Small Amplitude Dust Acoustic Waves Research Articles

The study of nonlinear dust acoustic wave propagation in a Lorentzian dusty Vlasov plasma in the presence of negative ions

Applying a reductive perturbation analysis in the Vlasov–Poisson model, a Korteweg–de Vries (KdV) equation has been derived for small amplitude dust acoustic waves in a Lorentzian dusty plasma composed of electrons, positive ions, negative ions and charged dust particles. In this paper, two models have been considered, one containing negative and the other containing positive grain charges. Nonlinear propagation of dust acoustic waves in both cases of negative and positive grain charges is governed by KdV equation which gives dust acoustic soliton solution. This dust acoustic soliton solution is rarefied for negative equilibrium dust charge and compressive for positive equilibrium dust charge. Our investigation also shows that the amplitude of dust acoustic soliton in both cases is less than their amplitudes if they are obtained by fluid theory. Thus, our kinetic model captures the nonlinear damping effect of dust acoustic soliton which is absent in fluid theory. The effect of kappa index and dust temperature on the soliton amplitude and width are also studied.

Nonlinear Dust Acoustic Waves in Dissipative Space Dusty Plasmas with Superthermal Electrons and Nonextensive Ions

The nonlinear characteristics of the dust acoustic (DA) waves are studied in a homogeneous, collisionless, unmagnetized, and dissipative dusty plasma composed of negatively charged dusty grains, superthermal electrons, and nonextensive ions. Sagdeev pseudopotential technique has been employed to study the large amplitude DA waves. It (Sagdeev pseudopotential) has an evidence for the existence of compressive and rarefractive solitons. The global features of the phase portrait are investigated to understand the possible types of solutions of the Sagdeev form. On the other hand, the reductive perturbation technique has been used to study small amplitude DA waves and yields the Korteweg-de Vries-Burgers (KdV-Burgers) equation that exhibits both soliton and shock waves. The behavior of the obtained results of both large and small amplitude is investigated graphically in terms of the plasma parameters like dust kinematic viscosity, superthermal and nonextensive parameters.

Complex Korteweg-de Vries equation and nonlinear dust-acoustic waves in a magnetoplasma with a pair of trapped ions

The nonlinear propagation of dust-acoustic (DA) waves in a magnetized dusty plasma with a pair of trapped ions is investigated. Starting from a set of hydrodynamic equations for dust fluids as well as kinetic Vlasov equations for ions, and applying the reductive perturbation technique, a Korteweg-de Vries (KdV)-like equation with a complex coefficient of nonlinearity is derived, which governs the evolution of small-amplitude DA waves in plasmas. The complex coefficient arises due to vortex-like distributions of both positive and negative ions. An analytical as well as numerical solution of the KdV equation are obtained and analyzed with the effects of external magnetic field, the dust pressure as well as different mass and temperatures of ions.

Nonlinear acoustic waves in a collisional self-gravitating dusty plasma

Using the reductive perturbation method, we investigate the small amplitude nonlinear acoustic wave in a collisional self-gravitating dusty plasma. The result shows that the small amplitude dust acoustic wave can be expressed by a modified Korteweg-de Vries equation, and the nonlinear wave is instable because of the collisions between the neutral gas molecules and the charged particles.

Small amplitude nonlinear electrostatic waves in a collisional complex plasma with positively charged dust

The effect of collision on small amplitude dust-acoustic waves is investigated for a plasma with positively charged dust grains. Taking into account the presence of different electron populations in thermal equilibrium, a modified Korteweg–de Vries equation is established. The existence conditions and nature of the waves, i.e., rarefactive or compressive, are found to be mainly dependent on the temperature and the density of the cold electrons. The present model is used to understand the salient features of the fully nonlinear dust-acoustic waves in the lower region of the Earth’s ionosphere, at an altitude of ∼85 km with the presence of an external heating source.

Effects of obliqueness and external magnetic field on the large amplitude solitary waves in a dusty plasma

The nonlinear excitation of large amplitude dust-acoustic (DA) solitary waves in a magnetized hot dusty plasma consisting of fast ions and charged dust grains is revisited to take into account the effects of embedding external magnetic field. The DA solitary wave is assumed to propagate obliquely to the magnetic field. Sagdeev's approach, which is valid for arbitrary amplitude solitary waves, is used. Both compressive and rarefactive solitary structures are shown to coexist by the effects of obliqueness and nonthermal or fast ions. It is found that as the percentage of fast particles ( β ) increases, the critical Mach number ( M c ) increases and the increase is more effective at the higher value of the direction cosine ( L z ). The solitary wave solutions for small amplitude DA waves exhibit distinct behaviors for different values of dust fluid temperature, β and L z .

