Strongly Coupled Dusty Plasma Research Articles

Compressibility effects on Rayleigh-Taylor instability in magnetized strongly coupled dusty plasma

The compressibility effects have been studied on the internal wave modes and Rayleigh-Taylor (R-T) instability in a magnetized strongly coupled dusty plasma (SCDP). A dusty fluid model is constructed considering the effects of weakly coupled electrons/ions and strongly coupled dust grains under the influence of the gravitational field. The effects of the magnetic field and viscoelastic coefficients have been incorporated under the generalized hydrodynamic (GH) fluid description in a quasineutral dusty plasma. The dispersion relation of R-T instability is derived analytically and discussed in the strongly coupled limit. The compressibility effects have appeared in the internal wave modes, significantly modifying the R-T instability criterion and growth rates. The Coulomb coupling parameter and dust magnetosonic speed suppress the growth rate of the R-T instability in a compressible SCDP.

Propagation characteristics of longitudinal modes in dusty plasmas

The space-time correlation function has been obtained in strongly coupled dusty plasmas (SCDPs) using equilibrium molecular dynamics (EMD) simulations. The simulated results for three-dimensional (3D) SCDPs with suitable normalization are computed over a wide domain of plasma parameters (Γ, κ) in a microcanonical ensemble. The EMD simulations indicate that different modes of propagated wave in SCDPs are analyzed for four different values of wave number (k). New investigations of normalized longitudinal current correlation function CL(k, t) show that the amplitude of oscillation and frequency of propagated modes increase with an increase in k. The obtained results for longitudinal modes of oscillation indicate that the dust particles remain in damping behavior at the low Γ, damped oscillation with decreasing amplitude inside decaying exponential envelope at intermediate Г, and sinusoidal oscillation at high Г, depending on κ. The system size (N) does not significantly affect the propagated modes of oscillation, while the periodic oscillation shifts toward higher Γ with increasing N and κ. The computations show that normalized longitudinal CL(k, t) current correlation particularly depend on Coulomb coupling (Γ), Debye screening (κ), and wave number (k). In our simulations, the frequency and the amplitude of oscillation of the dust particles decrease with an increment of κ and system size (N), but the frequency increases and the amplitude decreases with increasing Γ, as expected. It has been demonstrated that the EMD method is used to study the different propagated modes in dusty plasma systems and can be used to predict the damping behavior, damped oscillation, and periodic phenomena in 3D strongly coupled SCDPs.

Phase plane analysis of the dust-acoustic waves for the Burgers equation in a strongly coupled dusty plasma

Phase plane analysis of dust-acoustic waves (DAWs) for the Burgers equation is investigated in a strongly coupled dusty plasma (SCDP) for the first time. The Burgers equation is obtained applying the reductive perturbation technique under the class of generalized hydrodynamic equations. The dynamical system of the Burgers equation is obtained using the traveling wave transfiguration. A phase plot containing a pair of heteroclinic orbits and a family of periodic orbits is presented for DAWs employing the concept of bifurcation theory through phase plane analysis. The analytical forms of kink and anti-kink wave solutions are derived by the tanh method. Analytical form of the periodic wave solution for the Burgers equation is derived for the first time in a SCDP. The parameters such as coupling parameter ( $$\Gamma$$ ), viscosity coefficient ( $$~\eta$$ ), dust–neutral collisional frequency ( $$\nu _{dn}$$ ), temperature of dusts ( $$T_d$$ ) and speed of wave (v) have significant effects on the dust-acoustic kink, anti-kink and periodic wave solutions.

