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).     

Effects of dust size distribution on nonlinear waves in a dusty plasma

For two-dimensional unmagnetized dusty plasmas with many different dust grain species, a Kadomtsev--Petviashvili (KP) equation, a modified KP (mKP) equation and a coupled KP(cKP) equation for small, but finite amplitude dust-acoustic solitary waves are obtained for different physical conditions respectively. The influence of an arbitrary dust size distribution described by a polynomial expressed function on the properties of dust-acoustic solitary waves is investigated numerically. How dust size distribution affects the sign and the magnitude of nonlinear coefficient A(D) of KP (mKP) equation is also discussed in detail. It is noted that whether a compressive or a rarefactive solitary wave exists depends on the dust size distribution in some dusty 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.     

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.     

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.     

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.     

Propagation features of head-on collision dust acoustic solitary waves in four-component quantum plasmas

ABSTRACT

In framework of the extended Poincaré–Lighthill–Kuo, the properties of dust acoustic (DA) solitary wave’s interaction are investigated in four-component quantum dusty plasma. Two Korteweg–de Vries equations describing the colliding DA solitary waves are derived by eliminating the secularities. By knowing the explicit form of the solitary wave solutions, the leading phase changes, trajectories and phase shifts are obtained, accordingly. The effects of various physical parameters such as the quantum mechanical parameters, the charge ratio between positive and negative dust particles, the mass ratio between negative and positive dust particles and the ratio of electron to ion temperatures are studied extensively. Our findings showed that these parameters play a significant role on the characteristics and basic features of DA solitary waves such as phase shifts in trajectories due to collision. The obtained results may be beneficial to understand well the collision of DA solitary waves that may occur in laboratory plasmas, space plasma as well as in plasma applications.     

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。     

Kinetic treatment of acoustic waves in a four‐component dusty plasma

A kinetic formulation is developed to investigate low‐frequency dust ion acoustic waves (DIAWs) and dust acoustic waves (DAWs) as well as numerically for a four‐component, collisionless, unmagnetized dusty plasma, using the linearized Vlasov–Poisson model for species obeying the Maxwellian distribution. In particular, the dynamics of low‐frequency DIAWs is investigated by considering two cases. In the first case, ions and positive dust particles are assumed to be dynamically adiabatic while the negative dust particles are static in the background. In second case, the ions are taken adiabatic, while both positive and negative dust particles are static in the background. For DAWs, the ions are assumed to be isothermal, while both positive and negative dust species are considered adiabatic. Electrons are assumed to be isothermal in all cases. The linear characteristics and Landau damping rates for DIAWs and DAWs are investigated with effects of the dust particle concentrations and different temperature ratios. It is noted that for higher values of positive dust concentration, DIAWs (DAWs) are less (more) damped. It is also observed that the damping rate increases (decreases) as T_i approaches T_e for DIAWs (DAWs). It is worth adding here that the theoretical results presented here are supported by numerical analyses and illustrations. The relevance of the study to laboratory and cosmic plasmas is also pointed out.     

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.     

Arbitrary amplitude dust acoustic solitary waves in a dusty plasma with an ion beam

Propagation regimes of an arbitrary amplitude dust acoustic solitary wave in a dusty plasma with an ion beam are analyzed by employing the Sagdeev potential technique. Two domains of the Mach numbers are defined depending on the ion beam and plasma parameters. Only a rarefactive soliton solution is found in a low velocity regime. Numerical solutions are presented that illustrate the dependence of soliton characteristics on practically interesting plasma and ion beam parameters. The findings of this investigation could be useful in understanding the nonlinear interaction of external ion beam and dusty plasma observed in laboratory plasma experiments.     

Influence of external magnetic field on dust acoustic waves in a capacitive RF discharge

This paper reports experiments on self-excited dust acoustic waves (DAWs) and its propagation characteristics in a magnetized rf discharge plasma. The DAWs are spontaneously excited in dusty plasma after adding more particles in the confining potential well and found to propagate in the direction of streaming ions. The spontaneous excitation of such low-frequency modes is possible due to the instabilities associated with streaming ions through the dust grain medium. The background E-field and neutral pressure determine the stability of excited DAWs. The characteristics of DAWs strongly depend on the strength of external magnetic field. The magnetic field of strength B < 0.05 T only modifies the characteristics of propagating waves in dusty plasma at moderate power and pressure, P = 3.5 W and p = 27 Pa, respectively. It is found that DAWs start to be damped with increasing the magnetic field beyond B > 0.05 T and get completely damped at higher magnetic field B ∼ 0.13 T. After lowering the power and pressure to 3 W and 23 Pa respectively, the excited DAWs in the absence of B are slightly unstable. In this case, the magnetic field only stabilizes and modifies the propagation characteristics of DAWs while the strength of B is increased up to 0.1 T or even higher. The modification of the sheath electric field where particles are confined in the presence of the external magnetic field is the main cause of the modification and damping of the DAWs in a magnetized rf discharge plasma.     

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.     

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.     

