Problems of Dust Grains Charging to Negative Potentials

The presence of dust grains is a common phenomenon in the space environment. Grains can be charged by many different processes (e.g., photoemission, attachment of electrons/ions, the secondary emission, etc.). If the grain's surface potential becomes high enough, one can observe field emission of ions or electrons. We are trapping a single dust grain in a Paul trap, expose it to a low-energy electron beam, and investigate the evolution of its charge-to-mass ratio with respect to the energy of primary electron beam. We use micron-sized (D = 2–11 m) glass grains and charge them up to -300 V of surface potentials; it corresponds to the electric field strength of about 10⁸ V/m. Analysis of the charging/discharging processes has shown that (1) the effect of the field enhanced secondary emission is negligible in the case of insulators and (2) the effective work function for electron field emission from charged insulators is as low as 1 eV.     

An application of the dust grain charging model to determination of secondary electron spectra

Dust grains – objects of different shapes with a size distribution from micro to nanometers – are generally considered as a part of many space as well as laboratory plasmas. Among various dust charging processes, electron-induced secondary emission plays an important role in plasmas containing a noteworthy portion of high-energy electrons. Since a part of secondary electrons has not the energy high enough to overcome the surface potential barrier, the resulting grain charge is determined not only by the secondary emission yield (related to the grain material and size) but also by the secondary electron spectrum. We have developed a model of secondary electron emission from small dust grains. In the present contribution, we discuss the profile of a secondary emission yield that can be received from the model and the measured equilibrium grain charge, both as functions of an incident electron beam energy. A comparison of these quantities leads to an estimation of secondary electron spectra. We have found that: (1) the energy spectrum of secondary electrons does not change with the energy of primary electrons and (2) the energy spectrum depends on the target material being harder for gold and silver than for glass grains.     

Resistive drift instability and Rayleigh-Taylor instability in a dusty plasma

The resistive drift instability and the Rayleigh-Taylor instability are studied self-consistently in a magnetized inhomogeneous dusty plasma. The effect of grain charge fluctuations is taken into consideration. It is found that the presence of the dust grains in the plasma can significantly affect the resistive drift instability but less significantly the Rayleigh-Taylor instability. Further, the grain charge fluctuation has a tendency to stabilize both instabilities.     

Role of stochastic fluctuations in the charge on macroscopic particles in dusty plasmas

The currents which charge a macroscopic particle placed in a plasma consist of discrete charges; hence, the charge can undergo random fluctuations about its equilibrium value. These random fluctuations can be described by a simple model which, if the mechanisms for charging of macroscopic particles are known, makes it possible to determine the dependence of the temporal and amplitude characteristics of the fluctuations on the plasma parameters. This model can be used to study the effect of charge fluctuations on the dynamics of the macroscopic particles. The case of so-called plasma-dust crystals (i.e., highly ordered structures which develop because of strong interactions among macroscopic particles) in laboratory gaseous discharge plasmas is considered as an example. The molecular dynamics method shows that, under certain conditions, random fluctuations in the charge can effectively heat a system of macroscopic particles, thereby impeding the ordering process. Zh. éksp. Teor. Fiz. 115, 2067–2079 (June 1999)     

Thermal condensation mode in a dusty plasma

In the present work, the radiative condensation instability is investigated in the presence of dust charge fluctuations. We find that the charge variability of the grain reduces the growth rate of radiative mode only for fluctuation wavelength smaller or of the order of the Debye length and this reduction is not very large. Far from the Debye sphere, radiative mode can damp due to thermal conduction of electrons and ions     

Effect of electron emission on the charge and shielding of a dust grain in a plasma: A continuum theory

The continuum approximation is used to analyze the effect of electron emission from the surface of a spherical dust grain immersed in a plasma on the grain charge by assuming negligible ionization and recombination in the disturbed plasma region around the grain. A parameter is introduced that quantifies the emission intensity regardless of the emission mechanism (secondary, photoelectric, or thermionic emission). An analytical expression for the grain charge Z _d is derived, and a criterion for change in the charge sign is obtained. The case of thermionic emission is examined in some detail. It is shown that the long-distance asymptotic behavior of the grain potential follows the Coulomb law with a negative effective charge Z _eff, regardless of the sign of Z _d. Thus, the potential changes sign and has a minimum if Z _d > 0, which implies that attraction is possible between positively charged dust grains.     

