Complex plasmas: III. Experiments on strong coupling and long-range correlations

This paper continues a series of review papers devoted to the physics of complex plasmas, in which one of the components (dust) is in a crystalline or liquid state, while the others (electron, ions, and neutral atoms) are in a gaseous state. This review is devoted to the experimental investigations of new phenomena incomplex plasmas. The experiments are explained using estimates based on the theory of elementary processes in complex plasmas, including the new phenomena considered in the previous parts of the review. The paper describes (i) the experiments on multilayer plasma crystals, including the study of their structure and phase transitions; (ii) the experiments on dust monolayer crystals; (iii) the experiments on plasma clusters formed by small number of dust grains; (iv) the experiments on dust ion-sound waves, dust acoustic waves, dust lattice waves, and dust shear waves; (v) the experiments on shock waves; (vi) the experiments on the ionization instabilities and the creation of dust voids and dust clumps; and (vii) the experiments on Mach cones excited either by fast grains or laser radiation.     

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.     

One-dimensional nonlinear self-organized structures in dusty plasmas

Dusty plasmas, which are open systems, can form stable one-dimensional self-organized structures. Absorption of plasma by dust particles results in the plasma flux from the plasma regions where the dust is absent. It is found that, in a one-dimensional dust layer, this flux is completely determined by the number of dust particles per unit area of the layer surface. This number determines all of the other parameters of the steady-state dust structure; in particular, it determines the spatial distributions of the dust density, dust charge, electron and ion densities, and ion drift velocity. In these structures, a force and electrostatic balance is established that ensures the necessary conditions for confining the dust and plasma particles in the structure. The equilibrium structures exist only for subthermal ion flow velocities. This criterion determines the maximum possible number of dust particles per unit area in the steady-state structure. The structures have a universal thickness, and the dust density changes sharply at the edge of the structure. The structures with a size either less than or larger than the ion mean free path with respect to ion-neutral collisions, quasi-neutral and charged structures, and soliton-and anti-soliton-like structures are investigated. Laboratory experiments and observations in extraterrestrial plasma formation are discussed in relation to dust structures.     

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.     

Excitation of dissipative drift turbulence in dusty plasmas

Drift instability in dusty plasma due to plasma density inhomogeneity and inhomogeneities of dust distributions in densities and charges is studied analytically. An explicit general expression for the growth rate of instability is derived. It is found that the growth rate of the dissipative drift instability is substantially enhanced and the threshold of the instability is lowered in the presence of dust.     

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.     

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.     

Nonlinear equilibrium spherical dust structures I: Basic equations and criterion for the existence of self-organized structures

Basic equations for dust structures are formulated that account for the balance of the forces, plasma fluxes, and grain charges with allowance for nonlinearity in the screening of individual grains and possible violation of quasineutrality due to the interaction of collective fields with plasma fluxes. A theory of non-linear drag forces exerted by plasma fluxes on dust grains is developed for moderate drift flux velocities, higher than the mean ion thermal velocity but much lower than the acoustic speed. It is shown that equilibrium dust structures have finite sizes and negative charges and that they can exist only in a certain range of intensities of external fluxes on their surfaces. When there is no additional volume ionization, the size of the structures is determined by the intensity of the external flux. A study is made of a weakly ionized dusty plasma in which the interaction of its components with neutral gas atoms plays a major role. The ion, electron, and dust density distributions, as well as the distributions of the dust grain charges and plasma fluxes, are calculated self-consistently as functions of the distance from the center of a structure.     

Surface activity of dust with variable charge

A simple model is developed for the self-consistent charging of a dust layer in an electrode plasmasheath, as well as for the force balance in this layer. The anisotropy of the plasma pressure near the plasmaboundary makes it possible to introduce the notion of surface tension. The equilibrium charge, the height atwhich the dust layer levitates above the electrode, and the plasma surface tension are calculated numerically as functions of the dust density. In all of the cases under analysis, the presence of dust is shown to increase the plasma surface tension, which indicates that the plasma sheath may become structurally unstable.     

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.     

The influence of gravity and wind on land plant evolution

Aspects of the engineering theory treating the elastic stability of vertical stems and cantilevered leaves supporting their own weight and additional wind-induced forces (drag) are reviewed in light of biomechanical studies of living and fossil terrestrial plant species. The maximum height to which arborescent species can grow before their stems elastically buckle under their own weight is estimated by means of the Euler-Greenhill formula which states that the critical buckling height scales as the 1/3 power of plant tissue-stiffness normalized with respect to tissue bulk density and as the 2/3 power of stem diameter. Data drawn from living plants indicate that progressively taller plant species employ stiffer and lighter-weight plant tissues as the principal stiffening agent in their vertical stems. The elastic stability of plants subjected to high lateral wind-loadings is governed by the drag torque (the product of the drag force and the height above ground at which this force is applied), which cannot exceed the gravitational bending moment (the product of the weight of aerial organs and the lever arm measured at the base of the plant). Data from living plants indicate that the largest arborescent plant species rely on massive trunks and broad, horizontally expansive root crowns to resist drag torques. The drag on the canopies of these plants is also reduced by highly flexible stems and leaves composed of tissues that twist and bend more easily than tissues used to stiffen older, more proximal stems. A brief review of the fossil record suggests that modifications in stem, leaf, and root morphology and anatomy capable of simultaneously coping with self-weight and wind-induced drag forces evolved by Devonian times, suggesting that natural selection acting on the elastic stability of sporophytes occurred early in the history of terrestrial plants.     