Studies of weak external force on thermal conductivity of complex liquids using homogenous perturbed simulations

A modified Evan-Gillan homogenous perturbed scheme was employed to measure the thermal response and corresponding normalized plasma thermal conductivity (λ0) of strongly coupled dusty plasmas (SCDPs). Homogenous perturbed molecular dynamics (HPMD) approach was employed to analyze the efficiency and compared the obtained outcomes of perturbed heat flux vector to the outcomes computed through equilibrium molecular dynamics (EMD) approach. Our new outcomes show that the thermal response of heat energy current through HPMD and EMD approaches is an excellent agreement with each other for SCDPs at much low value of normalized external perturbation (F*). The obtained HPMD simulations demonstrate that the presented approach provides good outcomes with fast convergence and small system size for low-tointermediate plasma couplings (Γ) at very weak F*. It was found that the measured plasma λ0 outcomes at nearly equilibrium weak F* (= 0.00005) are in reasonable agreement with earlier results obtained from EMD, homogenous and inhomogeneous nonequilibrium molecular dynamics simulations and theoretical predictions and generally overpredicted the plasma λ0 by ~1%–~24% depending on the arrangement of plasma parameters (Г, к). It was shown that the HPMD is an excellent approach to calculate the plasma λ0 and to recognize the elementary patterns in 3D SCDPs.

Stability of three-dimensional dust acoustic waves in a strongly coupled dusty plasma including kappa distributed superthermal ions and electrons

A rigorous theoretical investigation of multi-dimensional instability of dust acoustic (DA) solitary waves in strongly coupled dusty plasma (SCDP) composed of superthermal distributed ions and electrons is presented. The dynamics of linear and nonlinear electrostatic excitations are studied. The dispersion properties of linear DA solitary waves are discussed in details. A nonlinear Zakharov-Kuznetsov (ZK) equation adequate for describing DA solitary waves is also derived. At the vicinity of the critical phase velocity, an extended ZK (EZK) equation is derived. The effects of the electrons and ions superthermality, the strongly and weakly coupling cases, and the ion-to-electron temperature ratio are discussed. The growth rate of the produced waves is calculated. It is found that the DA phase velocity decreases as the ion-to-electron temperature ratio increases. The contrary is occurred for strongly coupled system. The instability growth rate increases (decreases) by increasing the ion-to-electron temperature ratio (the superthermal parameters). The present investigation could be helpful in understanding the propagation and the instability of the detected DA solitary waves in laboratory, space and astrophysics mediums where superthermal particles are present.

The rotating Rayleigh-Taylor instability in a strongly coupled dusty plasma

The linear Rayleigh-Taylor instability (RTI) in a uniformly rotating strongly coupled dusty plasma (SCDP) is investigated both analytically and numerically. The influence of the Coriolis force on the dust particles is considered mainly owing to the drag force of the magnetized ions. The dispersion relation is analytically derived using appropriate boundary conditions and velocity profile. The dispersion characteristics are analyzed in the strongly coupled (kinetic) limit, and it is observed that the criterion of linear RTI is modified due to the presence of rotation and shear velocity comprising strong correlation effects. It is found that in the presence of intermediate magnetic field in SCDP, dust cloud rotation and strong correlation effects altogether stabilize the growth rate of linear RTI. The analytical growth rate of RTI shows a good agreement with the growth rate calculated numerically.

Modified Potential Around a Moving Test Charge in Strongly Coupled Dusty Plasma

The theory of dynamical (wake) potential behind a moving test charge in a weakly coupled dusty plasma is extended to that including of strong interaction between dust grains. Such strong interaction is included in the dielectric response function by a generalized hydrodynamic (GH) fluid model. It is shown that the strong interaction between dusts including the lattice spacing correction has a significant effect on the wake potential in dusty plasma. This may be used to investigate basic features of phase transition and possibility of lattice formation of dusty plasma.

