M. R. Gupta

Instability of dust acoustic wave due to nonthermal ions in a charge varying dusty plasma

The effects of nonthermal ions with excess of fast (energetic) ions on linear dust acoustic (DA) wave propagation has been investigated incorporating the dust charge variation and the isothermal dust pressure variation. It is seen that due to the dust charge variations in the presence of nonthermal ions, instead of the usual damping, there is a growth of the DA wave if the ion nonthermality parameter a>15(1+σi)/(8−72σi), σi(=Ti/Te≪1), Ti(Te) is the ion (electron) temperature, and there may occur, under certain conditions, exponentially growing mode with zero real frequency. It is also seen that in the absence of dust charge variations there also occurs a zero real frequency, exponentially growing mode if the ion nonthermality parameter a>1. In absence of dust charge variations or in the presence of adiabatic dust charge variations, finite dust temperature Td can stabilize the instability. However, in the presence of nonadiabatic dust charge variations Td cannot stabilize the instability.

Nonlinear properties of small amplitude dust ion acoustic solitary waves

In this paper some nonlinear characteristics of small amplitude dust ion acoustic solitary wave in three component dusty plasma consisting of electrons, ions, and dust grains have been studied. Simultaneously, the charge fluctuation dynamics of the dust grains under the assumption that the dust charging time scale is much smaller than the dust hydrodynamic time scale has been considered here. The ion dust collision has also been incorporated. It has been seen that a damped Korteweg–de Vries (KdV) equation governs the nonlinear dust ion acoustic wave. The damping arises due to ion dust collision, under the assumption that the ion hydrodynamical time scale is much smaller than that of the ion dust collision. Numerical investigations reveal that the dust ion acoustic wave admits only a positive potential, i.e., compressive soliton.

Effect of nonadiabatic dust charge variations on nonlinear dust acoustic waves with nonisothermal ions

The effect of nonadiabatic dust charge variation on the nonlinear dust acoustic wave in a dusty plasma consisting of warm adiabatic dust grains, isothermal electrons and nonisothermal ions have been investigated by reductive perturbation technique. It has been shown that due to the nonadiabatic dust charge variation and also for the presence of nonisothermal ions, nonlinear dust acoustic wave is governed by a modified Korteweg–de Vries Burger (mKdVB) equation. The Burger term arises due to the nonadiabatic dust charge variation, whereas the nonlinear terms are modified due the different effects of nonisothermal ions. Numerical integration of mKdVB equation shows that the nonlinear dust acoustic wave admits negative potentials with the oscillatory (dispersion dominant) or monotonic (dissipation dominant) shock transition and exhibits compressional shock wave.

Dust acoustic shock wave at high dust density

Dust acoustic (DA) shock wave at high dust density, i.e., the dust electroacoustic (DEA) or dust Coulomb (DC) shock wave has been investigated incorporating the nonadiabatic dust charge variation. The nonlinear DEA (DC) shock wave is seen to be governed by the Korteweg–de Vries Burger equation, in which the Burger term is proportional to the nonadiabaticity generated dissipation. It is seen that the shock strength decreases but after reaching minimum, it increases as the dust space charge density |qdnd| increases and the shock strength of DA wave is greater than that of DEA (DC) wave. Moreover the DEA (DC) shock width increases appreciably with increase mass mi of the ion component of the dusty plasma but for DA shock wave the effect is weak.

Small-amplitude nonlinear dust acoustic wave a magnetized dusty plasma with charge fluctuation

Some properties of nonlinear dust acoustic waves in magnetized dusty plasma with variable charges by reductive perturbation technique have been studied. The effect of adiabatic dust charge variations under the assumption that the ratio of dust charging time to the dust hydrodynamical time is very small, and the nonadiabatic dust charges variations under the assumption that the same ratio is small but finite, are also incorporated. It is seen that the magnetic field and the dust charge variations significantly modify the wave amplitude. It is also seen that in case of adiabatic charge variations, the Korteweg-de Vries (KdV) equation governs the nonlinear dust acoustic wave, whereas in case of nonadiabatic dust charge variations, the wave is governed by the KdV Burger equation. Nonadiabaticity generated anomalous dissipative effect causes generation of the dust acoustic shock wave. Numerical integration of KdV Burger equation shows that the dust acoustic wave admits oscillatory (dispersion dominant) or monotone (dissipation dominant) shock solutions depending on the magnitude of the coefficient of the Burger term.

