Hot Dusty Plasma Research Articles

Propagation characteristics of (2 + 1) dimensional dust acoustic solitary waves in hot dusty plasma

The propagation characteristics of (2 + 1) dimensional nonlinear dust acoustic solitary wave in an unmagnetized hot dusty plasma composed of dust particles, electrons and nonthermal ions are studied in the paper. Firstly, the Kadomtsev-Petviashvili (KP) equation, which is used to describe the (2 + 1) dimensional nonlinear dust acoustic solitary wave, is derived by the reduced perturbation method, and the phase diagram and the Sagdeev potential equation of the system are obtained by using the traveling wave solution method. Then, the effects of different parameters in the hot dusty plasma system on the nonlinear coefficient, dispersion coefficient of the KP equation, system phase diagrams, Sagdeev potential function and the solitary wave solution in isothermal and adiabatic states are discussed by using numerical simulation and analysis method of mathematical software. Finally, the results show that the mass of dust particles, temperature, number density and distribution state of electrons and nonthermal ions have important effects on the amplitude, width and waveform of the nonlinear dust acoustic solitary wave under isothermal and adiabatic conditions.

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

Abstract In the present work, employing the nonlinear field equations of a hot dusty plasma in the presence of nonthermal electrons and trapped ions, we studied the amplitude modulation of nonlinear waves in such a plasma medium by use of the reductive perturbation method and obtained the modified nonlinear Schrodinger equation. The modulational instability (MI) was investigated and the effects of the proportion of the fast electrons (α), the trapping parameter (b) and the plasma parameters such as the dust-ion temperature ratio (σd), the partial unperturbed electron to dust density (δ), and the ion-electron temperature ratio (σi) on it was discussed. For the investigation of modulational instability problems three parameters P/Q, Kmax and Γmax play the central role. The variations of these parameters with the wave number k and the other physical parameters are discussed and the possibility of occurence of modulational instability is indicated.

Multidimensional Instability of Dust‐Acoustic Solitary Waves in a Magnetized Hot Dusty Plasma with Superthermal Electrons and Ions

AbstractMultidimensional instability of dust‐acoustic solitary wave (DASW) in magnetized dusty plasma with superthermal electrons and ions and micron size hot dust particles is investigated. The Zakharov‐Kuznetsov (ZK) equation, describing the small but finite amplitude DASW, was derived using the reductive perturbation method and its solitary answers was introduced. Effects of electrons and ions superthermality as well as the external magnetic field on the nature of DASW are discussed in detail. Dispersion relation, threshold condition, and growth rate of multidimensional instability of DASW were derived using small‐k (long wavelength plane wave) perturbation expansion method. We found that the direction and strength of external magnetic field extremely affect the growth rate and instability criterion. Results show that growth rate of instability decreases with increasing the number of superthermal electrons and increases with increasing the number of superthermal ions. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Shock wave solution in a hot adiabatic dusty plasma having negative and positive non-thermal ions with trapped electrons

In this report an investigation of the properties of a dust acoustic (DA) shock wave propagating in an adiabatic dusty plasma, including the effect of the negative-ion-rich non-thermal ions and trapped electrons, is presented. The reductive perturbation method is employed to derive the modified Burgers equation and a new form of the lower-order nonlinear modified Burgers equation for DA shock waves in a homogeneous, unmagnetized and collisionless plasma whose constituents are electrons, singly-charged positive ions, singly-charged negative ions and massive, charged dust particles. The stationary analytical solution of the Burgers equation and the new analytical solution of the lower-order nonlinear modified Burgers equation are numerically analyzed, and the effects of various dusty plasma constituents on the DA shock wave’s propagation are taken into account. Both positive and negative ions in the dusty plasma are observed to play a key role in the formation of both positive, as well as negative, DA shock waves, and the ion concentration can be used to control the transformation from negative to positive potentials of the waves.