Modified gravitational instability of degenerate and non-degenerate dusty plasma

The gravitational instability of strongly coupled dusty plasma (SCDP) is studied considering degenerate and non-degenerate dusty plasma situations. The SCDP system is assumed to be composed of the electrons, ions, neutrals, and strongly coupled dust grains. First, in the high density regime, due to small interparticle distance, the electrons are considered degenerate, whereas the neutrals, dust grains, and ions are treated non-degenerate. In this case, the dynamics of inertialess electrons are managed by Fermi pressure and Bohm potential, while the inertialess ions are by only thermal pressure. Second, in the non-degenerate regime, both the electrons and ions are governed by the thermal pressure. The generalized hydrodynamic model and the normal mode analysis technique are employed to examine the low frequency waves and gravitational instability in both degenerate and non-degenerate cases. The general dispersion relation is discussed for a characteristic timescale which provides two regimes of frequency, i.e., hydrodynamic regime and kinetic regime. Analytical solutions reveal that the collisions reduce the growth rate and have a strong impact on structure formation in both degenerate and non-degenerate circumstances. Numerical estimation on the basis of observed parameters for the degenerate and non-degenerate cases is presented to show the effects of dust-neutral collisions and dust effective velocity in the presence of polarization force. The values of Jeans length and Jeans mass have been estimated for degenerate white dwarfs as Jeans length LJ=1.3×105 cm and Jeans mass MJ=0.75×10−3M⊙ and for non-degenerate laboratory plasma Jeans length LJ=6.86×1016 cm and Jeans mass MJ=0.68×1010M⊙. The stability of the SCDP system is discussed using the Routh-Hurwitz criterion.

Nonlinear coupling of acoustic and shear mode in a strongly coupled dusty plasma with a density dependent viscosity

The nonlinear propagation of low frequency waves, in a collisionless, strongly coupled dusty plasma (SCDP) with a density dependent viscosity, has been studied with a proper Galilean invariant generalized hydrodynamic (GH) model. The well known reductive perturbation technique (RPT) has been employed in obtaining the solutions of the longitudinal and transverse perturbations. It has been found that the nonlinear propagation of the acoustic perturbations govern with the modified Korteweg-de Vries (KdV) equation and are decoupled from the sheared fluctuations. In the regions, where transversal gradients of the flow exists, coupling between the longitudinal and transverse perturbations occurs due to convective nonlinearity which is true for the homogeneous case also. The results, obtained here, can have relative significance to astrophysical context as well as in laboratory plasmas.

Stability characteristics of a non-Newtonian strongly coupled dusty plasma in the presence of shear flow

A visco-elastic medium, such as a strongly coupled dusty plasma (SCDP), permits both the propagation of longitudinal dust acoustic mode due to compressibility and transverse shear mode due to elasticity. In the presence of finite velocity shear, these two modes get coupled with each other and eventually the coupled mode becomes unstable. In a non-Newtonian dust fluid, it has been found that the viscosity gradient has a modulating effect on this shear-driven instability under various parametric regimes. A detailed investigation has been carried out on the effect of viscosity gradient on the stability characteristics of a strongly coupled dusty plasma by using the conventional dust fluid equations; both analytically and numerically. These results can be helpful in understanding the phenomena associated with mechanical instabilities in highly viscous fluids; such as metallic glasses, Earth's mantle etc.

Jeans instability in collisional strongly coupled dusty plasma with radiative condensation and polarization force

The influence of dust-neutral collisions, polarization force, and electron radiative condensation is analysed on the Jeans (gravitational) instability of partially ionized strongly coupled dusty plasma (SCDP) using linear perturbation (normal mode) analysis. The Boltzmann distributed ions, dynamics of inertialess electrons, charged dust and neutral particles are considered. Using the plane wave solutions, a general dispersion relation is derived which is modified due to the presence of dust-neutral collisions, strong coupling effect, polarization force, electron radiative condensation, and Jeans dust/neutral frequencies. In the long wavelength perturbations, the Jeans instability criterion depends upon strong coupling effect, polarization interaction parameter, and thermal loss, but it is independent of dust-neutral collision frequency. The stability of the considered configuration is analysed using the Routh–Hurwitz criterion. The growth rates of Jeans instability are illustrated, and stabilizing influence of viscoelasticity and dust-neutral collision frequency while destabilizing effect of electron radiative condensation, polarization force, and Jeans dust-neutral frequency ratio is observed. This work is applied to understand the gravitational collapse of SCDP with dust-neutral collisions.

