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.     

Analysis of the influence of sheath positions,flight parameters and incident wave parameters on the wave propagation in plasma sheath

The plasma sheath covering hypersonic vehicles has a significant effect on the propagation of electromagnetic waves. Based on the calculation of the flow field of a conical cylindrical, this work studies the propagation of electromagnetic waves in plasma sheath at L-band and Ku-band, and discusses the propagation characteristics in the head, side and tail of the sheath. The dielectric properties of plasma sheath are related to flight speed and altitude. A flight condition corresponds to a unique distribution of dielectric properties. For the conical cylindrical, the results show that flight speed is generally negatively correlated with the transmissivity of the plasma sheath. The reflection characteristics of electromagnetic waves at the L-band and Ku-band when obliquely incident to the plasma sheath show a downward trend. When the frequency is increased to Ku-band, the propagation characteristics of electromagnetic waves in the plasma sheath are related to the position of the sheath.     

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.     

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.     

Kinetic simulation study of one dimensional collisional bounded plasma

A self-consistent kinetic simulation study of one dimensional collisional bounded plasma is presented.The formation of stable of stable sheath potential is investigated.It is found that mass ratio of electron and ion not only affects the level of sheath potential.but also affects the ion temnperature of system.It is clarified that the effects of secondary emission electron on both the total potential drop and the temperature are not important.     

Study of Characteristics of the Radio-Frequency Sheath over a Substrate with a Circular Trench

Since processed substrates usually exhibit nonplanar surface structures in Micro-Electro-Mechanical-Systems (MEMS) etching, a two-dimensional (2D) fluid model is developed to simulate the characteristics of the sheath near a conductive substrate with a circular trench, which is placed in an argon discharge powered by a radio-frequency (rf) current source. The model consists of 2D time-dependent fluid equations, the Poisson equation, and a current balance equation that can self-consistently determine the instantaneous voltage on the substrate placed on a powered electrode. The effects of both the aspect ratio (depth/width) and the structure of the trench on the characteristics of the sheath are simulated. The time-averaged potential and electric field in the sheath are calculated and compared for different discharge parameters. The results show that the radial sheath profile is not uniform and always tends to adapt to the contour of the substrate, which is believed to be the moulding effect. Affected by the structure of the substrate surface, the potential and electric field near the inner and outer sidewalls of the trench exhibit obvious non-uniformity, which will inevitably lead to non-uniformity in etching, such as notching. Furthermore, with a fixed amplitude of the rf current source, the potential drops and the sheath thickness decrease with an increase in aspect ratio.     

On the electron sheath theory and its applications in plasma–surface interactions

In this work, an improved understanding of electron sheath theory is provided using both fluid and kinetic approaches while elaborating on their implications for plasma–surface interactions. A fluid model is proposed considering the electron presheath structure, avoiding the singularity in electron sheath Child–Langmuir law which overestimates the sheath potential. Subsequently, a kinetic model of electron sheath is established, showing considerably different sheath profiles in respect to the fluid model due to non-Maxwellian electron velocity distribution function and finite ion temperature. The kinetic model is then further generalized and involves a more realistic truncated ion velocity distribution function. It is demonstrated that such a distribution function yields a super-thermal electron sheath whose entering velocity at the sheath edge is greater than the Bohm criterion prediction. Furthermore, an attempt is made to describe the electron presheath–sheath coupling within the kinetic framework, showing a necessary compromise between a realistic sheath entrance and the inclusion of kinetic effects. Finally, the secondary electron emissions induced by sheath-accelerated plasma electrons in an electron sheath are analysed and the influence of backscattering is discussed.     

Occurrence of ionization instability associated with plasma bubble in glow discharge magnetized plasma

Floating potential fluctuations of glow discharge magnetized plasma are found to expose mixed mode oscillations(MMOs) in the existence of plasma bubble. Plasma bubble has been formed by emerging density gradient in the form of a sheath around a cylindrical and spherical grid to a critical value of applied potential. Two Langmuir probes, LP_1 and LP_2, are retained in the ambient plasma to collect the plasma floating potential fluctuations at two different locations of the plasma system. The perceived instability pattern shows regular-irregular-regular MMOs under various imposed conditions. Furthermore, various nonlinear techniques such as phase space plot, recurrence plot and Hurst exponent have been executed to understand the underlying dynamical behavior of the system. Low-frequency(~200–1200 Hz) oscillations are also supposed and are inferred as ion-acoustic waves excited by ionization instability. The observed results are then validated with the theory of the instability based on a fluid hydrodynamic approach.     

