Dust grains in plasma with coulomb collisions

Dust-grain charging in a dense plasma with electron and ion concentration up to 10¹⁶cm^?3, where the electron transport cross section is dominated by Coulomb collisions, was investigated. It was established that the charge of an isolated dust grain increases with electron concentration, whereas its potential is almost constant in the range 10¹⁴–10¹⁶cm^?3 of electron concentrations studied. It is shown that the self-consistent electric-field potential at moderate and large distances from the dust grain is well approximated by the Debye expression, but the screening radius is appreciably larger than even the electron Debye radius. The region of parameters of a dense photoresonance sodium plasma, where the dust-grain ensemble may crystallize, was established.     

Charge screening in a plasma with an external ionization source

An asymptotic theory for the screening of the electric field of a dust particle or a spherical probe in a plasma with an external steady and/or internal (proportional to the electron density) gas ionization source has been developed for the first time. It has been established that the screening of the charge of a spherical body adsorbing the charge of the incident plasma particles is described by a superposition of two exponentials with different screening constants. The two exponentials are retained even in the absence of nonequilibrium fluxes on the macroparticle and only in the special case of an isothermal plasma does the screening become Debye one. The screening length is determined by the ratio of the electron-ion, β_ei, and Langevin, β_L = 4πeμ_i (where μ_i is the ion mobility), recombination coefficients. If β_L ? β_ei, then it is much larger than the electron Debye length. The ions in an isothermal plasma have been found to give the same contribution to the screening as the electrons if the electron-ion recombination coefficient exceeds the Langevin ion recombination coefficient by a factor of 2 or more, β_ei ≥ 2β_L. The Vlasov equation is used to analyze the asymptotic behavior of the macroparticle potential in a collisionless plasma.     

Possibility of weakly charged nonlinear solitary dust clouds near the continuum threshold of dust population in a quasi-neutral dusty plasma

Considering the Boltzmann response of the plasma ions and electrons and inertial dynamics of the charged dust grains, the possibility of very weak compressive soliton near the continuum limit of the dust population has been inferred. It is concluded that the behaviour of such coherent structures could be well described by the numerical analysis of the derived nonlinear classical energy integral equation for bounded solutions. These seem to be higher order dispersive structures within acoustic limit of the nonlinear turbulence. It is observed that the dust density enhancement beyond the continuum threshold causes regular increment in width and amplitude of the soliton structures. It is found that the soliton amplitude sensitively depends on the massive impurity’s population. These coherent structures could be visualized as weakly charged solitary dust clouds of finite extension (∼ plasma Debye length) within Boltzmann environment of plasma particles in their local surroundings. The seeding mechanism of such clouds may be attributed to some plasma instabilities driven by either internal or external free energy sources. Numerical analysis of the problem concludes that the experimental observations of such clouds could be possible in low density plasma regime. It is deduced that for plasma density ∼ 10⁶ cm^-3 at temperatures of a few electron volts and for micron to l0nm sized dust grains, the observation of such structures could be possible within wide range variability of the dust population density.     

尘埃颗粒与等离子体鞘层相互作用的数值模拟

通过求解一维稳态的尘埃等离子体鞘层模型,得到了等离子体鞘层势、正离子密度、电子密度和尘埃颗粒密度随一维横向的分布,Bohm判据及鞘层边界无量纲Bohm速度随尘埃密度的变化曲线,尘埃颗粒的带电量和尘埃密度的关系,尘埃颗粒的温度对尘埃颗粒自身在鞘层中分布的影响。结果表明,随着尘埃密度的增加,鞘层的厚度在减小,鞘层内的电子密度在下降,而且尘埃颗粒的带电量也在逐渐减少;随着尘埃温度的增加,鞘层的厚度减小,电子密度下降,而且鞘层附近的尘埃颗粒在逐渐增多。     

Nonstationary macroparticle charging in an arc plasma jet

The charging of liquid metal macroparticles in the rarified part of a vacuum arc plasma jet is studied. The sheath in the vicinity of the macroparticle is collisionless and the problem with different Debye length to macroparticle radius ratios is analyzed. Maxwellian velocity distribution functions with different temperatures for the electrons and ions in an arbitrary ratio are allowed in the model. By solving the equation for the electric field together with the equation for ion and electron flux, the charging time and the near electric field of the macroparticles were calculated. The kinetics of the macroparticle charging are controlled by the ion and electron flux to the macroparticle, which depend on the potential distribution in the sheath. The potential falls off slower than 1/r² in the case of the large Debye length to macroparticle radius ratio, and falls off more rapidly than 1/r² in the other case. The charge which accumulates on a macroparticle at distances of about 10 cm from a 100-Å cathode is about 10^-16 C and the charging time is about 10^-5 s. The influence of the plasma drift velocity on the macroparticle charging is small. The model presented here agrees well with an experimental study of macroparticle repulsion from biased substrates     

