Dust Acoustic Solitary Waves Research Articles

Stability of three-dimensional obliquely propagating dust acoustic waves in dusty plasma including the polarization force effect

Propagation of dust acoustic solitary waves (DASWs) in a magnetized dusty plasma consisting of extremely massive, negatively/positively charged dust fluid and Boltzmann distributed electrons and ions is studied. A nonlinear Zakharov-Kuznetsov (ZK) equation adequate for describing the solitary waves is derived by applying a reductive perturbation technique. Moreover, an extended Zakharov Kuznetsov (EZK) equation is derived at the vicinity of the critical phase velocity. The effects of the polarization force are explicitly discussed and the growth rate of the produced waves is calculated. It is found that the physical parameters have strong effects on the instability criterion as well as on the growth rate. It is noted that the phase velocity decreases as the polarization force, the effective-to-ion temperature ratio, and the ion-to-electron temperature ratio increase. Moreover, the nonlinearity coefficient and the critical phase velocity increase by increasing the polarization force. The relevance of these findings to a recent plasma experiment and astrophysical plasma observations is briefly discussed.

On the rogue waves propagation in non-Maxwellian complex space plasmas

The implications of the non-Maxwellian electron distributions (nonthermal/or suprathermal/or nonextensive distributions) are examined on the dust-ion acoustic (DIA) rogue/freak waves in a dusty warm plasma. Using a reductive perturbation technique, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation. The latter is used to study the nonlinear evolution of modulationally unstable DIA wavepackets and to describe the rogue waves (RWs) propagation. Rogue waves are large-amplitude short-lived wave groups, routinely observed in space plasmas. The possible region for the rogue waves to exist is defined precisely for typical parameters of space plasmas. It is shown that the RWs strengthen for decreasing plasma nonthermality and increasing superthermality. For nonextensive electrons, the RWs amplitude exhibits a bit more complex behavior, depending on the entropic index q. Moreover, our numerical results reveal that the RWs exist with all values of the ion-to-electron temperature ratio σ for nonthermal and superthermal distributions and there is no limitation for the freak waves to propagate in both two distributions in the present plasma system. But, for nonextensive electron distribution, the bright- and dark-type waves can propagate in this case, which means that there is a limitation for the existence of freak waves. Our systematic investigation should be useful in understanding the properties of DIA solitary waves that may occur in non-Maxwellian space plasmas.

The nonadiabatic dust charge variation on dust acoustic solitary and shock waves in strongly coupled dusty plasmas

The combined effects of nonadiabatic dust charge fluctuation and strongly coupled dust particles on the nonlinear propagation of dust acoustic (DA) waves in dusty plasma consisting of nonthermal electrons and trapped ions with vortex-like distribution are presented here. We use generalized viscoelastic hydrodynamic model for dust particles. In the weak nonlinearity limit, a modified Korteweg–de Vries (KdV) equation with a damping term and a KdV–Burger equation have been derived in the kinetic regime and hydrodynamic regime, respectively. The approximate analytical solitary solution of modified KdV equation is derived in the weak nonadiabatic dust charge variation limit, which shows that the amplitude of DA solitary waves decreases with time. The presence of viscosity due to strong coupling stands for the formation of DA shock waves in the hydrodynamic regime. The results show that the DA shock waves will be oscillating one for weak viscosity and will become monotonic ones for large viscosity.

Effect of dust charge fluctuation on multidimensional instability of dust-acoustic solitary waves in a magnetized dusty plasma with nonthermal ions

Simultaneous effects of dust charge fluctuation and nonthermal ions on the threshold point and growth rate of three-dimensional instability of dust-acoustic solitary waves (DASW) in magnetized dusty plasma have been investigated. In this model, dusty plasma consists of Maxwellian electrons, nonthermal ions, and micron size negatively charged dust particles. Modified Zakharov-Kuznetsov equation for DASW was derived employing a reductive perturbation method and its solitary answer under the influence of dust charge fluctuation and nonthermal ions has been studied. The dispersion relation of DASW has been derived using a small-k perturbation method. Results show that the direction and the magnitude of external magnetic field at which the instability takes place are strongly affected by the rate of dust charge fluctuation and nonthermality of ions. With increasing the number of nonthermal ions, the growth rate of instability decreases, while increasing the dust charge fluctuation increases the growth rate of instability.