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.     

The structure of an electronegative magnetized plasma sheath with non-extensive electron distribution

In this paper, an electronegative magnetized plasma sheath model with non-extensive electron distribution is established, and the Bohm criterion affected by the non-extensive parameter q is theoretically derived. The ion Mach number varies with q. The numerical simulation results show that compared with electronegative magnetized plasma sheath with Maxwell distribution (q = 1), the sheath structures with super-extensive distribution (q < 1) and sub-extensive distribution (q > 1) are different. The physical quantities including the sheath potential distribution, ion density distribution, the electron density distribution, negative ion density distribution and the net space charge density distribution are discussed. It is shown that the non-extensive parameter q has a significant influence on the structure of the electronegative magnetized plasma sheath. Due to the Lorentz force, both the magnitude and the angle of the magnetic field affect the structure of the sheath, whether the electrons are Maxwell distributed or non-extensively distributed.     

Analytical Determination of Collisionless Sheath Properties for Triple Frequency Capacitively Coupled Plasma

A triple frequency capacitively coupled plasma(TF-CCP) has been considered to investigate the behavior of the sheath parameters.A self-consistent time-independent collisionless model has been developed.The sheath width and potential are calculated using the present model and compared with those calculated using a single-frequency(SF),a dual-frequency(DF)and a triple-frequency(TF) model for time independent collisionless cases.The sheath motion and sheath potential are found to be larger compared with those of SF and DF CCPs for an inhomogeneous sheath,and that of TF CCP for a homogeneous sheath.The effects of the source parameters,i.e.,current magnitudes,frequencies and phase difference,on the sheath parameters are investigated.The sheath parameters show higher values at higher source currents whereas they decrease with the increase of excitation frequencies.It has also been found that,by the proper choice of source frequencies and phase differences,it is possible to adjust the energy of ions when they hit the electrode.     

Transmissivity of electromagnetic wave propagating in magnetized plasma sheath using variational method

A variational method is introduced to analyze the transmissivity of an electromagnetic wave propagating in the magnetized plasma sheath. The plasma density is modeled by two parabolic inhomogeneous regions separated by one homogeneous region. The Lagrangian density of the system is constructed based on the fluid energy density and the electromagnetic energy density.The total variation of the Lagrangian density is derived. The fluid and electromagnetic fields are numerically solved by expansion in piecewise polynomial function space. We investigate the effect of an external magnetic field on the transmissivity of the electromagnetic wave. It is found that the transmissivity is increased when an external magnetic field is applied. The dependence of transmissivity on the collision frequency between the electrons and the neutral particles has also been studied. We also show that the external magnetic field causes a shift in the critical frequency of the plasma sheath.     

Two-dimensional self-consistent numerical simulation of the whole discharge region in an atmospheric argon arc

A 2D self-consistent numerical model of the whole argon-arc discharge region that includes electrodes is developed in this work to facilitate analysis of the physical processes occurring in atmospheric arc plasma. The 2D arc column model contains the ionization and thermal non-equilibrium, which is coupled with a 1D electrode sheath model. The influence of plasma-species diffusion near the electrode region is investigated based on Maxwell–Stefan equations and the generalized Ohm's law. The numerical results of argon free-burning arcs at atmospheric pressure are then investigated. The simulation shows that the plasma is obviously in the state of thermal and ionization equilibrium in the arc core region, while it deviates from thermal and ionization equilibrium in the arc fringe region. The actual electron density decreases rapidly in the near-anode and near-cathode regions due to non-equilibrium ionization, resulting in a large electron number gradient in these regions. The results indicate that electron diffusion has an important role in the near-cathode and near-anode regions. When the anode arc root gradually contracts, it is easy to obtain a positive voltage drop of the anode sheath (I = 50 A), while it remains difficult to acquire a positive anode sheath voltage drop (I = 150 A). The current–voltage characteristics predicted by our model are found to be identical to the experimental values.     

