The Kinetic of Dust with Different Sizes in a Magnetized Collisional Plasma Sheath

The characteristics of dust are investigated in a magnetized plasma sheath with taking into account the gravitational force and collisions between dust and neutral. The model is based on using fluid method and solving the basic equations of fluid method numerically. As the Lorentz, gravitational and collisional forces depend on the dust radius, the numerical calculations are done for different values of dust radius. It enables us to study the effects of dust size on dust dynamics in a magnetized plasma sheath.     

Dynamics of Dust in a Plasma Sheath with Magnetic Field

Dynamics of dust in a plasma sheath with a magnetic field was investigated using a single particle model. The result shows that the radius, initial position, initial velocity of the dust particles and the magnetic field do effect their movement and equilibrium position in the plasma sheath. Generally, the dust particles with the same size, whatever original velocity and position they have, will locate at the same position in the end under the net actions of electrostatic, gravitational, neutral collisional, and Lorentz forces. But the dust particles will not locate in the plasma sheath if their radius is beyond a certain value.     

Characteristics of Positive Ions in the Sheath Region of Magnetized Collisional Electronegative Discharges

A hydrodynamic model is used to investigate the characteristics of positive ions in the sheath region of a low-pressure magnetized electronegative discharge. Positive ions are modeled as a cold fluid, while the electron and negative ion density distributions obey the Boltzmann distribution with two different temperatures. By taking into account the ion-neutral collision effect in the sheath region and assuming that the momentum transfer cross section has a power law dependence on the velocity of positive ions, the sheath formation criterion （modified Bohm＇s criterion） is derived and it is shown that there are specified maximum and minimum limits for the ion Mach number M. Considering these two limits of M, the behaviors of electrostatic potential, charged particle density distributions and positive ion velocities in the sheath region are studied for different values of ion-neutral collision frequency.     

Modeling of magnetized collisional plasma sheath with nonextensive electron distribution and ionization source

The properties of an atmospheric-pressure collisional plasma sheath with nonextensively distributed electrons and hypothetical ionization source terms are studied in this work. The Bohm criterion for the magnetized plasma is extended in the presence of an ion–neutral collisional force and ionization source. The effects of electron nonextensive distribution, ionization frequency, ion– neutral collision, magnetic field angle and ion temperature on the Bohm criterion of the plasma sheath are numerically analyzed. The fluid equations are solved numerically in the plasma–wall transition region using a modified Bohm criterion as the boundary condition. The plasma sheath properties such as charged particle density, floating sheath potential and thickness are thoroughly investigated under different kinds of ion source terms, contributions of collisions, and magnetic fields. The results show that the effect of the ion source term on the properties of atmosphericpressure collisional plasma sheath is significant. As the ionization frequency increases, the Mach number of the Bohm criterion decreases and the range of possible values narrows. When the ion source is considered, the space charge density increases, the sheath potential drops more rapidly, and the sheath thickness becomes narrower. In addition, ion–neutral collision, magnetic field angle and ion temperature also significantly affect the sheath potential profile and sheath thickness.     

Surface Potential of Dust Grains at the Sheath Edge of Electronegative Dusty Plasmas

In this paper we investigate the dust surface potential at the sheath edge of electronegative dusty plasmas theoretically, using the standard fluid model for the sheath and treating electrons and negative ions as Boltzmann particles but positive ions and dust grains as cold fluids. The dust charging model is self-consistently coupled with the sheath formation criterion by the dust surface potential and the ion Mach number, moreover the dust density variation is taken into account. The numerical results reveal that the dust number density and negative ion number density as well as its temperature can significantly affect the dust surface potential at the sheath edge.     

