Dust Charge Variation Research Articles

Spherical solitons in Earth’S mesosphere plasma

Soliton formation in Earth’s mesosphere plasma is described. Nonlinear acoustic waves in plasmas with two-temperature ions and a variable dust charge where transverse perturbation is dealt with are studied in bounded spherical geometry. Using the perturbation method, a spherical Kadomtsev–Petviashvili equation that describes dust acoustic waves is derived. It is found that the parameters taken into account have significant effects on the properties of nonlinear waves in spherical geometry.

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.

Dust acoustic and drift waves in a non-Maxwellian dusty plasma with dust charge fluctuation

The properties of dust acoustic and drift waves are investigated in a charge varying magnetized dusty plasma. The plasma is composed of non-thermal electrons and ions with dynamic dust particles. The mathematical expression which describes the dust charge fluctuation is obtained using ${\it\kappa}$-distribution for both the electrons and ions. A dispersion relation is derived and analysed numerically by choosing space plasma parameters. It is found that the inclusion of variable dust charge along with the non-thermal effects of electrons and ions significantly affect linear/nonlinear properties of the dust acoustic and dust drift waves. The effects of different physical parameters including spectral index (${\it\kappa}$), dust charge number ($Z_{d}$), electron density ($n_{e}$) and ion temperature ($T_{i}$) on the wave dispersion and instability are presented. It is found that the presence of the non-thermal electron and ion populations reduce the growth rate of the instability which arises due to the dust charging effect. In addition, the nonlinear vortex solutions are also obtained. For illustration, the results are analysed by using the dusty plasma parameters of Saturn’s magnetosphere.

Jeans instability of a dusty plasma with dust charge variations

The effect of the dust charge variations on the stability of a self-gravitating dusty plasma has been theoretically investigated. The dispersion relation for the dust-acoustic waves in a self-gravitating dusty plasma is obtained. It is shown that the dust charge variations have significant effects. It increases the growth rate of instability and the instability cutoff wavenumbers. It is found that by increasing the value of the ions temperature and the absolute value of the equilibrium dust charge, the cutoff wavenumber decreases and the stability region is extended.

Modeling of nonlinear envelope solitons in strongly coupled dusty plasmas: Instability and collision

Modeling of instability and collision of nonlinear dust-acoustic (NDA) envelope solitons in strongly coupled dusty plasmas (SCDPs) is theoretically investigated. The SCDPs consists of strongly correlated negatively variable-charged dust grains and weakly correlated Boltzmann electrons and ions. Using the derivative expansion perturbation technique, a nonlinear Schrödinger-type (NLST) equation for describing the propagation of NDA envelope solitons is derived. Moreover, the extended Poincaré–Lighthill–Kuo (EPLK) method is employed to deduce the analytical phase shifts and the trajectories after the collision of NDA envelope solitons. In detail, the results show that both modulation instability and phase shift after collision of NDA envelope solitons will modify with the increase in the effects of the viscosity, the relaxation time, and the dust charge fluctuation. Crucially, the modeling of dust-acoustic envelope solitons collision, as reported here, is helpful for understanding the propagation of NDA envelope solitons in strongly coupled dusty plasmas.

Dust-ion acoustic shock waves in a dusty multi-ion plasma with negatively dust-charge fluctuation

The nonlinear propagation of dust-ion acoustic shock waves in a collisionless, unmagnetized multi-ion dusty plasma contains Botlzemann-distributed electrons, negative and positive ions with extremely massive and stationary negative charge dust grains with dust charge fluctuations is investigated. By employing the reductive perturbation method, we obtain a Burgers equation that describes the two-ion fluid dynamics. The dust charge variation is found to play an important role in the formation of such dust-ion acoustic shock structures. The viscosity only affects the thickness of the shock waves. The dependences of the shock wave’s velocity, height and thickness on the system parameters are investigated.

Collisionless damping of dust-acoustic waves in a charge varying dusty plasma with nonextensive ions

The charge variation induced nonlinear dust-acoustic wave damping in a charge varying dusty plasma with nonextensive ions is considered. It is shown that the collisionless damping due to dust charge fluctuation causes the nonlinear dust acoustic wave propagation to be described by a damped Korteweg-de Vries (dK-dV) equation the coefficients of which depend sensitively on the nonextensive parameter q. The damping term, solely due to the dust charge variation, is affected by the ion nonextensivity. For the sake of completeness, the possible effects of nonextensivity and collisionless damping on weakly nonlinear wave packets described by the dK-dV equation are succinctly outlined by deriving a nonlinear Schrodinger-like equation with a complex nonlinear coefficient.