Kinematic dust viscosity effect on linear and nonlinear dust-acoustic waves in space dusty plasmas with nonthermal ions

Linear and nonlinear dust-acoustic (DA) waves are studied in a collisionless, unmagnetized and dissipative dusty plasma consisting of negatively charged dust grains, Boltzmann-distributed electrons, and nonthermal ions. The normal mode analysis is used to obtain a linear dispersion relation illustrating the dependence of the wave damping rate on the carrier wave number, the dust viscosity coefficient, the ratio of the ion temperature to the electron temperatures, and the nonthermal parameter. The plasma system is analyzed nonlinearly via the reductive perturbation method that gives the KdV-Burgers equation. Some interesting physical solutions are obtained to study the nonlinear waves. These solutions are related to soliton, a combination between a shock and a soliton, and monotonic and oscillatory shock waves. Their behaviors are illustrated and shown graphically. The characteristics of the DA solitary and shock waves are significantly modified by the presence of nonthermal (fast) ions, the ratio of the ion temperature to the electron temperature, and the dust kinematic viscosity. The topology of the phase portrait and the potential diagram of the KdV-Burgers equation is illustrated, whose advantage is the ability to predict different classes of traveling wave solutions according to different phase orbits. The energy of the soliton wave and the electric field are calculated. The results in this paper can be generalized to analyze the nature of plasma waves in both space and laboratory plasma systems.

Multidimensional Instability of Dust‐Acoustic Solitary Waves in a Magnetized Hot Dusty Plasma with Superthermal Electrons and Ions

AbstractMultidimensional instability of dust‐acoustic solitary wave (DASW) in magnetized dusty plasma with superthermal electrons and ions and micron size hot dust particles is investigated. The Zakharov‐Kuznetsov (ZK) equation, describing the small but finite amplitude DASW, was derived using the reductive perturbation method and its solitary answers was introduced. Effects of electrons and ions superthermality as well as the external magnetic field on the nature of DASW are discussed in detail. Dispersion relation, threshold condition, and growth rate of multidimensional instability of DASW were derived using small‐k (long wavelength plane wave) perturbation expansion method. We found that the direction and strength of external magnetic field extremely affect the growth rate and instability criterion. Results show that growth rate of instability decreases with increasing the number of superthermal electrons and increases with increasing the number of superthermal ions. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dust Acoustic Compressive Waves in a Warm Dusty Plasma Having Non-Thermal Ions and Non-Isothermal Electrons

In this article an investigation is presented on the properties of dust acoustic (DA) compressive solitary wave propagation in an adiabatic dusty plasma, including the effect of non-thermal positive and negative ions and non-isothermal electrons. The reductive perturbation method has been employed to derive the lower degree modified Kadomtsev-Petviashivili (mK-P), 3D Schamel-Korteweg-de-Vries equation or modified Kadomtsev-Petviashivili (mK-P) equations for dust acoustic solitary waves in a homogeneous, unmagnetized and collisionless plasma whose constituents are non-isothermal electrons, singly charged positive and negative non-thermal ions and massive charged dust particles. The stationary analytical solutions of the lower degree mK-P and mK-P equations are numerically analyzed, where the effect of various dusty plasma constituents on DA solitary wave propagation is taken into account. It is observed that both the ions in dusty plasma play a key role in the formation of DA compressive solitary waves, and also the ion concentration and non-isothermal electrons control the transformation of the compressive potentials of the waves.