A 90° laser scattering experiment for measuring temperature and density of ions and electrons in a cold dense theta pinch plasma

In a 90° scattering experiment performed on a plasma with a density of some 10¹⁷cm^?3 and a temperature of some eV a scattering spectrum is expected which consists essentially of an intense central part and two very weak satellite peaks. In this investigation the spectrum of the central part (ion line) was resolved. From the ion line alone which was in good agreement with calculated spectra, the ion temperature, electron temperature and electron density were determined. At some plasma parameters only a few particles were included in the Debye volume. Also in these cases no deviations from calculated spectra have been observed. In addition the position and half-width of the satellites were measured. The position of the satellites yields an independent value of the electron density which agrees very well with that determined from the ion line. The half-width of the satellites was much broader than expected theoretically due to fluctuations of the electron density within the scattering volume. The measurement was performed on a theta pinch plasma. The energy of the condensor bank was 7.5 kJ, the voltage 18 kV. As a light source aQ-switch laser was used with a power of about 100 MW. Because of beam stops to prevent stray light only a fourth of the whole power reached the plasma.     

Interactions of charged dust particles in clouds of charges

Two charged dust particles inside a cloud of charges are considered as Debye atoms forming a Debye molecule. Cassini coordinates are used for the numerical solution of the Poisson-Boltzmann equation for the charged cloud. The electric force acting on a dust particle by the other dust particle was determined by integrating the electrostatic pressure on the surface of the dust particle. It is shown that attractive forces appear when the following two conditions are satisfied. First, the average distance between dust particles should be approximately equal to two Debye radii. Second, attraction takes place when similar charges are concentrated predominantly on the dust particles. If the particles carry a small fraction of total charge of the same polarity, repulsion between the particles takes place at all distances. We apply our results to the experiments with thermoemission plasma and to the experiments with nuclear-pumped plasma.     

Screening and attraction of dust particles in plasmas

The potential around a dust particle in a plasma is found using the collisional hydrodynamic equations of dusty plasmas, taking into account ion-dust and ion-neutral collisions and considering the plasma source proportional to the dust density. The linear screening is strongly influenced by the collisions and can substantially differ from Debye screening. Attraction of negatively charged dust particles can occur due to overscreening by the ion fluxes in the presence of friction forces.     

Ultrahigh charging of dust particles in a nonequilibrium plasma

Charging of dust particles in a plasma with the two-temperature energy distribution of electrons has been studied. It has been shown that the dust-particle potential divided by the electron temperature decreases with increasing electron temperature in the plasma with cold ions. Owing to this behavior, the potential of the dustparticle surface increases with the electron temperature more slowly than the linear function and is lower than the electron temperature (divided by the elementary charge) for T _e > 5.5 eV in hydrogen and for T _e > 240 eV in argon. The fraction of fast electrons at which these electrons begin to contribute to the charge of dust particles has been determined. It has been shown that the charge of micron particles can reach 10⁶ elementary charges. The effect of the cold and thermal field emission on the charge of dust particles has been analyzed. The possibility of obtaining ultrahigh charges (to 10⁷ elementary charges on dust particles with a radius of 50–100 μm irradiated by a 25-keV 1-mA electron beam has been demonstrated.     

Potential around a dust grain placed in the plasma sheath

We present a theory for potential distributions around a charged dust grain in a plasma with flowing ions. For this purpose, we account for absorption of ions by the grain surface and derive a kinetic ion density response for ion flow speed lying between the electron and ion thermal speeds. Poisson's equation is then solved to obtain the potential distribution close and far from the dust grain. It is found that at distances smaller than half the Debye radius, the potential remains spherically symmetric, while at large distances the potential becomes assymetric.     

