Behavior of a dust grain in the double layer of an electric probe in a gas-discharge plasma

Equations for the motion of an individual dust grain in the double layer of a negatively charged cylindrical probe in a glow discharge plasma are derived and solved numerically. The distribution of the electric potential near the probe is determined, and the grain charge is calculated as a function of the distance from the probe for different probe potentials. The trajectories of grains with different initial energies are traced. An analysis of the grain trajectories shows that, at a certain distance from the probe, high-energy grains may be recharged; i.e., the grain charge may change sign. The grains are found to have no direct effect on the probe current in a dusty plasma of a glow discharge.     

Positive column of a glow discharge in neon with charged dust grains (a review)

The effect of charged micron-size dust grains (microparticles) on the electric parameters of the positive column of a low-pressure dc glow discharge in neon has been studied experimentally and numerically. Numerical analysis is carried out in the diffusion-drift approximation with allowance for the interaction of dust grains with metastable neon atoms. In a discharge with a dust grain cloud, the longitudinal electric field increases. As the number density of dust grains in an axisymmetric cylindrical dust cloud rises, the growth of the electric field saturates. It is shown that the contribution of metastable atoms to ionization is higher in a discharge with dust grains, in spite of the quenching of metastable atoms on dust grains. The processes of charging of dust grains and the dust cloud are considered. As the number density of dust grains rises, their charge decreases, while the space charge of the dust cloud increases. The results obtained can be used in plasma technologies involving microparticles.     

Numerical simulations of ion and electron transport in a low-temperature dusty plasma

Charged particle transport and kinetic processes in a low-temperature dusty plasma are numerically simulated. Dust grains are represented as spheres with a given radius. The self-consistent electric field in the plasma surrounding a charged dust grain is calculated taking into account the perturbations of plasma quasineutrality near the grains. It is shown that applying an external electric field leads to a rearrangement of the plasma space charge and a break of the spherical symmetry of the electron and ion density distributions around the grain. The mutual influence of two identical charged dust grains is considered, and the energy of the electrostatic interaction between the grains is calculated. It is shown that this energy has a minimum at a certain finite distance between the grains.     

Formation of vortex dust structures in inhomogeneous gas-discharge plasmas

A generalized analytical model of instabilities in a dusty plasma with a nonzero grain charge gradient in a field of nonelectrostatic forces is considered. A review is given of different experimental observations of the dust self-oscillations that occur in the plasmas of an rf capacitive discharge and a dc glow discharge and whose appearance can be explained in terms of the proposed model. It is shown that the change in the grain charge gives rise to dynamic dust structures in laboratory gas-discharge plasmas. Attention is focused on the analysis of the onset of vortex motion of the dust grains.     

Properties of dust-plasma structures formed in a glow discharge above the lower wall of the discharge chamber

The properties are studied of dusty plasma structures formed in a glow discharge in a dust trap above the lower wall of the side branch of the discharge tube, near the turn of the discharge channel. The dust structure is three-dimensional with a characteristic size of up to 3 cm and contains about 30000 dust grains. Depending on the experimental conditions, dust-acoustic, dissipative, and charge-gradient instabilities can develop in such a structure. When using highly polydisperse dust grains of arbitrary shape, the effect of selection of dust grains by the plasma with respect to their mean size and shape was discovered. This effect was studied quantitatively in two gases by using the method of gathering and extraction of the dust grains levitating in the trap. The morphology of the dust structures was determined from the pair correlation functions of the horizontal cross sections containing long-range order peaks and elements of a hexagonal lattice. Stratification of a uniform structure accompanied by convective rotation caused by the grain charge gradient was observed. Applications of the dusty plasma created in this type of device are discussed.     