Erratum to: Dust-acoustic solitary and rogue waves in a Thomas-Fermi degenerate dusty plasma

In our original paper (Irfan et al. 2014), we have found that the KdV based nonlinear Schrodinger (NLS) equation does not satisfy the criteria of modulational instability (i.e., PQ > 0) and the existence of rogue waves, where P and Q are the dispersion and nonlinearity coefficients of NLSE. We therefore have made a remedy correction for this situation in this erratum and applied a well-known multiscale reductive perturbation method (Moslem et al. 2011) to fluid equations of Irfan et al. (2014), analyzing the rogue waves in a Thomas-Fermi dusty plasma. In the previous literature (El-Labany et al. 2012; Rahman et al. 2013; Rahman and Ali 2014; El-Awady and Moslem 2011; ElAwady et al. 2014; Panwar et al. 2013; Panwar and Ryu 2014; Bains et al. 2014 etc.), it was shown that the KdV based NLS Equation holds the condition PQ > 0 for the existence of rogue waves. However, it is later on realized (El-Tantawy and Moslem 2014) that the KdV based NLS equation does not admit the rogue waves, for which the product PQ < 0 holds. Thus, to use a multiscale reductive perturbation method, we consider the expansion S = S0 + ∑∞n=1 e ∑l=∞ l=−∞ S (n) l (ζ, τ ) exp(ilΘ) for dependent variables and the stretching ζ = e(r − Vgt), and τ =

Nonplannar Nonlinear Dust ion Acoustics Solitary and Shock Waves in a Dusty Multi-ion Plasma

We have presented a stern theoretical exploration of the nonplannar and nonlinear propagation of dust-ion acoustic (DIA) waves in a dusty multi-ion plasma. We studied the progation of nonplannar non-linear DIA waves by the reductive perturbation method which leads to the the derivation of the Burgers [Korteweg de-Vries (K-dV)] equation for the shock (solitary) wave propagation. The shock (solitary) waves are found to be formed in a multi-ion dusty plasma due to the balance between nonlinearity and dissipation (dispersion), and that the dissipation (dispersion) arises due to the dust charge fluctuation (deviation of charge neutrality condition). We have analized the effects of nonplannar and nonlinear geometry on the DIA shock and solitary waves propagating in such a dusty multi-ion plasma. We have shown that the nonplanar (cylindrical and spherical) solitary and shock structures are significantly different from planner ones.

Nonlinear dust acoustic travelling waves in dusty plasmas due to dust charge fluctuations

Dust acoustic solitary waves, blow-up solitary waves and periodic waves have been investigated in unmagnetized dusty plasmas with Maxwell-distributed electrons and ions, considering dust charge fluctuations using the bifurcation theory of planar dynamical systems. The basic equations are transformed to an ordinary differential equation involving the electrostatic potential. Applying the bifurcation theory of planar dynamical systems, we have established the existence of solitary, blow-up solitary and periodic waves. Four exact solutions of the solitary, blow-up solitary and periodic waves are derived depending on the physical parameters. Regarding the solitary, blow-up solitary and periodic waves, we have presented the combined effects of the density ratio of electrons and ions (${\it\alpha}$), the temperature ratio of electrons and ions $({\it\beta})$ and the speed of the travelling wave ($v$) on the characteristics of dust acoustic solitary, blow-up solitary and periodic waves.

Effects of strong electrostatic interaction on multi-dimensional instability of dust-acoustic solitary waves in a magnetized strongly coupled dusty plasma

The effects of strong electrostatic interaction among highly charged dust on multi-dimensional instability of dust-acoustic (DA) solitary waves in a magnetized strongly coupled dusty plasma by small-k perturbation expansion method have been investigated. We found that a Zakharov-Kuznetsov equation governs the evolution of obliquely propagating small amplitude DA solitary waves in such a strongly coupled dusty plasma. The parametric regimes for which the obliquely propagating DA solitary waves become unstable are identified. The basic properties, viz., amplitude, width, instability criterion, and growth rate, of these obliquely propagating DA solitary structures are found to be significantly modified by the effects of different physical strongly coupled dusty plasma parameters. The implications of our results in some space/astrophysical plasmas and some future laboratory experiments are briefly discussed.

