Orbital-motion-limited theory of dust charging and plasma response
Xian-Zhu Tang, Gian Luca Delzanno
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7 pages, 4 figures Copyright (2015) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Phys. Plasmas 21, 123708 (2014) and may be found at http://scitation.aip.org/content/aip/journal/pop/21/12/10.1063/1.4904404
The foundational theory for dusty plasmas is the dust charging theory that provides the dust potential and charge arising from the dust interaction with a plasma. The most widely used dust charging theory for negatively charged dust particles is the so-called orbital motion limited (OML) theory, which predicts the dust potential and heat collection accurately for a variety of applications, but was previously found to be incapable of evaluating the dust charge and plasma response in any situation. Here we report a revised OML formulation that is able to predict the plasma response and hence the dust charge. Numerical solutions of the new OML model show that the widely-used Whipple approximation of dust charge-potential relationship agrees with OML theory in the limit of small dust radius compared with plasma Debye length, but incurs large (order-unity) deviation from the OML prediction when the dust size becomes comparable with or larger than plasma Debye length. This latter case is expected for the important application of dust particles in a tokamak plasma.
Charging of dust grains in low-pressure plasmas is reviewed critically. A theory based on the Fokker-Planck equation and orbital motion limited approximation is proposed. The theory predicts that dust grains can acquire a positive charge in low-pressure electropositive plasmas having a sufficiently high plasma potential, in agreement with experimental observations. It is also shown that variations in the plasma potential (electron temperature) can lead to spatial regions in which grains have opposite charges.
The charging of conducting or alternatively insulating dust grains in a supersonic plasma flow with a directed photon flux is studied by the particle-in-cell method. The electron emission modifies the surface charge distribution on a grain and in the surrounding plasma. The charge and potential distributions on and around a dust grain are studied for different photon fluxes and different angles of the incident unidirectional photons with respect to the plasma flow velocity vector. Continuous and pulsed radiations are considered. We show that photoemission allows controlling the charge on condu…
Dust particulates immersed in a quasineutral plasma can emit electrons in several important applications. Once electron emission becomes strong enough, the dust enters the positively charged regime where the conventional Orbital-Motion-Limited (OML) theory can break down due to potential well effects on trapped electrons. A minimal modification of the trapped-passing boundary approximation in the so-called OML$^+$ approach is shown to accurately predict the dust charge and heat collection flux for a wide range of dust size and temperature.
It is well known that the form of grain size distribution strongly influences the linear dielectric response of a dusty plasma. In previous results [IEEE Trans. Plasma Sci. 29, 182 (2001)], it was shown that for a class of size distributions, there is an equivalence to a Lorentzian distribution of mono-sized particles. The electrostatic response to a slowly moving test charge, using a second order approximation can then be found [Phys. Lett. A 305, 79 (2002)]. It is also well known [Phys. Plasmas 10, 3484 (2003)] that the dynamical charging of grains in a dusty plasma enhances the shielding of…
The charging of spinning insulating objects by plasma and photoemission is studied with the particle-in-cell method. Unidirectional photon flux, different angular velocities of the object, and different plasma flow speeds are considered. Photoemission can lead to a positive total charge and electric dipole moment on the object. The spinning of the object redistributes the surface charge. The total object charge oscillates in time with the period matching the period of the object rotation. Plasma potential and density in the vicinity of the object oscillate with the same frequency. The plasma i…
Combining a particle-particle, particle-cluster and cluster-cluster agglomeration model with an aggregate charging model, the coagulation and charging of dust particles in various plasma environments relevant for proto-planetary disks have been investigated. The results show that charged aggregates tend to grow by adding small particles and clusters to larger particles and clusters, leading to greater sizes and masses as compared to neutral aggregates, for the same number of monomers in the aggregate. In addition, aggregates coagulating in a Lorentzian plasma (containing a larger fraction of h…
A general derivation of the charging equation of a dust grain is presented, and indicated where and when it can be used. A problem of linear fluctuations of charges on the surface of the dust grain is discussed.
