Numerical simulations of ion and electron transport in a low-temperature dusty plasma

Charged particle transport and kinetic processes in a low-temperature dusty plasma are numerically simulated. Dust grains are represented as spheres with a given radius. The self-consistent electric field in the plasma surrounding a charged dust grain is calculated taking into account the perturbations of plasma quasineutrality near the grains. It is shown that applying an external electric field leads to a rearrangement of the plasma space charge and a break of the spherical symmetry of the electron and ion density distributions around the grain. The mutual influence of two identical charged dust grains is considered, and the energy of the electrostatic interaction between the grains is calculated. It is shown that this energy has a minimum at a certain finite distance between the grains.     

Nonlinear Wave Structures and Plasma−Dust Effects in the Earth’s Atmosphere

The interaction of charged dust grains with nonlinear vortical structures in the Earth’s atmosphere is analyzed. Certain aspects of the atmosphere?ionosphere interaction, in particular, mechanisms for the appearance of dust grains at ionospheric altitudes, are discussed. It is shown that, at certain altitudes, there are regions in the wavenumber space in which conditions leading to the excitation of acoustic?gravity waves are satisfied. The interaction of nonlinear acoustic?gravity waves with dust grains of meteoric origin at ionospheric altitudes, which leads to the mixing and redistribution of dust grains over the region where vortices exist, is investigated. The possibility of formation of vertical and horizontal dust flows in dusty ionospheric plasma as a result of modulational instability is analyzed. The dynamics of dust grains in dust devils frequently arising in the atmosphere above well-heated surfaces is modeled. The vortical structure of such a dust devil is characterized by a reduced pressure in the center, which facilitates the lifting of small dust grains from the surface. The formulated model is used to calculate the trajectories of dust grains in dust devils with allowance for the influence of the electric field generated in the vortex by colliding dust grains. The calculations show that dust devils play an important role in the transport of dust grains.     

Behavior of a dust grain in the double layer of an electric probe in a gas-discharge plasma

Equations for the motion of an individual dust grain in the double layer of a negatively charged cylindrical probe in a glow discharge plasma are derived and solved numerically. The distribution of the electric potential near the probe is determined, and the grain charge is calculated as a function of the distance from the probe for different probe potentials. The trajectories of grains with different initial energies are traced. An analysis of the grain trajectories shows that, at a certain distance from the probe, high-energy grains may be recharged; i.e., the grain charge may change sign. The grains are found to have no direct effect on the probe current in a dusty plasma of a glow discharge.     

Potential of a test charge in a dust-electron plasma

The potential of a slowly moving test charge in a positive-dust-electron plasma is calculated taking into account dust grain charge fluctuations, as well as collisions between neutral atoms and electrons and dust grains. The results should be useful for understanding the shielding in a dusty plasma sheath with levitated grains.     

Wave processes during the interaction of the Earth’s magnetotail with dusty plasma near the lunar surface

The wave processes that take place under the interaction of the Earth’s magnetosphere with dusty plasma near the lunar surface are considered. It is shown that the waves can be excited for the photoelectron parameters corresponding to the quantum yield of the lunar regolith reported by Willis et al. [Photon and Particle Interactions with Surfaces in Space, Ed. by R. J. L. Grard (Reidel, Dordrecht, 1973), p. 389]. Ion-acoustic waves are excited in the regions of the transient magnetic and/or boundary magnetospheric layers due to the onset of linear hydrodynamic instability, whereas dust-acoustic waves are generated due to the onset of linear kinetic instability in the entire region of magnetotail interaction with dusty plasma near the Moon. In both cases, instability is caused by the relative motion of the magnetospheric ions and charged dust grains. The dynamics of the development of ion-acoustic and dust-acoustic turbulence is investigated. Ion-acoustic turbulence is described in terms of strong turbulence theory, while dust-acoustic turbulence is described in terms of weak turbulence theory. The energy density of oscillations, the effective collision frequencies, and the electric fields arising in the system are determined for both ion-acoustic and dust-acoustic turbulences. It is shown that the development of ion-acoustic turbulence in the dusty plasma system near the Moon can lead to the generation of electric fields that are somewhat weaker than those arising near the lunar surface due to the charging of the Moon’s surface under the action of solar radiation, but still sufficiently strong to affect the electric field pattern above the Moon. The obtained effective collision frequencies should be taken into consideration when deriving hydrodynamic equations for dusty plasma ions with allowance for turbulent plasma heating.     