Landau damping of Gardner solitons in a dusty bi-ion plasma

The effects of linear Landau damping on the nonlinear propagation of dust-acoustic solitary waves (DASWs) are studied in a collisionless unmagnetized dusty plasma with two species of positive ions. The extremely massive, micron-seized, cold, and negatively charged dust particles are described by fluid equations, whereas the two species of positive ions, namely, the cold (heavy) and hot (light) ions are described by the kinetic Vlasov equations. Following Ott and Sudan [Phys. Fluids 12, 2388 (1969)], and by considering lower and higher-order perturbations, the evolution of DASWs with Landau damping is shown to be governed by Korteweg-de Vries (KdV), modified KdV (mKdV), or Gardner (KdV-mKdV)-like equations. The properties of the phase velocity and the Landau damping rate of DASWs are studied for different values of the ratios of the temperatures (σ) and the number densities (μ) of hot and cold ions as well as the cold to hot ion mass ratio m. The distinctive features of the decay rates of the amplitudes of the KdV, mKdV, and Gardner solitons with a small effect of Landau damping are also studied in different parameter regimes. It is found that the Gardner soliton points to lower wave amplitudes than the KdV and mKdV solitons. The results may be useful for understanding the localization of solitary pulses and associated wave damping (collisionless) in laboratory and space plasmas (e.g., the F-ring of Saturn), in which the number density of free electrons is much smaller than that of ions and the heavy, micron seized dust grains are highly charged.

Instability of nonplanar modulated dust acoustic wave packets in a strongly coupled nonthermal dusty plasma

Cylindrical and spherical amplitude modulations of dust acoustic (DA) solitary wave envelopes in a strongly coupled dusty plasma containing nonthermal distributed ions are studied. Employing a reductive perturbation technique, a modified nonlinear Schrödinger equation including the geometrical effect is derived. The influences of nonthermal ions, polarization force, and the geometries on the modulational instability conditions are analyzed and the possible rogue wave structures are discussed in detail. It is found that the spherical DA waves are more structurally stable to perturbations than the cylindrical ones. Possible applications of these theoretical findings are briefly discussed.

Erratum: Existence and damping of dust acoustic solitary waves in a bounded geometry [Phys. Rev. E87, 063101 (2013)

Erratum: Existence and damping of dust acoustic solitary waves in a bounded geometry [Phys. Rev. E<b>87</b>, 063101 (2013)

Solitonic, Periodic and Quasiperiodic Behaviors of Dust Ion Acoustic Waves in Superthermal Plasmas

The solitonic, periodic, and quasiperiodic behaviors of dust ion acoustic waves in superthermal plasmas with q-nonextensive electrons are studied using the bifurcation theory of planar dynamical systems through direct approach. Using a Galilean transformation, model equations are transformed to a Hamiltonian system involving electrostatic potential. The existence of solitary and periodic waves is shown for the unperturbed Hamiltonian system. Analytical forms of these waves are presented depending on physical parameters q and μ. The effects of q and μ are studied on characteristics of nonlinear dust ion acoustic solitary and periodic waves. It is observed that parameters q and μ significantly influence the characteristics of nonlinear dust ion acoustic solitary and periodic structures. Considering an external periodic perturbation, the quasiperiodic behavior of the perturbed Hamiltonian system for dust ion acoustic waves is studied. It is seen that the unperturbed Hamiltonian system has the solitary and periodic wave solutions whereas the perturbed Hamiltonian system has quasiperiodic motion for same values of parameters q,μ and v.

