Strong Dependency of Ion Acceleration on Ion Beam Divergency in Magnetized Collisionless Plasma Sheath

The ion acceleration inside the collisionless plasma sheath is investigated at the presence of external magnetic field. By using the fluid model, the number and momentum equations of the ions and the Boltzmann and Poisson equations are solved numerically in the case that the ion beam has a small divergency at the plasma sheath boundary. It is shown that the kinetic energy of the ions has a strong dependency to the magnitude of divergency when the magnetic field has a small component parallel to the 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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Sheath Characteristic in ECR Plasma Nitriding

1. IntroductionThe plasma sheath is an important and complexregion for nearly all plasma applications in materials processing. The theoretical and experimental research on the features of sheath is important for making the processing mechanism clear and for selectingthe best processing conditions.The main process Of plasma nitriding has been noal.widely accepted as being dominated b3' the excitednitrogen molecules, ions= and nitrogen atoms [l-41.As to their formation, Aloll [5] thought that i…     

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.     

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.     

Numerical study on characteristics of radio-frequency discharge at atmospheric pressure in argon with small admixtures of oxygen

In this paper, a 1D fluid model is developed to study the characteristics of a discharge in argon with small admixtures of oxygen at atmospheric pressure. This model consists of a series of equations, including continuity equations for electrons, positive ions, negative ions and neutral particles, the energy equation, and the Poisson equation for electric potential. Special attention has been paid to the electron energy dissipation and the mechanisms of electron heating, while the admixture of oxygen is in the range of 0.1%–0.6%. It is found that when the oxygen-to-argon ratio grows, the discharge is obviously divided into three stages: electron growth, electron reduction and the electron remaining unchanged. Furthermore, the cycle-averaged electric field,electron temperature, electron Ohmic heating, electron collisionless heating, electron energy dissipation and the net electron production are also studied in detail, and when the oxygen-toargon ratio is relatively larger(R?=?0.6%), double value peaks of electron Ohmic heating appear in the sheath. According to the results of the numerical simulation, various oxygen-to-argon ratios result in different amounts of electron energy dissipation and electron heating.     

Effects of pulsed magnetic field on density reduction of high flow velocity plasma sheath

A three-dimensional model is proposed in this paper to study the effect of the pulsed magnetic field on the density distribution of high flow velocity plasma sheath. Taking the typical parameters of plasma sheath at the height of 71 km as an example, the distribution characteristics and time evolution characteristics of plasma density in the flow field under the action of pulsed magnetic field, as well as the effect of self-electric field on the distribution of plasma density, are studied. The simulation results show that pulsed magnetic field can effectively reduce the density of plasma sheath. Meanwhile, the simulation results of three-dimensional plasma density distribution show that the size of the density reduction area is large enough to meet the communication requirements of the Global Position System(GPS) signal. Besides, the location of density reduction area provides a reference for the appropriate location of antenna. The time evolution of plasma density shows that the effective density reduction time can reach 62% of the pulse duration, and the maximum reduction of plasma density can reach 55%. Based on the simulation results, the mechanism of the interaction between pulsed magnetic field and plasma flow field is physically analyzed. Furthermore, the simulation results indicate that the density distributions of electrons and ions are consistent under the action of plasma self-electric field.However, the quasi neutral assumption of plasma in the flow field is not appropriate, because the self-electric field of plasma will weaken the effect of the pulsed magnetic field on the reduction of electron density, which cannot be ignored. The calculation results could provide useful information for the mitigation of communication blackout in hypersonic vehicles.     

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.     

Effect of pulse waveform on plasma sheath expansion in plasma-based ion implantation

In this paper, the effect of the pulse waveform on plasma sheath evolution around a diamond-shaped target has been simulated using fluid dynamic model in the context of plasma-based ion implantation (PBII). The implanted parameters of ions such as ion-implanted energy, impact angle and impact current have also been studied under different pulse shapes. Understandably, the longer pulse rise time would result in the lower ion impact energy, and less sheath expanding extent. By comparing the sheath structure under different pulse rise time, we found that long pulse rise time would enhance the conformation of the sheath to the target at the earlier stage of the pulse and would reduce the tendency of the ion depletion in the plasma sheath. Accordingly increase the ion impact current at the later stage of the pulse, which is quite important for the PBII process, when the ions have been accelerated adequately.     

Effects of resonant magnetic perturbations on the loss of energetic ions in tokamak pedestal

Resonant magnetic perturbations (RMPs) are extensively applied to mitigate or suppress the edge localized mode in tokamak plasmas, but will break the axisymmetric magnetic field configuration and increase the loss of energetic ions. The mechanism of RMPs induced energetic ion loss has been extensively studied, and is mainly attributed to resonant effects. In this paper, in the perturbed non-axisymmetric tokamak pedestal, we analytically derive the equations of guiding center motion for energetic ions including the bounce/transit averaged radial drift velocity and the toroidal precession frequency modified by strong radial electric field. The loss time of energetic ions is numerically solved and its parametric dependence is analyzed in detail. We find that passing energetic ions cannot escape from the plasma, while deeply trapped energetic ions can escape from the plasma. The strong radial electric field plays an important role in modifying the toroidal precession frequency and resulting in the drift loss of trapped energetic ions. The loss time of trapped energetic ions is much smaller than the corresponding slowdown time in DIII-D pedestal. This indicates that the loss of trapped energetic ions in the perturbed non-axisymmetric pedestal is important, especially for the trapped energetic ions generated by perpendicular neutral beam injection.     

Particle Trajectories and Energy Distribution from a New IEC Fusion Device: A Many-Body Approach

This paper reports the explorations on the particle dynamics, ion distribution, energy spectra and temperature in a new-designed inertial electrostatic confinement fusion device in case of low azimuthal magnetic field. The proposed design has six bar-sized cathodes at the vicinity of the central region and a central DC current-carrying bar injects a homogeneous azimuthal magnetic flux on the particles. The cylindrical device is simulated in the fully ionized Deuterium media. Following the 3D design of the chamber, the real-time simulations have been performed by the time integration of the electrical and magnetic forces. The model uses the many-body approach with the particle–particle and particle–chamber interactions. To implement the particle–chamber interaction, the finite difference method has been applied. Besides, the model includes reflection effects of particles from the electrically grounded chamber wall. According to the simulations, the particle trajectories exhibit complex fluctuations in the central region and nearby the chamber walls. The ion temperature has been calculated around T _i  = 35 keV for the source potential V = ?150 kV. In addition, the ion distribution indicates that 68 % of ions can be collected in the central region. According to the velocity distribution, there exists a double Gaussian distribution with a low velocity peak. In addition, nearly 61 % of ions stay in the energy scale between 2 keV ≤ E ≤ 39 keV. The averaged neutron rate is estimated as 5.96 × 10⁵ n/s.     

Transient Behavior of Negative Hydrogen Ion Extraction from Plasma

For plasma source,the extraction of negative ions is quite diferent from that of positive ions.To understand the efect of extraction field on plasma,the time-dependent behavior of negative hydrogen ion extraction from a negative ion source has been studied by particle-in-cell simulation in the collisionless limit.The simulations have shown that,due to the diference in dynamics between electrons and ions,the imbalance of the numbers of charged particles occurs in the source,results in the broadening of plasma sheath and the great increase of plasma potential.The resultant high sheath field and the ambipolar electric field in plasma make the negatively charged particles congregate inside the sheath and move toward the extraction outlet.The emission area of negative ions is much smaller than that of the extraction aperture,which is in sharp contrast to the case of positive ion extraction.