Modeling of voids in colloidal plasmas

Dust-void formation in a dc glow discharge

Experimental investigations of dusty plasma parameters of a dc glow discharge were performed in a vertically oriented discharge tube. Under certain conditions, dust-free regions (voids) were formed in the center of the dust particle clouds that levitated in the strong electric field of a stratified positive column. A model for radial distribution of dusty plasma parameters of a dc glow discharge in inert gases was developed. The behavior of void formation was investigated for different discharge conditions (type of gas, discharge pressure, and discharge current) and dust particle parameters (particle radii and particle total number). It was shown that it is the ion drag force radial component that leads to the formation of voids. Both experimental and calculated results show that the higher the discharge current the wider dust-free region (void). The calculations also show that more pronounced voids are formed for dust particles with larger radii and under lower gas pressures.

Simulating the dynamics of complex plasmas

Complex plasmas are low-temperature plasmas that contain micrometer-size particles in addition to the neutral gas particles and the ions and electrons that make up the plasma. The microparticles interact strongly and display a wealth of collective effects. Here we report on linked numerical simulations that reproduce many of the experimental results of complex plasmas. We model a capacitively coupled plasma with a fluid code written for the commercial package comsol. The output of this model is used to calculate forces on microparticles. The microparticles are modeled using the molecular dynamics package lammps, which we extended to include the forces from the plasma. Using this method, we are able to reproduce void formation, the separation of particles of different sizes into layers, lane formation, vortex formation, and other effects.

Sheath structure and formation of dust voids in cylindrical plasma discharges

Using a self-consistent two-dimensional fluid model the structure of the plasma sheath in a cylindrical system is investigated. The results show that there is a bumping potential in the central axis resulting in the larger outward directing ion drag force with respect to the opposite electric field force. And the process of the formation of dust voids is studied in the sheath by molecular-dynamics simulation.

Successive generations of dust in complex plasmas: a cyclic phenomenon in the void region

Dust formation and growth in plasmas are in most cases continuous cyclic phenomena. We show that the growth of new dust generations takes place in a dust-free region, usually called a void, in the dust cloud. The three-step process of new dust generation is detailed thanks to the correlation between electrical, optical, and ex situ diagnostics. The strong inhomogeneity of both the plasma and the dust cloud during this process is underlined.

Obliquely propagating dust-density waves

Self-excited dust-density waves are experimentally studied in a dusty plasma under microgravity. Two types of waves are observed: a mode inside the dust volume propagating in the direction of the ion flow and another mode propagating obliquely at the boundary between the dusty plasma and the space charge sheath. The dominance of oblique modes can be described in the frame of a fluid model. It is shown that the results fom the fluid model agree remarkably well with a kinetic electrostatic model of Rosenberg [J. Vac. Sci. Technol. A 14, 631 (1996)]. In the experiment, the instability is quenched by increasing the gas pressure or decreasing the dust density. The critical pressure and dust density are well described by the models.

Multiple void formation in plasmas containing multispecies charged grains

Self-organized separation of charged-dust species in two-dimensional dusty plasmas is studied by means of molecular-dynamics simulation. The multispecies dust grains, interacting through a screened Coulomb potential with a long-range attractive component, are confined by an external quadratic potential and subjected to a radially outward ion drag force. It is found that, in general, the species are spatially separated by bandlike dust-free (or void) regions, and grains of the same species tend to populate a common shell. At large ion drag and/or large plasma screening, a central disklike void as well as concentric bandlike voids separating the different species appear. Because of the outward drag and the attractive component of the dust-dust interaction forces, highly asymmetrical states consisting of species-separated dust clumps can also exist despite the fact that all the forces are either radial or central.

Dust transport in a magnetized radio-frequency discharge under microgravity conditions

Dust is found in plasmas used in industrial applications, such as microelectronics and solar cell manufacturing, in fusion plasmas, where it is usually the result of plasma-wall interactions, and in plasmas in space, such as planetary atmospheres, cometary tails, planetary rings, interstellar molecular clouds, and star and planet formation regions. In plasma applications, magnetic fields are occasionally used, mainly to confine the plasma. In space, however, magnetic fields are very often present and they may strongly influence the behavior of dusty plasma, for instance in the formation of stars and planets. We extended a fully self-consistent two-dimensional fluid model for radio-frequency discharges by adding a homogeneous axial magnetic field and the effect it has on the transport of plasma species in a low-temperature dusty discharge. We show that the magnetic field has an important effect on the (ambipolar) diffusion of ions and electrons in the bulk of the discharge. This causes an important change in the force balance of the dust particles and in the time scales of the formation of a dust-free void. Finally, we compare the parameters of the modeled discharge with the parameters of a planet formation region around a young stellar object (YSO). We conclude that a magnetic field in both low-temperature rf discharges under micro-gravity conditions and dusty plasmas around YSO's has an important effect on the transport of dust and must be important for the formation of planets and stars.

Dust-free regions around Langmuir probes in complex plasmas under microgravity

Dust-free regions around a Langmuir probe are studied in a complex plasma under microgravity. The dust particles settle in the presheath of the probe, where an equilibrium of the electric field force and the ion-drag force is established. The size and shape of the dust cloud are discussed with simple models. A more sophisticated presheath model is solved numerically to analyze the acting forces and the equilibrium position of the dust. The formation of distinct particle layers in the dust shell can be explained by the force gradients of the effective potential well.

