Linear and nonlinear excitations in complex plasmas with nonadiabatic dust charge fluctuation and dust size distribution

Both linear and nonlinear excitation in dusty plasmas have been investigated including the nonadiabatic dust charge fluctuation and Gaussian size distribution dust particles. A linear dispersion relation and a Korteweg-de Vries-Burgers equation governing the dust acoustic shock waves are obtained. The relevance of the instability of wave and the wave evolution to the dust size distribution and nonadiabatic dust charge fluctuation is illustrated both analytically and numerically. The numerical results show that the Gaussian size distribution of dust particles and the nonadiabatic dust charge fluctuation have strong common influence on the propagation of both linear and nonlinear excitations.     

Effect of dust charge variation on dust—acoustic solitary waves in a magnetized two—ion—temperature dusty plasma

The effect of dust charge variation on the dust-acoustic solitary structures is investigated in a warm magnetized two-ion-temperature dusty plasma consisting of a negatively and variably charged extremely massive dust fluid and ions of two different temperatures. It is shown that the dust charge variation as well as the presence of a second component of ions would modify the properties of the dust-acoustic solitary structures and may exite both dust-acoustic solitary holes (soliton waves with a density dip) and positive solitons (soliton waves with a density hump).     

量子尘埃等离子体中尘埃充电对尘埃声波的影响

采用流体动力学方程组和尘埃充电方程组成的自洽模型系统,对量子尘埃等离子体中的尘埃声波波动性质进行了研究。通过线性理论分析方法得到系统的尘埃声波波动方程及其色散关系,并对色散关系进行了数值分析。研究表明：充电效应定性地修正了尘埃声波的色散特性,引起尘埃声波的耗散,其耗散强度主要与尘埃等离子体的参数有关。最后,分析了引起尘埃声波耗散的物理原因。     

Effects of the dust size distribution in one-dimensional quantum dusty plasma

The effects of the dust size distribution in ultracold quantum dusty plasmas are investigated. The amplitude φ_m and width ω of quantum dust acoustic waves are studied with different dust size distributions in the system. The φ_m and ω of the quantum dust acoustic waves are found to increase as the total number density increases. The φ_m and ω are greater for unusual dusty plasmas than for typical dusty plasmas. Moreover, as the Fermi temperature of the dust grains increases, the φ_m of the wave decreases. The ω of quantum dust acoustic waves increases as the speed u₀ of the wave increases.     

Variable‐size dust grains with generalized (r,q) electrons in a dusty plasma

The effect of the generalized (r, q) distribution on the non‐linear propagation of dust acoustic waves (DAWs) in a dusty plasma consisting of variable‐size dust grains is discussed. A Korteweg–de Vries (KdV) equation is derived using the reductive perturbation technique (RPT). The dust size obeys the power‐law dust size distribution (DSD). The present results reveal that rarefactive and compressive waves can propagate in the proposed plasma model. It is found that the spectral indices r and q influence the main properties of DAWs. Especially, the velocity, amplitude, and width of the DAW change drastically with r compared to changes in q.     

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.     

Effects of dust size distribution in ultracold quantum dusty plasmas

The effect of dust size distribution in ultracold quantum dusty plasmas are investigated in this paper. How the dispersion relation and the propagation velocity for the quantum dusty plasma vary with the system parameters and the different dust distribution are studied. It is found that as the Fermi temperature of the dust grains increases the frequency of the wave increases for large wave number dust acoustic wave. The quantum parameter of H_d also increases the frequency of the large wave number dust acoustic wave. It is also found that the frequency ω₀ and the propagation velocity v₀ of quantum dust acoustic waves all increase as the total number density increases. They are greater for unusual dusty plasmas than those of the usual dusty plasma.     

Effect of multicomponent dust grains in a cold quantum dusty plasma

By employing the quantum hydrodynamic model for electron-ion-dust plasma,we derive a dispersion relation of the quantum dusty plasma.The effects of the dust size distribution on the dispersion relation in a cold quantum dusty plasma are studied.Both analytical and numerical results are given to compare the differences between the dusty plasma by considering the dust size distribution and the mono-sized dusty plasma.It is shown that many system parameters can significantly influence the dispersion relation of the quantum dusty plasma.     