Modeling of nonlinear envelope solitons in strongly coupled dusty plasmas: Instability and collision

Modeling of instability and collision of nonlinear dust-acoustic (NDA) envelope solitons in strongly coupled dusty plasmas (SCDPs) is theoretically investigated. The SCDPs consists of strongly correlated negatively variable-charged dust grains and weakly correlated Boltzmann electrons and ions. Using the derivative expansion perturbation technique, a nonlinear Schrödinger-type (NLST) equation for describing the propagation of NDA envelope solitons is derived. Moreover, the extended Poincaré–Lighthill–Kuo (EPLK) method is employed to deduce the analytical phase shifts and the trajectories after the collision of NDA envelope solitons. In detail, the results show that both modulation instability and phase shift after collision of NDA envelope solitons will modify with the increase in the effects of the viscosity, the relaxation time, and the dust charge fluctuation. Crucially, the modeling of dust-acoustic envelope solitons collision, as reported here, is helpful for understanding the propagation of NDA envelope solitons in strongly coupled dusty plasmas.

Nonplanar dust acoustic solitary waves in a strongly coupled dusty plasma with superthermal ions

The nonplanar amplitude modulation of dust acoustic (DA) envelope solitary waves in a strongly coupled dusty plasma (SCDP) has been investigated. By using a reductive perturbation technique, a modified nonlinear Schrödinger equation (NLSE) including the effects of geometry, polarization, and ion superthermality is derived. The modulational instability (MI) of the nonlinear DA wave envelopes is investigated in both planar and nonplanar geometries. There are two stable regions for the DA wave propagation strongly affected by polarization and ion superthermality. Moreover, it is found that the nonlinear DA waves in spherical geometry are the more structurally stable. The larger growth rate of the nonlinear DA MI is observed in the cylindrical geometry. The salient characteristics of the MI in the nonplanar geometries cannot be found in the planar one. The DA wave propagation and the NLSE solutions are investigated both analytically and numerically.

Frequency-dependent shear viscosity of a liquid two-dimensional dusty plasma

The viscoelasticity of a two-dimensional (2D) liquid stronglycoupled dusty plasma is studied experimentally, without macroscopic shear. Positions and velocities of the dust particles, measured by video microscopy, are used as the inputs to the generalized Green-Kubo relation to obtain the complex viscosity η(ω). The real part of η(ω) (which corresponds to dissipation) diminishes gradually with frequency, while the imaginary part (which corresponds to elasticity) is peaked at a frequency below the 2D dusty plasma frequency. The viscoelastic approximation is found to accurately describe the 2D experimental results for η(ω), yielding the Maxwell relaxation time τ(M)=0.10 s. Results for η(ω) are compared to 2D molecular dynamics Yukawa simulations and to a previous experiment that was performed using an oscillating macroscopic shear.

Test of the Stokes-Einstein Relation in a Two-Dimensional Yukawa Liquid

The Stokes-Einstein relation, relating the diffusion and viscosity coefficients D and eta, is tested in two dimensions. An equilibrium molecular-dynamics simulation was used with a Yukawa pair potential. Regimes are identified where motion is diffusive and D is meaningful. The Stokes-Einstein relation, Deta proportional k(B)T, was found to be violated near the disordering transition; under these conditions collective particle motion exhibits dynamical heterogeneity. At slightly higher temperatures, however, the Stokes-Einstein relation is valid. These results may be testable in strongly coupled dusty plasma experiments.

Instability of Longitudinal Wave in Magnetized StronglyCoupled Dusty Plasma

Instability of longitudinal wave in magnetized strongly coupled dustyplasmas is investigated. The dust charging relaxation is taken intoaccount. It is found that there exists threshold of interdust distancefor the instability of wave, which is determined significantly by thedust charging relaxation, the coupling parameter of high correlation ofdust as well the strength of magnetic field.

Mean spherical model for strongly coupled dusty plasmas

A solution of the mean spherical model is presented for particles interacting with a pair potential which is repulsive at short-range and attractive at long-range. The solution can be used for the description of the structure of strongly-coupled dusty plasmas, represented as one component systems of dust particles with an interaction potential determined by the plasma dynamics; a screened Coulomb repulsive interaction at short distances and a long-range attraction due to a screened “shadow effect” on the plasma fluxes to the dust particles. A comparison with recent experimental results shows a better agreement when the attractive potential is present.