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.     

The effects of vortex like distributed electron in magnetized multi-ion dusty plasmas

The nonlinear propagation of small but finite amplitude dust-ion-acoustic solitary waves in a magnetized, collisionless dusty plasma is investigated theoretically. It has been assumed that the electrons are trapped following the vortex-like distribution and that the negatively and positively charged ions are mobile with the presence of charge fluctuating stationary dusts, where ions mass provide the inertia and restoring forces are provided by the thermal pressure of hot electrons. A reductive perturbation method was employed to obtain a modified Korteweg-de Vries (mK-dV) equation for the first-order potential and a stationary solution is obtained. The effect of the presence of trapped electrons, negatively and positively charged ions and arbitrary charged dust grains are discussed.     

Nonplanar dust ion-acoustic solitary and shock waves in a dusty plasma with electrons following a vortex-like distribution

Properties of nonplanar (viz. cylindrical and spherical) dust ion-acoustic (DIA) solitary and shock waves propagating in a dusty plasma containing charge fluctuating stationary dust, inertial warm ions, and non-isothermal electrons following a vortex-like distribution, are investigated by the reductive perturbation method. It has been shown that all the basic features of the DIA solitary and shock waves are significantly modified by the effects of vortex-like electron distribution, dust charge fluctuation, and nonplanar cylindrical and spherical geometries. The implications of our results in some space and laboratory dusty plasma environments are briefly discussed.     

Effect of dust size distribution and dust charge fluctuation on dust ion-acoustic shock waves in a multi-ion dusty plasma

The effects of dust size distribution and dust charge fluctuation of dust grains on the small but finite amplitude nonlinear dust ion-acoustic shock waves, in an unmagnetized multi-ion dusty plasma which contains negative ions, positive ions and electrons, are studied in this paper. A Burgers equation and its stationary solutions are obtained by using the reductive perturbation method. The analytical and numerical results show that the height with polynomial dust size distribution is larger than that of the monosized dusty plasmas with the same dust grains, but the thickness in the case of different dust grains is smaller than that of the monosized dusty plasmas. Furthermore, the moving speed of the shock waves also depend on different dust size distributions.     

K-P-Burgers equation in negative ion-rich relativistic dusty plasma including the effect of kinematic viscosity

The stationary solution is obtained for the K–P–Burgers equation that describes the nonlinear propagations of dust ion acoustic waves in a multi-component, collisionless, un-magnetized relativistic dusty plasma consisting of electrons, positive and negative ions in the presence of charged massive dust grains. Here, the Kadomtsev–Petviashvili(K–P) equation, threedimensional(3D) Burgers equation, and K–P–Burgers equations are derived by using the reductive perturbation method including the effects of viscosity of plasma fluid, thermal energy, ion density, and ion temperature on the structure of a dust ion acoustic shock wave(DIASW). The K–P equation predictes the existences of stationary small amplitude solitary wave,whereas the K–P–Burgers equation in the weakly relativistic regime describes the evolution of shock-like structures in such a multi-ion dusty plasma.     

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

The nonlinear propagation of the dust-electron-acoustic waves in a dusty plasma consisting of cold and hot electrons, stationary and streaming ions, and charge fluctuating stationary dust 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-electron-acoustic shock waves in such a dusty plasma. The basic features of such dust-electron-acoustic shock waves have been identified. It has been proposed to design a new laboratory experiment which will be able to identify the basic features of the dust-electron-acoustic shock waves predicted in this theoretical investigation.     

Nonlinear propagation of dust-acoustic solitary waves in a dusty plasma with arbitrarily charged dust and trapped electrons

A theoretical investigation of dust-acoustic solitary waves in three-component unmagnetized dusty plasma consisting of trapped electrons, Maxwellian ions, and arbitrarily charged cold mobile dust was done. It has been found that, owing to the departure from the Maxwellian electron distribution to a vortex-like one, the dynamics of small but finite amplitude dust-acoustic (DA) waves is governed by a nonlinear equation of modified Korteweg–de Vries (mKdV) type (instead of KdV). The reductive perturbation method was employed to study the basic features (amplitude, width, speed, etc.) of DA solitary waves which are significantly modified by the presence of trapped electrons. The implications of our results in space and laboratory plasmas are briefly discussed.     

