Theoretical model for the effect of dust grains on self‐filamentation of a gaussian electromagnetic beam in a fully ionized plasma

A theoretical model for the effect of dust grains on the self‐filamentation of a Gaussian electromagnetic beam propagating in a fully ionized plasma has been developed by employing the energy balance of the plasma constituents, perturbed electron and ion concentrations, and temperature. In this model, neutral atom ionization, re‐integration and accumulation of electrons and ions, photoelectric emission of electrons from the surface of dust grains, as well as elastic and charging collisions have also been considered. The effective dielectric constant in the presence of dust grains has been constructed. The effect of temporal growth of dust grains on various plasma parameters for different values of the dust density has been explored. The variation of the beam width with the normalized channel of propagation has been observed for distinct dust densities and dust charge states. It is observed that the non‐linearity induced by the effective dielectric constant in the presence of dust grains increases the self‐filamentation of the beam, thus enhancing the effective critical power with the dust density. Some of the outcomes of our approach are in line with experimental observations. These outcomes may be useful for explaining space and laboratory plasma experiments as well as for future studies in complex plasmas.     

Linear propagation of dust acoustic modes in the presence of an electron beam

The physical and optical properties of plasmas are depended on dynamics of species in the discharge volume. Then, the presence of an electron beam, as a separate component, in a dusty plasma can modify the plasma structures through altering the discharge parameters. In this report, the linear propagation of acoustic modes in a collisionless dusty plasma contains electrons, ions and charged dust grains is investigated in the presence of an electron beam. Our analysis indicates that the electron beam can modify the dispersion relations of dust acoustic modes which resulted different data transportation in dusty plasmas. The obtained results are also examined for negative and positive charged dust grains with different number densities. The charge of dust grains represents an important role in the dynamics of the low frequency waves. Additionally, our findings reveal that the propagation of acoustic waves in dusty plasmas can be controlled by adjusting the electron number density of the beam and the cathode potential. Lastly, we obtian the destabilizing effects, originated from dust charge fluctuation, by reconsidering the dispersion relations of both dust acoustic modes.     

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.     

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.     

Metastable states of dust plasma

The free energy of three-component dust plasma has been calculated analytically based on the spherical model of an elementary electroneutral volume. It has been shown that metastable states of dust particles, ions, and simultaneously all plasma particles can exist for finite interparticle distances. These states can be attained due to spatial correlation of electrons, while some states can be attained due to the correlation of ions. A large charge of dust particles, high electron temperature, and a small fraction of the charge of the electrons compared to the total absolute charge of the plasma particles are important conditions for the existence of metastable states. A possible connection between the existence of metastable states of particles in the plasma and their agglomeration has been analyzed.     

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.     

Surface waves in strongly irradiated dusty plasmas

High-frequency surface waves at the interface between two dusty plasmas subject to radiation are considered. Ultraviolet radiation with energy flux larger than the photoelectric work function of the dust surface causes photoemission of electrons. The dust charge and the overall charge balance of the plasma are thus modified. The dispersion properties of the surface waves are investigated for three parameter regimes distinguished by the charging mechanisms in the two plasmas. It is shown that photoemission can significantly affect the plasma and the surface waves.     

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     

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.     

Kinetic simulations of argon dusty plasma afterglow including metastable atom kinetics

The afterglow of a dusty plasma of rf discharge in argon is simulated by the particle-in-cell-Monte Carlo collision (PIC-MCC) method. The experimental observation that heavy dust contamination of plasma leads to an anomalous increase in the electron density at the beginning of afterglow is explained by release of electrons from the dust surface. Under the assumption that the floating potential of particles is in equilibrium with plasma conditions, the fast cooling of electrons in afterglow plasma due to a rapid escape of hot electrons from the volume leads to a decrease in the magnitude of the floating potential and hence to a loss of charge by dust. The intensive desorption of electrons from nanoparticles is the origin of anomalous behavior of the electron density. At the next stage of afterglow, when the electrons become cool, the plasma decay is defined by ambipolar diffusion. The effect of metastable argon atoms is also considered. Additional ionization due to metastable atom collisions affects the electron temperature but does not change the behavior of the electron density qualitatively.     

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.     

Compressive and Rarefactive Waves in Dust Plasma with Non-thermal Ions

The governing equation of the dust fluid with non-thermal ions and variable dust charge on dust particles in hot dust plasmas is obtained. Both the compressive and rarefactive waves in this system are investigated. They can be determined by plasma parameters including the temperatures of dust fluid, ions and electrons, as well as the non-thermal parameter of ions, and the number densities of the dust particles, the ions and the electrons, etc.     

Dust in Plasma II. Effects of Secondary Electrons: Ionization and Surface Emission

In this second paper, the effect of secondary electrons on the charge and potential of a dust particle immersed in plasma has been studied. The processes of electron‐induced ionization and those of photo‐electron and secondary electron emission from the particle surface as a function of primary electron temperature have been taken into account. Starting from temperatures as low as 6 eV in an Ar plasma, ionization produces an extra ion flux to the dust surface comparable to that of the ion charge exchange effect. For what concerns the surface emission, results show that a transition from negative to positive dust charge/potential takes place, and that the transition regime is characterized by a non‐monotonic behavior of the electric potential around the particle. In the case of photoelectric emission, the dust charge and potential are monotonic decreasing functions of the electron temperature, while in the case of emission induced by primary electrons a minimum charge/potential is reached before they grow towards positive values. In no case multiple dust charge states have been observed due to the presence of the potential well attached to the particle surface. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Slowing down of charged particles in dusty plasmas with power‐law kappa‐distributions

We study the slowing down of a particle beam passing through the dusty plasma with power‐law κ‐distributions. Three plasma components, electrons, ions, and dust particles, can have a different κ‐parameter. By using Fokker‐Planck theory, the deceleration factor and slowing down time are derived and expressed by a hyper‐geometric κ‐function. Numerically, we study the slowing down property of an electron beam in the κ‐distributed dusty plasma. We show that the slowing down in the plasma depends strongly on the κ‐parameters of plasma components, and dust particles play a dominant role in the deceleration effects. We also show dependence of the slowing down on mass and charge of a dust particle in the kappa‐distributed plasma.     