Charging-delay effect on longitudinal dust acoustic shock wave in strongly coupled dusty plasma

Taking into account the charging-delay effect, the nonlinear propagation characteristics of longitudinal dust acoustic wave in strongly coupled collisional dusty plasma described by generalized hydrodynamic model have been investigated. In the “hydrodynamic limit,” a Korteweg–de Vries Burger (KdVB) equation with a damping term arising due to dust-neutral collision is derived in which the Burger term is proportional to the dissipation due to dust viscosity through dust-dust correlation and charging-delay-induced anomalous dissipation. On the other hand, in the “kinetic limit,” a KdVB equation with a damping term and a nonlocal nonlinear forcing term arising due to memory-dependent strong correlation effect of dust fluid is derived in which the Burger term depends only on the charging-delay-induced dissipation. Numerical solution of integrodifferential equations reveals that (i) dissipation due to dust viscosity and principally due to charging delay causes excitation of the longitudinal dust acoustic shock ...

Small Amplitude Nonlinear Dust Acoustic Wave Propagation in Saturn's F, G and E Rings

Nonlinear properties of small amplitude dust acoustic waves, incorporatingboth the ion inertial effect and dust drift effect have been studied.The effect of dust charge variation is also incorporated. It is seen thatdue to the dust charge variation, a Korteweg-de Vries (KdV) equationwith positive or negative damping term depending on the wave velocityand the ring parameters governes the nonlinear dust acoustic wave. It isseen that the damping or growth arises due to the assumption that dusthydrodynamical time scale is much smaller than that of the dust chargingscale. This assumption is valid only for planetary rings such as SaturnsF, G and E rings. Numerical investigations reveal thatall the three rings in F, G and E, dust acoustic solitary wave admits both negative and positive potentials. Instability arises from the available freeenergy of drift motion of dust grains only for the wave with wave velocity λ

Ion acoustic shock waves in a collisional dusty plasma

The effect of ion–dust collisions on small amplitude nonlinear dust ion acoustic waves has been investigated. Analytical investigation shows that propagation of the small amplitude wave is governed by Korteweg–de Vries (KdV) Burger equation. It is found that the coefficient of the Burger term is proportional to the ion viscosity, which arises through ion–dust collisions and depends on the temperatures and number densities of the electrons, ions and also on the number density of dust grains, as seen in a recent experiment (Nakamura et al.). Numerical investigations on the basis of that experimental data show that the dust–ion acoustic wave exhibits both oscillatory and monotonic shocks depending on the number density of dust particles, as observed in that experiment [Nakamura et al., Phys. Rev. Lett. 83, 1602 (1999)].

Effect of magnetic field on temporal development of Rayleigh–Taylor instability induced interfacial nonlinear structure

The effect of magnetic field on the nonlinear growth rate of Rayleigh–Taylor instability induced two fluid interfacial structures has been investigated. The magnetic field is assumed to be parallel to the plane of the two fluid interface and acts in a direction perpendicular to the wave vector. If the magnetic field is restricted only to either side of the interface, the growth rate may be depressed (may almost disappear) or be enhanced depending on whether the magnetic pressure on the interface opposes the instability driving pressure difference g(ρh−ρl)y or acts in the same direction. If magnetic field is present on both sides of the two fluid interface, stabilization may also take place in the sense that the surface of separation undulates periodically when the force due to magnetic pressure on two sides is such as to act in opposite direction. This result differs from the classical linear theory result which predicts that the magnetic field parallel to the surface has no influence on the growth rate w...

Effect of compressibility on the Rayleigh–Taylor and Richtmyer–Meshkov instability induced nonlinear structure at two fluid interface

The effect of compressibility and of density variation on Rayleigh–Taylor and Richtmyer–Meshkov instability of the temporal development of two fluid interfacial structures such as bubbles and spikes have been investigated. It is seen that the velocity of the tip of the bubble or spike increases (destabilization) if the local Atwood number increases due to density variation of either of the fluids. The opposite is the result, i.e., the bubble or spike tip velocity decreases (stabilization) if the density variation leads to lowering of the value of the local Atwood number. The magnitude of stabilization or destabilization is an increasing function of the product of the wave number k and interfacial pressure p0. The effect of compressibility is quite varied. If the heavier (upper) fluid alone is incompressible (γh→∞), but the lighter fluid is compressible the growth rate is higher (destabilization) than when both the fluids are incompressible. Moreover the heavier fluid remaining incompressible the growth ra...