Multi-dimensional instability of electrostatic solitary waves in a warm multi-ion dust plasma

Study of dust ion acoustic waves in a magnetized dusty plasmas composed of negatively or positively charged static dust, positive and negative ions, as well as kappa distribution electrons is presented. The Zakharov–Kuznetsov (ZK) equation is derived via reductive perturbation technique. The solitary wave solution of ZK equation is given and the multi-dimensional instability of these solitary waves is investigated via small k perturbation method. The instability criterion and growth rate relying on obliqueness, superthermality, positive ion thermal pressure, relative ion number density, magnetic field strength, and direction cosines are discussed for five cases. The results are beneficial to understand different nonlinear characteristics of unstable electrostatic disturbances in laboratory and space plasmas.     

Nonlinear interaction phenomenon of dust acoustic solitary and shock waves in dusty plasma

The effects of head-on collision on dust acoustic (DA) solitary and shock waves in dusty plasma are investigated considering positively charged inertial dust, Boltzmann distributed negatively charged heavy ions, positively charged light ions, and superthermal electrons in the plasma system. The nonlinear Korteweg-de-Vries (KdV) Burger equations are derived taking the extended Poincaré-Lighthill-Kuo method into account to study the characteristic properties of nonlinearity and production of solitary shock due to collisions. The study reveals that the amplitudes and widths of the DA shock waves are decreasing with increasing viscosity, electron to dust density ratio, and dust to ion temperature ratio, while they are increasing due to the presence of superthermal electrons. The nonlinearity of DA waves are enhanced with increasing density ratio of electron to dust and temperature ratio of dust to ion and electron, respectively, but it is reducing with superthermal electrons. The phase shifts of DA solitary waves are found to decrease with rising superthermality of electrons and increase with the density ratio of electron to dust.     

Shock waves in a rotating non-Maxwellian viscous dusty plasma

A theoretical model is presented to study the characteristics of dust acoustic shock in a viscous, magnetized, rotating dusty plasma at both fast and slow time scales. By employing the reductive perturbation technique, the non-linear Zakharov–Kuznetsov–Burger (ZKB) equation is derived for both cases when the dust is inactive and dynamic (fast and slow time scales). Both electrons and ions are considered to follow the kappa/Cairns distribution. It is observed that in both cases, i.e. when dust is in the background and active, viscosity plays a key role in dissipation for the propagation of acoustic shock. Magnetic field and rotation are responsible for the dispersive term. Superthermality is found to affect significantly the formation of the shock wave along with viscous nature of plasma, whereas the dust charge affects the non-linear coefficient of the ZKB equation. The present investigation may be beneficial to the understanding of the rotating plasma, in particular the experiments being carried out.     

Interaction of solitary waves in magnetized warm dusty plasmas with dust charging effects

In consideration of adiabatic dust charge variation, the combined effect of the external magnetized field and the dust temperature on head-on collision of the three-dimensional dust acoustic solitary waves is investigated. By using the extended Poincar\'e--Lighthill--Kuo method, the phase shifts and the trajectories of two solitons after the collision are obtained. The effects of the magnitude and the obliqueness of the external magnetic field and the dust temperature on the solitary wave collisions are discussed in detail.     

Effects of double spectral electron distribution and polarization force on dust acoustic waves in a negative dusty plasma

The nonlinear features of dust acoustic waves (DAWs) propagating in a multicomponent dusty plasma with negative dust grains, Maxwellian ions, and double spectral electron distribution (DSED) are investigated. A Korteweg de Vries Burgers equation (KdVB) is derived in the presence of the polarization force using the reductive perturbation technique (RPT). In the absence of the dissipation effect, the bifurcation analysis is introduced and various types of solutions are obtained. One of these solutions is the rarefactive solitary wave solution. Additionally, in the presence of the dissipation effects, the tanh method is employed to find out the solution of KdVB equation. Both of the monotonic and the oscillatory shock structures are numerically investigated. It is found that the correlation between dissipation and dispersion terms participates strongly in creating the dust acoustic shock wave. The limit of the DSED to the Maxwell distribution is examined. The distortional effects in the profile of the shock wave that result by increasing the values of the flatness parameter, r, and the tail parameter, q, are investigated. In addition, it has been shown that the proportional increase in the value of the polarization parameter R enhances in both of the strength of the monotonic shock wave and the amplitude of the oscillatory shock wave. The effectiveness of non-Maxwellian distributions, like DSED, in several of plasma situations is discussed as well.     