Ion-acoustic solitons in dusty plasma

The dynamics of dust ion-acoustic solitons is analyzed in a wide range of dusty plasma parameters. The cases of both a positive dust grain charge arising due to the photoelectric effect caused by intense electromagnetic radiation and a negative grain charge established in the absence of electromagnetic radiation are considered. The ranges of plasma parameters and Mach numbers in which ??conservative?? (nondissipative) solitons can exist are determined. It is shown that, in dusty plasma with negatively charged dust grains, both compression and rarefaction solitons can propagate, whereas in plasma with positively charged dust grains, only compression solitons can exist. The evolution of soliton-like compression and rarefaction perturbations is studied by numerically solving the hydrodynamic equations for ions and dust grains, as well as the equation for dust grain charging. The main dissipation mechanisms, such as grain charging, ion absorption by dust grains, momentum exchange between ions and dust grains, and ion-neutral collisions are taken into account. It is shown that the amplitudes of soliton-like compression and rarefaction perturbations decrease in the course of their evolution and their velocities (the Mach numbers) decrease monotonically in time. At any instant of time, the shape of an evolving soliton-like perturbation coincides with the shape of a conservative soliton corresponding to the current value of the Mach number. It is shown that, after the interaction between any types of soliton-like perturbations, their velocities and shapes are restored (with a certain phase shift) to those of the corresponding perturbations propagating without interaction; i.e., they are in fact weakly dissipative solitons.     

Formation of quasi-two-dimensional dust structures in an external electric field

Conditions are considered under which quasi-two-dimensional extended structures are formed consisting of charged dust grains that are suspended in a gravitational field by an external electric field. Formulas are derived that describe the relationships between the parameters of the intergrain interaction potential, the number of dust grains, and the gradients of the linear electric field of the device. A criterion is proposed that determines the onset of a new dust layer in a quasi-two-dimensional dust system.     

Formation of chain structures in systems of charged grains interacting via isotropic pair potentials

Conditions for the formation of chain structures of charged grains confined in the gravitational field by external electric fields are studied analytically and numerically. The relationships between the parameters of the pair interaction potential, the number of grains, and the electric field gradient in the trap are found. A criterion for the violation of stable equilibrium in a quasi-one-dimensional chain of grains and the formation of a new configuration in the system is proposed.     

Dusty Plasma near the Martian Satellite Deimos

The formation of dusty plasma in the near-surface layer above the illuminated part of the Deimos, the satellite of Mars, due to photoelectric and electrostatic processes is analyzed. Using a physicomathematical model self-consistently describing the densities of photoelectrons and dust grains above the illuminated part of Deimos, the distribution function of photoelectrons near its surface is calculated and the altitude dependences of the electric field, as well as of the number density, charge, and size of dust grains, are determined. It is noted that, due to the lower gravity, substantially larger grains are lifted above the surface of Deimos compared to those lifted above the Moon’s surface. In this case, adhesion, which is believed to significantly hamper the detachment of dust grains from the lunar surface, plays a substantially smaller role on Deimos.     