Effect of anisotropic dust pressure and superthermal electrons on propagation and stability of dust acoustic solitary waves

Employing the reductive perturbation technique, Zakharov–Kuznetzov (ZK) equation is derived for dust acoustic (DA) solitary waves in a magnetized plasma which consists the effects of dust anisotropic pressure, arbitrary charged dust particles, Boltzmann distributed ions, and Kappa distributed superthermal electrons. The ZK solitary wave solution is obtained. Using the small-k expansion method, the stability analysis for DA solitary waves is also discussed. The effects of the dust pressure anisotropy and the electron superthermality on the basic characteristics of DA waves as well as on the three-dimensional instability criterion are highlighted. It is found that the DA solitary wave is rarefactive (compressive) for negative (positive) dust. In addition, the growth rate of instability increases rapidly as the superthermal spectral index of electrons increases with either positive or negative dust grains. A brief discussion for possible applications is included.

Nonlinear Dust Acoustic Waves in Strongly Coupled Quantum Dusty Plasmas

Using a set of fluid equations to describe the inertial dust grain component in dense collisionless unmagnetized quantum dusty plasmas, where the electrons and ions obey the Thomas-Fermi density distribution, the propagation characteristics of dust acoustic solitary waves (DASWs) are studied. First, a linear dispersion of dust acoustic wave (DAW) is obtained, and it is shown that the DAW is modified by a strongly coupled parameter. Then for small amplitude solitary waves, the Korteweg-de Vries equation is obtained by applying the reductive perturbation technique. For arbitrary amplitude solitary waves, the Sagdeev potential method is employed and the Sagdeev potential is analyzed. In both cases, the effect of dust coupling parameters on the characteristics of DASWs in our system are analyzed.

Coexistence of DA shock and solitary waves in dusty plasmas with two-temperature-ions

The nonlinear propagation characteristics of cylindrical and spherical shock waves in an unmagnetized dusty plasma comprising of inertial negative dust, Boltzmann electrons, and ions with two distinct temperatures, are rigorously investigated by deriving the modified Burgers (mB) equation. Later, the nonplanar KdV-Burgers (nKdVB) equation is derived to show the presence of dispersive and dissipative effects on nonlinear waves. The standard reductive perturbation method is employed to derive the mB and nKdVB equations. The basic features of nonplanar dust-acoustic (DA) waves (viz. amplitude, profile structure, etc.) are discussed. The present analysis can play important role to understand the basic features of nonlinear electrostatic waves in astrophysical plasmas.

Compressive and rarefactive dust-ion-acoustic Gardner solitons in a multi-component dusty plasma

The linear and nonlinear propagations of dust-ion-acoustic solitary waves (DIASWs) in a collisionless four-component unmagnetized dusty plasma system containing nonextensive electrons, inertial negative ions, Maxwellian positive ions, and negatively charged static dust grains have been investigated theoretically. The linear properties are analyzed by using the normal mode analysis and the reductive perturbation method is used to derive the nonlinear equations, namely, the Korteweg-de Vries (K-dV), the modified K-dV (mK-dV), and the Gardner equations. The basic features (viz., polarity, amplitude, width, etc.) of Gardner solitons (GS) are found to exist beyond the K-dV limit and these dust-ion-acoustic GS are qualitatively different from the K-dV and mK-dV solitons. It is observed that the basic features of DIASWs are affected by various plasma parameters (viz., electron nonextensivity, negative-to-positive ion number density ratio, electron-to-positive ion number density ratio, electron-to-positive ion temperature ratio, etc.) of the considered plasma system. The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear structures and the characteristics of DIASWs propagating in both space and laboratory plasmas.

Pseudopotential approach for dust acoustic solitary waves in dusty plasmas with kappa-distributed ions and electrons and dust grains having power law size distribution

Sagdeev's pseudopotential method is used to study small as well as arbitrary amplitude dust acoustic solitons in a dusty plasma with kappa distributed electrons and ions with dust grains having power law size distribution. The existence of potential well solitons has been shown for suitable parametric region. The criterion for existence of soliton is derived in terms of upper and lower limit for Mach numbers. The numerical results show that the size distribution can affect the existence as well as the propagation characteristics of the dust acoustic solitons. The effect of kappa distribution is also highlighted.