Jeans-Buneman instability in a dusty plasma

A self consistent formulation of the Jeans instability of a dusty plasma with proper inclusion of charge dynamics is described. It is shown that charge fluctuations significantly affect the Jeans as well as the Buneman mode. For plasma particles (electrons and ions) in local thermal equilibrium, the Jeans lengthλ _J is given byλ _J≈λ _g F(R, ε, β/η), whereλ _g is the Debye length of the charged grains,R is the square of the ratio of the Jeans to the plasma frequency of the grains,ε is the square of the ratio of the Debye length of the grains and the plasma particles andβ/η is the ratio of the attachment to the decay frequency of the electronic charges to the grain surface. The functional form ofF is given in the text. Numerical investigation of the Jeans-Buneman mode for a two and three component plasma shows that the Jeans mode dominates atkλ _D≪1 (wherek is the wave number andλ _D is the Debye length of plasma particles), whereas atkλ _D≫1 only the Buneman mode operates. Charge fluctuations reduce the area of overlap of the two modes. Furthermore, in the absence of gravity, there exists a new, charge fluctuation induced unstable mode in a streaming dusty plasma. Astrophysical applications of the results are discussed.     

The Bohm criterion for a dusty plasma sheath

The formation of the sheath in a dusty plasma is investigated. The Bohm criterion is derived for two different cases: (a) when electrons are in thermodynamic equilibrium and dust grains provide the immobile, stationary background and (b) when both electrons and ions are in thermodynamic equilibrium and dust grains are moving. In the first case, Bohm criterion gets modified due to the fluctuation of the charge on the grain surface. In the second case, the collisional and Coulombic drag play important role in determining the Bohm criterion.     

The influence of ion bombardment on emission properties of small dust grains

Dust grains that are present in many plasma and vacuum systems and in the space usually carry a non-negligible charge. Their charging significantly depends on surface properties of the grain material. In cold plasma, charging is mainly given by electron attachment, nevertheless, when plasma becomes hot, other processes (secondary electron emission, field emission, etc.) take place. Emission properties of the grain surface could be modified by grain baking or by ion bombardment. Our study is carried out at the dust charging experiment dealing with a single dust grain electro-dynamically levitated in a 3D quadrupole trap. The grain can be exposed to the ion beam in the energy range of 100 eV–5 keV and to the electron beam in the energy range of 100 eV–10 keV. We have chosen He⁺ and Ar⁺ ions for the surface treatment and the observed influence on the surface properties is discussed in terms of secondary emission. A non-negligible shift of the secondary electron emission yield, as well as a change of energy distribution of secondary electrons, were measured after Ar⁺ bombardment. A preliminary study suggests that the effects of He⁺ and Ar⁺ are comparable.     

Low-frequency variable charge solitary waves in a collisionless dusty plasma with a Cairns-Gurevich ion velocity distribution

In this paper, the problem of large amplitude dust acoustic (DA) solitons has been addressed in a charge varying dusty plasma with ions following a Cairns-Gurevich distribution. Based on the orbit motion limited approach, the correct Cairns-Gurevich ion charging current is presented for the first time. The expression relating the variable dust charge to the plasma potential is given in terms of the Lambert function and we take advantage of this transcendental function to, carefully, analyse DA solitons in a charge varying dusty plasma with trapped nonthermal ions. Our results show that the spatial patterns of the variable charge solitary wave are significantly changed due to the presence of ion population modelled by the Cairns-Gurevich distribution. An addition of a small concentration of trapped nonthermal ions makes the solitary structure less spiky, grows the net negative charge residing on the dust grain surface, and contributes to the electron depletion. Finally, our investigation is extended to highlight the effect of the grain dust charge variation. We have shown that under certain conditions, the impact of dust charge fluctuation may furnish an alternate physical mechanism rasing anomalous dissipation, which becomes more strong and may predominate over the dispersion as the nonthermal character of ions following the Cairns-Gurevich distribution increases.     