Collisional Sheath in the Electronegative Radio-Frequency Plasma

A model of collisional RF sheath with negative ions is discussed in this paper. The influences of collision and negative ions on the parameters of the sheath are studied through numerical simulation. It is found that when the collision coefficient increases and the RF power is fixed, the electrode potential and sheath electric field potential increase, the electrode current and thickness of the sheath decrease. When the negative ion content changes, the same phenomenon Occurs,     

Characteristics of Collision, Capacitive Radio Frequency Sheath

A simple collisional radio frequency (rf) sheath fluid model, which is not restricted by the ratio of rf frequency to ion plasma frequency (β = ωrf/ωpi), was established and solved numerically. In the ion balance equation, the effect of the collision on the ion and the ion velocity is assumed to be a direct ratio to ion velocity. The ion energy distributions (IEDs) calculated in the model in comparison with the experimental data [M. A. Sobolewski, J. K. Olthoff, and Y. C. Wang, J. Appl. Phys. 85, 3966 (1999)], proved the validity of the model. And the effect of the collision on the sheath characteristic was obtained and discussed. This paper demonstrates that the collision frequency is another crucial parameter as well as the ratio β to determine the rf sheath characteristics and the shape of IEDs.     

Ion Temperature Effect on Weakly Collisional DC Plasma Sheath

Using a collisional two-fluid model, we investigate the ion temperature effect on the sheath formation criterion as well as the sheath structure in electropositive plasmas. In this work, temperature dependence of the characteristics of a weakly collisional DC plasma sheath is examined numerically. It will be shown in the constant cathode electric potential, the more the ion temperature, the low the thickness of sheath. Moreover, for a special set of physical parameters, the sheath formation criterion is not fulfilled for ion temperature under a minimum value.     

Effect of Negative Ion Parameters on Sheath Formation Criterion in Electronegative Plasmas

Using a fluid model for three types of particles, the plasma-sheath formation criterion has been analyzed in collisional electronegative plasma, and the effects of the negative ion temperature and density are examined on the positive ion transition velocity. It is shown that in the collisional sheath, there will be an allowable interval for the positive ion velocity between two upper and lower limits as the plasma-sheath formation criterion; by increasing the mean temperature of the negative charge carriers, this velocity interval decreases. To confirm the correction of the allowable interval, the plasma sheath equations are numerically solved, and the negative ion temperature effect for example, is examined on the sheath formation.     

Instability of Velocity Distributions of Slightly Ionized Gases in Electric Fields

If a slightly ionized gas is subject to a constant electric field the (time- and space independent) distribution function for the electrons may be double-humped if the cross section for electron-molecule interactions is changing sufficiently rapidly with velocity. Accordingly “inverse Landau-damping” can make the distribution function unstable with respect to longitudinal waves if the collisional damping is not too large. The results in the present paper indicate that the plasma can be unstable and parameters involved are estimated in order to get the conditions for instability.     

Modelling of electronegative collisional warm plasma for plasma-surface interaction process

An electronegative collisional plasma having warm and massive positive ions, non-extensive distributed electrons and Boltzmann distributed negative ions is modelled for the plasma-surface interaction process that is used for the surface nitriding. Specifically the sheath formation is evaluated through the Bohm's criterion, which is found to be modified, and the variation of the sheath thickness and profiles of the density of plasma species and the net space charge density in the sheath region in addition to the electric potential. The effect of ion temperature, nonextensivity and collisional parameter is examined in greater detail considering the collisional cross-section to obey power-law dependency on the positive ion velocity. The positive ions are found to enter in the sheath region at lower velocities in the collisional plasma compared to the case of collision-less plasma; this velocity sees minuscule reduction with increasing nonextensivity. The increasing ion temperature and collisional parameter lead to the formation of sheath with smaller thickness.     

压力容器环形下降段内含硼溶液流动混合特性的数值模拟分析

发生堆芯应急冷却安注时,外部注入的含硼冷却剂与稀释水团将在环形下降段内发生混合,含硼冷却剂与稀释水团混合不均匀可能导致堆芯重返临界。本文基于Fluent 18.0对环形下降段内的流动混合特性进行分析。横截面的速度分布显示,入口截面的水平方向速度随周向位置的增加而显著衰减,而环形下降段下部区域横截面的速度分布趋于平缓;三维流线图显示,流体进入压力容器后在环腔内壁发生剧烈碰撞,随后绕环形下降段呈放射状流动。通过自定义硼酸溶液,并模拟其与稀释水团之间混合,数值结果与相关的实验研究结果较为一致;三维浓度分布显示,雷诺数较低时入口硼酸溶液将停滞在环形下降段上部空间,增加入口雷诺数有利于搅混均匀。     

