Instability In Dusty Plasma Research Articles

Suppression of the Kelvin–Helmholtz instability due to polarization force in nonuniform magnetized sheared dusty plasmas

The Kelvin–Helmholtz (K–H) instability in a magnetized nonuniform velocity sheared dusty plasma is investigated accounting for the effects of dust polarization force due to inhomogeneity in background plasma number densities. A three-component fluid model for dusty plasma is formulated considering Boltzmann electron/ion fluids and flowing magnetized dust fluids whose dynamics are affected due to the presence of dust polarization force. A dispersion relation for the K–H instability is derived by applying normal mode analysis on the linearized perturbation equations of the system. It is found that the polarization parameter dependent dust acoustic mode significantly modifies the dispersion relation of the K–H instability. The critical shear required to excite the K–H instability (S > Scrit) decreases with an increase in the dust polarization parameter and dust cyclotron frequency. The growth rate of the K–H instability is observed to be suppressed due to the presence of the dust polarization parameter. The results have been discussed for experimental magnetized dusty plasmas, which shows that under considered parametric limits, one cannot ignore the presence of dust polarization force on the excitation of the K–H instability in dusty plasmas. The astrophysical consequences are also discussed in Saturn’s E-ring in the limiting case of varying dust grain size.

Simulations of a low frequency beam-cyclotron instability in a dusty plasma

The nonlinear development of a low frequency beam-cyclotron instability in a collisional plasma composed of magnetized ions and electrons and unmagnetized, negatively charged dust is investigated using one-dimensional particle-in-cell simulations. Collisions of charged particles with neutrals are taken into account via a Langevin operator. The instability, which is driven by an ion $\boldsymbol{E}\times \boldsymbol{B}$ drift, excites a quasi-discrete wavenumber spectrum of waves that propagate perpendicular to the magnetic field with frequency of the order of the dust plasma frequency. In the linear regime, the unstable wavelengths are of the order of the ion gyroradius. As the wave energy density increases, the dominant modes shift to longer wavelengths, suggesting a transition to a Hall-current-type instability. Parameters are considered that reflect the ordering of plasma and dust quantities in laboratory dusty plasmas with high magnetic field. Comparison with the nonlinear development of this beam cyclotron instability in a collisionless dusty plasma is also briefly discussed.

Effect of ion drag on Jean's instability in dusty plasma

The effect of ion drag on the Jeans instability of the dust in the plasma background is examined. It is shown that the ion drag force significantly enhances the Jeans instability and the gravitational collapse of the dust. If the drag force exceeds a critical value, the length scale threshold on Jeans instability is removed and the arbitrary small condensation of dust may occur. The relevance of these results to the planetesimal formation in molecular clouds is briefly discussed.

Recombination Waves in Dusty Plasma of a Non-Self-Sustained Discharge

The steady-state, spatially periodic, structures generated by the evolution of the nonlinear stage of recombination instability in dusty plasma of a non-self-sustained discharge are studied. The research has revealed two types of structures typical for this kind of discharge; they differ in the rates of the increment of recombination instability. The features of each type of structure are described, and the mechanism of their formation is presented. It is shown that the calculation results qualitatively and, with a small variation of discharge parameters, quantitatively agree with the experimental data.

Effect of Coriolis force on the self-gravitational instability of dusty plasma in the presence of magnetic field

In view of the importance of Coriolis force in an astrophysical context, the problem of self-gravitational instability of dusty plasma in the presence of magnetic field is investigated. Equations of the problem are stated and the dispersion relation has been derived with the help of linearized perturbation equations. We find that the Jeans criterion of instability remains valid but the expression of the critical Jeans wave-number is modified. Mathematical calculations have been performed and some figures are plotted between the growth rate of instability and wave numbers. From the curves, it is found that dust sonic speed has a stabilizing effect.

Effect of ion radiative cooling on Jeans instability of partially ionized dusty plasma with dust charge fluctuation

In this paper, the effect of ion radiative cooling on the gravitational instability of dusty plasma is studied, incorporating dust charge fluctuation with dust-neutral, neutral-ion, and ion-neutral collisions. The basic equations are linearized using normal mode analysis to obtain a general dispersion relation. The general dispersion relation is analytically and numerically discussed to explain the role of ion radiative cooling in the structure formation through gravitational instability. The Jeans collapse criteria are found to be modified due to ion and electron radiative cooling, dust charge fluctuations, and collisions effects. It is determined from the analytical and numerical calculations that the support of radiative cooling of ions drives thermal fluctuations and gives instability to the system. The electron cooling effect remains dominating over ion cooling effect, and thus, it enhances the collapse more efficiently than ion cooling effect. Although the radiative cooling is slow, it may precede the collapse in molecular cloud, which further leads to the structure formation. The present work is relevance for the structure formation in the molecular cloud.