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.     

Theory of mach cones in magnetized dusty plasmas with strongly correlated charged dust grains

A theory for the formation of Mach cones in a magnetized dusty plasma with strongly correlated charged dust grains has been presented. We use the electron and ion susceptibilities for weakly correlated magnetized electrons and ions as well as the strongly correlated unmagnetized dust grain susceptibilities which are obtained by means of the quasilocalized charge approximation and a generalized hydrodynamic model. The plasma dielectric response of the present system reveals the parametric regimes for which Mach cones in a strongly coupled laboratory dusty magnetoplasma can be formed. We suggest conducting experiments in radiofrequency dusty plasma discharges with superconducting magnets for verifying the theoretical prediction of Mach cones that is made herein.     

Electrodynamics and dispersion properties of a magnetoplasma containing elongated and rotating dust grains

The electrodynamics and dispersion properties of a magnetized dusty plasma containing elongated and rotating charged dust grains are examined. Starting from an appropriate Lagrangian for dust grains, a kinetic equation for the dust grain and the corresponding equations of motion are derived. Expressions for the dust charge and dust current densities are obtained with the finite size (the dipole moment) of elongated and rotating dust grains taken into account. These charge and current densities are combined with the Maxwell-Vlasov system of equations to derive dispersion relations for the electromagnetic and electrostatic waves in a dusty magnetoplasma. The dispersion relations are analyzed to demonstrate that the dust grain rotation introduces new classes of instabilities involving various low-frequency waves in a dusty magnetoplasma. Examples of various unstable low-frequency waves include the electron whistler, the dust whistler, dust cyclotron waves, AlfvÉn waves, electromagnetic ion-cyclotron waves, as well as lower-hybrid, electrostatic ion cyclotron, modified dust ion-acoustic waves, etc. Also found is a new type of unstable waves whose frequency is close to the dust grain rotation frequency. The present results should be useful in understanding the properties of low-frequency waves in cosmic and laboratory plasmas that are embedded in an external magnetic field and contain elongated and rotating charged dust grains.     

Statistic of a Gaussian beam from an arbitrary rough target in the single passage atmospheric turbulence

The extended Huygens-Fresnel principle and Goodman model was utilized for target surface to derive the mutual coherence function (MCF) of a Gaussian beam reflected from an arbitrary rough target in atmospheric turbulence. According to the MCF, expressions of the mean irradiance and average speckle size at the receiver were obtained. The analysis indicated that the mean intensity is closely related to the ratio of root mean square (rms) height to the lateral correlation length. In addition, the speckle size at the receiver is associated with turbulence strength, propagation distance and roughness of the target. The results can be reduced to the result of a Gaussian beam illuminating rough target and scattering from a target in free space.     

Collision and recombination driven instabilities in variable charged dusty plasmas

The dust-acoustic instability driven by recombination of electrons and ions on the surface of charged and variably-charged dust grains as well as by collisions in dusty plasmas with significant pressure of background neutrals have been theoretically investigated. The recombination driven instability is shown to be dominant in the long wavelength regime even in the presence of dust-neutral and ion-neutral collisions, while in the shorter wavelength regime, the dust-neutral collision is found to play a major role. In an earlier research work, the dust-neutral collision was neglected in comparison to the effect due to the recombination for estimating the dust-acoustic instability; later the other report shows that the recombination effect is negligible in the presence of dust-neutral collisions. In line of this present situation our investigation revealed that the recombination is more important than dust-neutral collisions in laboratory plasma and fusion plasma, while the dust-neutral collision frequency is dominant in the interstellar plasmas. The effects of ion and dust densities and ion streaming on the recombination and collision driven mode in parameter regimes relevant for many experimental studies on dusty plasmas have also been calculated.     

Fluctuations of the charge on a dust grain in a plasma

A dust grain in a plasma acquires an electric charge by collecting electron and ion currents. These currents consist of discrete charges, causing the charge to fluctuate around an equilibrium value 〈Q〉. Electrons and ions are collected at random intervals and in a random sequence, with probabilities that depend on the grain's potential. We developed a model for these probabilities and implemented it in a numerical simulation of the collection of individual ions and electrons, yielding a time series Q(t) for the grain's charge. Electron emission from the grain is not included, although it could be added easily to our method. We obtained the power spectrum and the RMS fluctuation level, as well as the distribution function of the charge. Most of the power in the spectrum lies at frequencies much lower than 1/τ, the inverse charging time. The RMS fractional fluctuation level varies as 0.5 |〈N〉|^-1/2, where 〈N〉=〈Q〉/e is the average number of electron charges on the grain. This inverse square-root scaling means that fluctuations are most important for small grains. We also show that very small grains can experience fluctuations to neutral and positive polarities, even in the absence of electron emission