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.     

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.     

Kinetic simulation of an electronegative plasma with a cut-off distribution and modified Bohm criterion

A kinetic simulation model has been employed to study the properties of an electronegative magnetized plasma sheath assuming the cut-off distribution of electrons and negative ions. The fundamental kinetic Bohm condition for the electronegative magnetized plasma has paramount importance for the formation of a stationary plasma sheath near the material wall. The presence of an oblique magnetic field in an electronegative plasma affects the ion distribution at the plasma injection side and at the wall. The temperature profile of negative charged particles has a non-uniform distribution, which determines the energy flow towards the wall.     

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.     

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.     

Characteristics of inductively coupled plasma(ICP) and helicon plasma in a singleloop antenna

Large area uniform plasma sources, such as high-density magnetized inductively coupled plasma(ICP) and helicon plasma, have broad applications in industry. A comprehensive comparison of ICP and helicon plasma, excited by a single-loop antenna, is presented in this paper from the perspectives of mode transition, hysteresis behavior, and density distribution. The E-H mode transition in ICP and the E-H-W mode transition in helicon plasma are clearly observed in the experiments. Besides, the considerable variation of hysteresis behavior from inverse hysteresis to normal hysteresis by the influence of the magnetic field is explored. The bi-Maxwellian and Maxwellian electron energy distribution functions in each discharge are used to explain this phenomenon, which is essentially related to the transition from a nonlocal kinetic property to a local kinetic property of electrons. In addition, we notice that the plasma density, in the radial direction, is peaked in the center of the tube in ICP, but a complicated distribution is formed in helicon plasma. In the axial direction, the maximum plasma density is still in the center of the antenna in ICP, whereas the highest plasma density is located downstream, far away from the antenna, in helicon plasma. It is believed that the reflected electrons in the sheath and pre-sheath by the upper metallic endplate and downstream propagated helicon wave will be responsible for this plasma density profile in helicon plasma. Due to the constrained electron motion in the magnetic field, an extremely uniform density distribution will be obtained with an appropriate axial magnetic field in the wave discharge mode.     

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.     

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.     

Set－up of a Pure Electron Plasma Device

An electron Penning-Malmberg trap,which can confine an electron column and provide a good platform to investigate the cross-filed transportation of strongly magnetized electron plasma ,has been set up.With the device,an electron plasma with a density of 10^7 cm^-3 can be confined for a relatively long time.The structure of the trap,electron source,as well as the way how th measure electron plasma density profile and velocity distrbustion are introduced in detail.     

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.     

Simulations of standing wave effect,stop band effect,and skin effect in large-area very high frequency symmetric capacitive discharges

In this paper, Maxwell equations are coupled with a radially localized global model and an analytical sheath model to investigate the electromagnetic effects under various frequencies and electron powers in large-area very high frequency symmetric capacitive argon discharges.Simulation results indicate that both the vacuum wavelength and the sheath width decrease with frequency, leading to the reduced surface wavelength. As a result, the standing wave effect becomes pronounced, causing the fact that the radial profiles of the electron density, radio frequency voltage, and sheath width shift from uniform over center-high to multiple-node. When the frequency is close to or higher than the series resonance frequency, the surface waves cannot propagate to the radial center because of the significant radial damping. Due to the lack of power deposition near the radial center, the electron density is nearly zero there, i.e. the stop band effect. As power increases, the higher electron density leads to the decrease of the skin depth.Therefore, the importance of the skin effect gradually exceeds that of the standing wave effect,giving rise to the transition from the center-high to edge-high electron density profiles. The method proposed in this work could help to predict the plasma distribution under different discharge conditions in a few minutes, which is of significant importance in optimizing the plasma processing.     

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.     

Characteristics of Langmuir Probe in Low Temperature, Weakly Magnetized Plasmas

The systematic Langmuir probe measurements for a weakly magnetized plasma have been carried out in the Linear Magnetized Plasma Device for different magnetic fields. By comparing the ion current density of probes with different sizes, the sheath thickness can be evaluated. It is found that while the ratio of cylindrical probe‘s dimension to ion Larmor radius is not more than 2, the model of probe for non-magnetized plasma is still applicable.     

Study of obliquely propagating electron acoustic shock waves with non-extensive electron population

Obliquely propagating electron acoustic shock waves in magnetized plasma composed of stationary ions, cold and non-extensive hot electrons are investigated by deriving Korteweg–de Vries Burgers(KdVB) equation. The tangent hyperbolic method is used to solve the KdVB equation in dissipative medium. The dissipation effect is introduced in the model by means of kinematic viscosity term. The analytical calculations of the KdVB equation shows that the structures(amplitude, velocity and width) of the shock waves are modified significantly with kinematic viscosity(η_0), obliqueness(k_z) and magnetic field(ω_c). Since plasmas are ubiquitously permeated with magnetic field, it is pertinent to explore the characteristics of KdVB equation in a magnetized plasmas.     

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.     

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.     

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.     

Dust Divertor for a Tokamak Fusion Reactor

Micron-size tungsten particulates find their equilibrium position in the magnetized plasma sheath in the normal direction of the divertor surface, but are convected poloidally and toroidally by the sonic ion flow drag parallel to the divertor surface. The natural circulation of the dust particles in the magnetized plasma sheath can be used to set up a flowing dust shield that absorbs and exhausts most of the tokamak heat flux to the divertor. The size of the particulates and the choice of materials offer substantial room for optimization.     

Diagnosing the Fine Structure of Electron Energy Within the ECRIT Ion Source

The ion source of the electron cyclotron resonance ion thruster(ECRIT) extracts ions from its ECR plasma to generate thrust, and has the property of low gas consumption(2 sccm,standard-state cubic centimeter per minute) and high durability. Due to the indispensable effects of the primary electron in gas discharge, it is important to experimentally clarify the electron energy structure within the ion source of the ECRIT through analyzing the electron energy distribution function(EEDF) of the plasma inside the thruster. In this article the Langmuir probe diagnosing method was used to diagnose the EEDF, from which the effective electron temperature, plasma density and the electron energy probability function(EEPF) were deduced. The experimental results show that the magnetic field influences the curves of EEDF and EEPF and make the effective plasma parameter nonuniform. The diagnosed electron temperature and density from sample points increased from 4 eV/2×10~(16)m~(-3) to 10 eV/4×10~(16)m(-3) with increasing distances from both the axis and the screen grid of the ion source. Electron temperature and density peaking near the wall coincided with the discharge process. However, a double Maxwellian electron distribution was unexpectedly observed at the position near the axis of the ion source and about 30 mm from the screen grid. Besides, the double Maxwellian electron distribution was more likely to emerge at high power and a low gas flow rate. These phenomena were believed to relate to the arrangements of the gas inlets and the magnetic field where the double Maxwellian electron distribution exits. The results of this research may enhance the understanding of the plasma generation process in the ion source of this type and help to improve its performance.