Self-gravitational instability of dusty plasma with dissipative effects

The influence of resistivity and viscosity effects on Jeans self-gravitational instability of dusty plasma is studied. The governing equations are constructed using magnetohydrodynamic model for dusty plasma. The general dispersion relation and Jeans criteria for instability are obtained employing the plane wave solutions on linearized perturbation equations. The Jeans criterion is found to be unaffected due to resistivity and viscosity parameter. The dispersion relation is analyzed for various directions of propagation with respect to magnetic field. The numerical calculations have been performed to show the effects of resistivity and viscosity on the growth rate of Jeans instability. It is observed that the presence of resistivity has destabilizing influence while viscosity has stabilizing effects on the growth rate of the Jeans instability. The analytical results are verified by the numerical analysis using both real and normalized astrophysical parameters. The present work is applicable to various space and astrophysical plasma systems, particularly for molecular clouds, protostellar disks, interstellar & circumstellar clouds and the ionosphere of the earth, etc.

Optogalvanic control of instabilities in dusty plasma

This paper presents experimental results on the control of periodic contraction of the void border and proposes a hypothesis on its mechanism, based on the distinctive features of a dusty plasma - its heterogeneity and the presence of the volumetric sink in it.

Connecting the wakefield instabilities in dusty plasmas.

The wakefield, or ion focus, formed by ions streaming past dust particles trapped in the plasma sheath leads to two types of instabilities: the Schweigert instability in multilayer systems and the mode-coupling instability that already appears in single-layer dust systems. Here, a model is presented that treats both types of instability in a common description. The parameter space for the onset of the instabilities is determined. A new variant of the mode-coupling instability is found to arise from the interaction among the layers. For weak confinement, all instabilities continuously merge into each other. For stronger confinement of the dust mainly the Schweigert type of instability is observed.

Effects of the relative motion of different particles on the wave instability in dusty plasmas

Theoretical study is carried out for the dust acoustic waves in a dusty plasma. The dispersion relation is obtained from the fluid dynamical model. It is found that the wave frequency depends on the electron number density, wave number, and the speed of electrons or ions. The dependencies of the instability on the system parameters are also discussed. It is found that the long wavelength wave is usually unstable, which may be useful in the plasma physics, especially in the magnetic confined fusion system or the charged beam dynamics in the accelerated driven system.

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 Schrodinger 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.

Effect of magnetic field and radiative condensation on the Jeans instability of dusty plasma with polarization force

The Jeans instability of self-gravitating dusty plasma with polarization force is investigated considering the effects of magnetic field, dust temperature and radiative condensation. The condition of Jeans instability and expression of critical Jeans wave number are obtained which depend upon polarization force and dust temperature but these are unaffected by the presence of magnetic field. The radiative heat-loss functions also modify the Jeans condition of instability and expression of critical Jeans wave number. It is observed that the polarization force and ratio of radiative heat-loss functions have destabilizing while magnetic field and dust temperature have stabilizing influence on the growth rate of Jeans instability.

Dissipative drift instability in dusty plasma

An investigation has been done on the very low-frequency electrostatic drift waves in a collisional dusty plasma. The dust density gradient is taken perpendicular to the magnetic field \documentclass[12pt]{minimal}\begin{document}$\overrightarrow{B_{0}}$\end{document}B0⃗, which causes the drift wave. In this case, low-frequency drift instabilities can be driven by \documentclass[12pt]{minimal}\begin{document}$\overrightarrow{E_{1}}\times \overrightarrow{B_{0}}$\end{document}E1⃗×B0⃗ and diamagnetic drifts, where \documentclass[12pt]{minimal}\begin{document}$\overrightarrow{E_{1}}$\end{document}E1⃗ is the perturbed electric field. Dust charge fluctuation is also taken into consideration for our study. The dust- neutral and ion-neutral collision terms have been included in equations of motion. It is seen that the low-frequency drift instability gets damped in such a system. Both dust charging and collision of plasma particles with the neutrals may be responsible for the damping of the wave. Both analytical and numerical techniques have been used while developing the theory.

Observation of the Taylor instability in a dusty plasma

Observations of the Taylor instability in a laboratory dusty plasma are presented. The dust cloud, formed in a dc argon glow-discharge plasma, is stratified into regions of high and low dust densities. The instability was triggered by a spontaneous intrusion of the low density dust fluid into the high density dust fluid at the interface. The instability in the dust fluid was phenomenologically similar to the hydrodynamic Taylor instability that occurs when a light fluid is accelerated into a heavy fluid.