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.     

Measurement of the charging of individual dust grains in a plasma

An experiment is described for investigating the charging of dust grains in a plasma. The apparatus is a double plasma device into which single dust grains are dropped from the top. The dust charge is detected and measured by a sensitive electrometer attached to a Faraday cup on the bottom. Experiments with electrons from the emissive filaments but without plasma indicate that the grains charge to approximately the filament potential for filament bias voltages smaller in absolute value than -70 V. The charge is of order 10⁶ electrons for SiC grains 30-150 μm in diameter. At higher bias voltage the charge is reduced due to secondary emission. The charge on grains increases with grain size and is nearly independent of the filament emission current. With plasma in the device, the grains charge both positively and negatively     

有互感和电源的介观耦合电路的量子涨落

通过正则变换和幺正变换的方法研究了有互感和电源存在的情况下的介观电容耦合电路的量子涨落.结果表明电荷和电流的量子涨落与电源无关;互感的有无对涨落的影响很大;适当选取回路中电器件的参数,可以控制耦合系数K对涨落的影响.并且,每个回路中电荷和电流的量子涨落是相互制约的.     

Shock Waves due to Grain-Charge Variation in Dusty Plasmas

Nonlinear electrostatic wave structures in plasmas containing variable-charge dust grains, Boltz-mann electrons, and inertial ions are investigated. The charge variation is assumed to be caused by electron and ion currents at the grains. It is found that intense shock waves can exist. The dissipation in such shock waves originate from the process of dust charging.     

Collective Grain Interactions II. Non‐linear Collective Drag Force

It is found that the collective effects operating at large distances from the grain surface can produce substantial scattering of the ion flux and create an additional collective drag force dominant for large grain densities. The consideration is restricted to large grain charges β = Z_de ²a /T_iλ_Di ? 1 and T_i /T_e ? 1 (–eZ_d being the grain charge in units of electron charge, a being the grain size, λ_Di being the ion Debye radius and T_e,i being electron and ion temperatures, respectively). For present dusty plasma experiments β ≈ 10–50, the large charges of grains are screened non‐linearly and the ion scattering creates non‐linear drag force. The present investigation considers effects of scattering by collective grain fields at large distances from the grains. It is found that the physical reason of the importance of collective drag force, calculated in this paper, is related to presence of weakly screened collective field of grains outside the non‐linear screening distance depending on grain densities. The amplitude of this collective fields of the grains is determined by non‐linear screening at non‐linear screening radius. It is shown that for dust densities of present experiments the collective drag force related to this scattering can be of the order of the non‐linear drag force caused by scattering inside the non‐linear screening radius or even larger. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Absence of an abrupt phase change from polycrystalline to amorphous in silicon with deposition temperature.

Using fluctuation electron microscopy, we have observed an increase in the mesoscopic spatial fluctuations in the diffracted intensity from vapor-deposited silicon thin films as a function of substrate temperature from the amorphous to polycrystalline regimes. We interpret this increase as an increase in paracrystalline medium-range order in the sample. A paracrystal consists of topologically crystalline grains in a disordered matrix; in this model the increase in ordering is caused by an increase in the grain size or density. Our observations are counter to the previous belief that the amorphous to polycrystalline transition is a discontinuous disorder-order phase transition.     

