Drift dissipative instability in planetary and cometary dusty plasmas

In a magnetized inhomogeneous dusty plasma drift dissipative instability may play an important role. We have examined the dependence of frequencies and growth rates on dust parameters. The marginal instability for such a dusty plasma seems to show some interesting results. The relevance of the investigation is discussed to understand the wave phenomena in planets and cometary environments.     

Finite larmor-radius effects on Rayleigh-Taylor instability of a dusty magnetized plasma

This paper discusses the Rayleigh-Taylor (RT) instability of an infinitely conducting medium having an exponential density distribution which includes the effects of finite ion Larmor-radius (FLR) corrections and suspended particles in the presence of a uniform horizontal magnetic field. The relevant equations of the problem are linearized and from the linearized perturbation equations a dispersion relation is obtained, using appropriate boundary conditions. It has been found that the criterion for the stable density stratification remains uninfluenced by the simultaneous inclusion of the FLR corrections and suspended particles. The stability of the medium has been proved for the case of stable stratification when the FLR corrections are not considered in the analysis. The growth rate of unstable RT modes with increasing relaxation frequency of the suspended particles is evaluated analytically. It has been shown that the presence of suspended particles in the medium suppresses the growth rate of the unstable RT modes, thereby implying a stabilizing influence of the particles on the considered configuration.     

Ion-acoustic instability in a dusty negative ion plasma

The ion-acoustic instability in a dusty negative ion plasma is investigated, focusing on the parameter regime in which the negative ion density is much larger than the electron density. The dynamics of the massive dust grains are neglected, but collisions of electrons and ions with dust grains in addition to other collisional processes are taken into account. The presence of a population of charged dust can change the frequency of the fast wave, lead to additional damping due to ion–dust collisions, and change the conditions for wave growth. Applications to dusty negative ion plasmas in the laboratory and in space are discussed.     

Self-gravitational instability in magnetized finitely conducting viscoelastic fluid

The linear self-gravitational instability of finitely conducting, magnetized viscoelastic fluid is investigated using the modified generalized hydrodynamic (GH) model. A general dispersion relation is obtained with the help of linearized perturbation equations using the normal mode analysis and it is discussed for longitudinal and transverse modes of propagation. In longitudinal propagation, we find that Alfven mode is uncoupled with the gravitating mode. The Jeans criterion of instability is determined which depends upon shear viscosity and bulk viscosity while it is independent of magnetic field. The viscoelastic effects modify the fundamental Jeans criterion of gravitational instability. In transverse mode of propagation, the Alfven mode couples with the acoustic mode, compressional viscoelastic mode and gravitating mode. The growth rate of Jeans instability is compared in weakly coupled plasma (WCP) and strongly coupled plasma (SCP) which is larger for SCP in both the modes of propagations. The presence of finite electrical resistivity removes the effect of magnetic field in the condition of Jeans instability and expression of critical Jeans wavenumber. It is found that Mach number and shear viscosity has stabilizing while finite electrical resistivity has destabilizing influence on the growth rate of Jeans instability.     

The Kelvin-Helmholtz instability in dusty plasmas

The Kelvin-Helmholtz instability in magnetized, dusty plasmas is examined, for both negatively and positively charged dust. The critical shear in the ion velocity along the magnetic field is computed as a function of the charge residing on dust grains.     

Dust-ion-acoustic solitary waves and their multi-dimensional instability in a magnetized dusty electronegative plasma with trapped negative ions

A theoretical investigation has been made on obliquely propagating dust-ion-acoustic solitary waves (DIASWs) in magnetized dusty electronegative plasma containing Boltzmann electrons, trapped negative ions, cold mobile positive ions, and arbitrarily charged stationary dust. The reductive perturbation method has been employed to derive the modified Zakharov-Kuznetsov (MZK) equation which admits solitary wave solution under certain conditions. The multi-dimensional instability of these solitary waves is also studied by the small-k (long wavelength plane wave) perturbation-expansion technique. The basic properties (speed, amplitude, width, instability, etc.) of small but finite amplitude DIASWs are significantly modified by the effects of external magnetic field, obliqueness, polarity of dust, and trapped negative ions. The implications of our results in space and laboratory plasmas are briefly discussed.     