Nonlinear waves in a self-gravitating charge-varying collisional dust molecular cloud in presence of diverse equilibrium inhomogeneities

An evolutionary model for investigating the nonlinear gravito-electrostatic waves in a self-gravitating inhomogeneous planar collisional dust molecular cloud on the Jeans scales of space and time is theoretically proposed. It includes dust-charge variation and weak but finite inertia of the thermal electrons and ions. All the equilibrium gradients and inhomogeneities arising from the dynamics of the electrons, ions, neutral and charged grains are considered simultaneously for the first time. So, any conventional homogenization assumption for mathematical simplification is avoided. By standard inhomogeneous multiple scaling techniques, it is methodologically shown that the fluctuations are collectively governed by a new gravito-electrostatically coupled pair of driven Korteweg–de Vries (d-KdV) equations with new gradient-driven variable coefficients and self-consistent linear sources. A numerical analysis portrays the eigenmode excitations as oscillatory shock- and soliton-like structures. In addition, depending on the explicit regions of the varied plasma parameter space and inhomogeneities, a new shape-transition from soliton to shock and vice versa occurs. Our nonlinear wave analyses could be applied to explain multispace satellite observations and predictions made by others in the past.

Auto-Backlund transformations and New Exact Soliton Solutions of KdV Equation for Nonlinear Dust Acoustic Solitary Waves in Dust Plasma with Variable Dust Charge

The nonlinear properties of dust acoustic solitary waves in unmagnetized dust plasma consisting of negative charged dust particles , Boltzmann distributed electrons and non-thermal distributed ions with variable dust charge are investigated. By using the reductive perturbation theory, a Korteweg-de Veries (KdV) equation is derived. The

Conditions for reflection and transmission of an ion acoustic soliton in a dusty plasma with variable charge dust

Modified Korteweg-de Vries (mKdV) equations are derived for the incident, reflected, and transmitted waves in order to examine the soliton reflection and its transmission through an inhomogeneous plasma comprising ions, dust grains with fluctuating charge and two types of electrons, namely nonisothermal electrons and isothermal electrons. All the mKdV equations are coupled at the point of reflection and solved for the reflected soliton. Unlike others, a relation is established between the velocity shifts of the incident, reflected and transmitted solitons, and based on a critical value of the shift of incident soliton the strengths of the soliton reflection and transmission are talked about. Conditions are obtained for the soliton reflection and its transmission, and a comparative study is made for the two cases of fixed and fluctuating charges on the dust grains.

Reflection of ion acoustic solitary waves in a dusty plasma with variable charge dust

An inhomogeneous plasma comprising ions, two temperature electrons and dust grains with variable charge is explored for its unperturbed state for ions’ drift due to density gradient and perturbed state for the evolution of ion acoustic solitary waves and their reflection under the effect of an external magnetic field. The ion drift velocity is found to depend on the plasma parameters and magnetic field. The perturbed state of plasma supports two types of ion acoustic waves, which evolve into fast and slow compressive solitary structures under certain conditions. However, only the fast solitary wave is observed to be reflected and acquired opposite polarity to that of the incident solitary wave. The solitary waves are found to be downshifted after their reflection. The reflection coefficient acquires higher values in the case of dust grains of fixed charge in comparison with the case of fluctuating charge on the dust grains. It means the reflection becomes stronger when the charge on the dust grains does not fluctuate and remains fixed. The effect of dust grain density is to enhance the amplitude of solitary waves but to weaken their reflection. The amplitudes of both the incident and reflected solitons remain higher for the case of fluctuating charge on the dust grains in comparison with the case of fixed charge. The effective temperature of the plasma is also found to alter the solitary structures significantly in the case of dust grains having fluctuating charge.

Effects of variable dust size, charge and mass on the characteristics of dust acoustic solitary waves in a magnetized dusty plasma

The effect of dust size, mass and charge distributions on the characteristics of nonlinear dust acoustic solitary waves (DASW) in a two-temperature ion dusty plasma has been studied analytically. The mass and electrical charge of dust particles are assumed to be proportional with their size. Plasma is embedded in an external magnetic field with variable direction. Using a reductive perturbation method, the Zakharov–Kuznetsov (ZK) equation is derived and its solitary answers are extracted. The coefficients of the nonlinear term of the ZK equation are affected strongly by the size of dust particles when the relative size (the ratio of the largest dust radius to smallest dust radius) is less than 2. Both the width and amplitude of DASW increase with increasing relative size. The cyclotron frequency of the dust changes with the relative size of the dust particles. DASW width is influenced by the magnitude as well as direction of the external magnetic field, while its amplitude is independent of the magnitude of the external magnetic field. At each strength of the external magnetic field, there is an optimum magnitude for its direction at which the width of DASW is maximum.

Ion-temperature-gradient driven modes in dust-contaminated plasma with nonthermal electron distribution and dust charge fluctuations

The effect of nonthermal electrons on ion-temperature-gradient (ITG) driven modes is investigated in the presence of variable dust charge and ion shear flow. The dust charge fluctuating expression is obtained in the presence of kappa distributed electrons. A dispersion relation is derived and analyzed numerically by choosing space plasma parameters of Jupiter/Saturn magnetospheres. It is found that the presence of nonthermal electrons population reduces the growth rate of ITG mode driven instability. The effects of ion temperature, electron density and magnetic field variation on the growth rate of ITG instability are presented numerically. It is also pointed out that the present results will be useful to understand the ITG driven modes with variable dust charge and kappa distributed electrons, present in most of the space plasma environments.

