Instabilities in Yukawa Liquids

A strongly coupled Yukawa liquid is a system of charged particles which interact via a screened Coulomb interaction and in which the electrostatic energy between neighboring particles is larger than their thermal energy but not large enough for crystallization. Various plasma systems including ultracold neutral plasmas and complex (dusty) plasmas can exist in this strongly coupled liquid phase.Here we investigate instabilities driven by the relative streaming of plasma components in three‐dimensional Yukawa liquids with a focus on complex plasmas. This includes a dust acoustic instability driven by weakly coupled ions streaming through the dust liquid, and a dust‐dust instability driven by the counter‐streaming of strongly coupled dust grains. Compared to the Vlasov behavior we find there can be a substantial modification of the unstable wavenumber spectrum due to strong coupling effects (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ion-Temperature-Gradient-Driven Modes with Nonthermal Electron Distributions in Bi-ion Dusty Magnetoplasma

The effect of nonthermal distributions of electrons on ion-temperature-gradient (ITG)-driven drift modes in the presence of tiny dust particles for bi-ion magneto plasmas is investigated. The dynamics of bi-ions and dust particles is considered for the study of low-frequency (less than the gyrofrequencies of dust and ions) ITG mode. A new dispersion relation is derived and analyzed numerically as well as analytically. Three different distributions for nonthermal electrons (Kappa, q, and Cairns distribution) are used. It is found that the presence of nonthermal electrons in bi-ion dusty magnetoplasma reduces the growth rate of the ITG instability. These results should be useful for laboratory and space plasmas where nonthermal electrons and dust is always present.     

Suspended Particles and the Gravitational Instability of Rotating Magnetised Medium

The effect of uniform rotation on the self gravitational instability of an infinite homogeneous magnetised gas particle medium in the presence of suspended particles is investigated. The equations of the problem are linearized and the general dispersion relation for such system is obtained. The rotation is assumed along two different directions and separate dispersion relation for each case is obtained. The dispersion relation for propagation parallel and perpendicular to the uniform magnetic field along with rotation is derived. The effect of suspended particles on the different modes of propagation is investigated. It is found that in presence of suspended particles, magnetic field, rotation and viscosity, Jeans' criterion determines the condition of gravitational instability of gas-particle medium.     

Jeans stability of dusty space plasmas

The Jeans stability of dusty plasmas is re-considered. In contrast to a gas, a dusty plasma can support a plethora of wave modes each potentially able to impart to the dust particles the randomising energy necessary to avoid Jeans collapse on some length scale. Consequently, the analysis of the stability to Jeans collapse is many-fold more complex in a dusty plasma than it is for a charge-neutral gas. After recalling some of the fundamental ideas related to the ordinary Jeans instability in neutral gases, we extend the discussion to plasmas containing charged dust grains. Besides the usual Jeans criterion based upon thermal agitation, we consider two other ways of countering the gravitational collapse: (i) via the excitation of dust-acoustic modes and (ii) via a novel Alfvén-Jeans instability, where perturbations of the dust mass-loaded magnetic field counter the effects of self-gravitation. These two mechanisms yield different minimum threshold length scales for the onset of instability/condensation. It is pointed out that for the study of the Jeans instability produced by density enhancements induced in the plasma by the presence of normal wave modes, even more prohibitive plasma size constraints must necessarily be satisfied.     

Spherically symmetric free fall collapse

The general dynamical equations for spherical gravitational collapse are derived by introducing the eigenvalue of the conformal Weyl tensor in the 2-2 component of the Einstein tensor and assuming the material content of the models to be a perfect fluid. Since this eigenvalue is coupled always with the material energy density, it has been interpreted as theenergy density of the free gravitational field whose presence is related with anisotropy and inhomogeneity. As a particular case, the collapse of a spherically symmetric dust (zero pressure) with vanishing radial acceleration (free fall collapse) is discussed. It is shown that the model is inhomogeneous with non-vanishing shear of the congruence of world lines of the dust particles. The model contains gravitational radiation by Szekere’s criterion since both shear invariant and the spatial gradient of density are non-vanishing. This is in contrast to the Oppenheimer-Synder model for which both the above mentioned characteristics are absent. A particular solution which is anisotropic and inhomogeneous has been given to prove the emission of gravitational radiation by the freely falling dust and in this case the energy density of the free gravitational field contains a typeN term superposed on the coulombian field.     

Nonlinear analytical calculation of the equilibrium shape of a charged drop uniformly accelerated in an electrostatic field

An analytical asymptotic expression for the equilibrium shape of a charged drop of an ideal incompressible conducting liquid uniformly accelerated in collinear electrostatic and gravitational fields is derived in an approximation quadratic with respect to the deviation of the equilibrium shape of the drop from a sphere. It is found that the equilibrium shape of the drop is close to a prolate spheroid when its self-charge and the external electric field strength are far from their values critical in terms of instability against the self-charge and induced charge. This spheroid experiences an insignificant pear-shaped distortion even when the charge of the drop and the electrostatic field strength are high.     