Levitation and dynamics of a collection of dust particles in afully ionized plasma sheath

Examines the dynamics of a collection of charged dust particles in the plasma sheath above a large body in a fully ionized space plasma when the radius of the large body is much larger than the sheath thickness. The dust particles are charged by the plasma, and the forces on the dust particles are assumed to be from the electric field in the sheath and from gravitation only. These forces will often act in opposite directions and may balance, making dust suspension and collection possible. The dust particles are supplied by injection or by electrostatic levitation. The ability of the sheath to collect dust particles, will be optimal for a certain combination of gravitation and plasma and dust particle parameters. In a dense dust sheath, the charges on the dust particles contribute significantly to the total space charge, and collective effects become important. These effects will reduce the magnitude of the sheath electric field strength and the charge on the dust particles. As dust particles are collected, the dust sheath is stretched and the largest dust particles may drop out, because the sheath is no longer able to suspend them. In a tenuous dust sheath, the inner layer, from the surface and about one Debye length thick, will be unstable for dust particle motion, and dust will not collect there. In a dense dust sheath, collective effects will decrease the thickness of this inner dust-free layer, making dust collection closer to the surface possible. By linearization of the force and current equations, the necessary and sufficient conditions for a stable dust sheath are found. The authors consider conditions which resemble those of planetary system bodies, but the results may also be of relevance to some laboratory plasmas     

Screening of a charged dust particle within a nonlocal charging theory

We study the influence of the nonlocality of the electron energy distribution function on the dust particle charge screening in a two-component plasma of various inert gases and nitrogen at atmospheric pressure. For our analytical and numerical calculations, we have chosen the point sink model in the diffusion-drift approximation, which, in addition to the bulk production and loss of electrons and ions, also includes the heterogeneous processes of their absorption by a dust particle. We have established that the dust particle potential distribution in the problem under consideration is a superposition of three Debye exponentials with three different screening constants. The first constant practically coincides with the inverse Debye length. The second constant is determined by the inverse length travelled by the electrons and ions in the ambipolar diffusion process in the characteristic recombination time. The third constant coincides with the inverse characteristic distance of electron energy transfer through heat conduction in the characteristic time of electron energy establishment in the processes of heating by a beam of fast electrons and energy losses in elastic and inelastic collisions. We compare our numerical calculations of the screening constants with the analytical estimates obtained in the ambipolar diffusion approximation.     

Stopping of heavy ions in plasmas at strong coupling

Standard approaches to the energy loss of ions in plasmas like the dielectric linear response or the binary collision model are strictly valid only in the regimes where the plasma is close to ideal and the coupling between projectile-ion and the plasma target is sufficiently weak. In this review we explore the stopping power in regimes where these conditions are not met. Actually relevant fields of application are heavy ion driven inertial fusion and the cooling of beams of charged particles by electrons. The conventional linear mean-field treatments are extended by many-body methods and particle simulations to account for strong correlations between the particles and for nonlinear coupling. We report the following important results in connection with the stopping at strong coupling: The energy loss of an ion scales with its charge approximately like Z^1.5, the effective screening length depends on Z and is larger than the Debye length. Slow highly charged ions are surrounded by a cloud of electrons trapped by many body collisions. Quantum effects like the wave nature of the electrons and Pauli-blocking reduce the stopping power by mollifying the effective interactions.     

Interaction of charged dust particles in clouds of thermodynamically equilibrium charges

The solution of the Poisson-Boltzmann equation for a cloud of charges surrounding two charged dust particles treated as Debye atoms forming a Debye molecule is investigated numerically using Cassini coordinates. The electric force exerted on a dust particle by the other dust particle was determined by integrating the electrostatic pressure on the surface of the dust particle. It is shown that attractive forces appear when the following two conditions are satisfied. First, the Debye radius (corresponding to the electron density at half the mean distance between the dust particles) must be approximately equal to half the mean distance between the dust particles. Attraction between the dust particles emerges at a distance equal approximately to half the mean distance between the dust particles. Second, attraction takes place when like charges are concentrated predominantly on the dust particles. If the particles carry a small fraction of charge of the same polarity, repulsion between the particles takes place at all distances.     

Screening of the dust-particle charge in a plasma with an external ionization source

An asymptotic theory of the screening of the dust-particle charge in a plasma with an external ionization source has been developed. It has been shown analytically that the screening of the charge of a dust particle adsorbing the charge of charged plasma particles that fall on it is not generally described by the Debye theory. The screening radius is determined by the relation between the coefficients β_ei and β_L = 4πek _i (k _i is the ion mobility) of the electron-ion and Langevin recombinations, respectively. When β_L ? β _ei , the screening radius is much larger than the electron Debye radius. It has been shown that the contribution of the ion component of an isothermal plasma to screening is equal to the electron contribution if the coefficient of the electron-ion recombination is twice or more larger than the Langevin coefficient of the ion recombination, β_ei ≥ 2β_L.     

