma with electrons having kappa velocity distribution. We use hot ions with equilibrium streaming speed and a fast superthermal electron charging current derived from orbit limited motion (OLM) theory. It is found that the presence of superthermal electrons does not only significantly modify the basic properties of shock waves, but also causes the existence of shock profile with only positive potential in such plasma with parameter ranges corresponding to Saturn?s rings. It is also shown that the strength and steepness of the shock waves decrease with increase of the size of dust grains and ion temperature.     

Problems of Dust Grains Charging to Negative Potentials

The presence of dust grains is a common phenomenon in the space environment. Grains can be charged by many different processes (e.g., photoemission, attachment of electrons/ions, the secondary emission, etc.). If the grain's surface potential becomes high enough, one can observe field emission of ions or electrons. We are trapping a single dust grain in a Paul trap, expose it to a low-energy electron beam, and investigate the evolution of its charge-to-mass ratio with respect to the energy of primary electron beam. We use micron-sized (D = 2–11 m) glass grains and charge them up to -300 V of surface potentials; it corresponds to the electric field strength of about 10⁸ V/m. Analysis of the charging/discharging processes has shown that (1) the effect of the field enhanced secondary emission is negligible in the case of insulators and (2) the effective work function for electron field emission from charged insulators is as low as 1 eV.