Vortices in dust clouds under microgravity: A simple explanation

Clouds of dust particles in radio frequency discharges often show a periodic vortexlike motion, especially near the edges of the electrodes or near the tip of an electrostatic probe. These vortices often last as long as the discharge is powered. In a previous paper we have followed a small number of individual dust particles in a discharge under microgravity conditions, moving under the influence of forces computed by means of a self-consistent two-dimensional hydrodynamic model, and interacting via a screened Coulomb potential. The resulting motion showed the vortexlike rotation. In this paper we discuss this phenomenon in more detail, using a simplified model with harmonic forces, but extending the simulations to three dimensions. Stable vortices are observed, which show a more chaotic behavior than in the two-dimensional situation. Particles frequently jump up and down between two counterrotating vortices. The generation of the vortices can be ascribed to a nonzero rotation of the net global force vector field, which is the sum of the ion drag force, the electric force, and the thermophoretic force in case of the experiments. Comparison of experimental data with simulations using a model potential may open a way to unravel the forces inside a cloud of dust particles.

Modeling the effect of dust on the plasma parameters in a dusty argon discharge under microgravity

A dusty radio-frequency argon discharge is simulated with the use of a two-dimensional fluid model. In the model, discharge quantities, such as the fluxes, densities, and electric field are calculated self-consistently. The charge and density of the dust are calculated with an iterative method. During the transport of the dust, its charge is kept constant in time. The dust influences the electric potential distribution through its charge and the density of the plasma through recombination of positive ions and electrons on its surface. Results are presented for situations in which the dust significantly changes the discharge characteristics, both by a strong reduction of the electron density and by altering the electric potential by its charge. Simulations for dust particles having a radius of 7.5 microm show that a double space charge layer is created around the sharp boundary of the dust crystal. A central dust-free region (void) is created by the ion drag force. Inside this void a strong increase of the production of argon metastables is found. This phenomenon is in agreement with experimental observations, where an enhanced light emission is seen inside the void.

Modeling of self-excited dust vortices in complex plasmas under microgravity

A two-dimensional hydrodynamic model for a dusty argon plasma in which the plasma and dust parameters are solved self-consistently has been supplemented with a separate dust particle tracing module to study the behavior of dust vortices. These coherent vortices appear in plasma crystal experiments performed under microgravity conditions. The nonconservative total force exerted by the discharge on the dust particles is responsible for the generation of the vortices. The contribution of the thermophoretic force driven by the gas temperature gradient plays an insignificant role in the generation of the vortices, even when the gas heating via the dust particles is taken into account. The forces related to the electric field, including the ion drag force, are dominant.

Fokker-Planck equation for Boltzmann-type and active particles: transfer probability approach

A Fokker-Planck equation with velocity-dependent coefficients is considered for various isotropic systems on the basis of probability transition (PT) approach. This method provides a self-consistent and universal description of friction and diffusion for Brownian particles. Renormalization of the friction coefficient is shown to occur for two-dimensional and three-dimensional cases, due to the tensorial character of diffusion. The specific forms of PT are calculated for Boltzmann-type and absorption-type collisions (the latter are typical in dusty plasmas and some other systems). The validity of the Einstein's relation for Boltzmann-type collisions is analyzed for the velocity-dependent friction and diffusion coefficients. For Boltzmann-type collisions in the region of very high grain velocity as well as it is always for non-Boltzmann collisions, such as, absorption collisions, the Einstein relation is violated, although some other relations (determined by the structure of PT) can exist. The generalized friction force is investigated in dusty plasmas in the framework of the PT approach. The relation among this force, the negative collecting friction force, and scattering and collecting drag forces is established. The concept of probability transition is used to describe motion of active particles in an ambient medium. On basis of the physical arguments, the PT for a simple model of the active particle is constructed and the coefficients of the relevant Fokker-Planck equation are found. The stationary solution of this equation is typical for the simplest self-organized molecular machines.

Nonlinear theory of void formation in colloidal plasmas

A nonlinear time-dependent model for void formation in colloidal plasmas is proposed. For experimentally relevant initial conditions, the model describes the nonlinear evolution of a zero-frequency linear instability that grows rapidly in the nonlinear regime and subsequently saturates to form a void. A number of features of the model are consistent with experimental observations under laboratory and microgravity conditions.

Vibrational modes in plasma crystals due to nonlinear temperature distribution in gas discharge plasmas

It is shown that a nonlinear temperature distribution in gas discharge plasma leads to a specific low-frequency mode of a quasi-two-dimensional plasma crystal. Linear dispersion characteristics of the mode are obtained. The characteristics of the mode can depend strongly on the temperature gradients and therefore can be effectively controlled by the experimental conditions.

Ion drag force in complex plasmas

The problem of calculating the ion drag force in complex plasmas is considered. It is shown that the standard theory of Coulomb scattering usually fails for the ion-dust elastic collisions. A simple approach to extend this theory is proposed. This leads to a considerable enhancement in the ion-dust elastic scattering cross section and, hence, increases the ion drag force in comparison with the previous analytical results. Analysis shows that the ion drag usually exceeds the electrostatic force in the limit of weak electric field. We suggest that this is the cause of the central "void" observed in microgravity complex plasma experiments.