Two-Dimensional Fluid Simulation of Collisional Plasma sheath over rf Powered Electrode with Cylindrical Hole

The characteristics of collisional radio-frequency (rf) sheath dynamics over an electrode with a cylindrical hole is simulated by means of a self-consistent model which consists of two-dimensional time-dependent fluid equations coupled with Poisson equation. In addition, an equivalent-circuit model is coupled to the fluid equations in order to self-consistently determine relationship between the instantaneous potential at the rf-biased electrode and the sheath thickness.Two-dimensional profiles of the potential, the ion fluid velocity, and the distributions of the ion and electron densities within the sheath are computed under various discharge conditions, such as the discharge powers and the gas pressures. The results show that the existence of the cylindrical hole on the electrode significantly affects the sheath structure and generates a potential trap in the horizontal direction, which is particularly strong when the sheath thickness is comparable to the depth of the hole. Moreover, it is found that the collisional effects have a significant influenc eon the sheath characteristics.     

Kinetic-theory-based investigation of electronegative plasma–wall transition with two populations of electrons

Kinetic theory has been employed to investigate the magnetized plasma-sheath structure and its characteristics in the presence of more than one species of negatively charged particles: hot electrons,cold electrons, and negative ions. The cold electrons and negative ions are considered to obey a Maxwellian distribution, whereas the hot electrons follow a truncated Maxwellian distribution. The Bohm sheath condition has been extended for the case of more than one species of negatively charged particles, in which the concentration of hot electrons has a crucial role in achieving the Bohm velocity. The thermal motion of hot electrons is much higher compared to cold electrons and negative ions, such that the variation of hot electron concentrations and the temperature ratio of hot to cold electrons play a key role in the determination of the plasma-sheath parameters: particle densities,electrostatic potential, the flow of positive ions towards the wall, and sheath thickness. We have estimated the deviation of the resultant drift velocity of positive ions on the plane perpendicular to the wall from the parallel component at the presheath–sheath interface. It is found that the deviation between the two velocity components increases with an increase in the obliqueness of the magnetic field. Furthermore, the results obtained from the kinetic trajectory simulation model are compared with the results obtained using a fluid model; the results are qualitatively similar, although the potential varies by less than 4% in terms of the magnitude at the wall.     

Ion Temperature Effect on Bohm Criterion for Magnetized Plasma Sheath

A two-fluid model has been used to study the characteristics of the plasma sheath in the presence of an external magnetic field and by taking into account both the ion temperature and the ion-neutral collision force. The model is solved numerically and sheath characteristics are obtained. The dependence of the Bohm magnetized sheath criterion to ion temperature is examined. Then it is concluded that the ion temperature has significant effects on the sheath characteristics such as ion velocity, particles densities and electric potential.     

Effects of Magnetic Field and Ion Velocity on SPT Plasma Sheath Characteristics

The distribution of magnetic field in Hall thruster channel has significant effect on its discharge process and wall plasma sheath characteristics. By creating physical models for the wall sheath region and adopting two-dimensional particle in cell simulation method, this work aims to investigate the effects of magnitude and direction of magnetic field and ion velocity on the plasma sheath characteristics. The simulation results show that magnetic field magnitudes have small impact on the sheath potential and the secondary electron emission coefficient, magnetic azimuth between the magnetic field direction and the channel radial direction is proportional to the absolute value of the sheath potential, but inversely proportional to the secondary electron emission coefficient. With the increase of the ion incident velocity, secondary electron emission coefficient is enhanced, however, electron density number, sheath potential and radial electric field are decreased. When the boundary condition is determined, with an increase of the sinmlation area radial scale, the sheath potential oscillation is aggravated, and the stability of the sheath is reduced.     