Broadening of carbon ionic lines in a low-temperature dense plasma

The broadening of the spectral lines of singly ionized carbon obtained in a plasma jet of a capillary discharge with an evaporating wall is studied in a wide range of electron concentrations ((6.5 × 10¹⁶)?(3.5 × 10¹⁹) cm^?3). With increasing plasma density, all the experimentally observed lines show a decrease in the half-width in comparison with the half-width calculated in the approximation of slight nonideality. It is experimentally established that a change in the character of the Stark broadening with increasing electron concentration is connected with a strong charge screening occurring when the distance between charged plasma particles decreases to ten diameters of the electron cloud of an emitting ion. Based on the experimentally determined applicability limits of the Griem formula for different energy states of the C II ion, a semiempirical expression for the spectral profile taking into account the Debye screening is proposed.     

Mechanism of diffusion of positively charged dust particles in a photoemission cell under microgravity conditions

The decay of a dusty plasma in a photoemission cell under microgravity conditions is investigated on the basis of the method of nonlocal moments. It is founds that plasma decay in space experiments occurs in accordance with the mechanism of free electron diffusion followed by dust particle drift. An analytic solution is found for the evolution of radial distributions of the dust particle concentration and the electric field under the experimental conditions. The effect of abnormally high temperatures of dust particles is considered. The effect of axial magnetic fields on the decay of dusty plasma is investigated. It is shown that the plasma decay in a magnetic field is governed by the ambipolar diffusion mechanism, the decay being prolonged up to 10³ s in a magnetic field on the order of 10³–10⁴ G in strength.     

On the charge of dust particles in a low-pressure gas discharge plasma

Self-consistent molecular-dynamics calculations of the charge of micron-size particles in a low-pressure gas-discharge plasma are performed. It is shown that charge exchange of ions on neutrals starts to affect the charge of dust particles at pressures corresponding to ion mean free paths much greater than the Debye radius. The computational results show that the potential of a particle depends nonmonotonically on the pressure and on the particle size.     

Energy loss of tens keV charged particles traveling in the hot dense carbon plasma

The energy loss of charged particles, including electrons, protons, and α-particles with tens keV initial energy E0, traveling in the hot dense carbon(C) plasma for densities from 2.281 to 22.81 g/cm3 and temperatures from 400 to 1500 eV is systematically and quantitatively studied by using the dimensional continuation method. The behaviors of different charged particles are readily distinguishable from each other. Firstly, because an ion is thousands times heavier than an electron, the penetration distance of the electron is much longer than that of proton and α-particle traveling in the plasma. Secondly, most energy of electron projectile with E0 100 keV deposits into the electron species of C plasma, while for the cases of proton and α-particle with E0 100 keV,about more than half energy transfers into the ion species of C plasma. A simple decreasing law of the penetration distance as a function of the plasma density is fitted, and different behaviors of each projectile particle can be clearly found from the fitted data.We believe that with the advanced progress of the present experimental technology, the findings shown here could be confirmed in ion-stopping experiments in the near future.     

Stress state of silver nanoparticles embedded in a silicate glass matrix investigated by HREM and EXAFS spectroscopy

Ag particles of 3.9 and 5.1 nm mean size in silicate glasses were produced by ion exchange and subsequent annealing at 480 and 600 ^°C. These thermal treatments may induce stresses in matrix and particles in addition to the well known effect of surface atoms because of the thermal expansion mismatch of both materials. Structural characterisation of the particles by high-resolution electron microscopy revealed a size-dependent lattice dilatation quite opposite to the so far observed lattice contraction of similar metal/glass composites. This result, confirmed by X-ray absorption spectroscopy at the Ag K-edge, is discussed in terms of an Ag-Ag bond length increase near the particle surface. The temperature-dependent EXAFS spectra (10-300 K) indicate an increased thermal expansion coefficient of the particles with an increased mean particle size calculated on the basis of an anharmonic Einstein model. With that the bond length increase can be explained. The results can be interpreted by a combination of both the particle size effects and the influence of the surrounding matrix. Received 30 November 2000