Effects of polarization force and nonthermal ions on dust-acoustic (DA) shock waves in a strongly coupled dusty plasma with positively charged dust

The nonlinear propagation of the dust-acoustic (DA) waves in a strongly coupled dusty plasma containing Maxwellian electrons, nonthermal ions, and positively charged dust is theoritically investigated by a Burgers equation. The effects of the polarization force (which arises due to the interaction between electrons and highly positively charged dust grains) and nonthermal ions are studied. DA shock waves are found to exist with positive potential only. It represents that the strong correlation among the charged dust grains is a source of dissipation, and is responsible for the formation of DA shock waves. The effects of polarization force and nonthermal ions significantly modified the basic features of DA shock waves in strongly coupled dusty plasma.     

Wake potential with mobile positive/negative ions in multicomponent dusty plasmas

We employ the test charge approach to calculate the electrostatic potential for a test charge in a multicomponent dusty plasma, whose constituents are the Boltzmann distributed electrons, mobile positive and negative ions, and immobile positive/negative charged dust particles. By using the modified dielectric constant of the dust-ion-acoustic (DIA) waves, the Debye screening and wake potentials are obtained. It is found that the presence of mobile negative ions significantly modify the DIA speed and the wake potential. The present results are relevant to polar mesosphere and microelectronic in the context of charged particle attraction and repulsion.     

尘埃等离子体中非线性波的叠加效应及稳定性问题

研究了小的有限振幅的无磁场尘埃等离子体中的非线性波.在一维情况下由Kortewegde Veries(KdV)方程来描述,考虑了二维情况下尘埃等离子体中尘埃颗粒上电荷的变化效应以及双温度离子效应后,尘埃等离子体受到横向高阶扰动后动力学方程由Kadomtsev-Petviashvili(KP)方程来描述.在此基础上,研究了以任意夹角传播的两个及三个孤立子的相互作用问题,考虑非线性效应后振幅相等的双孤立子在相互作用区域内振幅最大值是单个孤立子振幅的4倍,振幅相等的三孤立子在相互作用区域内振幅最大值是单个孤立子振幅的9倍.研究还表明波的传播方向受到横向高阶扰动后是稳定的.     

Effects of bi-kappa distributed electrons on dust-ion-acoustic shock waves in dusty superthermal plasmas

The basic properties of dust-ion-acoustic （DIA） shock waves in an unmagnetized dusty plasma （containing inertial ions, kappa distributed electrons with two distinct temperatures, and negatively charged immobile dust grains） are investi- gated both numerically and analytically. The hydrodynamic equation for inertial ions has been used to derive the Burgers equation. The effects of superthermal bi-kappa electrons and ion kinematic viscosity, which are found to modify the basic features of DIA shock waves significantly, are briefly discussed.     

Large-amplitude dust acoustic solitons in an opposite polarity dusty plasma with generalized polarization force

Linear and nonlinear dust acoustic(DA)waves have been investigated in an opposite polarity dusty plasma comprising negatively and positively charged dust grains,Maxwellian electrons and ions,including the generalized polarization force effect.The properties of linear DA waves have been significantly altered by the dual dust polarity and polarization force.Large amplitude DA solitons have been discussed in the framework of the Sagdeev potential technique.Our results show that both rarefactive and compressive solitons can exist in such a dusty plasma.The basic features of the Sagdeev potential have been examined under the effect of the polarization force parameter R,the ratio of the charge number of the positive dust to that of the negative dust Z,and the Mach number M.The results show that these parameters play a significant role in determining the region of existence of large amplitude DA solitons.     

Propagation of dust-acoustic waves in weakly ionized plasmas with dust-charge fluctuation

For an unmagnetized partially ionized dusty plasma containing electrons, singly charged positive ions, micron-sized massive negatively charged dust grains and a fraction of neutral atoms, dispersion relations for both the dust-ion-acoustic and the dustacoustic waves have been derived, incorporating dust charge fluctuation. The dispersion relations, under various conditions, have been exhaustively analysed. The explicit expressions for the growth rates have also been derived. International Conference on the Frontiers of Plasma Physics and Technology, 9–14 December 2002, Bangalore, India.     

Modulational instability of dust acoustic waves in a dusty plasma with nonthermal electrons and ions

Effects of nonadiabaticity of variable dust charge, dust fluid temperature, trapped electrons as well as nonisothermality of ions on the amplitude modulation of dust acoustic waves in an unmagnetized dusty plasma are investigated. A modified nonlinear Schr?dinger equation (NLSE) is obtained by the standard reductive perturbation technique and is solved numerically by the split-step Fourier method. The modulational instability and the envelope solitary wave structure are found to be modified somewhat by the effects of nonthermally distributed ions and trapped electrons.     