Multi-dimensional instability of electrostatic solitary waves in a warm multi-ion dust plasma

Study of dust ion acoustic waves in a magnetized dusty plasmas composed of negatively or positively charged static dust, positive and negative ions, as well as kappa distribution electrons is presented. The Zakharov–Kuznetsov (ZK) equation is derived via reductive perturbation technique. The solitary wave solution of ZK equation is given and the multi-dimensional instability of these solitary waves is investigated via small k perturbation method. The instability criterion and growth rate relying on obliqueness, superthermality, positive ion thermal pressure, relative ion number density, magnetic field strength, and direction cosines are discussed for five cases. The results are beneficial to understand different nonlinear characteristics of unstable electrostatic disturbances in laboratory and space plasmas.     

Studies of the dynamic behaviour of charged dust particles in high electric fields using laser Doppler velocimetry

As a preliminary study for the collection of dust particles in an electrostatic precipitator, laser Doppler velocimetry has been used to measure the velocity of small dust particles charged in the high electric field of a model electrostatic precipitator. A differential optical system is adopted for the velocimeter. The period-measuring system is used to analyse Doppler beat signals and to obtain velocity data from them. By means of the laser Doppler velocimeter, the dynamic behaviour of the velocity and direction of moving dust particles is fully revealed as a function of the applied electric voltage in the entire collecting space of the model electrostatic precipitator, and is shown in vectorial flow diagrams of particle velocity.     

Electrostatic force of dust deposition originating from contact between particles and photovoltaic glass

Charged photovoltaic glass produces an electrostatic field. The electrostatic field exerts an electrostatic force on dust particles, thus making more dust particles deposited on the glass. In this paper, the contact electrification between the deposited dust particles and the photovoltaic glass is studied. Meanwhile, the surface charge density model of the photovoltaic glass and the electrostatic force of charged particles are analyzed. The results show that with the increasing of the particle impact speed and the inclination angle of the photovoltaic panel, the charges on particles increase to different degrees.Under a given condition, the electrostatic forces acting on the charged particles at different positions above the glass plate form a bell-shaped distribution at a macro level, and present a maximum value in the center of the plate. As the distance between the particle and the charged glass decreases, the electrostatic force exerted on the particle increases significantly and fluctuates greatly. However, its mean value is still higher than the force caused by gravity and the adhesion force,reported by some studies. Therefore, we suggest that photovoltaic glass panels used in the severe wind-sand environment should be made of an anti-static transparent material, which can lessen the dust particles accumulated on the panels.     

On the instability against the surface charge of a liquid meniscus at the end of a capillary

The subject of consideration is instability of the flat meniscus of a viscous liquid at the end of a capillary in the gravitational field and an electrostatic field when the symmetry axis of the capillary is arbitrarily oriented relative to the direction of free-fall acceleration. It is shown that, if the electrostatic field strength is high, the development of meniscus instability does not depend on the orientation of the capillary. The instability growth rate versus wavenumber dependence for annular waves of different types on the meniscus surface is found to be nonmonotonic.     

Simulation of Dust Particle Trajectories in an Electrostatic Probe with the Purpose of Increasing Its Efficiency

Formation of dust particles and clusters is observed in almost all modern fusion devices. Accumulation of dust in next-generation thermonuclear installations can significantly affect plasma parameters and lead to accumulation of unacceptably large amounts of tritium. The use of a specially developed electrostatic probe is planned in the international thermonuclear experimental reactor ITER to collect dust for further analysis. The article describes a numerical model of movement of dust particles in an electrostatic probe. Dust particle trajectories inside the probe are analyzed. Several electrostatic probe design modifications are proposed on the basis of the analysis in order to increase the efficiency of dust collection.     

Large amplitude ion-acoustic double layers in a plasma havingvariable-charge dust grain particles

The dust grain charging effect on large amplitude ion-acoustic double layers in a dusty plasma are investigated by the numerical calculation. The nonlinear structures of ion-acoustic double layers are examined, showing that the characteristics of the double layer sensitively depend on the dust charging effect, the influence of the ion temperature, the electrostatic potential, and the Mach number. The flow of the plasma current to the surface of dust particles increases the dust charge numbers. The effect of the ion temperature decreases the propagation speed of the ion-acoustic double layers and decreases the dust charge numbers. It is found that rarefactive double layers can propagate in this system. New findings of large amplitude ion-acoustic double layers with the dust charging effect and finite ion temperature in a dusty plasma are predicted     