The deflection of interstellar dust grains in the magnetic field near the heliopause has been investigated based on the assumption that interstellar grains are homogeneous spheres. However, remote observations have shown that interstellar grains are more likely to be composites of a large number of subunits. This has profound significance when interpreting data obtained through in-situ measurements, for the deflection of interstellar grains depends on their charge-to-mass ratio, and aggregates acquire different surface charges from spheres due to their complex structure. In this paper, the cha…
A one dimensional Vlasov Poisson simulation code is employed to investigate the plasma sheath considering electron induced secondary electron emission (SEE) and backscattering. The SEE coefficient is commonly treated as constant in a range of plasma simulations, here improved SEE model of a charged dielectric wall is constructed which includes the wall charging effect on SEE coefficient and the energy dependency of SEE coefficient. Pertinent algorithms to implement above SEE model in plasma simulation are studied in detail. It is found that the SEE coefficient increases with the amount of nega…
Low frequency longitudinal wave instability in magnetized high correlation dusty plasmas is investigated. The dust charging relaxation is taken into account. It is found that the instablity of wave is determined significantly by the frequency of wave, the dust charging relaxation, the shear viscosity and viscoelastic relaxation time, the coupling parameter of high correlation of dust as well the strength of magnetic field.
The influence of charge trap states in the dielectric boundary material on capacitively coupled radio frequency plasma discharge is investigated with theory and Particle in cell/Monte Carlo Collision simulation. It is found that the trap states of the wall material manipulated discharge properties mainly through the varying ion induced secondary electron emission (SEE) coefficient in response to dynamic surface charges accumulated within solid boundary. A comprehensive SEE model considering surface charging is established first, which incorporates the valence band electron distribution, electr…
The role of hot electrons in charging of dust grains is investigated in a two-temperature hydrogen plasma. A variety of dust particles are introduced into the system and secondary electron emission (SEE) from each of the dust grains has been reported. A cylindrical Langmuir probe is used for determining the plasma parameters and a Faraday cup is connected to an electrometer in order to measure the dust current. The electrometer readings confirm the electron emission from the dust and SEE is observed from the tungsten dust in a low-pressure experimental plasma device for the first time.
A kinetic equation for dust particles with a new kinetic variable - the mass of grains - is suggested for the description of processes with changing mass in dusty plasmas and neutral systems.
The dust charging processes in the collections of electrons and ions in the nonequilibrium dusty plasma with power-law distributions are investigated on the basic of a new q-distribution function theory in nonextensive statistics. Electrons and ions obey the power-law distributions and are with q-parameters different from each other. We derive the generalized formulae for the dust charging currents in which the nonextensive effects play roles. Further we investigate the dust charging processes taking place in the homogeneous dusty plasma where only the particle velocities are power-law distrib…
Numerical simulations of monolayer dust crystals in an RF complex plasma were performed to examine the crystal structure and quantify the effects of including the collision enhanced ion current in the charging model. A GEC cell similar to a previous experimental work was modeled for a range of RF voltages, using a continuum description for the plasma and a particle description for dust grains. The time history of each dust grain was monitored. The dust charge was computed using both the OML and the collision enhanced charging (CEC) model applicable to the sheath region. The dust model accounte…
The Orbital-Motion-Limited (OML) theory has been modified to predict the dust charge and the results were contrasted with the Whipple approximation [Tang and Delzanno, Phys. Plasmas 21, 123708 (2014)]. To further establish its regime of applicability, in this paper the OML predictions (for a non-electron-emitting, spherical dust grain at rest in a collisionless, unmagnetized plasma) are compared with Particle-In-Cell simulations that retain the absorption radius effect. It is found that for large dust grain radius $r_d$ relative to the plasma Debye length $λ_D$, the revised OML theory remains …
