Dust Surface Potential Research Articles

Study of plasma sheath in the presence of dust particles in a magnetic mirror-like field configuration

The properties of a plasma sheath in the presence of dust grains and a magnetic mirror-like field configuration have been investigated in this study. All the plasma species viz. electrons, ions, and dust grains are described by fluid equations. The system of equations involved in the study is solved numerically using the Runge-Kutta fourth-order (RK4) method to explore the sheath properties. The results of the study suggest that in the presence of a magnetic mirror-like field configuration, the component of ion velocity perpendicular to the wall decreases near the surface, and consequently, the ion density increases. To the best of our knowledge, such observations have not been reported anywhere previously. This utterly different observation is due to the magnetic field configuration alone. Such a behavior can be used to control the dynamics of the ions in the sheath. Moreover, ion-neutral collisions tend to reduce the effect of the magnetic field on the properties of the sheath. The study may be helpful to understand the interactions of plasma with the wall in different plasma-assisted industrial applications containing dust grains as contaminants. Besides, the study will play a significant role in controlling the dynamics of positive ions and negatively charged dust grains in the sheath. The space charge shows an unusual behavior near the sheath. In the usual scenario, the space charge slightly decreases near the wall. But in the present context, the space charge increases. Further, it has been observed that the dust surface potential near the wall becomes less negative with the increase in magnetic field strength. The magnetic field and ion-neutral collisions tend to restrict the movement of the ions toward the wall when acting separately, but their combined effect leads to a different kind of behavior altogether.

Influence of Xenon–Fluorine–Sulfur Hexafluoride (Xe+–F−–SF6−) and Argon-Fluorine-Sulfur Hexafluoride (Ar+–F−–SF6−) Streaming on Dust Surface Potential (DSP) That Has Cairn–Tsallis Distributed Plasmas

The dust grain surface potential is examined analytically and numerically in dusty plasmas containing negative/positive ion species by using the Cairn Tsallis (non-Maxwellian) dusty plasma. The equations for the dust-charging process are derived to solve the current balance equation for the xenon–fluorine–sulfur hexafluoride and argon–fluorine–sulfur hexafluoride plasmas. The charging process affected by plasma properties such as spectral indices α and q, in addition to positive ion streaming (UAr+ and UXe+) and negative ion streaming (UF− and USF6−) of both types of plasmas, is examined. Our findings suggest that considering a wide range of Xe+−F−−SF6− and Ar+−F−−SF6− masses is critical for understanding plasma physics, specifically multi-component plasmas.

Effect of ion beam current on dust charge fluctuations and ion-acoustic waves in electronegative dusty plasmas

The effects of ion beam current associated with the streaming positive ions on the dust charge fluctuations and ion acoustic wave propagation in quiescent electronegative dusty plasma have been investigated using fluid theory. The dust charging phenomenon and unstable mode of ion waves are modified for two streaming conditions of positive ions which are extended and graphically illustrated. The dependencies of the growing and damping rate of ion waves on dust density and the size of dust grains are studied. The evolution of dust surface potential is found in the negative domain with the increase in concentration of negative ions and the instability rate for ion wave decreases. Furthermore, it is shown that the dust surface potential shifts into positive domain as the electrons are significantly depleted (and the plasma becomes ion-ion plasma) from the electronegative plasma and thus ion waves exhibit a damping phenomenon.

Tadpole type motion of charged dust in the Lagrange problem with planet Jupiter

We investigate the dynamics of charged dust interacting with the interplanetary magnetic field in a Parker spiral type model and subject to the solar wind and Poynting–Robertson​ effect in the vicinity of the 1:1 mean motion resonance with planet Jupiter. We estimate the shifts of the location of the minimum libration amplitude solutions close to the location of the L4 and L5 points of the classical – gravitational – problem and provide the extension of the ‘librational regimes of motion’ and the width of the resonance in dependency of the nongravitational parameters related to the dust grain size and surface potential of the particles. Our study is based on numerical simulations in the framework of the spatial, elliptic restricted three-body problem and semi-analytical estimates obtained by averaging of Gauss’ planetary equations of motion.