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.     

Possibility of weakly charged nonlinear solitary dust clouds near the continuum threshold of dust population in a quasi-neutral dusty plasma

Considering the Boltzmann response of the plasma ions and electrons and inertial dynamics of the charged dust grains, the possibility of very weak compressive soliton near the continuum limit of the dust population has been inferred. It is concluded that the behaviour of such coherent structures could be well described by the numerical analysis of the derived nonlinear classical energy integral equation for bounded solutions. These seem to be higher order dispersive structures within acoustic limit of the nonlinear turbulence. It is observed that the dust density enhancement beyond the continuum threshold causes regular increment in width and amplitude of the soliton structures. It is found that the soliton amplitude sensitively depends on the massive impurity’s population. These coherent structures could be visualized as weakly charged solitary dust clouds of finite extension (∼ plasma Debye length) within Boltzmann environment of plasma particles in their local surroundings. The seeding mechanism of such clouds may be attributed to some plasma instabilities driven by either internal or external free energy sources. Numerical analysis of the problem concludes that the experimental observations of such clouds could be possible in low density plasma regime. It is deduced that for plasma density ∼ 10⁶ cm^-3 at temperatures of a few electron volts and for micron to l0nm sized dust grains, the observation of such structures could be possible within wide range variability of the dust population density.     

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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。     

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。     

The dust acoustic wave in a bounded dusty plasma with strong electrostatic interactions between dust grains

The dispersion relation for the dust acoustic wave (DAW) in an unmagnetized dusty plasma cylindrical waveguide is derived, accounting for strong electrostatic interactions between charged dust grains. It is found that the boundary effect limits the radial extent of the DAW. The present result should be helpful for understanding the frequency spectrum of the DAW in a dusty plasma waveguide with strongly coupled charged dust grains.     

Effects of the dust size distribution on shock waves in dusty plasma

By using a Korteweg-deVries-Burgers(KdV-Burgers) equation and considering the dust size distribution, we have studied effects of the dust size distribution on the shock wave in dusty plasma. The dependence of characteristics of the shock wave on different dust size distributions has been given. It is found that the speed and amplitude of a shock wave considering the dust size distribution are larger than that of the dusty plasma with the averaged dust size. However, the width of a shock wave considering the dust size distribution is smaller than that of the dusty plasma with the averaged dust size.     

Low-frequency variable charge solitary waves in a collisionless dusty plasma with a Cairns-Gurevich ion velocity distribution

In this paper, the problem of large amplitude dust acoustic (DA) solitons has been addressed in a charge varying dusty plasma with ions following a Cairns-Gurevich distribution. Based on the orbit motion limited approach, the correct Cairns-Gurevich ion charging current is presented for the first time. The expression relating the variable dust charge to the plasma potential is given in terms of the Lambert function and we take advantage of this transcendental function to, carefully, analyse DA solitons in a charge varying dusty plasma with trapped nonthermal ions. Our results show that the spatial patterns of the variable charge solitary wave are significantly changed due to the presence of ion population modelled by the Cairns-Gurevich distribution. An addition of a small concentration of trapped nonthermal ions makes the solitary structure less spiky, grows the net negative charge residing on the dust grain surface, and contributes to the electron depletion. Finally, our investigation is extended to highlight the effect of the grain dust charge variation. We have shown that under certain conditions, the impact of dust charge fluctuation may furnish an alternate physical mechanism rasing anomalous dissipation, which becomes more strong and may predominate over the dispersion as the nonthermal character of ions following the Cairns-Gurevich distribution increases.