Influence of charging current fluctuations on the grain velocity distribution in weakly-ionized plasmas

The distribution function of dust particles immersed in a weakly-ionized plasma is calculated with regard to electron and ion absorption by grains and fluctuations of grain-charging currents. The dust-particle energy is shown to undergo abrupt changes due to specific velocity dependence of the grain friction coefficient and stochastic character of grain charging. Their effect can crucially influence the state of the grain. This model can give some indication concerning the possibility of structure formation and melting of a dusty crystal structure. The hysteresis in the transition from the one-peak distribution function to twin-peak distribution function can be observed with changing of plasma parameters.     

Self-Consistent Consideration of Fluctuations in Singlet Superconducting Phases with s and d Symmetry

We analyze the behavior of thermal fluctuations of the superconducting order parameter with extended s-wave and $${{d}_{{{{x}^{2}} - {{y}^{2}}}}}$$-wave symmetry. For this purpose, we develop a method of self-consistent consideration of the order parameter fluctuations and charge carrier scatterers by fluctuations of coupled electron pairs using the theory of functional integration. The study is performed based on the quasi-two-dimensional one-band model with attraction between electrons located at neighboring sites. We obtain the distribution functions of the phase fluctuation probabilities depending on temperature, charge carrier concentrations, and model parameters. It is shown that the phase of the order parameter in the superconducting region is coherent, and the density of states has a dip at the Fermi level. In approaching the incoherent region of the phase diagram, the dip in the density of states disappears simultaneously with the loss of phase coherence. At the same time, the order parameter amplitude averaged over fluctuations remains finite at any temperature and concentration of charge carriers. Our results show that the pseudogap state cannot be explained in the frames of this scenario.     

金属离子掺杂对TiO2/白云母纳米复合材料中TiO2的颗粒形态及相组成的影响

采用化学液相沉积法制备了系列未掺杂和掺杂不同金属离子的TiO2白云母纳米复合材料.利用扫描电子显微镜(SEM),x射线衍射(XRD)对其TiO2薄膜的TiO2颗粒形态和相组成进行了详细研究.结果表明,TiO2颗粒在15—50nm之间;除球形颗粒外,掺杂Mn2+,Zn2+的样品中还出现有金红石柱状颗粒.TiO2薄膜中相组成以锐钛矿、金红石共存为特征;掺杂金属离子对TiO2相组成的影响取决于金属离子的离子半径、电荷及配位体特征. 关键词： 金属离子掺杂 TiO2 颗粒形态 相组成     

Effect of granularity and inhomogeneity in excess conductivity of YBa2Cu3O7−δ+xBaTiO3 superconductor

Synthesis of polycrystalline YBCO+xBaTiO₃ (x=1.0, 2.5, 5.0) superconductor has been done and the effects of granularity and inhomogeneities due to inclusions of nano-BaTiO₃ in excess conductivity are reported in this work. The phase formation, texture and grain alignments were analyzed through XRD and SEM techniques. SEM results reveal that the grain size is reduced and morphology is improved with the incorporation of nano-BaTiO₃ particles. Superconducting order parameter fluctuation (SCOPF) studies on the electrical conductivity were investigated from the resistivity vs. temperature data in the experimental domain relatively above T_c. Log(Δσ) vs. log(ε) plots show that the 2D to 3D crossover temperature (T_LD) that demarcates dimensional nature of fluctuation inside the grains is influenced by BaTiO₃ incorporation in YBCO matrix. An upward shift of T_LD in the mean field region has been observed as a consequent dominance of 3D region with increase in 1 wt% BaTiO₃ in the composites as compared to higher inclusions. It has been analyzed that microscopic inhomogeneities produced as a result of diffusion of a fraction of Ti ions into the grains affect fluctuations in the excess conductive region. The interplay of microscopic inhomogeneities produced inside the grains and mesoscopic inhomogeneities in the grain boundaries on the excess conductivity has been explained in terms of thermal fluctuations for the composites.