Electrostatic sheath at the boundary of a collisional dusty plasma

Considering the Boltzmann response of the ions and electrons in plasma dynamics and inertial dynamics of the dust charged grains in a highly collisional dusty plasma, the nature of the electrostatic potential near a boundary is investigated. Based on the fluid approximation, the formation as well as the characteristic behaviours of the sheath is studied. It is expected that the presence of dust charged grains will lead to a very different behaviour of the sheath as compared to that of electron-ion plasma. Moreover, the collisions of the dust charged grains with the neutrals are expected to exhibit novel features.     

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.     

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)     

Dynamics of sheath evolution in magnetized charge-fluctuating dusty plasmas

The evolution of sheath in plasma contaminated with varying dust charges under the effect of an external magnetic field is studied. Study of Sagdeev potential through pseudoptential approach has been attempted with a view to deriving the sheath equation. Numerical analysis has been carried out to study the potential variation with sheath-ward distance for various plasma parameters. A unique finding of the study is that the presence of dust particles as well as the magnetic field drastically modifies the Bohm sheath criterion for plasma sheath formation as obtained earlier in unmagnetised two-component plasma. The results have more realistic interpretation in showing explicitly the interaction of magnetic field and impurity caused by dust charge variation, with the possibility of its impact in various technological applications including plasma-material interaction, material processing and electro-mechanical devices.     

Characteristics of Dust Plasma Sheath in an Oblique Magnetic Field

The characteristics of dust plasma sheath in an oblique magnetic field are investigated with a fluid model. Hot electrons, cold ions, neutral particles, and dust grains are taken into account in this system. We perform a numerical simulation of the sheath. The results reveal that the magnetic field has significant effects on the sheath structure, and it also makes the suspension position of dust shift away from the wall.     

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.     

Measurement of temperature of a dusty plasma from its configuration

A new concept called “configurational temperature” is introduced in the context of dusty plasma, where the temperature of the dust particles submerged in the plasma can be measured directly from the positional information of the individual dust particles and the interaction potential between the dust grains. This method does not require the velocity information of individual particles, which is a key parameter to measure the dust temperature in the conventional method. The technique is initially tested using two-dimensional (2D) OpenMP parallel molecular dynamics and Monte Carlo simulation and then compared with the temperature evaluated from experimental data. The experiment have been carried out in the Dusty Plasma Experimental (DPEx) device, where a 2D stationary plasma crystal of melamine formaldehyde particles is formed in the cathode sheath of a DC glow discharge argon plasma. The kinetic temperature of the dust is calculated using the standard particle image velocimetry technique at different pressures. An extended simulation result for the three-dimensional case is also presented, which can be employed for the temperature measurement of a three-dimensional dust crystal in laboratory devices.     

Charge and Levitation of Grains in Plasma Sheath with Dust Thermic Emission

By taking into account thermic emission current from hot dust surface, the problem involved in dust charging and levitation of dust grains in plasma sheath has been researched. The results are compared to that without including thermal emission current while the system parameters are same. It is found that the thermal emission current has played a significant role on modifying the dust charging and balance levitations. Both of the charging numbers of dust and the dust radius in balance are dramatically reduced. The stability of dust levitation is also analyzed and discussed.     

Charge and Levitation of Grains in Plasma Sheath with Dust Thermic Emission

By taking into account thermic emission current from hot dust surface, the problem involved in dust charging and levitation of dust grains in plasma sheath has been researched. The results are compared to that without including thermal emission current while the system parameters are same. It is found that the thermal emission current has played a significant role on modifying the dust charging and balance levitations. Both of the charging numbers of dust and the dust radius in balance are dramatically reduced. The stability of dust levitation is also analyzed and discussed.     

Ordered dust structures in glow discharge plasmas

Ordering of dust grains suspended in glow discharge plasmas into quasi-steady liquid-or crystallike structures in an external field is considered. The self-consistent electric field generated by free electrons, ions, and dust grains is found. An estimate is obtained for the confining potential required to hold dust grains in the direction perpendicular to the discharge axis. It is shown that the potential energy of interaction between ordered dust particles has the form characteristic of ionic crystals. Critical parameters are estimated for a liquidlike dust structure. The correlation function calculated for a dusty plasma by using this approach is compared with a measured one.     

Three-dimensional wake potential in a streaming dusty plasma

The oscillatory wake potential for a slowly moving or static test dust particulate in a finite temperature, collisionless and unmagnetized dusty plasma with a continuous flow of ions and dust particles has been studied. The collective resonant interaction of the moving test particle with the low-frequency and low-phase-velocity dust-acoustic mode is the origin of the periodic attractive force between the like polarity particulates along and perpendicular to the streaming ions and dust grains resulting into dust-Coulomb crystal formation. This wake potential can explain the three-dimensional dust-Coulomb crystal formation in the laboratory conditions.     

