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 Charging and Dynamics in Tokamaks

Fundamental characteristics of charging of a dust particle and its dynamics in SOL/divertor plasma in tokamaks are studied. According to the OML (orbit motion limited) theory, the charging process is extremely faster, with a charging time of nanoseconds, than the dynamics process of the dust particle in SOL/divertor plasma, with a characteristic time of milliseconds, which means that the local charge state can be taken as the equilibrium charge state. It was clarified that the equilibrium charge Zd,eq can be determined in the form of Zd,eq / Rd Te, which is a function of both the normalized relative speed of plasma ion flow with respect to the velocity of the dust particle and the plasma temperature ratio. After the investigation of dominant forces acting on dust particles, the friction forces due to the plasma ion absorption and ion Coulomb scattering are found of the same order for the case of low relative speed. The critical radius of a dust particle, for which the gravity is larger than the friction forces due to plasma ions, is obtained.     

Dust Acoustic Compressive Waves in a Warm Dusty Plasma Having Non-Thermal Ions and Non-Isothermal Electrons

In this article an investigation is presented on the properties of dust acoustic(DA)compressive solitary wave propagation in an adiabatic dusty plasma,including the effect of nonthermal positive and negative ions and non-isothermal electrons.The reductive perturbation method has been employed to derive the lower degree modified Kadomtsev-Petviashivili(mK-P),3D Schamel-Korteweg-de-Vries equation or modified Kadomtsev-Petviashivili(mK-P) equations for dust acoustic solitary waves in a homogeneous,unmagnetized and collisionless plasma whose constituents are non-isothermal electrons,singly charged positive and negative non-thermal ions and massive charged dust particles.The stationary analytical solutions of the lower degree mK-P and mK-P equations are numerically analyzed,where the effect of various dusty plasma constituents on DA solitary wave propagation is taken into account.It is observed that both the ions in dusty plasma play a key role in the formation of DA compressive solitary waves,and also the ion concentration and non-isothermal electrons control the transformation of the compressive potentials of the waves.     

Nonplanar dust acoustic solitary and rogue waves in an ion beam plasma with superthermal electrons and ions

The propagation characteristics of dust acoustic solitary and rogue waves are investigated in an unmagnetized ion beam plasma with electrons and ions following kappa-type distribution in nonplanar geometry. The reductive perturbation method(RPM) is employed to derive the cylindrical/spherical Korteweg–de Vries(KdV) equation, which is further transformed into standard KdV equation by neglecting the geometrical effects. Using new stretching coordinates,nonlinear Schr?dinger equation(NLSE) has been derived from the standard KdV equation to study the different order rational solutions of dust acoustic rogue waves(DARWs). The impact of various physical parameters on the characteristics of dust acoustic solitary waves(DASWs) is elaborated specifically in nonplanar geometry. Further, the effects of ion beam and superthermality of electrons/ions on the characteristics of DARWs are studied. The results obtained in the present investigation may be useful in comprehending a variety of phenomena in Earth's magnetosphere polar cap region where the presence of positive ion beam has been detected and also in other regions of space/astrophysical environments where dust along with superthermal electrons and ions exists.     

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.     

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.     

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.     

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.     

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.     

Dust acoustic shock waves in magnetized dusty plasma

We have presented a theoretical study of the dust acoustic(DA) shock structures in a magnetized,electron depleted dusty plasma in the presence of two temperature superthermal ions. By deriving a Korteweg–de Vries–Burgers equation and studying its shock solution, we aim to highlight the effects of magnetic field and obliqueness on various properties of the DA shock structures in the presence of kappa-distributed two temperature ion population. The present model is motivated by the observations of Geotail spacecraft in the Earth?s magnetotail and it is seen that the different physical parameters such as superthermality of the cold and hot ions, the cold to hot ion temperature ratio, the magnetic field strength, obliqueness and the dust kinematic viscosity greatly influence the dynamics of the shock structures so formed. The results suggest that the variation of superthermalities of the cold and hot ions have contrasting effects on both positive and negative polarity shock structures.Moreover, it is noted that the presence of the ambient magnetic field affects the dispersive properties of the medium and tends to make the shock structures less wide and more abrupt. The findings of present investigation may be useful in understanding the dynamics of shock waves in dusty plasma environments containing two temperature ions where the electrons are significantly depleted.     

