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.     

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.     

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.     

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.     

Sheath Structures of Strongly Electronegative Plasmas

The sheath structures of strongly electronegative plasmas axe investigated on basis of the accurate Bohm criterion obtained by Sagdeev potential. It is found that the presheath transition between the bulk plasma and the sheath almost does not exist there, and that distributions of electrons, negative and positive ions in the sheath form a pure positive ion sheath near the boundary of the electrode. Furthermore, the density distribution of space net charge has a peak near the sheath edge, the spatial potential within the sheath falls faster, and the sheath thickness becomes thinner.     

离子初始速度对等离子体鞘层厚度的影响

本文从理论上研究了离子初始速度对等离子体鞘层厚度的影响,建立了理论计算公式和数值模拟方法,考察了离子初始速度对鞘层厚度的影响因子。在离子初始能量为3.2 eV情况下,用粒子模拟程序进行了数值模拟,模拟与理论计算得到的空间电场分布十分接近。     

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.     

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.     

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.     

The Electrostatic Cylindrical Sheath in a Plasma

The electrostatic sheath with a cylindrical geometry in an ion-electron plasma is investigated. Assuming a Boltzmann response to electrons and cold ions with bulk flow, it is shown that the radius of the cylindrical geometry do not affect the sheath potential significantly. We also found that the sheath potential profile is steeper in the cylindrical sheath compared to the slab sheath. The distinct feature of the cylindrical sheath is that the ion density distribution is not monotonous. The sheath region can be divided into three regions, two ascendant regions and one descendant region.     

Sheath Criterion for an Electronegative Plasma Sheath in an Oblique Magnetic Field

The sheath criterion for an electronegative plasma composed of hot electrons,hot negative ions and cold positive ions in an oblique magnetic field is investigated.We discuss the effects of negative ions and external magnetic field on the sheath criterion.We find that the ion Mach number is of relatively low value because of Coulomb attraction between positive and negative ions.Also the ion Mach number depends on the magnitude and the angle of the magnetic field as well as the initial velocity of ion flow.     

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.     

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.     

Influence of the Collisions on the Dusty Plasma Sheath in the Presence of an Oblique Magnetic Field

The dust dynamics in a magnetized collisional plasma-sheath are numerically studied by using the fluid model. Isothermal electrons, cold fluid ions, cold fluid dust grains and immobile neutral particles are taken into account in the sheath. As dust can be created by detaching small pieces of the wall limiting plasma, naturally, these grains can have different sizes. Therefore, the influence of dust size on the sheath characteristics is considered. Assuming the dust–neutral collision cross section has a power law dependency on the dust velocity. The comparison of the effect of the dust radius in both specific collisional models shows that in the constant cross section model, dust size plays a more role with respect to the constant collision frequency. The effect of the dust size on dust velocity is investigated for different values of the power factor. It shows that dust velocity when reaching near the wall in constant cross section model is much less than constant mobility model, and the velocity of the smaller dust is lower on the wall. If dust density is very small, the kind of collisional model has no significant influence on the electric potential. But by increasing dust density, a little fall in the local electric potential and a little rise in the sheath thickness are seen in constant cross section model.     

Combined Effect of Ion Temperature and Magnetic Field on Collisionless Sheath Structure

A steady state two-fluid model has been used to study the characteristics of the collisionless plasma sheath in the presence of an external magnetic field and by taking into account both the ion temperature and the ion drift velocity at the sheath edge. The number and momentum equations of ions, the Boltzmann distribution of electrons and Poisson equations are solved numerically. The dependence of the Bohm magnetized sheath criterion to ion temperature is examined. It is shown that the ion temperature has significant effects on the sheath characteristics such as ion velocity, charged particles densities and electric potential. In the specific orientations of the magnetic field, it is found that by increasing the ion temperature, the ions do not achieve energy and the kinetic energy of the ions in the depth direction reaches the specific value at bigger distance from the plasma-sheath boundary.     

