Ionization instability and dusty plasma structurization

In the presence of ionization processes, a homogeneous equilibrium dust distribution often appears as a balance between plasma generation by ionization and plasma absorption by dust particles. It is shown that such equilibrium, often present in laboratory plasmas, is generally unstable against the formation of dust clumps separated by dust-free regions (dust voids). The driving force that separates an initially homogeneous dusty plasma into dust clumps and dust voids is the drag force produced by ions flowing out from the regions with reduced dust density. The lower the dust density, the lower the electron absorption by dust particles and the larger the ionization rate proportional to the electron density. An increase in the ion drag force leads to a further decrease in the dust density and, thus, drives the instability. In the nonlinear stage, the instability creates structures—dust clouds separated by dust voids. The dependence of the instability growth rate on the wavenumber (or, in other words, on the size of the dust-free and dust-containing regions) is investigated. It is shown that, for sufficiently small wavenumbers, a homogeneous distribution is always unstable. An analogy with a gravitational-like instability related to shadowing of the plasma flux by dust particles is pointed out. This effect, which is due to collective shadowing of the plasma flux, dominates the shadowing by individual dust particles discussed previously. Similar to the usual gravitational instability, perturbations with the largest scales are always unstable. Contrary to the usual gravitational instability, the largest growth rate corresponds not to the largest possible scale but to the size close to the mean free path of plasma particles colliding with dust particles. A special investigation is undertaken to determine the influence of the ion-neutral collisions on the growth rate of the instability.     

Magnetorotational instability of a weakly ionized accretion disk with vertical and azimuthal magnetic fields

Magnetorotational instability of a weakly ionized accretion disk with an admixture of charged dust grains in a magnetic field with the axial and toroidal components is analyzed. The dispersion relation for perturbations perpendicular to the disk plane is derived with allowance for both the Hall current and the finite transverse plasma conductivity. It is shown that dust grains play an important role in the disk magnetic dynamics. Due to the effect of dust grains, the Hall current can reverse its direction as compared to the case of electron-ion plasma. As a result, the instability threshold shifts toward the short-wavelength range. Under certain conditions, electromagnetic fluctuations of any length can become unstable. It is established that the instability criterion for waves of any scale length is satisfied within a finite interval of the density ratio between the dust and electron plasma components. The width of this interval and the instability growth rate as functions of the plasma parameters and the configuration of the magnetic field in the disk are analyzed.     

Modulational excitation of low-frequency dust acoustic waves in the Earth’s lower ionosphere

During the observation of Perseid, Leonid, Gemenid, and Orionid meteor showers, stable low-frequency lines in the frequency range of 20–60 Hz were recorded against the radio-frequency noise background. A physical mechanism for this effect is proposed, and it is established that the effect itself is related to the modulational interaction between electromagnetic and dust acoustic waves. The dynamics of the components of a complex (dusty) ionospheric plasma with dust produced from the evolution of meteoric material is described. The conditions for the existence of dust acoustic waves in the ionosphere are considered, and the waves are shown to dissipate energy mainly in collisions of neutral particles with charged dust grains. The modulational instability of electromagnetic waves in a complex (dusty) ionospheric plasma is analyzed and is found to be driven by the nonlinear Joule heating, the ponderomotive force, and the processes governing dust charging and dynamics. The conditions for the onset of the modulational instability of electromagnetic waves, as well as its growth rate and threshold, are determined for both daytime and nighttime. It is shown that low-frequency perturbations generated in the modulational interaction are related to dust acoustic waves.     

Reversal of the hall current and amplification of the magnetorotational instability in a weakly ionized plasma

A criterion for the development of a magnetorotational instability in a weakly ionized dusty plasma is considered. A dispersion relation for the wavenumber and the growth rate of an unstable perturbation is derived for an arbitrary angle between the wave vector and magnetic field. It is shown that the presence of dust grains can reverse the direction of the Hall current in the plasma and can shift the instability threshold to shorter wavelengths. Under certain conditions, Alfvén fluctuations of arbitrary scale can be unstable. The Hall current reversal is found to have a strong effect on the development of a magnetorotational instability when the Alfvén resonance frequency in a weakly ionized plasma is close to the rotation frequency of the accretion disk.     