We study the secondary electron emissions induced by the impact of electrons on dust grains and the resulting dust charging processes in the nonequilibrium dusty plasma with power-law distributions. We derive new expressions of the secondary emitted electron flux and the dust charging currents that are generalized by the power-law q-distributions, where the nonlinear core functions are numerically studied for the nonextensive parameter q. Our numerical analyses show that the power-law q-distribution of the primary electrons has a significant effect on the secondary emitted electron flux as wel…
In the past years, EUV lithography scanner systems have entered High-Volume Manufacturing for state-of-the-art Integrated Circuits (IC), with critical dimensions down to 10 nm. This technology uses 13.5 nm EUV radiation, which is transmitted through a near-vacuum H2 background gas, imaging the pattern of a reticle onto a wafer. The energetic EUV photons excite the background gas into a low-density H2 plasma. The resulting plasma will locally change the near-vacuum into a conducting medium, and can charge floating surfaces and particles, also away from the direct EUV beam. This paper will discu…
The role of quantum tunneling effect in the electron accretion current onto a negatively charged grain immersed in isotropic plasma is analyzed, within the quasiclassic approximation, for different plasma electron distribution functions, plasma parameters, and grain sizes. It is shown that this contribution can be small (negligible) for relatively large (micron-sized) dust grains in plasmas with electron temperatures of the order of a few eV, but becomes important for nano-sized dust grains (tens to hundreds nm in diameter) in cold and ultracold plasmas (electron temperatures ~ tens to hundred…
Micron-sized dust grains have been successfully employed as non-perturbative probes to measure variations in plasma conditions on small spatial scales, such as those found in plasma sheaths. The dynamics of the grains can be used to map the forces due to electric fields present in the sheath, but the particle charge and electric field are difficult to measure independently. The problem is further complicated by the ion wake field which develops downstream of the dust grains in a flowing plasma. Within a sheath, ions are accelerated towards the charged boundary, and this ion flow creates a posi…
Coagulation growth kinetics of nanoparticles in plasma is affected by inter-particle electrostatic forces due to charging phenomenon. In stationary plasmas, unipolar charging of particles results in retardation of particles growth and may result in limitation on a particle size. We demonstrate opposite effect of enhanced particles growth in atmospheric pressure non-stationary arc discharge. Modeling of the nanoparticles growth kinetics revealed the formation of bipolar charge distribution. As a result, reversed (attractive) Coulomb forces promote formation of micrometer size particles in a mil…
The nanoparticle charging processes along with background spatial-temporal plasma profile have been investigated with 3DPIC simulation in a pulsed EUV exposure environment. It is found that the particle charge polarity (positive or negative) strongly depends on its size, location and background transient plasma conditions. The particle (100 nm diameter) charge reaches steady state in a single pulse (20 us) within the EUV beam in contrast to particles outside the beam that requires multiple pulses. The larger the particle size, the less number of pulses are required to reach steady state. It is…
In this article we are going to consider dust acoustic wave in dusty plasma whose constituents are inertial negative charged dust particles, Boltzmann distributed electrons and non-thermal distributed ions with variable dust charge. Using reductive perturbation method, we have obtained Korteweg-de Veries (kdv) and modified kdv(mkdv) equations. A Sagdeev potential for the system and stability conditions for solitonic solution are also derived.
The impacts of dust density inhomogeneity and dust size distribution (DSD) on linear dust acoustic (DA) wave propagation have been investigated theoretically in an inhomogeneous unmagnetized dusty plasma having powerlaw DSD. Two different types of wave modes, viz. slow and fast mode, are found to propagate in this inhomogeneous medium. It is shown that the linear dispersion characteristics of the DA waves are substantially affected by the DSD and density inhomogeneity. Also, it is found that the phase velocity increases with increasing dust density.