Auto-Backlund transformations and new exact travelling wave solutions of Kadomtsev-Petviashvili equation for nonlinear dust acoustic solitary waves in dust plasmas with variable dust charge and two temperature ions

Auto-Backlund transformations and new exact travelling wave solutions of Kadomtsev-Petviashvili equation for nonlinear dust acoustic solitary waves in dust plasmas with variable dust charge and two temperature ions

Effect of Second Nonthermal Ion on the Characteristics of Dust Acoustic Solitary Waves in a Magnetized Dusty Plasma with Variable Dust Charge

AbstractThe nonlinear dust acoustic solitary waves in a magnetized dusty plasma with nonthermal ions and variable dust electric charge is studied analytically. Using reductive perturbation method the Zakharov‐Kuznetsov (ZK) equation is derived and effect of nonthermal coefficient, external magnetic field, and variable dust electric charge on the amplitude and width of soliton in dusty plasma is investigated. With increasing the rate of dust charge variation with respect of plasma potential, the amplitude of generated solitary waves in magnetized dusty plasma increases to a constant magnitude while its width decreases. Increasing the nonthermal ions coefficient leads to a noticeable decrease in the amplitude of solitons while the width of soliton increases. The amplitude of generated solitary waves in such a dusty plasma is independent of applied external magnetic field but we will have more localized solitons with increasing the external magnetic field strength. It is found that solitons are strongly influenced by the direction of external magnetic field. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dust acoustic solitons in a charge varying dusty plasma in the presence of ion nonthermality and background nonextensivity

Dust acoustic (DA) solitons are addressed in a charge varying dusty plasma in the presence of ion nonthermality and background nonextensivity. A physically meaningful nonthermal nonextensive ion distribution is outlined. The correct non-Maxwellian ion charging current is derived based on the orbit-limited motion theory. Under grain-current balance, the variable dust charge is expressed in terms of the Lambert function. It is found that nonthermality and its nonextensive nature may act concurrently and influence the restoring force and hence the soliton profile. Due to the flexibility provided by the nonextensive parameter, we think that our model should provide a better fit of the space observations.

Modulational instability of dust acoustic solitary waves for variable-charge dust grains in an ion beam–dusty plasma

A theoretical study is presented for the nonlinear self-modulation of low-frequency electrostatic dust acoustic (DA) waves propagating in a dusty plasma exposed to an external ion beam. By employing the derivative expansion perturbation method, a nonlinear Schrödinger equation (NLSE) is derived for the electric potential wave amplitude. Both dispersion and nonlinearity coefficients of the NLSE are explicit functions of the carrier wavenumber and of relevant physical parameters background species density and temperature, and dust charging fluctuation. The modulation instability of the NLSE is investigated. It is found that the presence of the ion beam species reduces the stable domain of the DA waves and the stable DA waves are created at higher wavenumber, k. Increasing ion beam temperature results as an increment of the wave dispersion and nonlinearity and the wave frequency. Also it widens the stability domain of the DA waves. Including the dust charge fluctuations changes drastically the domain where one can find stable DA wave envelopes. A brief conclusion is provided related to the application of the current findings in laboratory plasma experiments.

Dust acoustic solitary waves in a dusty plasma with variable dust charge and an arbitrary streaming ion beam

Conditions for the existence of dust acoustic solitary waves have been investigated on the nonlinear, unmagnetized homogeneous dusty plasma with variable dust charge and an arbitrary streaming ion beam. The Sagdeev’s pseudopotential has been derived in terms of ud, the dust fluid flow velocity. It is found that there exists a critical value of \(u_{d_{0}} \)(≠0), the value of ud at which (ud′)2 = 0, beyond which the solitary waves cease to exist. This critical value of ud depends on other parameters like dust temperature, etc.

Head-on collision of dust acoustic solitary waves with variable dust charge and two temperature ions in an unmagnetized plasma

The head-on collision of dust acoustic solitary waves (DASWs) in an unmagnetized dusty plasma with single electrons, two-temperature ions, variable dust charge is investigated using the extended Poincare-Lighthill-Kuo (PLK) method. The effects of the dust charge fluctuation and two temperature ion are studied. It is found that the dust charge fluctuation and two temperature ion have the significant role on the phase shift.

The effect of dust size distribution and dust charge fluctuation on dust acoustic solitary waves in a magnetized dusty plasma

Dust acoustic solitary waves in a magnetized dusty plasma are studied taking into account the effect of dust size and dust charge variations. Using the analytical and numerical results the influence of different plasma parameters on dust acoustic solitary waves are examined. It is observed that the dust size distribution and dust charge variation have significant contributions on the characteristics of dust acoustic solitary waves.