强耦合尘埃等离子体中正电扰动下的尘埃声激波

研究了强耦合尘埃等离子体的尘埃声波的线性色散关系和尘埃声孤波的非线性传播。考虑一个包含电子、离子、正电扰动尘埃颗粒的完全电离的三成分模型等离子体。假定其电子、离子数密度服从玻尔兹曼分布,而大质量的尘埃成分用一组经典流体方程描述,对系统方程进行线性化,得到了尘埃声波的线性色散关系,发现离子的集中参数对色散关系的影响很大。用约化摄动法对系统方程进行展开,得到了描述小振幅孤波的伯格斯方程。基于伯格斯方程研究了尘埃声孤波的基本特性,发现尘埃颗粒的强耦合效应对尘埃声孤波有很大的修正作用。该研究结果有助于理解尘埃空间等离子体中局域波的一些特性。     

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研究了强耦合尘埃等离子体的尘埃声波的线性色散关系和尘埃声孤波的非线性传播。考虑一个包含电子、离子、正电扰动尘埃颗粒的完全电离的三成分模型等离子体。假定其电子、离子数密度服从玻尔兹曼分布,而大质量的尘埃成分用一组经典流体方程描述,对系统方程进行线性化,得到了尘埃声波的线性色散关系,发现离子的集中参数对色散关系的影响很大。用约化摄动法对系统方程进行展开,得到了描述小振幅孤波的伯格斯方程。基于伯格斯方程研究了尘埃声孤波的基本特性,发现尘埃颗粒的强耦合效应对尘埃声孤波有很大的修正作用。该研究结果有助于理解尘埃空间等离子体中局域波的一些特性。     

Effects of adiabaticity of electrons and ions on dust-ion-acoustic solitary waves

The nonlinear propagation of dust-ion-acoustic (DIA) waves in an adiabatic dusty plasma (containing adiabatic inertial-less electrons, adiabatic inertial ions, and negatively charged static dust) is investigated by the pseudo-potential approach. The combined effects of adiabatic electrons and negatively charged static dust on the basic properties (critical Mach number, amplitude, and width) of small as well as arbitrary amplitude DIA solitary waves are explicitly examined. It is found that the combined effects of adiabatic electrons and negatively charged static dust significantly modify the basic properties (critical Mach number, amplitude, and width) of the DIA solitary waves. It is also found that due to the effect of adiabaticity of electrons, negative DIA solitary waves [which are found to exist in a dusty plasma (containing isothermal electrons, cold ions, and negatively charged static dust) for α=zdnd0/ni0>2/3, where zd is the number of electrons residing onto a dust grain surface, nd0 is the constant (static) dust number density and ni0 is the equilibrium ion number density] disappears, i.e. due to the effect of adiabatic electrons, one cannot have negative DIA solitary waves for any possible set of dusty plasma parameters [0?α<1 and 0?σ=Ti0/Te0?1, where Ti0 (Te0) is electron (ion) temperature at equilibrium].     

Effect of viscosity on dust–ion acoustic shock wave in dusty plasma with negative ions

The properties of dust–ion acoustic (DIA) shock wave in a dusty plasma containing positive and negative ions is investigated. The reductive perturbation method has been used to derive the Korteweg–de Vries–Burgers equation for dust acoustic shock waves in a homogeneous, unmagnetized and collisionless plasma whose constituents are Boltzmann distributed electrons, singly charged positive ions, singly charged negative ions and cold static dust particles. The KdV–Burgers equation is derived and its stationary analytical solution is numerically analyzed where the effect of viscosity on the DIA shock wave propagation is taken into account. It is found that the viscosity in the dusty plasma plays as a key role in dissipation for the propagation of DIA shock.     

Modified KP-Burger and KP-Burger equations in coupled dusty plasmas with variable dust charge and non-isothermal ions

The modified Kodomtsev-Petviashvili-Burger (mKP-Burger) and Kodomtsev-Petviashvili-Burger equations are derived in strongly coupled dusty plasmas containing non-isothermal ions, Boltzmann distributed electrons and variable dust charge. We use reductive perturbation method and discuss on solitary waves and shock waves solutions of these equations.     

Lower order three-dimensional Burgers equation having non-Maxwellian ions in dusty plasmas

The dust acoustic(DA) shock wave with dust charge fluctuations, non-Maxwellian ions, and non-isothermal electrons is studied theoretically. The perturbation technique is employed to derive the lower order three-dimensional(3D) Burgers equation, and shock wave solution is explored by the tan-hyperbolic method. The effects of flat trapped and trapped electron distributions in the presence of Maxwellian and non-Maxwellian ions on characteristics shock waves are observed. The temperature ratio of non-Maxwellian ion temperature and non-isothermal electron temperature is found to play an important role in forming the shock-like structure.