On the instability of a two-dimensional plane plasma crystal

A study is made of the transverse instability of two-dimensional plane dust crystals with a simple (one particle per primitive cell) and a complex (two particles per primitive cell) lattice structure. The instability criteria (crystal melting conditions) are obtained for an arbitrary, spherically symmetric intergrain interaction potential. It is shown that, for simple lattices, the instability develops in the short-wavelength limit, whereas, for complex lattices, the instability growth rate is maximum in the long-wavelength limit. The structural instability of a square lattice is also considered.     

Linear theory of electron cyclotron instability of electromagnetic waves in a magnetoactive plasma waveguide

The linear stage of electron cyclotron instability of quasi-TE modes in a waveguide filled with a magnetoactive plasma is studied using a kinetic approach. The dispersion relation of the instability is derived analytically. It is shown that the presence of the plasma can reduce both the linear instability growth rate and the instability region; in this case, the maximum of the growth rate is displaced toward lower frequencies. The results obtained are compared with the available experimental observations. They can be useful for optimizing the operating regimes of high-power continuous-wave gyrotrons.     

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.     

On the growth rate of aperiodic instability in plasma with an anisotropic bi-Maxwellian electron velocity distribution

The growth rate of aperiodic instability of transverse and longitudinal-transverse electromagnetic field perturbations in plasma with an anisotropic bi-Maxwellian electron velocity distribution is studied. The boundaries of the instability domains in wave vector space are found, and the growth rates of field perturbations with configurations different from that corresponding to the maximum growth rate are determined.     

Global modes of flute instability of a rotating cylindrical plasma

The influence of rotation on the flute instability of a cylindrical gravitating plasma in a straight inhomogeneous magnetic field is studied in the framework of one-fluid magnetohydrodynamics. The dispersion relation and integral expression for the instability growth rate of eigenmodes are derived. It is shown that, in the framework of the given problem, rotation is a destabilizing factor, and the corresponding theorem is proved for the general case. For a linear radial profile of the rotation frequency, the structure of eigenmodes is calculated. The growth rate of these modes is shown to increase with increasing rotation velocity and azimuthal mode number. It is found that plasma rotation in the eigenmode localization region leads to the displacement of perturbation from the rotation region, which results in a decrease in the instability growth rate. The absence of eigenmodes (i.e., exponential instability of the system) for certain profiles of the density and rotation frequency is demonstrated.     

Saturation of two-stream instability of an electron beam in plasma

The development and nonlinear saturation of two-stream instability of a warm nonrelativistic electron beam in a cold plasma are investigated numerically in the framework of a one-dimensional model. It is shown that, for a sufficiently large velocity spread of the electron beam, instability develops and saturates according to a universal law, the wave phase velocity remains the same in the saturation stage, and the maximum field is somewhat lower than that predicted by classical estimates and depends in a different way on the growth rate. The damping of plasma oscillations not only changes the instability growth rate, but also substantially decreases the maximum wave field.     

Weibel instability in the field of a short laser pulse

The growth rate of Weibel instability in a plasma interacting with a high-frequency pulse with a duration less or comparable with the electron mean free time is determined. The growth rate is shown to decrease with decreasing pulse duration. It is found that instability can develop after the short pulse is switched off and the generated magnetic field no longer affects electron motion in the high-frequency field.     

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.     

Stability of dust acoustic wavepackets suffering from polarization force due to the presence of trapped ions

The combined effects of the polarization force, free and trapped ions, and dust charge variation are incorporated in a rigorous study of the nonlinear dust acoustic waves (DAWs) propagating in an unmagnetized dusty plasma. Owing to the departure from the Boltzmann ion distribution, it is found that the nonlinear DAWs are governed by a modified Korteweg?de Vries (mKdV) equation. The association between the mKdV solitary wave and the DAW envelope in the system under consideration is discussed. A modified nonlinear Schrödinger equation appropriate for describing the modulated DAWs is derived. The modulation instability (MI) and the dependence of the system physical parameters on the polarization force, trapped ions, and dust charge variation have been analyzed. It is found that the critical curve separating the stable/unstable regions is strongly influenced by both of the polarization and the ion trapping parameters. Moreover, increasing the polarization leads to an increase of the critical wave number, while increasing the trapping parameter yields the opposite effect. The MI maximum growth rate decreases (increases) as the polarization (trapped ion) increases. The obtained results may be helpful in better understanding of space observations of the solar energetic particle flows in interplanetary space and the energetic particle events in the Earth’s magnetosphere.     