Nonlinear screening of dust grains and structurization of dusty plasma

A review of theoretical ideas on the physics of structurization instability of a homogeneous dusty plasma, i.e., the formation of zones with elevated and depressed density of dust grains and their arrangement into different structures observed in laboratory plasma under microgravity conditions, is presented. Theoretical models of compact dust structures that can form in the nonlinear stage of structurization instability, as well as models of a system of voids (both surrounding a compact structure and formed in the center of the structure), are discussed. Two types of structures with very different dimensions are possible, namely, those smaller or larger than the characteristic mean free path of ions in the plasma flow. Both of them are characterized by relatively regular distributions of dust grains; however, the first ones usually require external confinement, while the structures of the second type can be self-sustained (which is of particular interest). In this review, they are called dust clusters and self-organized dust structures, respectively. Both types of the structures are characterized by new physical processes that take place only in the presence of the dust component. The role of nonlinearities in the screening of highly charged dust grains that are often observed in modern laboratory experiments turns out to be great, but these nonlinearities have not received adequate study as of yet. Although structurization takes place upon both linear and nonlinear screening, it can be substantially different under laboratory and astrophysical conditions. Studies on the nonlinear screening of large charges in plasma began several decades ago; however, up to now, this effect was usually disregarded when interpreting the processes occurring in laboratory dusty plasma. One of the aims of the present review was to demonstrate the possibility of describing the nonlinear screening of individual grains and take it into account with the help of the basic equations for the equilibrium between plasma components when analyzing equilibrium structures. The effect of plasma screening nonlinearity on both the diffusion processes and the forces of dust drag by plasma fluxes is analyzed. It is shown how self-organized dust structures form in these processes. In the limit of very small dust grain charges, the forces acting on the dusty plasma components and the set of basic equations for stationary dust structures (with allowance for nonlinear screening) take a standard form. New qualitative effects, such as the suppression of diffusion due to ion scattering from dust grains and the formation of structures of different configurations, are described. A detailed comparison with previous results is performed. It is shown that the solution of basic nonlinear equations for dust structures yields new qualitative effects. A number of new effects to be studied in future dusty plasma experiments with the formation of structures in spherical chambers are predicted (it is assumed that diffusion will play a significant role under microgravity conditions). Recent ground-based experiments, as well as experiments carried out onboard the International Space Station, directly confirm the nonlinear character of screening and the significant role played by this nonlinearity in the structurization of dusty plasma. Experiments on the formation of structures consisting of smaller dust grains within structures formed of larger grains are discussed. It is shown that those experiments can be interpreted only using the concept of nonlinear screening.     

Heat transfer in dust structures in an RF discharge plasma

Results are presented from experimental studies of heat transfer in liquid-like plasma-dust structures. The experiments were performed with aluminum oxide grains ～3–5 μm in size in an RF discharge plasma. The heat capacity of the dust grains in plasma is measured. The thermal conductivity and thermal diffusivity of liquid-like plasma-dust structures are deduced under the assumption that the observed temperature gradients and the propagation of a thermal perturbation in a dusty plasma are related to heat conduction within the dust component. The measured temperature dependences of the thermal conductivity and thermal diffusivity are in qualitative agreement with the results of numerical simulations performed in the model of a simple single-atom liquid. It is shown that quantitative discrepancy between the experimental and numerical results is related to the energy loss of dust grains in their collisions with the neutral particles of the ambient gas.     

Determination of the pairwise interaction potential between dust grains in plasma

Results are presented from measurements of the pairwise interaction potential between dust grains in plasma. The experiments were carried out with RF capacitive discharges over a wide range of dusty plasma parameters. All the experiments under analysis revealed a repulsive interaction potential that was close in shape to the screened Coulomb potential. The grain charges and the radii at which they were screened are determined.     

Solitary dust sound waves in a plasma with two-temperature ions and distributed grain size

The propagation of weakly nonlinear dust sound waves in a dusty plasma containing two different-temperature ion species is explored. The nonlinear equations describing both the quadratic and cubic plasma nonlinearities are derived. It is shown that the properties of dust sound waves depend substantially on the grain size distribution. In particular, for solitary dust sound waves with a positive potential to exist in a plasma with distributed grain size, it is necessary that the difference between the temperatures of two ion species be larger than that in the case of equal-size grains.     

Properties of dust-plasma structures formed in a glow discharge above the lower wall of the discharge chamber

The properties are studied of dusty plasma structures formed in a glow discharge in a dust trap above the lower wall of the side branch of the discharge tube, near the turn of the discharge channel. The dust structure is three-dimensional with a characteristic size of up to 3 cm and contains about 30000 dust grains. Depending on the experimental conditions, dust-acoustic, dissipative, and charge-gradient instabilities can develop in such a structure. When using highly polydisperse dust grains of arbitrary shape, the effect of selection of dust grains by the plasma with respect to their mean size and shape was discovered. This effect was studied quantitatively in two gases by using the method of gathering and extraction of the dust grains levitating in the trap. The morphology of the dust structures was determined from the pair correlation functions of the horizontal cross sections containing long-range order peaks and elements of a hexagonal lattice. Stratification of a uniform structure accompanied by convective rotation caused by the grain charge gradient was observed. Applications of the dusty plasma created in this type of device are discussed.     