Dust-ion-acoustic solitary waves and their multi-dimensional instability in a magnetized nonthermal dusty electronegative plasma

A rigorous theoretical investigation has been made on multi-dimensional instability of obliquely propagating electrostatic dust-ion-acoustic (DIA) solitary structures in a magnetized dusty electronegative plasma which consists of Boltzmann electrons, nonthermal negative ions, cold mobile positive ions, and arbitrarily charged stationary dust. The Zakharov-Kuznetsov (ZK) equation is derived by the reductive perturbation method, and its solitary wave solution is analyzed for the study of the DIA solitary structures, which are found to exist in such a dusty plasma. The multi-dimensional instability of these solitary structures is also studied by the small-k (long wave-length plane wave) perturbation expansion technique. The combined effects of the external magnetic field, obliqueness, and nonthermal distribution of negative ions, which are found to significantly modify the basic properties of small but finite-amplitude DIA solitary waves, are examined. The external magnetic field and the propagation directions of both the nonlinear waves and their perturbation modes are found to play a very important role in changing the instability criterion and the growth rate of the unstable DIA solitary waves. The basic features (viz. speed, amplitude, width, instability, etc.) and the underlying physics of the DIA solitary waves, which are relevant to many astrophysical situations (especially, auroral plasma, Saturn’s E-ring and F-ring, Halley’s comet, etc.) and laboratory dusty plasma situations, are briefly discussed.     

Dynamic fission instability of dissipative protoplanets

All theories of fission require a catastrophic, dynamic phase in order to produce two separate bodies. We have used nonlinear numerical and linear analytical calculations to show that the dynamic fission instability probably does not occur in dissipative protoplanets. The numerical calculations were performed with a three-spatial-dimension hydrodynamical code, with the proto-planet represented by a fluid with a Murnaghan equation of state. The kinetic energy in the protoplanet (other than rigid body rotation) is dissipated throughout the evolution in order to simulate the effects of viscous dissipation. Protoplanets rotating above the limit for dynamic instability were given initial asymmetric density perturbations; in each case the asymmetry did not grow during a time on the order of the rotational period. This dynamical stability has been verified by including the dissipative terms in the tensor-virial equation analysis for the stability of a Maclaurin spheroid: the dynamic instability vanishes when the dissipative terms are included, while the secular instability (with a growth time much larger than the rotational period) remains. The result applies to bodies of radius R with a kinematic viscosity ν? 4 × 10¹³ (R/6400 km)²cm²sec^?1, and hence may be applicable to any terrestrial protoplanet which is not totally molten. Current thermal histories for the Earth predict a partially molten mantle with a viscosity greater than this critical value. Depending on the detailed rheology of the early Earth, our results appear to rule out the possibility of forming the Earth-Moon system through a dynamic fission instability.     

Rayleigh-Taylor instability of a plasma with finite ion Larmor radius effects

The stability of an infinitely conducting plasma of variable density has been investigated taking into account the finiteness of the ion Larmor radius. The perturbations propagating along the ambient magnetic field are considered. It is established that, in general,n ² is necessarily real, wheren is the growth rate of disturbance, thus ruling out the possibility of overstability or damped oscillations. The solution is shown to be characterized by a variational principle, which provides the basis for obtaining an approximate solution of the problem. Two density distributions are considered: (i) a continuously stratified plasma layer and (ii) two semi-infinitely extending plasmas of constant densities separated by a horizontal interface. In both cases it has been shown that for the said disturbances the stability criterion remains unaffected by the inclusion of finite Larmor radius effects, though the amplified motion is strongly inhibited due to their inclusion.     

Gravitational instability of discs with dissipative coronae around supermassive black holes

We study the dynamical structure of a self-gravitating disc with coronae around a supermassive black hole. Assuming that the magnetorotational instability responsible for generating the turbulent stresses inside the disc is also the source for a magnetically dominated corona, a fraction of the power released when the disc matter accretes is transported to and dissipated in the corona. This has a major effect on the structure of the disc and its gravitational (in)stability according to our analytical and self-consistent solutions. We determine the radius where the disc crosses the inner radius of gravitational instability and forms the first stars. Not only the location of this radius which may extend to very large distances from the central black hole, but also the mass of the first stars highly depends on the input parameters, notably the viscosity coefficient, the mass of the central object and the accretion rate. For accretion discs around quasi-stellar objects (QSOs) and the Galactic Centre, we determine the self-gravitating radius and the mass of the first clumps. Comparing the cases with a corona and without a corona for typical discs around QSOs or the Galactic Centre, when the viscosity coefficient is around 0.3, we show that the self-gravitating radius decreases by a factor of approximately 2, but the mass of the fragments increases with more or less the same factor. The existence of a corona implies a more gravitationally unstable disc according to our results. The effect of a corona on the instability of the disc is more effective when the viscosity coefficient increases.     