非均匀尘埃等离子体中孤子的传播

运用约化摄动法研究了非均匀尘埃等离子体中孤子的传播情况. 在低阶近似下, 对于小的、但有限振幅的长波振动, 当分界面不连续变化时,孤子在不连续点的反射波与透射波均可由 KdV 方程来描述, 并给出了低阶近似情况下, 对于小的、但有限振幅的长波振动, 当入射波为单孤子时, 反射孤子与透射孤子的个数及其大小;当分界面是有限长度并连续变化时,对于小的、但有限振幅的长波振动, 尘埃声孤波由KdV型方程来描述,并由此给出了准孤子振幅、传播速度等参量在传播过程中的变化. 关键词： 尘埃等离子体 孤子 KdV方程 约化摄动法     

Formation of structures in a dusty ionosphere

An analysis of the evolution of microscopic particles (dust grains) in the Earth’s ionosphere and their effect on ionization in the middle atmosphere is presented. It is shown that summer conditions in the polar ionosphere, which are characterized by an ambient air temperature below 150 K and presence of supersaturated water vapor, facilitate the formation of dust structures in the middle atmosphere, such as noctilucent clouds and polar mesospheric summer echoes. The ionospheric plasma composition can change significantly in the regions occupied by these structures. Depending on photoelectric properties of the grains, their presence may lead to excess, or decrease in, electron concentration and complex behavior of ion concentration. The proposed self-consistent model of the ionosphere allows for grain growth, sedimentation, and charging and can be used to explain the behavior of ionization under summer conditions in the polar ionosphere.     

Evolution of a dust void in a radio-frequency plasma sheath

The onset and growth of a dust void are investigated in a radio-frequency (rf) sheath of a capacitively coupled argon plasma. A circularly symmetric void emerges and grows with increasing rf power and pressure in the central region of the dust cloud levitating in the sheath. Experimental measurements of the void diameter are compared with the predictions of a simple phenomenological theory, based on a balance of forces on dust grains.     

尘埃颗粒与等离子体鞘层相互作用的数值模拟

通过求解一维稳态的尘埃等离子体鞘层模型,得到了等离子体鞘层势、正离子密度、电子密度和尘埃颗粒密度随一维横向的分布,Bohm判据及鞘层边界无量纲Bohm速度随尘埃密度的变化曲线,尘埃颗粒的带电量和尘埃密度的关系,尘埃颗粒的温度对尘埃颗粒自身在鞘层中分布的影响。结果表明,随着尘埃密度的增加,鞘层的厚度在减小,鞘层内的电子密度在下降,而且尘埃颗粒的带电量也在逐渐减少;随着尘埃温度的增加,鞘层的厚度减小,电子密度下降,而且鞘层附近的尘埃颗粒在逐渐增多。     

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)     

等离子体鞘层中尘埃粒子的分布特性

采用柱槽状电极的流体模型，数值模拟了等离子体鞘层及鞘层中尘埃粒子的分布结构. 研究了尘埃粒子数、粒子大小、电极尺寸等因素对尘埃分布结构的影响. 研究表明：当等离子体密度较高时，鞘层较薄，反之鞘层较厚；当尘埃粒子数少时，尘埃分布形成一层结构，反之则形成多层结构；随电极尺寸的不同，尘埃粒子形成一些复杂而又有趣的结构. 关键词： 尘埃粒子 等离子体鞘层 电极     

两种带电尘埃颗粒的等离子体鞘层玻姆判据

采用流体方程和尘埃充电自洽模型研究了鞘边含有两种尘埃颗粒的等离子体玻姆判据. 通过拟牛顿法数值模拟了鞘边两种尘埃颗粒的存在对尘埃自身充电以及离子马赫数的影响. 两种尘埃颗粒中含量较少的尘埃颗粒数密度的增加, 导致两种尘埃颗粒表面悬浮势一个降低, 一个升高. 含量较少的尘埃颗粒的数密度越多和半径越小, 都会导致离子马赫数增大. 另外鞘边无论何种尘埃颗粒的速度增加, 鞘边离子马赫数都将减小. 关键词： 等离子体鞘层 尘埃颗粒 玻姆判据     

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.     

Theory of self-organized dust sheaths in edge plasmas

A concept of self-organisation is used to derive the structure of dust sheath close to the wall taking into account self-consistently dust charges and dust distribution together with electron, ion distributions and ion drift. It is shown that instead of Bohm criterion the dust sheath is determined by other criteria allowing Mach number to be in restricted value ranges. The total structure of the dust sheath in dimensionless variables is determined by the Mach number only. Dust sheaths can contain definite number of dust particles per unit area which are determined by the value of the Mach number. The dust sheaths change drastically the electrostatic potential distributions and are usually much thicker than the usual plasma sheaths. A theoretical model together with numerical computations gives all dust sheath parameter distributions and the global characteristics such as the total drop of the potential, the thickness of the sheath, the number of dust particles in the sheath and the criterion of dust levitation. The recent observations on “Textor 94” indicating the long time dust survival in edge region of the present tokamaks, the dust levitation and agglomeration in the volume of edge tokamak plasma are discussed.