New low-frequency waves and negative mass instability in dusty plasmas

AbstractLow-frequency dusty plasma waves with frequencies much smaller than the frequency of charging collisions of plasma particles with dust particles are considered taking into account elastic and charging collisions of plasma particles with dust and neutrals. The usual dust sound waves with an upper frequency equal to the dust plasma frequency are found to be present only for wavelengths much smaller than the plasma particle effective mean free path due to the effective collision frequency. The effectice collision frequency is found to be inversely proportional to the square root of the product of the charging frequency and the frequency of particle momentum losses, involving processes due to elastic plasma particle–dust collisions and collisions with neutrals. It is shown that when the wavelength of the wave is much larger than the mean free path for effective collisions, the properties of the waves are different from those considered previously. A negative mass instability is found in this domain of frequencies when the effective mean free path of ions is larger than the effective mean free path of electrons. In the absence of neutrals, this appears to be possible only if the temperature of ions exceeds the electron temperature. This can occur in laboratory experiments and space plasmas but not in plasma-etching experiments. In the absence of instability, a new dust oscillation, a dust charging mode, is found, whose frequency is almost constant over a certain range of wave numbers. It is inversely proportional to the dust mass and charging frequency of the dust. A new dust electron sound wave is found for frequencies less than the frequency of the dust charging mode. The velocity of the dust electron sound wave is determined by the electron temperature but not the ion temperature, as for the usual dust sound waves, with the electron temperature substantially exceeding the ion temperature.

Rayleigh Taylor instability in a dusty plasma

A non-local theory is developed to study the Rayleigh–Taylor instability in an inhomogeneous dusty plasma in the presence of a uniform magnetic field. Using the fluid equations and the dynamics of charged dust grains, an eigenmode equation is derived to study the stability of the mode. Typical space parameters in the vicinity of Saturn are used to investigate the stability of the mode. The growth rate of the Rayleigh–Taylor is found to be drastically higher in a dusty plasma than in a pure plasma. This might have a wider consequence in explaining the origin of low-frequency modes in various situations in the space atmosphere. The effects of the dust charge, and the dust density on the growth rate of the instability are also studied.

Mixed-Mode Oscillations in Complex-Plasma Instabilities

Instabilities in dusty plasmas are frequent phenomena. We show that some instabilities can be described by mixed-mode oscillations often encountered in chemical systems or neuronal dynamics and studied through dynamical system theories. The time evolution of these instabilities is studied through the change in the associated waveform. Frequency and interspike interval are analyzed and compared to results obtained in other scientific fields concerned by mixed-mode oscillations.

Self-excited void instability in dusty plasmas: plasma and dust cloud dynamics during the heartbeat instability

When a three-dimensional dust cloud is present in a plasma, a dust-free region, called a void, is usually obtained in the plasma centre. Under certain conditions, this region exhibits a self-excited unstable behaviour consisting of successive contractions and expansions of its size. In this paper, this low frequency instability (few Hz), called a ‘heartbeat’, is characterised by various diagnostics. Electrical and optical measurements both correlated with high speed imaging brought to the fore the main features of this instability. Forces involved in the void existence are an inward electrostatic force and an outward ion drag one. The force balance ensures an open void but this equilibrium can be disturbed, leading to the observed instabilities. As these forces are strongly dependent on local ionisation conditions, correlations between physical processes in the plasma volume and the dust cloud motion are investigated through experimental results.

Kinetic theory of the streaming instability in dusty plasmas

The free energy associated with the relative streaming of plasma and dust particles can feed streaming instabilities. Here we consider the case of an unmagnetized plasma and use the results of kinetic theory which consistently take into account the plasma particles-dust collisions and dust charge fluctuations. These are valid in the parameter regime where the plasma particles-dust collisions dominate with respect to the binary plasma collisions.

Effect of non-thermal ion distributions on the Jeans instability in dusty plasmas

Non-thermal ion distributions are a characteristic feature of space plasmas, and in the current work the influence of such non-thermal ion distributions on the Jeans instability is examined. Following previous general models, the electrons are taken to be Boltzmann on the timescales involved, whilst the negative dust component is modelled by the continuity and momentum equations. The ion dynamics are described via a non-thermal Cairns distribution. The linear dispersion relation is derived and analysed for varying degrees of deviation from ordinary thermal behaviour, determined by the characteristic parameter of the Cairns distribution.