Electrostatic solitary structures in a magnetized nonextensive plasma with q-distributed electrons

A rigorous theoretical investigation has been made of obliquely propagating electrostatic solitary structures in a magnetized plasma, taking into account the effect of nonextensive electrons. By employing the reductive perturbation method, the basic characteristics of obliquely propagating ion-acoustic (IA) solitary waves (SWs) in a cold magnetized electron-ion plasma (consisting of inertial ions and noninertial q-distributed electrons) have been addressed. The Korteweg-de Vries equation is derived and its numerical solution is obtained. It has been shown that the effects of electron nonextensivity and external magnetic field significantly modify the natures of the small but finite-amplitude IA SWs. The present analysis may be useful to understand and demonstrate the dynamical properties of IA SWs in different astrophysical and cosmological scenarios (viz. stellar polytropes, hadronic matter, quark-gluon plasma, protoneutron stars, dark-matter halos, etc.).     

Calculation of the grain charge fluctuations in a dusty plasma

The time characteristics of grain charging, namely, the relaxation time of the steady grain charge and the charge fluctuations of grains of different sizes, are computed from particle simulations. The results obtained are compared with some theoretical predictions (primarily those derived from the drift-diffusion model). The simulations are carried out for nonmoving and moving two-temperature argon plasmas.     

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.     

Ion acoustic cnoidal waves in a dusty plasma with a critical dust density

The propagation of nonlinear periodic ion acoustic waves in a dusty plasma is considered for conditions in which the coefficient in the nonlinear equation that describes the quadratic nonlinearity of the medium is zero. An equation that accounts for the cubic nonlinearity of the system is derived, and its solution is found. The dependence of the phase velocity of a cnoidal wave on its amplitude and modulus is determined. In describing the effect of higher order nonlinearities on the properties of a dust ion acoustic wave, two coupled equations for the first- and second-order potentials are obtained. It is shown that the nonlinear ion flux generated by a cnoidal wave propagating in a medium with a cubic nonlinearity is proportional to the fourth power of the wave amplitude.     

Cylindrical and spherical dust-ion-acoustic modified Gardner solitons in dusty plasmas with two-temperature superthermal electrons

A rigorous theoretical investigation has been performed on the propagation of cylindrical and spherical Gardner solitons (GSs) associated with dust-ion-acoustic (DIA) waves in a dusty plasma consisting of inertial ions, negatively charged immobile dust, and two populations of kappa distributed electrons having two distinct temperatures. The well-known reductive perturbation method has been used to derive the modified Gardner (mG) equation. The basic features (amplitude, width, polarity, etc.) of nonplanar DIA modified Gardner solitons (mGSs) have been thoroughly examined by the numerical analysis of the mG equation. It has been found that the characteristics of the nonplanar DIA mGSs significantly differ from those of planar ones. It has been also observed that kappa distributed electrons with two distinct temperatures significantly modify the basic properties of the DIA solitary waves and that the plasma system under consideration supports both compressive and rarefactive DIA mGSs. The present investigation should play an important role for understanding localized electrostatic disturbances in space and laboratory dusty plasmas where stationary negatively charged dust, inertial ions, and superthermal electrons with two distinct temperatures are omnipresent ingredients.     

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.     

Solitary waves in dusty plasmas with weak relativistic effects in electrons and ions

Two distinct classes of dust ion acoustic (DIA) solitary waves based on relativistic ions and electrons, dust charge Z _d and ion-to-dust mass ratio Q’ = m _i /m _d are established in this model of multicomponent plasmas. At the increase of mass ratio Q’ due to increase of relativistic ion mass and accumulation of more negative dust charges into the plasma causing decrease of dust mass, relativistic DIA solitons of negative potentials are abundantly observed. Of course, relativistic compressive DIA solitons are also found to exist simultaneously. Further, the decrease of temperature inherent in the speed of light c causes the nonlinear term to be more active that increases the amplitude of the rarefactive solitons and dampens the growth of compressive solitons for relatively low and high mass ratio Q’, respectively. The impact of higher initial streaming of the massive ions is observed to identify the point of maximum dust density N _d to yield rarefactive relativistic solitons of maximum amplitude.     

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.     

Structure of the fronts of strong collisional shock waves in an ideal two-temperature electron-ion plasma with ions of arbitrary charge

Solutions in the form of plane running waves are investigated numerically in the framework of a two-temperature hydrodynamic model of a fully ionized ideal plasma with ions of arbitrary charge number Z₀. Most simulations were carried out for simple boundary conditions corresponding to a cold immobile plasma at the front of a running wave. All the solutions obtained have a discontinuity in the form of an isoelectronic-thermal jump, whose parameters relax to their steady-state values in the course of calculation. The problem of finding numerical solutions in which all the quantities at infinity take on finite (equilibrium) values actually reduces to the problem of the front structure of a strong shock wave. For a plasma with singly changed ions (Z₀ = 1), numerical solutions were found to coincide with the previously known solution. For a plasma with arbitrarily charged ions (Z₀ > 1), numerical solutions were obtained for the first time on the basis of justified formulas for the electron thermal conductivity.     