Twisted electrostatic waves in a self‐gravitating dusty plasma

A generalized response (dielectric) function for twisted electrostatic waves is derived for an un‐magnetized self‐gravitating thermal dusty plasma, whose constituents are the Boltzmann‐distributed electrons and positive ions in the presence of negatively charged micrometre‐sized massive dust particulates. For this purpose, a set of Vlasov–Poisson coupled equations is solved along with the perturbed Laguerre–Gauss distribution function, as well as the electrostatic and gravitational potentials in the limit of paraxial approximation. For plane wave solution, the wavefronts of the dust‐acoustic (DA ) wave are assumed to have a constant phase with electric and gravitational field lines propagating straight along the propagation axis. On the other hand, non‐planar wave solutions show helical (twisted) wavefronts, in which field lines spiral around the propagation axis owing to the azimuthal velocity component to account for the finite orbital angular momentum (OAM ) states. The dispersion relation and damping rate for twisted DA waves are studied both analytically and numerically. It is shown that finite OAM states, the dust to electron temperature ratio, and dust self‐gravitation effects significantly affect the linear dispersion and Landau damping frequencies. In particular, the phase speed of twisted DA waves is reduced with the variation of the twist parameter η (= k /lq_ϕ ), dust concentration δ (= n_{d 0}/n_{i 0}), and dust self‐gravitation α (= ω_Jd /ω_pd ). The relevance of our findings to interstellar dust clouds is also discussed for micrometre‐sized massive dust grains.     

Jeans Instability of Self Gravitating Dust Cloud in Presence of Effective Electrostatic Pressure

The role of viscosity coefficient (η'), coulomb coupling parameter (Γ) and dust mass on the growth of jeans mode is investigated in strongly coupled dusty plasma using equations of Generalized Hydrodynamics (GH) Model. The novel aspect of this work is that the force arising due to electrostatic pressure caused by grain grain interaction has been included in the dynamics of dust particles. This force is found to play a significant role in counter balancing the self gravity effect, thereby reducing the growth rate of jeans instability. The present work may provide more physical insight in understanding the mechanisms behind formation of planetesimals, stars etc.     

Some properties of the gravitational fields of a hydrodynamical fluid and dust

Conditions are obtained on the four velocity of the particles of a medium in the gravitational fields of a hydrodynamical fluid and dust, and the nature of the motion of the medium in these fields is investigated. It is shown that the gravitational fields of a hydrodynamical fluid and dust do not admit conformal mapping onto Einstein spaces which are not conformally flat spaces (spaces of constant curvature).     

The Kadomtsev-Petviashvili equation for dust ion-acoustic solitons in pair-ion plasmas

Using the reductive perturbation method,we have derived the Kadomtsev-Petviashvili(KP) equation to study the nonlinear properties of electrostatic collisionless dust ion-acoustic solitons in pair-ion(p-i) plasmas.We have chosen the fluid model for the positive ions,the negative ions,and a fraction of static charged(both positively and negatively) dust particles.Numerical solutions of these dust ion-acoustic solitons are plotted and their characteristics are discussed.It is found that only the amplitudes of the electrostatic dust ion-acoustic solitons vary when the dust is introduced in the pair-ion plasma.It is also noticed that the amplitude and the width of these solitons both vary when the thermal energy of the positive or negative ions is varied.It is shown that potential hump structures are formed when the temperature of the negative ions is higher than that of the positive ions,and potential dip structures are observed when the temperature of the positive ions supersedes that of the negative ions.As the pair-ion plasma mimics the electron-positron plasma,thus our results might be helpful in understanding the nonlinear dust ion acoustic solitary waves in super dense astronomical bodies.     

Kadomtsev–Petviashvili equation for dust ion-acoustic solitons in pair-ion plasmas

Using the reductive perturbation method, we have derived the Kadomtsev-Petviashvili (KP) equation to study the nonlinear properties of electrostatic collisionless dust ion-acoustic solitons in the pair-ion (p-i) plasmas. We have chosen the fluid model for the positive ions, the negative ions, and a fraction of static charged (both positively and negatively) dust particles. Numerical solutions of these dust ion-acoustic solitons are plotted and their characteristics are discussed. It is found that only the amplitudes of the electrostatic dust ion-acoustic solitons vary when the dust is introduced in the pair-ion plasma. It is also noticed that the amplitude and the width of these solitons both vary when the thermal energy of the positive or negative ions is varied. It is shown that potential hump structures are formed when the temperature of the negative ions is higher than that of the positive ions, and potential dip structures are observed when the temperature of the positive ions supersedes that of the negative ions. As the pair-ion plasma mimics the electron-positron plasma, thus our results might be helpful in understanding the nonlinear dust ion acoustic solitary waves in super dense astronomical bodies.     

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.