Simulation of Plasma Focus Devices with Hemisphere Electrodes

A magneto-hydrodynamic simulation of a plasma focus device with hemisphere electrodes is constructed. The snowplow model is used with help of the momentum conservation equation to describe the motion of the plasma sheath between the two concentric hemispheres. The model simulates various plasma parameters like plasma temperature and plasma sheath velocity. The circuit equation is used to calculate the discharge current and electrodes voltage across the two hemisphere terminals. A comparison between the cylindrical and spherical devices is built. The results show that the current dip and the spike voltage is expected to be much pronounced in the spherical devices. It is found also that the plasma sheath velocity and temperature in the case of the cylindrical system are higher than that in the spherical one.     

Comparative analysis of the arc characteristics inside the converging-diverging and cylindrical plasma torches

A two-temperature thermal non-equilibrium model is used to simulate and compare the arc characteristics within the converging-diverging and traditional cylindrical plasma torches.The modeling results show that the presence of the constrictor within the converging-diverging torch makes the evolution characteristics of the arc significantly different from that of cylindrical torch.Compared with a cylindrical geometrical torch,a much higher plasma flow velocity and relatively longer high temperature region can be generated and maintained inside the converging-diverging torch.In the constrictor of converging-diverging torch,the normalized radius of arc column increases and the degree of thermodynamic equilibrium of the plasma is significantly improved with the increase of axial distance.The radial momentum balance analysis shows that for the cylindrical torch,the pressure gradient that drives the arc expansion and the Lorentz force that drives the arc contraction dominate the radial evolution of the arc.While at the converging and constrictor region of a converging-diverging plasma torch,the radial gas dynamic forces in arc fringes pointing toward the arc center enhance the mixing of the cold gas of boundary layer with the high temperature gas of the arc center,increasing the average gas temperature and decreasing the thickness of cold boundary layer,thereby facilitating the formation of diffusion type arc anode attachment at the diverging section of torch.     

Experimental Investigation of Surface Wave Plasma Excited by a Cylindrical Dielectric Rod

An improved surface wave plasma source equipped with a cylindrical quartz rod has been developed, which has great potential in processing inner wall of cylindrical workpieces. A cylindrical quartz rod not only excites the plasma around the rod, but also guides surface wave plasma along the rod. The distributions of plasma density and plasma temperature under different incident microwave powers and pressures are diagnosed by a Langmuir probe. The electron density near the rod is around the order of 10^11cm^-3. When the incident power is 450 W, the length of surface wave plasma column can reach up to 420 mm at 20 Pa.     

Dynamical evolution of cross phase of edge fluctuations and transport bifurcation

The dynamical evolution of edge turbulence during a transport bifurcation is explored using a flux-driven nonlinear fluid model with a geometry relevant to the plasma edge region. The simulations show that the self-generated mean shear flows can dramatically modify the phase angle between turbulent fluctuations. The changes in phase differences and amplitudes of edge fluctuations give rise to the modifications of turbulent edge transport. The statistical properties of flux and fluctuations are also investigated before and after edge shear flow generation.     

圆柱形与圆锥形放电腔室中氢等离子体组分与状态研究

采用圆柱形和圆锥形的放电腔室,使用氢气作为放电气体在不同的射频功率下进行了放电。使用质谱诊断和Langmuir探针诊断相结合的方法对两种放电腔室中的氢等离子体的离子组分、离子能量分布（IED）、等离子体电势、电子密度和有效电子温度进行了对比研究。根据等离子体的诊断结果,讨论了圆锥形与圆柱形两种放电腔室中的放电特性。结果表明：圆柱形放电腔室中含有更多的亚稳态氢原子H ^*,而圆锥形放电腔室中含有更多的H⁺离子。圆锥形放电腔室中等离子体具有更高的电子密度和离子密度及更低的等离子体电势。     

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.     

Some studies on transient behaviours of sheath formation in dusty plasma with the effect of adiabatically heated electrons and ions

Based on quasipotential analysis, a plasma sheath is studied through the derivation of the Sagdeev potential equation in dusty plasma coexisting with adiabatically heated electrons and ions. Salient features as to the existence of sheaths are shown by solving the Sagdeev potential equation through the Runge–Kutta method, with appropriate consideration of adiabatically heated electrons and ions in the dynamical system. It has been shown that adiabatic heating of plasma sets a limit to the critical dust speed depending on the densities and Mach number, and it is believed that its role is very important to the sheath. One present problem is the contraction of the sheath region whereby dust grains levitated into the sheath lead to a crystallization similar to the formation of nebulons and are compressed to a larger chunk of the dust cloud by shrinking of the sheath. Our overall observations advance knowledge of sheath formation and are expected to be of interest in astroplasmas.