Effect of dust size distribution on ion-acoustic solitons in dusty plasmas with different dust grains

Theoretical studies are carried out for ion acoustic solitons in multicomponent nonuniform plasma considering the dust size distribution. The Korteweg?de Vries equation for ion acoustic solitons is given by using the reductive perturbation technique. Two special dust size distributions are considered. The dependences of the width and amplitude of solitons on dust size parameters are shown. It is found that the properties of a solitary wave depend on the shape of the size distribution function of dust grains.     

Effect of microwave radiation on a dusty plasma

The effect of microwave radiation on a complex plasma produced by an external ionizer is studied using numerical simulations. It is shown that, as the radiation intensity increases, the scattering of the incident radiation by charged metal grains is enhanced and radiation at the second harmonic of the incident radiation appears in the scattered spectrum. This effect is associated with the grain charge oscillations caused by the nonlinear action of the microwave field. It is found that, under the action of strong microwave radiation, the grain charge can increase by one order of magnitude. It is shown that, when the microwave intensity is high enough, the distribution of the electric field near a dust grain is shown to change so radically that the field component normal to the grain surface can even change its sign.     

Nonlinear dynamics of drift structures in a magnetized dissipative plasma

A study is made of the nonlinear dynamics of solitary vortex structures in an inhomogeneous magnetized dissipative plasma. A nonlinear transport equation for long-wavelength drift wave structures is derived with allowance for the nonuniformity of the plasma density and temperature equilibria, as well as the magnetic and collisional viscosity of the medium and its friction. The dynamic equation describes two types of nonlinearity: scalar (due to the temperature inhomogeneity) and vector (due to the convectively polarized motion of the particles of the medium). The equation is fourth order in the spatial derivatives, in contrast to the second-order Hasegawa-Mima equations. An analytic steady solution to the nonlinear equation is obtained that describes a new type of solitary dipole vortex. The nonlinear dynamic equation is integrated numerically. A new algorithm and a new finite difference scheme for solving the equation are proposed, and it is proved that the solution so obtained is unique. The equation is used to investigate how the initially steady dipole vortex constructed here behaves unsteadily under the action of the factors just mentioned. Numerical simulations revealed that the role of the vector nonlinearity is twofold: it helps the dispersion or the scalar nonlinearity (depending on their magnitude) to ensure the mutual equilibrium and, thereby, promote self-organization of the vortical structures. It is shown that dispersion breaks the initial dipole vortex into a set of tightly packed, smaller scale, less intense monopole vortices-alternating cyclones and anticyclones. When the dispersion of the evolving initial dipole vortex is weak, the scalar nonlinearity symmetrically breaks a cyclone-anticyclone pair into a cyclone and an anticyclone, which are independent of one another and have essentially the same intensity, shape, and size. The stronger the dispersion, the more anisotropic the process whereby the structures break: the anticyclone is more intense and localized, while the cyclone is less intense and has a larger size. In the course of further evolution, the cyclone persists for a relatively longer time, while the anticyclone breaks into small-scale vortices and dissipation hastens this process. It is found that the relaxation of the vortex by viscous dissipation differs in character from that by the frictional force. The time scale on which the vortex is damped depends strongly on its typical size: larger scale vortices are longer lived structures. It is shown that, as the instability develops, the initial vortex is amplified and the lifetime of the dipole pair components-cyclone and anticyclone-becomes longer. As time elapses, small-scale noise is generated in the system, and the spatial structure of the perturbation potential becomes irregular. The pattern of interaction of solitary vortex structures among themselves and with the medium shows that they can take part in strong drift turbulence and anomalous transport of heat and matter in an inhomogeneous magnetized plasma.     

Dust ion acoustic solitary structures in the presence of isothermal positrons

The Sagdeev potential technique has been employed to study the dust ion acoustic solitary waves and double layers in an unmagnetized collisionless dusty plasma consisting of negatively charged static dust grains, adiabatic warm ions, isothermally distributed electrons, and positrons. A computational scheme has been developed to draw the qualitatively different compositional parameter spaces or existence domains showing the nature of existence of different solitary structures with respect to any parameter of the present plasma system. The present system supports both positive and negative potential double layers. The negative potential double layer always restricts the occurrence of negative potential solitary waves, i.e., any sequence of negative potential solitary waves having monotonically increasing amplitude converges to a negative potential double layer. However, there exists a parameter regime for which the positive potential double layer is unable to restrict the occurrence of positive potential solitary waves. As a result, in this region of the parameter space, there exist solitary waves after the formation of positive potential double layer, i.e., positive potential supersolitons have been observed.     

Collisionless expansion of a plasma with doubly charged ions in a rarefied magnetized plasma

The collisionless interaction between an expanding cylindrical plasma cloud containing singly and doubly charged ions and a magnetized background plasma is investigated numerically using a method combining the kinetic and hydrodynamic approaches. The results presented were obtained from simulations carried out under conditions corresponding to active space experiments on the expansion of plasma clouds in the Earth’s ionosphere.     