Effect of the shape of the electron energy distribution function on the dust grain charge and its screening in glow discharge plasmas

The dust grain charge in the plasma of a glow discharge in noble gases and nitrogen is calculated in the orbit motion limited model for reduced fields in the range of E/N = 1–20 Td. The calculations were performed using the electron energy distribution functions (EEDFs) obtained by solving the Boltzmann equation numerically with allowance for elastic and inelastic electron scattering and analytically with allowance for only elastic scattering and (for nitrogen) excitation of rotational levels, as well as using a Maxwellian EEDF. In the latter case, either the characteristic electron energy or mean electron energy multiplied by two thirds was used as the electron temperature. It is shown that the calculations with the use of a Maxwellian EEDF yield larger values of the grain charge as compared to those calculated with EEDFs obtained by solving the Boltzmann equation. The range of E/N values is determined in which analytical expressions for the EEDF obtained with allowance for elastic scattering and excitation of rotational levels are applicable to calculating the grain charge. The effect of the EEDF shape on the screening of the dust grain charge in plasma is investigated. The Debye screening length in case of a Maxwellian EEDF is shown to be shorter than that obtained with EEDFs calculated by numerically solving the Boltzmann equation.     

Dust grain charges in a nuclear-track plasma and the formation of dynamic vortex dust structures

Results are presented from Monte Carlo calculations of the electric charge of dust grains in a plasma produced during the slowing down of the radioactive decay products of californium nuclei in neon. The dust grain charging is explained for the first time as being due to the drift of electrons and ions in an external electric field. It is shown that the charges of the grains depend on their coordinates and strongly fluctuate with time. The time-averaged grain charges agree with the experimental data obtained on ordered liquidlike dust structures in a nuclear-track plasma. The time-averaged dust grain charges are used to carry out computer modeling of the formation of dynamic vortex structures observed in experiments. Evidence is obtained of the fact that the electrostatic forces experienced by the dust grains are potential in character.     

Development of a self-consistent model of dust grain charging at elevated pressures using the method of moments

A model of dust grain charging is constructed using the method of moments. The dust grain charging process in a weakly ionized helium plasma produced by a 100-keV electron beam at atmospheric pressure is studied theoretically. In simulations, the beam current density was varied from 1 to 10⁶ μA/cm². It is shown that, in a He plasma, dust grains of radius 5 μm and larger perturb the electron temperature only slightly, although the reduced electric field near the grain reaches 8 Td, the beam current density being 10⁶ μA/cm². It is found that, at distances from the grain that are up to several tens or hundreds of times larger than its radius, the electron and ion densities are lower than their equilibrium values. Conditions are determined under which the charging process may be described by a model with constant electron transport coefficients. The dust grain charge is shown to be weakly affected by secondary electron emission. In a beam-produced helium plasma, the dust grain potential calculated in the drift-diffusion model is shown to be close to that calculated in the orbit motion limited model. It is found that, in the vicinity of a body perturbing the plasma, there may be no quasineutral plasma presheath with an ambipolar diffusion of charged particles. The conditions for the onset of this presheath in a beam-produced plasma are determined. __________ Translated from Fizika Plazmy, Vol. 29, No. 3, 2003, pp. 214–226. Original Russian Text Copyright ? 2003 by Filippov, Dyatko, Pal’, Starostin.     

Experimental studies of the dynamics of dust grains in gas-discharge plasmas

Results of the experimental studies of the dynamics of dust grains in the plasmas of an rf capacitive discharge and a dc glow discharge are presented. The dusty plasma of a dc glow discharge was investigated in both ground-based experiments and experiments carried out under microgravity conditions (on board the Mir space station). The pair correlation function, temperature, and diffusion coefficient of dust grains are measured in a wide range of the dusty-plasma parameters. Dimensionless parameters responsible for the microscopic transport of dust-grains in a gas-discharge plasma are determined. A nonintrusive diagnostic technique for determining the dust-grain charges and screening lengths under the assumption of screened interaction between the grains is proposed. This technique is used to estimate the surface potential of dust grains of different size in a gas-discharge plasma.     

Photoelectric charging of dust grains

Photoemission from the surface of a dust grain in vacuum is considered. It is shown that the cutoff in the energy spectrum of emitted electrons leads to the formation of a steady-state electron cloud. The equation describing the distribution of the electric potential in the vicinity of a dust grain is solved numerically. The dust grain charge is found as a function of the grain size.     

