Nonlinear Dynamics in a Nonextensive Complex Plasma with Viscous Electron Fluids

Cylindrical and spherical dust-electron-acoustic(DEA) shock waves and double layers in an unmagnetized,collisionless,complex or dusty plasma system are carried out.The plasma system is assumed to be composed of inertial and viscous cold electron fluids,nonextensive distributed hot electrons,Maxwellian ions,and negatively charged stationary dust grains.The standard reductive perturbation technique is used to derive the nonlinear dynamical equations,that is,the nonplanar Burgers equation and the nonplanar further Burgers equation.They are also numerically analyzed to investigate the basic features of shock waves and double layers(DLs).It is observed that the roles of the viscous cold electron fluids,nonextensivity of hot electrons,and other plasma parameters in this investigation have significantly modified the basic features(such as,polarity,amplitude and width) of the nonplanar DEA shock waves and DLs.It is also observed that the strength of the shock is maximal for the spherical geometry,intermediate for cylindrical geometry,while it is minimal for the planar geometry.The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear phenomena associated with the nonplanar DEA waves in both space and laboratory plasmas.     

Nonlinear Structures in an Ion-Beam Plasmas Including Dust Impurities with Nonthermal Nonextensive Electrons

The properties of dust ion acoustic waves are investigated in an unmagnetized multicomponent plasma system consisting of ion beam, charged positive and negative ions, electrons obeying nonthermal-Tsallis distribution and stationary negatively charged dust grains by the conventional Sagdeev pseudopotential method, through which the condition for existence of several nonlinear structures is analyzed theoretically. The dispersion relation for electrostatic waves is derived and analyzed and an expression of the energy integral equation is obtained. It is reported here that our plasma model supports solitions, double layers and supersoliton solutions for certain range of parameters. Finally, the effects of different physical plasma parameters on these nonlinear structures are studied numerically. The present theory should be helpful in understanding the salient features of the electrostatic waves in space and in laboratory plasmas where two distinct groups of ions and non-Maxwellian distributed electrons are present.     

Ion-Acoustic Shock Waves in Nonextensive Multi-Ion Plasmas

The nonlinear propagation of ion-acoustic(IA) shock waves(SHWs) in a nonextensive multi-ion plasma system(consisting of inertial positive light ions as well as negative heavy ions, noninertial nonextensive electrons and positrons) has been studied. The reductive perturbation technique has been employed to derive the Burgers equation.The basic properties(polarity, amplitude, width, etc.) of the IA SHWs are found to be significantly modified by the effects of nonextensivity of electrons and positrons, ion kinematic viscosity, temperature ratio of electrons and positrons, etc.It has been observed that SHWs with positive and negative potential are formed depending on the plasma parameters.The findings of our results obtained from this theoretical investigation may be useful in understanding the characteristics of IA SHWs both in laboratory and space plasmas.     

Ion-Acoustic Shock Waves in Nonextensive Multi-Ion Plasmas

The nonlinear propagation of ion-acoustic (IA) shock waves (SHWs) in a nonextensive multi-ion plasma system (consisting of inertial positive light ions as well as negative heavy ions, noninertial nonextensive electrons and positrons) has been studied. The reductive perturbation technique has been employed to derive the Burgers equation. The basic properties (polarity, amplitude, width, etc.) of the IA SHWs are found to be significantly modified by the effects of nonextensivity of electrons and positrons, ion kinematic viscosity, temperature ratio of electrons and positrons, etc. It has been observed that SHWs with positive and negative potential are formed depending on the plasma parameters. The findings of our results obtained from this theoretical investigation may be useful in understanding the characteristics of IA SHWs both in laboratory and space plasmas.     

Large-amplitude double layers in a dusty plasma with an arbitrary streaming ion beam

Formation of large-amplitude double layers in a dusty plasma whose constituents are electrons, ions, warm dust grains and positive ion beam are studied using Sagdeev’s pseudopotential technique. Existence of double layers is investigated. It is found that both the temperature of dust particles and ion beam temperature play significant roles in determining the region of the existence of double layers.     

Electrostatic double layers in a warm negative ion plasma with nonextensive electrons

The electrostatic double layer (DL) structures are studied in negative ion plasma with nonextensive electrons q-distribution. The extended Korteweg–de Vries (EKdV) equation is derived using a reductive perturbation method. It is found that both fast (compressive) and slow (rarefactive) ion acoustic (IA) DLs can propagate in such type of plasmas. The effects of various plasma physical parameters; such as nonextensivity of electrons, presence of negative ions, temperature of both positive and negative ions and different mass ratios of positive to negative ions on the formation of DL structures are discussed in detail with numerical illustrations.     