Numerical investigation of sheath characteristics for electronegative magnetized plasma and dust charging

We have studied the effects of the magnetic field on the active electronegative plasma sheath properties and dust charging process in the sheath region for two different collisional models: constant ion mean free path and constant ion mobility using 1d3v fluid hydrodynamics model. It is found that the magnetic field strength and choice of collisional models have a significant effect on the active plasma sheath characteristics and charging of an isolated dust grain. The sheath criterion for an active electronegative magnetized plasma for both collisional models has been extended, and the effects of neutral gas pressure, source frequency, obliqueness of magnetic field, and initial electric field at sheath edge are graphically illustrated. There are two distinct regions observed in the sheath region: magnetic field and electric field dominant regions. The spatial distribution of plasma sheath parameters is systematically presented. It is found that the evolution of dust surface potential is affected by the magnitude of the magnetic field and collisional models. The stable levitation of dust grains in the sheath region is close to the sheath entrance. Moreover, the total force experienced by an isolated dust grain in the sheath region rapidly increases close to the material surface, and the magnitude of force is higher for larger dust grain.

Effect of levitated dust kinetics in the dynamic evolution of inhomogeneous plasma sheath

The main goal here is to study theoretically the formation of plasma sheath in an inhomogeneous dusty plasma. The effect of weak ionization of the dust grains as similar to the Townsend discharge has been incorporated to see how it influences the evolution of sheath. Sheath equation has been derived to describe the properties of sheath structures analytically and numerically. It has shown that the ionization along with the inhomogeneity affects significantly the growth of sheath which has been highlighted elaborately for some typical plasma parameters. After getting well defined sheath region, dynamical behaviour of levitated dust grains into the sheath has been studied. The totality of the findings has been centred around the estimation of dust surface potential, dust sizes along with the generation of net force on dust grains. Both inhomogeneous and ionization effects allow the dust grains in acquiring different potential to sustain equilibrium in different places. As a result of this, nebulons and the dust cloudlike structures are electrically charged.

Dust surface potential for the dusty plasma with negative ions and with a three-parameter non-Maxwell velocity distribution

We study the dust surface potential for the complex dusty plasma with negative ions and with a three-parameter non-Maxwell velocity distribution. The plasma contains electrons, positive ions, negative ions, and negatively charged dust particles. By using the current equilibrium condition, we derive the relationship between the normalized dust surface potential and the dusty plasma parameters such as the normalized dust number density, the temperature ratio of negative ions to electrons, the density ratio of negative ions to positive ions, and the charge number of negative ions. The numerical analyses show that the relationship depends evidently on the three parameters in the non-Maxwell distribution when the dust surface potential is relatively smaller, but with the increase of the potential, such dependence will weaken soon. The dust surface potential is negative and increases monotonously with the increase of the dust density, and for the complex dusty plasma with the three-parameter non-Maxwell distribution, it is generally greater than that in the same plasma with the kappa-distribution and the Maxwellian distribution.

A kinetic model for investigating the dielectric properties of rocket exhaust dusty plasmas

The electron kinetic model of rocket exhaust dusty plasma is developed based on the Boltzmann equation. Additional electron-dust elastic and inelastic collision processes are included in the kinetic equation except for the electron-neutral collisions. The dust surface potential and electron density are calculated according to the dust charging balance equation and the quasineutrality condition. The electron energy distribution function (EEDF) is calculated by solving the kinetic equation numerically. It shows that the obtained EEDF results for different dust densities deviate from the Maxwellian distribution obviously. In addition, the dielectric properties of rocket exhausts based on the obtained non-Maxwellian EEDFs are analyzed for different dust and plasma parameters. It is shown that the relative permittivity based on the EEDFs obtained from the kinetic model is larger than that based on Maxwellian distribution, while for the conductivity and attenuation constant, they become smaller. As for the influence of dust particles on the dielectric properties, a high ratio of dust and neutral density (10−9) leads to a smaller absolute value of relative permittivity, electrical conductivity, and attenuation constant for both Maxwellian distribution and EEDF obtained from the kinetic model. When the ratio is low (10−10), the dust particles almost have no influence on the dielectric properties. Meanwhile, it can be seen that the existence of dust particles makes the difference in dielectric properties obtained from the calculated EEDFs and Maxwellian distribution smaller.

Dust Charging and Propagation of Dust-Acoustic Waves in a Multicomponent Thermal Dusty Plasma System

An analytical model is developed with the aim to investigate the propagation of dust-acoustic (DA) waves in a multicomponent thermal dusty plasma system including ion species as well. Dust particles are considered positively charged by electron and ion currents, thermionic and UV photo-ionic processes. The model is applied to laboratory plasma as well as Martian atmospheric plasma to explain the nature of dust potential variation as well as characteristics of DA propagation modes within the linear and nonlinear regimes for given plasma parameters. In the nonlinear regime, the KdV equation is derived, and the equation is seen to support the propagation of compressive solitons in laboratory plasma system and rarefactive solitons in the case of Martian atmospheric plasma. The inclusion of ion species in the system is seen to have an important role in determining the propagation speed, the amplitude, and the corresponding width of solitons. The thermionic work function W, photon yield factor Y, and low value of flux density of UV photon beam J do not have an appreciable impact on dispersion relation and DA soliton structures. On the contrary, noticeable changes occur in the case of the dust surface potential obtained in both laboratory and Martian plasmas.