Effect of adiabatic variation of dust charges on dust acoustic solitary waves in magnetized dusty plasmas

The effect of dust charging and the influence of its adiabatic variation on dust acoustic waves is investigated. By employing the reductive perturbation technique we derived a Zakharov–Kuznetsov (ZK) equation for small amplitude dust acoustic waves. We have analytically verified that there are only rarefactive solitary waves for this system. The instability region for one-dimensional solitary wave under transverse perturbations has also been obtained. The obliquely propagating solitary waves to the z-direction for the ZK equation are given in this paper as well.

Effect of dust-charge variation on dust acoustic solitary waves in a dusty plasma with trapped electrons

The effect of variable dust charge, dust temperature and trapped electrons on small-amplitude dust acoustic waves is investigated. It is found that both compressive and rarefractive solitons as well as double layers exist depending on the non-isothermality parameter. A modified Korteweg de Vries (MKdV) equation is derived. Critical cases, at which the nonlinear coefficient is approximately zero, are derived. In the vicinity of the critical values, KdV and further MKdV (FMKdV) equations are obtained. Employing quasipotential analysis, the Sagdeev potential equation has been derived. Because of the presence of free and trapped electrons, the plasma acoustic wave exhibits different features of various solitary waves. The Sagdeev potential equation, at a small amplitude, shows that the ordering of non-isothermality in the dusty plasma plays a unique role. In the case of a plasma with first-order non-isothermality, the Sagdeev potential equation shows the compressive solitary-wave propagation while, for a plasma with higher-order non-isothermality, the solution of this equation reveals the coexistence of compressive and farefractive solitary waves. In addition, for certain plasma parameters, the solitary wave disappears and a double layer is expected. Again, with the better approximation in the Sagdeev potential equation, more features of solitary waves, known as spiky and explosive, along with the double layers, are also highlighted. The findings of this investigation may be useful in understanding laboratory plasma phenomena and astropbysical situations.

Dust acoustic solitary waves and double layers in a dusty plasma with trapped electrons

The effect of variable dust charge, dust temperature, and trapped electrons on small amplitude dust acoustic waves is investigated. It is found that both compressive and rarefactive solitons as well as double layers exist depending on the nonisothermality parameter. A modified Korteweg–de Vries is derived. At critical density, the Korteweg–de Vries equation is obtained. Employing quasipotential analysis, the Sagdeev potential equation with the inclusion of different new effects has been derived. Because of the presence of free and trapped electrons, the plasma acoustic wave has gained features of various solitary waves. The Sagdeev potential equation, at a small amplitude, shows that the ordering of nonisothermality plays a unique role. In the case of a plasma with first-order nonisothermality, the Sagdeev potential equation shows the compressive solitary wave propagation, while for plasma with higher-order nonisothermality, the solution of this equation reveals the coexistence of both compressive and rarefactive solitary waves. In addition, for certain plasma parameters, the solitary wave disappears and a double layer is expected. Again, with the better approximation in the Sagdeev potential equation, more features of solitary waves, e.g., spiky and explosive, along with the double layers, are also highlighted. The findings of this investigation may be useful in understanding laboratory plasma phenomena and astrophysical situations.

Dust acoustic shock waves in two-component dusty plasma

The effect of electron–dust collision on small-amplitude nonlinear dust acoustic (DA) wavesin two-component thermal dusty plasma consisting of positively charged (due to thermionicemission) dust grains and electrons has been investigated incorporating the nonadiabaticity ofdust-charge variation arising due to delays in the dust charging, i.e. due to small nonzero values ofωpd/νch, whereωpd is the dust-plasmafrequency and νch is the dust-charging frequency. The propagation of small-amplitude DA waves isgoverned by a modified Korteweg–de Vries–Burger equation in which the Burger termarising due to the charge delay induced dissipation. Numerical investigationsreveal that this equation has a shock-wave solution. Numerical investigations alsoreveal that in the absence of collision-induced dissipation the charge-delay-induceddissipation also causes the generation of a DA shock wave in two-component dustyplasma.

Dust acoustic solitary waves and double layers in a dusty plasma with an arbitrary streaming ion beam

The effects of variable dust charge, dust temperature and an arbitrary streaming ion beam on small amplitude dust acoustic waves are investigated. It is found that both compressive and rarefactive solitons as well as double layers exist. There exists a critical ion beam velocity below which the ion beam is unable to generate solitons. Korteweg–de Vries (KdV) equations with third and fourth-order nonlinearity at the critical values are derived and the properties of dust acoustic solitary waves are discussed. In the vicinity of the critical values, KdV-type with mixed nonlinearity is obtained. The quite dense positive ion, the dust temperature, the ion beam density, mass ratio and temperature govern the existence of dust acoustic waves. The findings of this investigation may be useful in understanding laboratory plasma phenomena and astrophysical situations.

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 Saturn'sF, 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 <V0, the drift velocity of the dust.