Modulational instability of dust ion acoustic waves in dusty plasmas with superthermal electrons

The propagation of dust ion acoustic waves is studied in plasmas composed of superthermal distributed electrons and stationary dust particles. The nonlinear Schrödinger equation is derived using the reductive perturbation technique and the modulational instability of dust ion acoustic waves is analyzed. Parametric investigations indicate that the presence of superthermal distributed electrons significantly modify the modulational instability and its growth rate. The effect of particle relative density on the wave characters is also investigated.     

Debye shielding in a dusty plasma

The phenomenon of Debye shielding is investigated in a dusty plasma consisting of Boltzmann electrons and ions, and negatively charged, massive dust grains. Both small and large amplitude electrostatic potentials are considered and a parameter study conducted.     

Envelope solitons and their modulational instability in dusty plasmas with two-temperature superthermal electrons

The modified ion-acoustic envelope solitons and their modulational instability in a multi-component unmagnetized plasma (consisting of negatively charged immobile dusts, inertial ions and superthermal electrons of two distinct temperatures) are theoretically investigated. A multiple scale (in space and time) perturbation technique is used to derive the cubic nonlinear Schrödinger equation (which describes the evolution of a slowly varying wave envelope with space and time). It is observed that the plasma system under consideration supports two types (bright and dark) envelope solitons. It is also found that the dark (bright) envelope solitons are modulationally stable (unstable). The variation of the growth rate of the unstable bright envelope solitons with various plasma parameters (e.g. wave number, temperature of superthermal electrons, etc.) are found to be significant. The modulational instability criterions of the modified ion-acoustic envelope solitons are also seen to be influenced due to the variation of the intrinsic plasma parameters. The implications of the results of this theoretical investigations in some space plasma systems (viz. Saturn’s magnetosphere) are briefly mentioned.     

Dust acoustic solitary waves in dusty plasma with nonthermal ions

In this paper, the characteristics of the dust acoustic solitary waves in dusty plasmas are studied. The distribution of ions is nonthermal, and the nonthermal parameter is treated as a variable. The pseudo-potential method has been used to investigate the possibility of soliton formation. We show that for some values of the nonthermal parameter there is no soliton.     

Shock waves in a dusty plasma with dust of opposite polarities

A four-component dusty plasma consisting of electrons, ions, and negative as well as positive dust particles has been considered. The basic features of shock waves that may exist in such a four-component dusty plasma have been theoretically investigated by the reductive perturbation method. The implications of our results in different regions of space (viz. cometary tails, mesosphere, Jupiter’s magnetosphere, etc.) are briefly discussed.     

Propagation of cylindrical acoustic waves in dusty plasma with positive dust

The hydrodynamic equations of positive and negative dust, Boltzmann electron and ion density distribution, and Poisson equation are used along with the reductive perturbation method to derive a cylindrical Kadomtsev-Petviashvili (CKP) equation. G′/G expansion method is used to obtain a new class of solutions. At certain condition, the solutions degenerate to solitary wave solutions. The effects of the physical parameters on the characteristics of solitary pulses are examined. The results give elucidation of the properties of dust acoustic solitary pulses in multicomponent space plasmas, particularly in interstellar dust clouds in a galactic disk and astrophysical plasma systems.     

Nonlinear potential structures in a dusty plasma

Fluid theory is used to investigate nonlinear potential structures in an inhomogeneous magnetized dusty plasma. Dipolar-vortex and modified convective cell structures are shown to exist.     

Small scale structures of a mesospheric dusty plasma

A dusty plasma model is presented to study the small scale structures of plasma densities in mesopause region associated with polar mesosphere summer echoes (PMSE). The heavy dust grains (ice particles) are treated as a flowing background of negative charge. Numerical results show that the electron and ion densities drop rapidly while the electric field increases dramatically within a short distance of several meters. The scalelengths of the electron density are comparable to the typical wavelength of the PMSE radars, which may be responsible for strong radar backscatter. Furthermore, the increase of the ice particle concentration results in the reduction of the density gradient and electric field.