The nonlocal electron kinetics for a low-pressure glow discharge dusty plasma

The nonlocal electron kinetic model based on the Boltzmann equation is developed in low-pressure argon glow discharge dusty plasmas. The additional electron-dust elastic and inelastic collision processes are considered when solving the kinetic equation numerically. The orbital motion limited theory and collision enhanced collection approximation are employed to calculate the dust surface potential. The electron energy distribution function (EEDF), effective electron temperature Teff, and dust surface potential are investigated under different plasma and dust conditions by solving the Boltzmann and the dust charging current balance equations self-consistently. A comparison of the calculation results obtained from nonlocal and local kinetic models is made. It is shown that the appearance of dust particles leads to a deviation of the EEDF from its original profile for both nonlocal and local kinetic models. With the increase in dust density and size, the effective electron temperature and dust surface potential decrease due to the high-energy electron loss on the dust surface. Meanwhile, the nonlocal and local results differ much from each other under the same calculation condition. It is concluded that, for low-pressure (PR ≤ 1 cm*Torr) glow discharge dusty plasmas, the existence of dust particles will amplify the difference of local and nonlocal EEDFs, which makes the local kinetic model more improper to determine the main parameters of the positive column. The nonlocal kinetic model should be used for the calculation of the EEDFs and dusty plasma parameters.

Electron energy probability function in the temporal afterglow of a dusty plasma

The kinetic description of the electron energy probability function (EEPF) in a dusty afterglow plasma is considered for two typical cases: when the rate of electron-neutral momentum-transfer collisions is independent of the electron energy and when it is a power function of the electron energy. The electron Boltzmann equation is solved using the method of characteristics and analytical expressions for the EEPF are obtained for different initial EEPFs (including both Maxwellian and Druyvesteyn distributions) at electron energies larger than the dust-surface potential. The analytical EEPF functions are then used to analyze several experimental parameter regimes of the dust radius and density, the dust-charge decay time, the afterglow duration, etc. It is also found that absorption of electrons by the dust particles plays an important role in determining the EEPF in a dusty afterglow.

Dust grains potential variation in a Vasyliunas Cairns-distributed plasmas with negative ions

Dust grains' potential variation is presented by using a non-equilibrium complex (dusty) plasma following the Vasyliunas Cairns (VC)-distribution, in which the components such as the electrons, ions [positive and negative], and dust grains have negative charge. For this reason, mathematical statement of currents is solved for dust grains having negatively charge to accomplish the equilibrium state value (viz., qd = constant) in the presence of VC-distributed plasmas. Indeed, the current balance equations are modified due to the streaming/nonequilibrium distributed negative ions. Numerically, it is assessed that the important plasma variable, for example, spectral index α, spectral index κ, negative ions streaming velocity (U0), and negative ions number density (ρ), significantly influences the dust grain surface potential (|ψd|) by: (i) increasing the value of spectral index kappa (κ) and negative ions density (ρ), the magnitude of dust surface potential (|ψd|) decreases and (ii) increasing the values of spectral index α and negative ions streaming velocity (U0), dust grains surface potential (|ψd|) increases. The relevance to low-temperature research center in a non-equilibrium dusty (complex) plasma is precisely discussed by associating oxygen ions (negative and positive) species.

Electron energy distribution in a dusty plasma: analytical approach.

Analytical expressions describing the electron energy distribution function (EEDF) in a dusty plasma are obtained from the homogeneous Boltzmann equation for electrons. The expressions are derived neglecting electron-electron collisions, as well as transformation of high-energy electrons into low-energy electrons at inelastic electron-atom collisions. At large electron energies, the quasiclassical approach for calculation of the EEDF is applied. For the moderate energies, we account for inelastic electron-atom collisions in the dust-free case and both inelastic electron-atom and electron-dust collisions in the dusty plasma case. Using these analytical expressions and the balance equation for dust charging, the electron energy distribution function, the effective electron temperature, the dust charge, and the dust surface potential are obtained for different dust radii and densities, as well as for different electron densities and radio-frequency (rf) field amplitudes and frequencies. The dusty plasma parameters are compared with those calculated numerically by a finite-difference method taking into account electron-electron collisions and the transformation of high-energy electrons at inelastic electron-neutral collisions. It is shown that the analytical expressions can be used for calculation of the EEDF and dusty plasma parameters at typical experimental conditions, in particular, in the positive column of a direct-current glow discharge and in the case of an rf plasma maintained by an electric field with frequency f=13.56MHz.