We consider the influence of dust charge fluctuations on damping of the dust-ion-acoustic waves. It is assumed that all grains have equal masses but charges are not constant in time - they may fluctuate in time. The dust charges are not really independent of the variations in the plasma potentials. All modes will influence the charging mechanism, and feedback will lead to several new interesting and unexpected phenomena. The charging of the grains depends on local plasma characteristics. If the waves disturb these characteristic, then charging of the grains is affected and the grain charge is …
We examine linear dust acoustic waves (DAWs) in a dusty plasma with strongly correlated dust grains, and discuss possibility of a twisted DA vortex beam carrying orbital angular momentum (OAM). For our purposes, we use the Boltzmann distributed electron and ion density perturbations, the dust continuity and generalized viscoelastic dust momentum equations, and Poisson's equation to obtain a dispersion relation for the modified DAWs. The effects of the polarization force, strong dust couplings, and dust charge fluctuations on the DAW spectrum are examined. Furthermore, we demonstrate that the D…
Simulations of dusty plasmas were performed using GRAPE-6, a special-purpose computer designed for gravitational N-body problems. The collective behaviour of dust particles, which are injected into the plasma, was studied by means of three-dimensional computer simulations. As an example of a dusty plasma simulation, we have calculated movement of dust particles in plasmas under microgravity conditions. In this simulation, a dust-free region called the "void" is observed in the dust cloud. Another example was to simulate experiments on Coulomb crystals in plasmas. Formation of a Coulomb crystal…
The nonlinear propagation of the dust-acoustic bright and dark envelope solitons in an opposite polarity dusty plasma system (composed of non-extensive $q$-distributed electrons, isothermal ions, and positively as well as negatively charged warm dust) have been theoretically investigated. The reductive perturbation method (which is valid for a small, but finite amplitude limit) is employed to derive the nonlinear Schrödinger equation. Two types of modes (namely, fast and slow dust-acoustic (DA) modes) have been observed. The conditions for the modulational instability (MI) and its growth rate …
We report an experimental observation of multiple co--rotating vortices in a extended dust column in the background of non--uniform diffused plasma. Inductively coupled RF discharge is initiated in the background of argon gas in the source region which later found to diffuse in the main experimental chamber. A secondary DC glow discharge plasma is produced to introduce the dust particles into the plasma. These micron sized poly-disperse dust particles get charged in the plasma environment and transported by the ambipolar electric field of the diffused plasma and found to confine in the potenti…
Effective potential of a charged dusty particle moving in homogeneous plasma has a negative part that provides attraction between similarly charged dusty particles. A depth of this potential well is great enough to ensure both stability of crystal structure of dusty plasma and sizable value of surface tension of a boundary surface of dusty region. The latter depends on the orientation of the surface relative to the counter-ion flow, namely, it is maximal and positive for the surface normal to the flow and minimal and negative for the surface along the flow. For the most cases of dusty plasma i…
The sheath region is probed in different complex plasma experiments using dust particles in addition to measurement of the optical emission originating from the plasma. The local maximum in optical emission coincides with the breaking of quasi-neutrality at the sheath boundary as indicated by the vertical force profile reconstructed from dust particle trajectories, as well as by the local onset of dust density waves in high density dust clouds suspended in a dielectric box.