Charge and potential of a dust grain versus the intergrain distance and establishment of the latter in a low-pressure plasma

Results from experimental studies of ordered dust structures in plasma are reviewed. The experimental conditions and the data on the grain size and intergrain distance in plasma dust crystals are analyzed. It is shown that intergrain distance is a function of the grain size. The range of the ratio of the dust grain size to the Debye radius within which plasma dust crystals can form is determined. A volume cell surrounding a dust grain in plasma is considered. It is found that the potential and charge of the grain depend substantially on the intergrain distance. The charge, potential, and potential energy of a dust grain in a plasma dust crystal, as well as the electrostatic force exerted by the plasma field on the grain, are calculated by the method of molecular dynamics as functions of the intergrain distance. The corresponding analytic approximations and the criterion for the establishment of a steady-state intergrain distance are proposed.     

Effect of microwave radiation on a dusty plasma

The effect of microwave radiation on a complex plasma produced by an external ionizer is studied using numerical simulations. It is shown that, as the radiation intensity increases, the scattering of the incident radiation by charged metal grains is enhanced and radiation at the second harmonic of the incident radiation appears in the scattered spectrum. This effect is associated with the grain charge oscillations caused by the nonlinear action of the microwave field. It is found that, under the action of strong microwave radiation, the grain charge can increase by one order of magnitude. It is shown that, when the microwave intensity is high enough, the distribution of the electric field near a dust grain is shown to change so radically that the field component normal to the grain surface can even change its sign.     

Investigation of the electron energy distribution function in hollow-cathode glow discharges in nitrogen and oxygen

The mechanism for the formation of the inverse electron distribution function is proposed and realized experimentally in a nitrogen plasma of a hollow-cathode glow discharge. It is shown theoretically and experimentally that, for a broad range of the parameters of an N₂ discharge, it is possible to form a significant dip in the profile of the electron distribution function in the energy range ε=2–4 eV and, accordingly, to produce the inverse distribution with df(ε)/d?>0. The formation of a dip is associated with both the vibrational excitation of N₂ molecules and the characteristic features of a hollow-cathode glow discharge. In such a discharge, the applied voltage drops preferentially across a narrow cathode sheath. In the main discharge region, the electric field E is weak (E<0.1 V/cm at a pressure of about p～0.1 torr) and does not heat the discharge plasma. The gas is ionized and the ionization-produced electrons are heated by a beam of fast electrons (with an energy of about 400 eV) emitted from the cathode. A high-energy electron beam plays an important role in the formation of a dip in the profile of the electron distribution function in the energy range in which the cross section for the vibrational excitation of nitrogen molecules is maximum. A plasma with an inverted electron distribution function can be used to create a population inversion in which more impurity molecules and atoms will exist in electronically excited states.     

Double layer in a cylindrical hollow-cathode discharge

A dc cylindrical coaxial glow discharge with an inner grid anode has been studied. The region between the two electrodes is seen dark, while a brightly glowing region forms inside the grid anode up to the center. The current-voltage characteristic of a dc cylindrical glow discharge in nitrogen is similar to that of a normal glow discharge, while the normal glow discharge voltage decreases with increasing pressure. The minimum plasma potentials are observed in the hollow cathode region due to the accumulation of electrons at the back of the grid anode. At the center, some of the passed electrons are converged, so their potential is decreased. These electrons have a sufficient time to be redistributed to form one group with a Maxwellian electron energy distribution function. The electron temperature measured by electric probes varies from 1.6 to 3.6 eV, while the plasma density varies from 3.9 × 10¹⁶ to 7 × 10¹³ m⁻³, depending on the discharge current and probe position. The plasma density increases as the electrons move radially from the grid toward the central region, while their temperature decreases.     

Measurements and calculations of the electron distribution function in the electronegative plasma of a hollow-cathode discharge in N<Subscript>2</Subscript>: SF<Subscript>6</Subscript> mixtures

Results are presented from measurements and numerical calculations of the electron energy distribution function in the plasma of a hollow-cathode glow discharge in N₂: SF₆ mixtures. It is shown that, when a small amount of SF₆ is added to nitrogen, the number of electrons in the inverse region of the distribution function (2–6 eV) increases by about one order of magnitude. As the electric field in plasma increases to ≈0.5 V/cm, the dip in the distribution function disappears and the inversion region vanishes.     