Shock structure formation in dusty plasmas

The problem of the evolution of a perturbation in a dusty plasma and its transformation into a nonlinear wave structure is considered. A computational method that allows one to solve the set of nonlinear evolutionary equations describing variable-charge dust grains, Boltzmann electrons, and inertial ions is developed. Exact steady-state solutions corresponding to ion-acoustic shock structures associated with anomalous dissipation originating from dust grain charging are found taking into account the effect of electron and ion charge separation. The role of this effect increases with the speed of the shock. The evolutions of an initial soliton (which is a steady-state wave solution in a plasma containing dust grains with a constant charge) and an initially immobile perturbation with a constant increased ion density are investigated. In a charge-varying dusty plasma, the soliton evolves into a nonsteady shock wave structure that propagates at a constant speed and whose amplitude decreases with time. The initially immobile perturbation with a constant increased ion density evolves into a shock structure similar to a steady-state shock wave. In the latter case, the compression shock wave is accompanied by a rarefaction region (dilatation wave), which finally leads to the destruction of the shock structure. The solution of the problem of the evolution of a perturbation and its transformation into a shock wave in a charge-varying dusty plasma opens up the possibility of describing real phenomena (such as supernova explosions) and laboratory and active space experiments.     

Experimental studies of the dynamics of dust grains in gas-discharge plasmas

Results of the experimental studies of the dynamics of dust grains in the plasmas of an rf capacitive discharge and a dc glow discharge are presented. The dusty plasma of a dc glow discharge was investigated in both ground-based experiments and experiments carried out under microgravity conditions (on board the Mir space station). The pair correlation function, temperature, and diffusion coefficient of dust grains are measured in a wide range of the dusty-plasma parameters. Dimensionless parameters responsible for the microscopic transport of dust-grains in a gas-discharge plasma are determined. A nonintrusive diagnostic technique for determining the dust-grain charges and screening lengths under the assumption of screened interaction between the grains is proposed. This technique is used to estimate the surface potential of dust grains of different size in a gas-discharge plasma.     

Nonlinear screening of dust grains and structurization of dusty plasma: II. formation and stability of dust structures

The second part of the review on dust structures (the first part was published in Plasma Phys. Rep. 39, 515 (2013)) is devoted to experimental and theoretical studies on the stability of structures and their formation from the initially uniform dusty plasma components. The applicability limits of theoretical results and the role played by nonlinearity in the screening of dust grains are considered. The importance of nonlinearity is demonstrated by using numerous laboratory observations of planar clusters and volumetric dust structures. The simplest compact agglomerates of dust grains in the form of stable planar clusters are discussed. The universal character of instability resulting in the structurization of an initially uniform dusty plasma is shown. The fundamental correlations described in the first part of the review, supplemented with effects of dust inertia and dust friction by the neutral gas, are use to analyze structurization instability. The history of the development of theoretical ideas on the physics of the cluster formation for different types of interaction between dust grains is described.     

Skin Effects in a Dusty Plasma

A multifluid MHD model is applied to study the magnetic field dynamics in a dusty plasma. The motion of plasma electrons and ions is treated against the background of arbitrarily charged, immobile dust grains. When the dust density gradient is nonzero and when the inertia of the ions and electrons and the dissipation from their collisions with dust grains are neglected, we are dealing with a nonlinear convective penetration of the magnetic field into the plasma. When the dust density is uniform, the magnetic field dynamics is described by the nonlinear diffusion equations. The limiting cases of diffusion equations are analyzed for different parameter values of the problem (i.e., different rates of the collisions of ions and electrons with the dust grains and different ratios between the concentrations of the plasma components), and some of their solutions (including self-similar ones) are found. The results obtained can also be useful for research in solid-state physics, in which case the electrons and holes in a semiconductor may be analogues of plasma electrons and ions and the role of dust grains may be played by the crystal lattice and impurity atoms.     

Heat exchange in dusty plasma

The effect of the charge of a dust grain on the exchange of its heat with plasma particles and with neutral gas particles in an anisotropic dusty plasma with dissipative flows is discussed. It is shown, in particular, that nonuniform heating of the grain surface gives rise to the radiometric force, which may be stronger than the ion wind force. Also, the grain charge causes the thermophoretic force to change its sign.