During the recent decade a steadily increasing number of papers devoted to so-called "quantum dusty plasmas" (QDP) appeared. These systems are combining the properties of dusty (i.e. micrometer to nanometer-sized particles containing) plasmas with quantum effects %(of electrons) appearing at high-density and/or low-temperature. Many exciting properties of QDP were predicted including nontrivial collective oscillations and linear and nonlinear waves. It was predicted that the results have relevance for dense astrophysical plasmas such as white dwarf stars, neutron stars, magnetars and laborator…
In this work linear stability analysis of a magnetized dusty plasma with an anisotropic dust component having transversal motions much stronger than motions parallel to the external magnetic field, and isotropic light plasma components is described. Such a situation presumably establishes in a shock compressed space dusty plasma downstream the shock front. Oblique low-frequency magneto-hydrodynamic waves ($ω\ll ω_{cd}$, $ω_{cd}$ being the dust cyclotron frequency) are shown to be undergone to the mirror instability. Consequences for nonthermal dust destruction behind shock fronts in the inters…
Complex plasmas consist of microparticles embedded in a low-temperature plasma and allow investigating various effects by tracing the motion of these microparticles. Dust density waves appear in complex plasmas as self-excited acoustic waves in the microparticle fluid at low neutral gas pressures. Here we show that various properties of these waves depend on the position of the microparticle cloud with respect to the plasma sheath and explain this finding in terms of the underlying ion-drift instability. These results may be helpful in better understanding the propagation of dust density waves…
We present an investigation of the combined effects of the Debye-Huckel (DH) repulsive and overlaping Debye spheres (ODS) attractive interaction potentials around charged dust particles on collective modes, phase separation and ordered dust structures in a strongly coupled dusty plasma. We obtain static and dynamical information via Molecular Dynamics simulations in the liquid and crystallized phases and identify the onset of an instability in the transverse collective mode, by using (zero-temperature) lattice summation method. The present results are useful for understanding the origin of coa…
An experimental investigation of the propagation characteristics of shock waves in an inhomogeneous dusty plasma is carried out in the Dusty Plasma Experimental (DPEx) device. A homogeneous dusty plasma, made up of poly-dispersive kaolin particles, is initially formed in a DC glow discharge Argon plasma by maintaining a dynamic equilibrium of the pumping speed and the gas feeding rate. Later, an equilibrium density inhomogeneity in the dust fluid is created by introducing an imbalance in the original dynamic equilibrium. Non-linear wave structures are then excited in this inhomogeneous dusty p…
We consider influence of finite size of ions on properties of classic plasmas. We focus our attention on the ion sound for electron-ion plasmas. We also consider dusty plasmas, where we account finite size of ions and particles of dust and consider the dispersion of dust acoustic waves. Finite size of particles affects classical plasma properties. Finite size of particles gives considerable contribution for small wave lengths, which is area of appearing of quantum effects. Consequently, it is very important to consider finite size of ions in quantum plasmas as well.
A versatile linear dusty (complex) plasma device is designed to study the transport and dynamical behavior of dust particles in a large volume. Diffused inductively coupled plasma is generated in the background of argon gas. A novel technique is used to introduce the dust particles in the main plasma by striking a secondary direct current (DC) glow discharge. These dust particles are found to get trapped in an electrostatic potential well which is formed due to the combination of the ambipolar electric field caused by diffusive plasma and the field produced by the charged glass wall of the vac…
The current-driven electrostatic ion-cyclotron (EIC) instability is studied in presence of a transverse dc electric fields in a collisional magnetized dusty plasma. We derive the appropriate charging equation self consistently by using the Vlasov equation.
The existence of magnetosonic solitons in dusty plasmas is investigated. The nonlinear magnetohydrodynamic equations for a warm dusty magnetoplasma are thus derived. A solution of the nonlinear equations is presented. It is shown that, due to the presence of dust, static structures are allowed. This is in sharp contrast to the formation of the so called shocklets in usual magnetoplasmas. A comparatively small number of dust particles can thus drastically alter the behavior of the nonlinear structures in magnetized plasmas.