单棒垂直方形通道临界热流密度实验研究

采用R134a作为流体工质,对单棒垂直方形通道临界热流密度（CHF）进行了实验研究。流道横截面为19 mm×19 mm的方形通道,内置外径为9.5 mm的单根加热棒,用来模拟压水堆中典型栅元通道。实验工况通过流体模化方法覆盖了压水堆典型运行工况。实验结果表明,R134a在方形通道内的CHF参数趋势与圆管中水的CHF参数趋势相同,R134a可以替代水作为模化工质;通过对圆管Bowring关系式和Katto & Ohno关系式进行冷壁因子修正,可用于预测带有冷壁的方形通道的CHF;Katto的流体模化方法适用于带有冷壁的方形通道。      

The Properties of the Space-Charge and Net Current Density in Magnetized Plasmas

A hydrodynamic model is used to investigate the properties of positive space-charge and net current density in the sheath region of magnetized, collisional plasmas with warm positive ions. It is shown that an increase in the ion-neutral collision frequency, as well as the magnitude of the external magnetic field, leads to an increase in the net current density across the sheath region. The results also show that the accumulation of positive ions in the sheath region increases by increasing the ion-neutral collision frequency and the magnitude of the magnetic field. In addition, it is seen that an increase in the positive ion temperatures causes a decrease in the accumulation of positive ions and the net current density in the sheath region.     

Inertia-Centric Stability Analysis of a Planar Uniform Dust Molecular Cloud with Weak Neutral-Charged Dust Frictional Coupling

This paper adopts an inertia-centric evolutionary model to study the excitation mechanism of new gravito-electrostatic eigenmode structures in a one-dimensional（1-D） planar self-gravitating dust molecular cloud（DMC） on the Jeans scale.A quasi-neutral multi-fluid consisting of warm electrons,warm ions,neutral gas and identical inertial cold dust grains with partial ionization is considered.The grain-charge is assumed not to vary at the fluctuation evolution time scale.The neutral gas particles form the background,which is weakly coupled with the collapsing grainy plasma mass.The gravitational decoupling of the background neutral particles is justifiable for a higher inertial mass of the grains with higher neutral population density so that the Jeans mode frequency becomes reasonably large.Its physical basis is the Jeans assumption of a self-gravitating uniform medium adopted for fiducially analytical simplification by neglecting the zero-order field.So,the equilibrium is justifiably treated initially as ＂homogeneous＂.The efficacious inertial role of the thermal species amidst weak collisions of the neutral-charged grains is taken into account.A standard multiscale technique over the gravito-electrostatic equilibrium yields a unique pair of Korteweg-de Vries（KdV） equations.It is integrated numerically by the fourth-order Runge-Kutta method with multi-parameter variation for exact shape analyses.Interestingly,the model is conducive for the propagation of new conservative solitary spectral patterns.Their basic physics,parametric features and unique characteristics are discussed.The results go qualitatively in good correspondence with the earlier observations made by others.Tentative applications relevant to space and astrophysical environments are concisely highlighted.     

Theoretical research on the transport and ionization rate coefficients in glow discharge dusty plasma

The electron kinetic model for investigating the transport and ionization rate coefficients of argon glow discharge dusty plasma is developed from the Boltzmann equation.Both of the electron-neutral and electron-dust collisions are considered as collision terms in the kinetic equation.The kinetic equation is simplified by employing the local approximation and nonlocal approach under the same discharge conditions,and the corresponding simplified kinetic equations are known as local and nonlocal kinetic equations respectively.Then the electron energy distribution function(EEDF)is obtained by numerically solving the local and nonlocal kinetic equations and the dust charging equations simultaneously.Based on the obtained EEDFs,the effective electron temperature,electron mobility,electron diffusion coefficient and ionization rate coefficient are calculated for different discharge conditions.It is shown that the EEDFs calculated from the local kinetic model clearly differ from the nonlocal EEDFs and both the local and nonlocal EEDFs are also clearly different with Maxwellian distributions.The appearance of dust particles results in an obvious decrease of high energy electrons and increase of low energy electrons when axial electric field is low.With the increase of axial electric field,the influence of dust particles on the EEDFs becomes smaller.The electron mobility and diffusion coefficients calculated on the basis of local and nonlocal EEDFs do not differ greatly to the dust-free ones.While,when dust density nd=10^6 cm^?3,the electron mobility increases obviously compared with the dust-free results at low axial electric field and decreases with the increasing axial electric field until they are close to the dust-free ones.Meanwhile,electron diffusion coefficients for dusty case become smaller and decrease with the increasing axial electric field.The ionization rate coefficients decrease when dust particles are introduced and they approach the dust-free results gradually with the increasing axial electric field.