The effect of a dust size distribution on electrostatic sheaths in unmagnetized dusty plasmas

In this work, the structure of plasma sheaths in presence of dust particles with different sizes is investigated numerically in a multifluid framework, where the dust size distribution is modeled by Gauss' law. For this, we have established a 1D, stationary, unmagnetized, and weakly collisional electronegative dusty plasma sheath model. The electrons and negative ions are considered in a local thermodynamic equilibrium, therefore, described by a Boltzmann distribution. On the other hand, positive ions and dust grains are described by fluid equations. The charging process is described by the orbit motion limited model. It is shown that taking into account dust grains with different sizes reduces considerably the sheath thickness. The behavior of dust surface potential is not affected, but the dust charge number is reduced, as well as the electrostatic force. It results in a decrease of layered structure. The presence of negative ions makes the structure of the electrostatic potential more oscillatory. The other physical parameters are also analyzed and discussed.

Effect of secondary electron emission on Jean's instability in a complex plasma in the presence of nonthermal ions

In this paper, we have investigated the role of secondary electron emission on Jean's instability in a complex plasma in the presence of nonthermal ions. The equilibrium dust surface potential has been considered negative and hence primary and secondary electron temperatures are equal. Such plasma consists of three components: Boltzman distributed electrons, nonthermal ions and negatively charged inertial dust grains. From the linear dispersion relation, we have calculated the real frequency and growth rate of Jean's instability. Numerically, we have shown that for strong ion nonthermality Jean's mode is unstable. Growth of the instability reduces and the real part of the wave frequency increases with increasing secondary electron emission from dust grains. Hence, strong secondary electron emission suppresses Jean's instability in a complex plasma even when ion nonthermality is strong and equilibrium dust charge is negative.

Kinetics of Complex Plasmas Having Dust of Different Materials With Corresponding Size Distribution

In this paper, the authors have presented a formulation of the kinetics of complex plasmas, having dust of different materials (different work functions) and size distributions, which is based on the number and energy balance of constituents; this is in deference to the present emphasis on considering complex plasma as an open system. The formulation is based on a size-independent dust surface potential; this simplifies the problem to a form, similar to that for the case of uniform size dust grains, characterized by the mean <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(a_{m})$</tex></formula> and the root mean square <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$(a_{rms})$</tex></formula> radius of the dust particles. Two cases, viz., complex plasma in thermal equilibrium and complex plasma irradiated by monochromatic radiation, have been considered in detail, and corresponding computations have been made for a mixture of two varieties of dust grains having high <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(\varphi_{2} &gt; h\nu)$</tex></formula> and low <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$(h\nu &gt; \varphi_{1})$</tex></formula> work functions. The relevance of the first case to flames and rocket exhausts has been pointed out. The fluctuation of charge corresponding to individual dust grains has also been evaluated. A discussion based on numerical results and conclusion have been also given.

Dust-acoustic soliton in electronegative complex plasmas with streaming positive ions

The Sagdeev potential approach is applied to investigate theoretically and numerically the dust acoustic soliton in electronegative dusty plasmas with streaming positive ions. The self-consistent dust charge variation is also taken into account. The lower and upper limits of Mach numbers are then derived. Moreover, it is found that both the positive ion streaming velocity and negative ion density can lower the two limits. The soliton profiles, involving the spatial potential, particle densities, dust surface potential, and space net charge distributions in various cases, are plotted and discussed.

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 Bohm criterion for the dusty plasma sheath

The hydrodynamic-fluid model and the self-consistent dust charging model are used to investigate the Bohm criterion for the dusty plasma sheath. The variation of the ion critical Mach number and the dust Mach number with dust density are presented, and the relation between the dust surface potential and the dust density at the sheath edge is discussed. It is shown that the ion velocity entering the sheath would exceed the ion sound velocity due to the existence of dust particles. The ion critical Mach number began declining after a maximum with the incessant increase of the dust density. The numerical results satisfy the qualitative analysis of the Sagdeev potential.

The Bohm criterion for the dusty plasma sheath

The Bohm criterion for the dusty plasma sheath is investigated with a fluid model. It is shown that the presence of dust particles near the interface between the bulk plasma and the sheath should have effects upon the ion Mach number. The dust particles charging and density variation are taken into account, and therefore the self-consistent relation between the dust surface potential and ion Mach number at the sheath edge is derived. The numerical results reveal that both the ion critical Mach number and the dust critical Mach number with variation of density ratio of dust-to-electron begin to decline after a maximum.