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.     

Effect of Dust Grains on Dust-Ion-Acoustic KdV Solitons in Magnetized Complex Plasma with Superthermal Electrons

In this paper, the propagation of dust-ion-acoustic (DIA) waves in a magnetized collisionless complex (dusty) plasma consisting of superthermal electrons are investigated. In the discharge plasma, the electron temperature is usually much greater than ion temperature. Thus, the electron distribution function DF), is generally nonmaxwellian, has to be modeled. For this purpose, the generalized Lorentzian ( $ \kappa $ )-DF is used to simulate the electron DF. Two types of modes (fast and slow DIA modes) exist in this plasma. By deriving Korteweg-de Vries (KdV) equation, using reductive perturbation method, both regions of solitary waves, rarefactive (dark) and compressive (bright) solitary waves, are allowed to be propagated in this plasma. Properties of DIA solitary waves are investigated numerically. How dust grains and superthermal electrons affect the sign and the magnitude of nonlinear coefficient of KdV equation is also discussed in detail. It is noted that the velocity, amplitude, and width of a DIA soliton is studied as well.     

Numerical simulation of RF discharges for plasma processing

In this paper, we present kinetic models for radio-frequency glow discharges. Discussed are models for bulk electrons and positive ions based on the solution of the Boltzmann equation in a one-dimensional geometry. The resulting spatiotemporal behaviour of the electrons is used to compute the plasma emission, which is compared with experimental data. The model for the ions is used to solve the coupled dynamics of the electric field and the ion density in the whole discharge as well as the ion velocity distribution at the electrodes. The results are compared with experimental data and with the results of a Monte Carlo code.     

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.     

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.     

Suppression of a spontaneous dust density wave by modulation of ion streaming

Synchronization of a self-excited dust density wave has been experimentally investigated in a strongly coupled dusty plasma. A dust density wave of frequency ~78 Hz is spontaneously generated from the dust void boundary due to the ion streaming instability. The electric field in the dust void region is measured, and the electric field force and ion drag force on the dust particles at the void boundary are estimated to explain the mechanism of spontaneous dust density wave excitation. Synchronization occurring through the suppression mechanism is observed by modulating the ion streaming by applying an external sinusoidal signal to the dust void. At sufficiently high modulation amplitude, the onset of period-doubling bifurcation is observed. Fast Fourier transform spectral analysis is done using time-series data obtained from high-speed video imaging. The van der Pol equation with a force term is used to correlate the observed suppression phenomena.     

Convoy electrons measured in coincidence with exit charge states in ion-surface scattering

Convoy electrons produced at glancing-angle scattering of 1.4–3.5 MeV Li ions from a SnTe(001) surface are measured in coincidence with scattered ions of different charge state q_e. Acceleration of the convoy electron due to the surface wake induced by the projectile ion is observed. The observed acceleration is found to be almost independent of q_e. This indicates that the memory of the charge state of the ion at convoy-electron emission is erased by subsequent charge-exchange processes at the surface. Using Bohr and Bohr-Lindhard models, it is concluded that the observed convoy electrons are mainly produced in the immediate vicinity of the surface.     

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.     

Dust Acoustic Shock Waves with Non-Thermal and Vortex-Like Ions in Dusty Plasma

A rigorous investigation is presented on the propagation characteristics of non-linear dust acoustic(DA)waves in an unmagnetized dusty plasma system containing non-thermal and vortex-like ions and Maxwellian electrons under the effect of a fluctuating charged dust fluid.The three-dimensional(3D)Burgers'equation and a new form of a lower degree modified 3D Burgers'equation with their analytical solutions are derived to study the features of shock waves in such plasmas.The effect of the population of non-thermal ions,the vortex-like ion parameter as well as the temperature ratios of ions and electrons on the evolution of shock waves in the presence of dust charge fluctuation is presented.This theoretical investigation might be effectively utilized to unveil the nature of many astrophysical plasma environments(Saturn's spokes etc.)where such plasmas are reported to have existed.     

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.