Large amplitude double layers in a four component dusty plasma with non-thermal ions

Dust acoustic double layers are studied in a four component dusty plasma. Positively and negatively charged mobile dust and Boltzmann distributed electrons are considered. The ion distribution is taken as nonthermal. The existence of compressive and rarefractive double layers is studied by pseudopotential approach. The effect of non-thermal ions on small amplitude and arbitrary amplitude double layers are also studied.     

Effects of axial magnetic field and nonextensivity on small amplitude dust acoustic solitary waves in dusty plasma

The nonlinear propagation of small amplitude dust‐acoustic (DA) solitary waves in magnetized dusty plasma consisting of negatively charged mobile dust fluid, and Boltzmann‐distributed electrons and ions with two distinct temperatures following a q‐nonextensive distribution are investigated. In this article, a number of nonlinear equations, namely, the Korteweg–de‐Vries (K‐dV) equations, have been derived by employing the reductive perturbation technique that is valid for a small but finite amplitude limit. The effects of nonextensivity of ions with two distinct temperatures and dust concentration on the amplitude and width of DA solitary waves are investigated theoretically. It is observed that both the nonextensive and low‐temperatures ions significantly modify the basic properties and polarities of DA solitary waves. It is shown that both positive and negative potential DA solitons occur in this case. The implications of these results to some astrophysical environments and space plasmas (e.g., stellar polytropes, peculiar velocity distributions of galaxies, and collisionless thermal plasma), and laboratory dusty plasma systems are briefly mentioned.     

Weak Ion Acoustic Double Layers in a Warm Plasma

The analytic solutions of the weak ion acoustic double layers in warm unmagnetized and magnetized plasma have been presented with the fluid equation for ions and an arbitrary equation of state for the hot electrons. It has been shown that double layers solutions exist for both magnetized and unmagnetized plasmas when two Boltzmann model for electrons are considered. The potential, the thickness and the velocity of such type of double layers have been calculated and compared with those for the cold plasma.     

Compressive and Rarefactive Waves in Dust Plasma with Non-thermal Ions

The governing equation of the dust fluid with non-thermal ions and variable dust charge on dust particles in hot dust plasmas is obtained. Both the compressive and rarefactive waves in this system are investigated. They can be determined by plasma parameters including the temperatures of dust fluid, ions and electrons, as well as the non-thermal parameter of ions, and the number densities of the dust particles, the ions and the electrons, etc.     

Bifurcation analysis of nonlinear and supernonlinear dust–acoustic waves in a dusty plasma using the generalized (r,q) distribution function for ions and electrons

Bifurcation analysis of dust acoustic (DA) periodic waves in three components, unmagnetized dusty plasma system is investigated using the generalized (r, q) distribution function for ions and electrons. Depending on the different parameters of the system considered, all possible phase portraits, including periodic, homoclinic, superperiodic, and superhomoclinic trajectories, are presented. The existence of rarefactive and compressive solitary waves is proved. Also, the plasma system under consideration supports both nonlinear and supernonlinear DA periodic waves. It has been found that the double spectral indices r and q play a decisive effect on the bifurcation of the waves.     

Nonplanar Shocks and Solitons in a Strongly Coupled Adiabatic Plasma: the Roles of Heavy Ion Dynamics and Nonextensitivity

An investigation has been made on heavy ion‐acoustic (HIA) nonplanar shocks and solitons in an unmagnetized, collisionless, strongly coupled plasma whose constituents are strongly correlated adiabatic inertial heavy ions, weakly correlated nonextensive distributed electrons and Maxwellian light ions. By using appropriate nonlinear equations for our strongly coupled plasma system and the well‐known reductive perturbation technique, a modified Burgers (mB) equation and a modified Korteweg‐de Vries (mK‐dV) equation have been derived. They are also numerically solved in order to investigate the basic features (viz. polarity, amplitude, width, etc.) of cylindrical and spherical shock/solitary waves in such a strongly coupled plasma system. The roles of heavy ion dynamics, nonextensivity of electrons, and other plasma parameters arised in this investigation have significantly modified the basic features of the cylindrical and spherical HIA solitary and shock waves. The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear phenomena associated with the cylindrical and spherical HIA waves both in space and laboratory plasmas. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Charging of a dust particle in a plasma with a nonextensive ion distribution function

The dust charge neutralization in a plasma with nonextensive ions is considered. The condition that the total current to a grain be zero is expressed in terms of the Lambert function. The fall-off of the net negative dust charge is then considered and a parameter study conducted, assuming hydrogen as well as argon plasma. Owing to ion nonextensivity, the dust charge reduction becomes much faster. Moreover, stronger is the ions correlation, more important is the involved electron depletion for a complete dust “decharging”.     