Ordered dusty structures in the plasma of an RF electrodeless gas discharge

Results are presented from the experimental studies and numerical simulations of the behavior of dust grains in the plasma of an inductive RF discharge. The experiments were carried out with neon at a pressure of 25–500 Pa and with 1.87-μm melamine formaldehyde grains. The discharge was excited by a ring inductor supplied from a generator operating at a 100-MHz frequency. The effective dust-grain interaction potential used in numerical simulations involved the spatial dependence of the grain charge on the plasma floating potential, grain-interaction anisotropy resulting from the focusing of the drift ion current by the negatively charged grains, and specific features of the shielding of the dust grains by the plasma electrons and ions recombining both in the plasma bulk and on the grain surface. The results of Monte Carlo simulations show that the dust grains form specific filament structures observed experimentally in the plasma of an inductive electrodeless discharge. __________ Translated from Fizika Plazmy, Vol. 26, No. 5, 2000, pp. 445–454. Original Russian Text Copyright ? 2000 by Zobnin, Nefedov, Sinel’shchikov, Sinkevich, Usachev, Filinov, Fortov.     

Glow intensity profile in a spherically stratified gas discharge

The glow intensity profile in a spherically stratified gas discharge is measured. It is shown that the boundaries of striations are thin spherical glowing shells, whose thickness is proportional to the striation radius. Based on the analysis of the optical-emission characteristics of spherical striations, the spatial distribution of the electric field in the stratified discharge region is estimated.     

Plasma parameters and existence conditions of monolayer dust structures in the electrode sheath of an RF discharge

The plasma parameters in the electrode sheath of an RF discharge were studied experimentally under the conditions of dust monolayer levitation. A new method is proposed for determining the plasma parameters, such as the average electric field, ion density, and ion velocity. The screening parameter and the dust grain charge are estimated. The criteria of stable levitation of a dust monolayer are considered. The obtained results are compared with the available theoretical and numerical data, as well as with the results obtained using other diagnostic methods.     

Nonlocal nature of the electron energy spectrum in a glow discharge in pure O2: I. Nonlocal character of the electron distribution function

Abstrac A study is made of the nonlocal nature of the electron energy distribution function in the positive column of a glow discharge in a tube filled with pure oxygen. The distribution function and the axial (E _z) and radial (E _r) electric fields as functions of radius are measured using an array of mobile probes. The experimentally obtained spatial profiles of the distribution function are used to test the applicability of the two-term approximation to the distribution function of the electrons with a nonlocal energy spectrum. The distribution function in a specified electric field E=E _z +E _r (where E _z ⊥ E _r) is calculated by solving the coordinate-dependent Boltzmann equation in the two-term approximation and by directly integrating the equations of electron motion using the Monte Carlo method. A comparison between the experimental data and the results of simulations carried out for a broad parameter range shows that, in the case of a highly nonlocal electron energy spectrum, the two-term approximation makes it possible to calculate the electron distribution function with a fairly good accuracy, in which case, however, in imposing the boundary conditions, the electron losses at the plasma surface should be treated in the kinetic approximation. It is shown that using the reflection coefficient of the plasma surface for electrons instead of the loss cone in space makes it possible to accurately calculate the electron energy distribution function over the entire parameter range under consideration, including the transient region in which the electron-energy relaxation length is comparable to the characteristic plasma dimension. __________ Translated from Fizika Plazmy, Vol. 26, No. 11, 2000, pp. 1038–1045. Original Russian Text Copyright ? 2000 by Ivanov, Klopovskii, Lopaev, Rakhimov, Rakhimova.     

Effect of ion collisions on the parameters of dust-plasma structures

A study is made of how collisions of ions with gas atoms affect the parameters of an ion flow and the interaction between dust grains, as well as their interaction with the flow. The ion velocity distribution in a gas discharge is analyzed with allowance for both resonant charge exchange of the ions with parent gas atoms and polarizing collisions. The interaction forces between a dust grain and an ion flow and among the grains due to the charge exchange of ions with gas atoms near the grain are examined.