A rigorous theoretical investigation is made to study the characteristics of dust-acoustic (DA) waves (DAWs) in an electron depleted unmagnetized opposite polarity dusty plasma system that contains super-thermal ($κ$-distributed) ions, mobile positively and negatively charged dust grains for the first time. The reductive perturbation method is employed to obtain the NLSE to explore the modulational instability (MI) conditions for DAWs as well as the formation and characteristics of gigantic rogue waves. The nonlinear and dispersion properties of the dusty plasma medium are the prime reasons be…
The nonlinear propagation of small but finite amplitude dust ion-acoustic waves (DIAWs) in an ion-beam driven plasma with Boltzmannian electrons, positive ions and stationary charged dust grains, is studied by using the standard reductive perturbation technique (RPT). It is shown that there exist two critical values $(γ_{c1}$ and $γ_{c2})$ of ion-beam to ion phase speed ratio $(γ)$, beyond which the beam generated solitons are not possible. The effects of the parameters, namely $γ$, the ratio of the ion-beam to plasma ion density $(μ_{i})$, the dust to ion density ratio $(μ_{d})$ as well as th…
The standard nonlinear Schrödinger equation (NLSE) is one of the elegant equations to find the information about the modulational instability criteria of dust-ion-acoustic (DIA) waves (DIAWs) and associated DIA rogue waves (DIARWs) in a three-component dusty plasma medium having inertialess super-thermal kappa distributed electrons, and inertial warm positive ions and negative dust grains. It can be seen that under the consideration of inertial warm ions along with inertial negatively charged dust grains, the plasma system supports both fast and slow DIA modes. The charge state and number dens…
The formation of the gigantic dust-acoustic rouge waves (DARWs) in an electron depleted unmagnetized opposite polarity dusty plasma system is theoretically observed for the first time. The nonlinear Schrödinger equation (derived by utilizing the reductive perturbation method) has been analytically as well as numerically analyzed to identify the basic features (viz., height, thickness, and modulational instability, etc.) of DARWs. The results obtained form this investigation should be useful in understanding the basic properties of these rouge waves which can predict to be formed in electron de…
Over the past decade, dust particulate contamination has increasingly become an area of concern within the fusion research community. In a burning plasma machine design like the International Thermonuclear Experimental Reactor (ITER), dust contamination presents problems for diagnostic integration and may contribute to tritium safety issues. Additionally due to ITER design, such dust contamination problems are projected to become of even greater concern due to dust/wall interactions and possible instabilities created within the plasma by such particulates. Since the dynamics of such dust can i…
A versatile table-top dusty plasma experimental (DPEx) device to study flow induced excitations of linear and nonlinear waves/structures in a complex plasma is presented. In this {$Π$}-shaped apparatus a DC glow discharge plasma is produced between a disc shaped anode and a grounded long cathode {tray} by applying a high voltage DC in the background of a neutral gas {(Argon)} and subsequently a dusty plasma is created by introducing micron sized dust particles that get charged and levitated in the sheath region. A flow of the dust particles is induced in a controlled manner by adjusting the pu…
Micron-size charged particles can be easily levitated in low-density plasma environments. At low pressures, suspended particles have been observed to spontaneously oscillate around an equilibrium position. In systems of many particles, these oscillations can catalyze a variety of nonequilibrium, collective behaviors. Here, we report spontaneous oscillations of single particles that remain stable for minutes with striking regularity in amplitude and frequency. The oscillation amplitude can also exceed 1 cm, nearly an order of magnitude larger than previously observed. Using an integrated experi…
The charge of micrometer-sized dust particles suspended in plasma above the powered electrode of radio-frequency (RF) discharges is studied. Using a self-consistent fluid model, the plasma profiles above the electrode are calculated and the electron depletion towards the electrode, as well as the increasing flow speed of ions towards the electrode, are considered in the calculation of the dust particle floating potential. The results are compared with those reported in literature and the importance of the spatial dust charge variation is investigated.
A phenomenological model using fluid theory is developed to show that the decay of two seemingly independent nonlinear structures namely the dust void and dust soliton strongly depends on the plasma ionization parameter in an unmagnetized complex plasma system. Numerical solution of model equations has shown that the evolution of dust voids and their subsequent decay in a time frame is intimately related with the ionization parameter. A similar result also holds good in case of dust solitons where stability of soliton is found to depend critically upon ionization parameter. Most importantly, i…
A standard nonlinear Schrödinger equation has been established by using the reductive perturbation method to investigate the propagation of electrostatic dust-acoustic waves, and their modulational instability as well as the formation of localized electrostatic envelope solitons in an electron depleted unmagnetized dusty plasma system comprising opposite polarity dust grains and super-thermal positive ions. The relevant physical plasma parameters (viz., charge, mass, number density of positive and negative dust grains, and super-thermality of the positive ions, etc.) have rigorous impact to re…