Dust acoustic waves in a nonequilibrium dusty plasma

With the use of the method of moments applicable for any values of the parameter of the nonideality of a dusty plasma and the hydrodynamic approach applicable only for small nonideality parameters, the theory of waves and oscillations of a complex plasma has been generalized to the case of a two-exponential interaction potential. It has been shown that the hydrodynamic approach and method of moments give the same dispersion relation for small nonideality parameters. It has been demonstrated that the velocity of dust acoustic waves in the long- and short-wavelength regions is determined by the small and large screening constants, respectively. It has been shown that the velocity of dust acoustic waves in nonequilibrium plasma is much higher than that obtained in the Debye screening theory for equilibrium plasma. In the hydrodynamic approach, the importance of the inclusion of the self-consistent mutual effect of the dust, electron, and ion components, and sinks of electrons and ions on dust particles, which lead to a noticeable change in the parameters of the interaction potential of dust particles, has been demonstrated.     

Theoretical model for the effect of dust grains on self‐filamentation of a gaussian electromagnetic beam in a fully ionized plasma

A theoretical model for the effect of dust grains on the self‐filamentation of a Gaussian electromagnetic beam propagating in a fully ionized plasma has been developed by employing the energy balance of the plasma constituents, perturbed electron and ion concentrations, and temperature. In this model, neutral atom ionization, re‐integration and accumulation of electrons and ions, photoelectric emission of electrons from the surface of dust grains, as well as elastic and charging collisions have also been considered. The effective dielectric constant in the presence of dust grains has been constructed. The effect of temporal growth of dust grains on various plasma parameters for different values of the dust density has been explored. The variation of the beam width with the normalized channel of propagation has been observed for distinct dust densities and dust charge states. It is observed that the non‐linearity induced by the effective dielectric constant in the presence of dust grains increases the self‐filamentation of the beam, thus enhancing the effective critical power with the dust density. Some of the outcomes of our approach are in line with experimental observations. These outcomes may be useful for explaining space and laboratory plasma experiments as well as for future studies in complex plasmas.     

Electron acoustic solitary waves in unmagnetized nonthermal plasmas

Electron acoustic(EA) solitary waves(SWs) are studied in an unmagnetized plasma consisting of hot electrons(following Cairns-Tsalli distribution), inertial cold electrons, and stationary ions.By employing a reductive perturbation technique(RPT), the nonlinear Korteweg–de Vries(KdV) equation is derived and its SW solution is analyzed. Here, the effects of plasma parameters such as the nonextensivity parameter(q), the nonthermality of electrons(α), and the cold-to-hot electron density ratio(β) are investigated.     

Electrostatic Double Layers in a Multicomponent Drifting Plasma Having Nonthermal Electrons

The pseudopotential technique is applied to a multicomponent plasma consisting of nonthermal electrons and warm positive and negative ions with drift motion with a view to studying ion-acoustic double layers. Conditions for the existence of such layers are obtained, two critical concentrations of negative ions being identified which control the formation and nature of the ion-acoustic double layers. The effects of nonthermal electrons, negative-ion concentration, and negative-ion temperature on the double layer formation and structure are also investigated. The nonthermal electrons and the negative ions are shown to contribute significantly to the excitation and structure of the double layers. The importance of the results in the context of magnetospheric and auroral plasmas is discussed.     

Dust-ion-acoustic shock waves due to dust charge fluctuation

A dusty plasma system containing Boltzmann electrons, mobile ions and charge fluctuating stationary dust has been considered. The nonlinear propagation of the dust-ion-acoustic waves in such a dusty plasma has been investigated by employing the reductive perturbation method. It has been shown that the dust charge fluctuation is a source of dissipation and is responsible for the formation of the dust-ion-acoustic shock waves. The basic features of such dust-ion-acoustic shock waves have been identified. The implications of our results in space and laboratory dusty plasmas are discussed.     

对含有非热力学平衡离子的尘埃等离子体中孤波特性的理论研究

得到了描述由尘埃颗粒电荷变化、非热力学平衡分布的离子和Boltzmann分布的电子组成的未磁化的热尘埃等离子体中的尘埃声波的修正的KdV (mKdV) 方程. 并对诸多的尘埃等离子体参数对尘埃声孤波结构的影响进行了理论研究，结果表明，尘埃等离子体参数决定着尘埃声孤波结构，且只在这些参数特别选定的一些区域，才会出现稳定的孤波. 关键词： 非热力学平衡离子 尘埃颗粒电荷变化 尘埃声孤波     

Nonplanar double layers in plasmas with opposite polarity dust

Nonplanar (cylindrical and spherical) double layers (DLs) in a four-component dusty plasma (composed of inertial positively and negatively charged dust, Boltzmann electrons and ions) are studied by employing the reductive perturbation method. The modified Gardner equation describing the nonlinear propagation of the dust-acoustic (DA) waves is derived, and its nonplanar double layer solutions are numerically analyzed. The parametric regimes for the existence of the DLs, which are found to be associated with positive potential only, are obtained. The basic features of nonplanar DA DLs, which are found to be different from planar ones, are also identified. The implications of our results to different space and laboratory dusty plasma situations, where opposite polarity dust are observed, are discussed.