Influence of the trapped ions on the screening effect and frictional force in a dusty plasma

The problem of screening of the charge acquired by a dust grain in a two-temperature plasma is considered. The influence of the trapped ions on the screening effect and on the frictional force exerted on a dust grain by an ion flow is investigated. It is shown that the ions trapped by a grain radically reduce the frictional force in the ion flow because their distribution is determined by the temperature of the cold buffer gas. The mechanism for the onset of the reactive force that accelerates the grain in the direction opposite to that of the flow is explained. It is based on the momentum transfer from the flow of the ions that are additionally accelerated in the grain field to the atoms of the buffer gas. As a result, the momentum carried by the charge-exchange atoms out of the “ions + grain” system exceeds the momentum they have carried into the system; this gives rise to a reactive force directed opposite to the ion flow (the negative frictional force). The magnitude of the reactive force is estimated.     

Ordered dusty structures in the plasma of an RF electrodeless gas discharge

Results are presented from the experimental studies and numerical simulations of the behavior of dust grains in the plasma of an inductive RF discharge. The experiments were carried out with neon at a pressure of 25–500 Pa and with 1.87-μm melamine formaldehyde grains. The discharge was excited by a ring inductor supplied from a generator operating at a 100-MHz frequency. The effective dust-grain interaction potential used in numerical simulations involved the spatial dependence of the grain charge on the plasma floating potential, grain-interaction anisotropy resulting from the focusing of the drift ion current by the negatively charged grains, and specific features of the shielding of the dust grains by the plasma electrons and ions recombining both in the plasma bulk and on the grain surface. The results of Monte Carlo simulations show that the dust grains form specific filament structures observed experimentally in the plasma of an inductive electrodeless discharge. __________ Translated from Fizika Plazmy, Vol. 26, No. 5, 2000, pp. 445–454. Original Russian Text Copyright ? 2000 by Zobnin, Nefedov, Sinel’shchikov, Sinkevich, Usachev, Filinov, Fortov.     

Dynamics of dust grains in a two-component dusty plasma induced by solar radiation under microgravity conditions

Results are presented from experimental studies of the dynamics of dust grains charged via photoemission under microgravity conditions. The experiments are performed with bronze grains exposed to solar radiation on board the Mir space station. The velocity distribution, temperature, mean charge, and friction and diffusion coefficients of dust grains are determined. An analysis of the data obtained shows that the polarization caused by the separation of opposite charges can significantly affect the transport processes in a two-component dusty plasma consisting of dust grains and the electrons emitted by them.     

Spatiotemporal evolution of vortex dust structures in a track plasma

Results are presented from experimental studies of the behavior of dust grains in a track plasma produced by an accelerated proton beam. Dynamic dust structures in such a plasma are obtained for the first time, and their spatiotemporal evolution is thoroughly investigated. The structures develop from a dust spiral, which abruptly transforms with increasing dust density into a differentially rotating dust cloud across which dust-sound waves (including spiral waves generated by the dense central core) propagate. As time elapses, the dust cloud loses its fragments and gradually vanishes. At constant experimental conditions, the lifetime of the structures attains a few minutes.     

Nonlinear dust-acoustic structures in space plasmas with superthermal electrons,positrons, and ions

Some features of nonlinear dust-acoustic (DA) structures are investigated in a space plasma consisting of superthermal electrons, positrons, and positive ions in the presence of negatively charged dust grains with finite-temperature by employing a pseudo-potential technique in a hydrodynamic model. For this purpose, it is assumed that the electrons, positrons, and ions obey a kappa-like (κ) distribution in the background of adiabatic dust population. In the linear analysis, it is found that the dispersion relation yield two positive DA branches, i.e., the slow and fast DA waves. The upper branch (fast DA waves) corresponds to the case in which both (negatively charged) dust particles and (positively charged) ion species oscillate in phase with electrons and positrons. On the other hand, the lower branch (slow DA waves) corresponds to the case in which only dust particles oscillate in phase with electrons and positrons, while ion species are in antiphase with them. On the other hand, the fully nonlinear analysis shows that the existence domain of solitons and their characteristics depend strongly on the dust charge, ion charge, dust temperature, and the spectral index κ. It is found that the minimum/maximum Mach number increases as the spectral index κ increases. Also, it is found that only solitons with negative polarity can propagate and that their amplitudes increase as the parameter κ increases. Furthermore, the domain of Mach number shifts to the lower values, when the value of the dust charge Z _d increases. Moreover, it is found that the Mach number increases with an increase in the dust temperature. Our analysis confirms that, in space plasmas with highly charged dusts, the presence of superthermal particles (electrons, positrons, and ions) may facilitate the formation of DA solitary waves. Particularly, in two cases of hydrogen ions H⁺ (Z _i = 1) and doubly ionized Helium atoms He²⁺ (Z _i = 2), the mentioned results are the same. Additionally, the mentioned dusty plasma does not support DA solitons with positive polarity (compressive solitons). Furthermore, our analysis confirms that DA double layers cannot exist in such a system. Moreover, the positron density has not a considerable effect on the behavior of DA solitons in our model.