Kinetic study of the linear stage of thermocurrent instability in the framework of the Boltzmann equation for a model gas

The linear stage of thermocurrent instability is investigated for a model gas in which the integral of inelastic collisions of electrons with gas particles has a divergent form and the frequencies of elastic and inelastic collisions are independent of the electron velocity. The proposed approach consists in the reduction of the Boltzmann equation for electrons in an inhomogeneous plasma to a set of equations for the moments of the electron velocity distribution function. The instability growth rate and the wave phase velocity as functions of the perturbation wavenumber are calculated, the maximum growth rate and the corresponding wavenumber are determined, and the dependence of these quantities on the degree of plasma quasineutrality is examined. It is demonstrated that the model satisfactorily (both qualitatively and quantitatively) describes the linear stage of thermocurrent instability in helium.     

Nonlinear theory of the excitation of azimuthal surface waves during dissipative instability

A theoretical study is made of the surface electromagnetic eigenmodes that are excited by an annular charged-particle beam due to dissipative instability and propagate across the external axial magnetic field in a cylindrical metal waveguide partially filled with plasma. A self-consistent set of differential equations for a cold low-density charged-particle beam moving above the plasma surface is constructed in the single-mode approximation and is solved numerically. It is shown that the larger the dissipation, the slower the instability growth rate and the larger the wave amplitude in the saturation stage of the instability. An increase in the transverse dimensions of a charged-particle beam results in a slower growth of the dissipative instability, in which case, however, the beam transfers a larger fraction of its kinetic energy to the wave.     

Ion-Flow-Induced Excitation of Electrostatic Cyclotron Mode in Magnetized Dusty Plasma

The stability of electrostatic cyclotron mode is investigated in a flowing magnetized dusty plasma in the presence of strong ion–neutral collisions. In the high magnetic field limit, when the dust magnetization becomes important, it is expected that the collective behavior of magnetized dust grains suspended in the near-sheath region substantially influences the dispersion properties of electrostatic modes. The growth/damping of the collective excitation is significantly controlled by such parameters as the ion–neutral collision frequency, Mach number, and magnetic field strength. In our case, the explicit dependence of the Mach number on the magnetic field and collision frequency has been taken into account and possible implications on the stability of the mode is analyzed. Streaming instability of cyclotron modes may be important to understand issues related to the interaction mechanism between dust grains and other associated phenomena like Coulomb crystallization, phase behavior, transport properties, etc., in the relatively strong magnetic field limit, which is currently accessible in the DPD (Kiel University) and MDPX (PSL, Auburn University) experiments.     

Raman scattering of laser radiation in magnetoactive plasma

Raman scattering in a subcritical plasma is simulated numerically for the case where the laser radiation propagates transversely to an external magnetic field. It is shown that, in the linear stage of Raman instability, the magnetic field decreases the instability growth rate for forward scattering and increases it for backward scattering. As the value of the magnetic field increases, the stochastic heating of plasma electrons is enhanced in the region of backscattering.     

Electrostatics of moving plasma

The stability of charge distribution over the surface of a conducting body in moving plasma is analyzed. Using a finite-width plate streamlined by a cold neutralized electron flow as an example, it is shown that an electrically neutral body can be unstable against the development of spontaneous polarization. The plasma parameters at which such instability takes place, as well as the frequency and growth rate of the fundamental mode of instability, are determined.     

Rayleigh-Taylor instability in quantum magnetized viscous plasma

Quantum effects on Rayleigh-Taylor instability of stratified viscous plasmas layer under the influence of vertical magnetic field are investigated. By linearly solving the viscous QMHD equations into normal mode, a forth-order ordinary differential equation is obtained to describe the velocity perturbation. Then the growth rate is derived for the case where a plasma with exponential density distribution is confined between two rigid planes. The results show that, the presence of vertical magnetic field beside the quantum effect will bring about more stability on the growth rate of unstable configuration for viscous plasma, which is greater than that of inviscous plasma.     

Parametric decay instability of an inhomogeneous plasma in a frequency-modulated pump wave

It is found experimentally that the broadening of the pump-wave spectrum affects the parametric instability in an inhomogeneous plasma more weakly than is predicted by theory. The suppression of the absolute instability is only observed for a pump-wave spectrum width of 2πΔf>100γ, which is much greater than the instability growth rate γ.