Rotational properties of annulus dusty plasma in a strong magnetic field

The collective dynamics of an annulus dusty plasma formed between a co-centric conducting (non-conducting) disk and ring configuration is studied in a strongly magnetized radiofrequency (rf) discharge. A superconducting electromagnet is used to introduce a homogeneous magnetic field to the dusty plasma medium. In the absence of the magnetic field, the dust grains exhibit thermal motion around their equilibrium position. The dust grains start to rotate in the anticlockwise direction with increasing magnetic field (B > 0.02 T ), and the constant value of the angular frequency at various strengths of the magnetic field confirms the rigid body rotation. The angular frequency of dust grains linearly increases up to a threshold magnetic field (B > 0.6 T ) and after that its value remains nearly constant in a certain range of magnetic field. Further increase in magnetic field (B > 1 T ) lowers the angular frequency. Low value of the angular frequency is expected by reducing the width of the annulus dusty plasma or the input rf power. The azimuthal ion drag force due to the magnetic field is assumed to be the energy source which drives the rotational motion. The resultant radial electric field in the presence of a magnetic field determines the direction of rotation. The variation of floating (plasma) potential across the annular region at given magnetic field explains the rotational properties of the annulus dusty plasma in the presence of a magnetic field.     

Effect of nonthermal ion distribution and dust temperature on nonlinear dust acoustic solitary waves

The effects of nonthermal ion distribution and finite dust temperature are incorporated in the investigation of nonlinear dust acoustic waves in an unmagnetized dusty plasma. Sagdeev pseudopotential method which takes into account the full nonlinearity of plasma equations, is used here to study solitary wave solutions. Possibility of co-existence of refractive and compressive solitons as a function of Mach number, dust temperature and concentration of nonthermal ions, is considered. For the fixed value of nonthermal ions, it is found that the effect of increase in dust temperature is to reduce the range of co-existence of compressive and refractive solitons. Particular concentration of nonthermal ions results in disappearance of refractive solitons while the decrease in dust temperature, at this concentration restores the lost refractive solitons.     

The effect of magnetic field on plasma particles in dusty plasma

In this work, we present the investigation of the formation features and internal structure of dust clouds created in plasma of glow discharge in the external magnetic field corresponding to a range of moderate and strong fields, at which the ion component is magnetized. The analysis of the plasma magnetization in the presence of dust components is carried out. We defined the values of magnetic induction at which the changes in dynamics of plasma particles in magnetic field in light inert gases are expected. The experimental setup was built in two versions. For the purpose of generating of magnetic field, the first setup was equipped with ordinary magnetic coils, and the second one included a superconducting solenoid. The discharge tubes, the main chambers where plasma was ignited and maintained in a glow discharge in lowered pressure, also have certain peculiarities, which we describe below. While using helium as a bulk gas, our study focused only on the dust trap in the region of narrowing discharge current. For neon, we used two traps: the striation trap and one just mentioned above placed in the narrowing of the discharge tube. As a result, the steady dust structures in a glow discharge under the magnetization of ions and electrons were obtained for the first time. Dust structures were rotated and tended to form a dust cluster and shell structure. A number of parameters of magnetization achieved in experiments were calculated.     

非均匀磁场尘埃等离子体中颗粒的复杂运动

本文研究了在非均匀磁场尘埃等离子体中不规则尘埃颗粒的复杂运动, 包括圆滚运动、尖头圆滚运动、圆周运动以及波浪运动等. 放置在电极上的圆柱形磁铁的主要作用是改变鞘层的径向分布, 进而对颗粒产生径向约束, 使尘埃颗粒悬浮于圆柱形磁铁周围, 其磁场并不足以磁化颗粒使其做圆滚运动. 通过与球形尘埃颗粒的对比实验发现, 圆滚运动是不规则尘埃颗粒在等离子体中特有的一种运动. 我们提出了一种新的机理: 由于不规则颗粒的自旋而引起的横向反Magnus力对颗粒的圆滚运动起了重要的作用. 文中通过受力分析定性地对实验中观察到的非球形颗粒的各种运动给出了合理的解释.     

Twisted electrostatic waves in a self‐gravitating dusty plasma

A generalized response (dielectric) function for twisted electrostatic waves is derived for an un‐magnetized self‐gravitating thermal dusty plasma, whose constituents are the Boltzmann‐distributed electrons and positive ions in the presence of negatively charged micrometre‐sized massive dust particulates. For this purpose, a set of Vlasov–Poisson coupled equations is solved along with the perturbed Laguerre–Gauss distribution function, as well as the electrostatic and gravitational potentials in the limit of paraxial approximation. For plane wave solution, the wavefronts of the dust‐acoustic (DA ) wave are assumed to have a constant phase with electric and gravitational field lines propagating straight along the propagation axis. On the other hand, non‐planar wave solutions show helical (twisted) wavefronts, in which field lines spiral around the propagation axis owing to the azimuthal velocity component to account for the finite orbital angular momentum (OAM ) states. The dispersion relation and damping rate for twisted DA waves are studied both analytically and numerically. It is shown that finite OAM states, the dust to electron temperature ratio, and dust self‐gravitation effects significantly affect the linear dispersion and Landau damping frequencies. In particular, the phase speed of twisted DA waves is reduced with the variation of the twist parameter η (= k /lq_ϕ ), dust concentration δ (= n_{d 0}/n_{i 0}), and dust self‐gravitation α (= ω_Jd /ω_pd ). The relevance of our findings to interstellar dust clouds is also discussed for micrometre‐sized massive dust grains.