Estimation of the rotational undamped natural frequency of bileaflet cardiac valve prostheses

The angular momentum balance is solved numerically for a size 29 mm CarboMedics prosthetic heart valve. The lift force is estimated from potential flow theory, while the drag force is estimated from the lift force and a blunt body empiricism. Buoyancy and gravitational effects are calculated based on the assumption of homogeneous leaflets. Other assumptions include uniform flow, negligible friction at the pivot axis, negligible viscous damping and fluid inertance, and a symmetry flow condition. Oscillations are predicted in the opening dynamics in the range of 2-25 Hz, for flow rates through one-half of the orifice in the range of 0.1-10.0 l/min. The frequency of these oscillations is dependent upon the orientation of the leaflet in relation to the gravitational field and the magnitude of the flow rate. In vivo and in vitro measurements by other investigators demonstrate similar effects of gravity and flow rate, with flutter frequencies of the order of 10-100 Hz. Excitation frequencies, based on vortex shedding, are estimated to be of the order 2-200 Hz, for the range of flow rates of the theoretical model. These results suggest that the natural frequency of this rotational second order system may, in theory, be a contributing factor to the flutter observed in bileaflet cardiac valve prostheses. The clinical significance of this finding is yet to be established.     

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.     

Dust-acoustic waves in a nonuniform adiabatic dusty plasma in the presence of polarization force

The linear propagation of the dust-acoustic (DA) waves in a nonuniform adiabatic dusty plasma, which consists of inertialess adiabatic electrons, inertialess adiabatic ions, and inertial negatively charged dust by taking into account the effects of polarization force, is theoretically investigated. It is found that the linear dispersion properties of the DA waves are significantly modified by the dust density nonuniformity, adiabaticity of electrons and ions, and the effects of the polarization force. It is shown that the phase speed of the DA waves is increased with the increase of adiabaticity of electrons and ions but decreased with the increase of the effects of polarization force. It is also shown that the dust density is enhanced with the increase of adiabatic index but depleted with the increase of polarization force. The scenarios relevant to dust-ion plasma in space environments are briefly addressed.     

Effect of rotation on plasma stability in the gas-dynamic trap

The effects of the centrifugal force and finite Larmor radius on plasma stability in the gas-dynamic trap are considered. Estimates show that the stability is governed by the strong effect of the finite Larmor radius of fast particles. If this stabilizing mechanism does not operate, then the instability ceases to be exponential when the sheared plasma rotation becomes sufficiently intense. In this case, the potential perturbation amplitude increases according to a power law, and the instability threshold remains unchanged. These effects do not influence the stability of the first azimuthal perturbation mode in a plasma with a free boundary. But when the plasma is in good electrical contact with the conducting wall of the device and when the plasma density profile is not too peaked at the axis, the first mode is stabilized by the finite Larmor radius effect because of the radial variation of the perturbed electric field.     

Stability of a Linear Plasma Crystal

Plasma Physics Reports - The stability of a linear chain of dust particles in an external confining force field is studied. It is assumed that the particles are located in a plasma with Maxwellian...     

Morphological adaptations of emergent plants to water flow: a case study with Typha angustifolia, Zizania latifolia and Phragmites australis

1. Water velocity plays an important role in shaping plant community structure in flowing waters although few authors have yet attempted to explain the adaptation of plants to flow. 2. We aimed to test two hypotheses, that: (i) some emergent macrophytes reconfigure their shoot distribution in fast currents and form clumps, and (ii) the shape and morphology of such clumps minimises drag caused by the current. The study focuses on three emergent macrophytes that co‐occur along a gradient of water velocity. 3. The species showed a clear zonation in response to water depth and current velocity. Phragmites australis occupied shallower and more slowly flowing water than Typha angustifolia and Zizania latifolia, which had similar preferences. 4. Both T. angustifolia and Z. latifolia shoots were more clumped at high velocity, whereas they were more randomly distributed at low flow or in stagnant water. Because of the low shoot density, water flowed more easily through T. angustifolia clumps, whereas Z. latifolia clumps had a high shoot density and large amounts of trapped litter, causing stagnant water in the centre of the clump. The clumps of Z. latifolia with a high density of shoots were longer and narrower than T. angustifolia clumps. Phragmites australis was less tolerant of flow than the other two species and large amounts of litter trapped in the clumps impaired flow. 5. The shoot distribution of both T. angustifolia and Z. latifolia is reconfigured at high flow and this minimises drag on the clumps.     

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.