Study on the characteristics of non-Maxwellian magnetized sheath in Hall thruster acceleration region

The secondary electron emission (SEE) and inclined magnetic field are typical features at the channel wall of the Hall thruster acceleration region (AR), and the characteristics of the magnetized sheath have a significant effect on the radial potential distribution, ion radial acceleration and wall erosion. In this work, the magnetohydrodynamics model is used to study the characteristics of the magnetized sheath with SEE in the AR of Hall thruster. The electrons are assumed to obey non-extensive distribution, the ions and secondary electrons are magnetized. Based on the Sagdeev potential, the modified Bohm criterion is derived, and the influences of the non-extensive parameter and magnetic field on the AR sheath structure and parameters are discussed. Results show that, with the decrease of the parameter q, the high-energy electron leads to an increase of the potential drop in the sheath, and the sheath thickness expands accordingly, the kinetic energy rises when ions reach the wall, which can aggravate the wall erosion. Increasing the magnetic field inclination angle in the AR of the Hall thruster, the Lorenz force along the $x$ direction acting as a resistance decelerating ions becomes larger which can reduce the wall erosion, while the strength of magnetic field in the AR has little effect on Bohm criterion and wall potential. The propellant type also has a certain effect on the values of wall potential, secondary electron number density and sheath thickness.     

Frequency Matching Effects on Characteristics of Bulk Plasmas and Sheaths for Dual-Frequency Capacitively Coupled Argon Discharges： One-Dimensional Fluid Simulation

A one-dimensional fluid model is proposed to simulate the dual-frequency capacitively coupled plasma for Ar discharges. The influences of the low frequency on the plasma density, electron temperature, sheath voltage drop, and ion energy distribution at the powered electrode are investigated. The decoupling effect of the two radio-frequency sources on the plasma parameters, especially in the sheath region, is discussed in detail.     

Effects of electron temperature on the ion extraction characteristics in a decaying plasma confined between two parallel plates

In this paper, a one-dimension particle-in-cell (PIC) code (EDIPIC) is employed to simulate the parallel-plate ion extraction process under an externally applied electrostatic field, focusing on the analysis of the influence of the initial electron temperature on the extracted ion fluxes to the metal plates during the ion extraction process. Compared with previously published results, the plasma oscillations on a timescale of the electron plasma period, and the excitation of the ion acoustic rarefaction waves resulting from the plasma oscillations originating from both the negative and positive electrodes, are studied for the first time. The modeling results show that both the negative and positive extractors can collect ions due to the plasma oscillations and the propagation of the ion acoustic rarefaction waves. With the increase of the initial electron temperature achieved by keeping other parameters unchanged, on the one hand, both the ion speed and flux to the negative and positive plates increase, which leads to a significant decrease of the ion extraction time, while on the other hand, the ion flux to the positive plate after the formation of a Child–Langmuir sheath is much more sensitive to an increase of the initial electron temperature than that to the negative plate. The PIC simulation results provide a deeper physical understanding of the influence of the initial electron temperature on the characteristics of the entire ion extraction process in a decaying plasma.     

Estimation of the sheath power dissipation induced by ion cyclotron resonance heating

During ion cyclotron resonance heating, the sheath power dissipation caused by ion acceleration in the radio frequency(RF) sheath is one of the main causes of RF power loss in the tokamak edge region. To estimate the power dissipation of an RF sheath in the ion cyclotron range of frequency(ICRF), a 1 D fluid model for the multi-component plasma sheath driven by a sinusoidal disturbance current in the ICRF is presented. By investigation of the sheath potential and ion flux at the wall, it is shown that the larger frequency and lower amplitude of the disturbance current can cause smaller sheath power dissipation. The effect of the energetic ion on the sheath power dissipation depends on the disturbance current. For large amplitude of disturbance current, the increase in the concentration and energy of the energetic ion leads to a decrease in sheath power dissipation. While for a small disturbance current, the sheath power dissipation demonstrates non-monotonic variation with the concentration and energy of the energetic ion. In addition, the sheath power dissipation is found to have a small increase in the presence of light impurity ions with low valence.     

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.