Effect of superthermal electrons on the characteristics of dust acoustic solitary waves in a magnetized hot dusty plasma with dust charge fluctuation

A nonlinear dust acoustic solitary wave (DASW) in a magnetized dusty plasma with superthermal electrons is studied analytically. In this model hot electrons are described by the kappa distribution function, but ions are taken to be Maxwellian and plasma pressure and dust-natural collisions have been taken into account. Using the reductive perturbation method the Zakharov–Kuznetsov equation is derived and effect of electrons’ hotness on the amplitude and width of soliton in dusty plasma is investigated. With decreasing energy of the hot electrons in the system, κ > 100, results coincide with the results of the dusty plasma system containing Maxwellian electrons. In this model anisotropy is caused by an external magnetic field while inhomogeneity is generated by ion density gradient in the plasma. The initial density decreases exponentially in the space along one direction. The amplitude of DASW is mainly affected by density inhomogenity rather than the electrons’ energy. With increasing energy of the system, the width of DASW increases significantly. Applying the effect of pressure in the model only rarefactive DASW may be generated in the dusty plasma.

Dust Acoustic Solitary Waves in Saturn F-ring's Region

Effect of hot and cold dust charge on the propagation of dust-acoustic waves (DAWs) in unmagnetized plasma having electrons, singly charged ions, hot and cold dust grains has been investigated. The reductive perturbation method is employed to reduce the basic set of fluid equations to the Kortewege-de Vries (KdV) equation. At the critical hot dusty plasma density Nh0, the KdV equation is not appropriate for describing the system. Hence, a set of stretched coordinates is considered to derive the modified KdV equation. It is found that the presence of hot and cold dust charge grains not only significantly modifies the basic properties of solitary structure, but also changes the polarity of the solitary profiles. In the vicinity of the critical hot dusty plasma density Nh0, neither KdV nor mKdV equation is appropriate for describing the DAWs. Therefore, a further modified KdV (fmKdV) equation is derived, which admits both soliton and double layer solutions.

Large-amplitude dust-acoustic solitary waves in an electron-depleted hot dusty plasma with trapped ions

A theoretical model is presented to show the existence, formation, and possible realization of large-amplitude dust-acoustic solitary potentials in electron-depleted hot dusty plasma with trapped ions. These nonlinear localized structures are self-consistent solutions of the Vlasov equation in which the ion response is non-Maxwellian due to the ion trapping in the large-amplitude plasma potentials. Emphasis is given to the role of the grain temperature. Interestingly, one finds that the effect of increasing the dust temperature is to restrict the domain of allowable Mach numbers. The latter enlarges when the relative amount of trapped ions is increased. Furthermore, the nonlinear potential shrinks and exhibits smaller depth and smaller width than the one involving cold dust grains. The strong localization of the dust particles becomes less pronounced when the dust temperature is increased. The results complement and provide new insights into previously published results on this problem and their relevance to space dusty plasmas is pointed out.PACS Nos.: 52.27.Lw; 52.35.Fp; 52.35.Sb; 52.35.Tc; 52.35.Mw

Dust-acoustic solitary waves in an adiabatic hot dusty plasma

An adiabatic hot dusty plasma (containing non-inertial adiabatic electron and ion fluids, and negatively charged inertial adiabatic dust fluid) is considered. The basic properties of arbitrary amplitude dust-acoustic (DA) solitary waves, which exist in such an adiabatic hot dusty plasma, are explicitly examined by the pseudo-potential approach. To compare the basic properties (critical Mach number, amplitude and width) of the DA solitary waves observed in a dusty plasma containing adiabatic electron, ion and dust fluids with those observed in a dusty plasma containing isothermal electron and ion fluids and adiabatic dust fluid, it has been found that the adiabatic effect of inertia-less electron and ion fluids has significantly modified the basic properties of the DA solitary waves, and that on the basic properties of the DA solitary waves, the adiabatic effect of electron and ion fluids is much more significant than that of the dust fluid.

Effects of obliqueness and external magnetic field on the large amplitude solitary waves in a dusty plasma

The nonlinear excitation of large amplitude dust-acoustic (DA) solitary waves in a magnetized hot dusty plasma consisting of fast ions and charged dust grains is revisited to take into account the effects of embedding external magnetic field. The DA solitary wave is assumed to propagate obliquely to the magnetic field. Sagdeev's approach, which is valid for arbitrary amplitude solitary waves, is used. Both compressive and rarefactive solitary structures are shown to coexist by the effects of obliqueness and nonthermal or fast ions. It is found that as the percentage of fast particles ( β ) increases, the critical Mach number ( M c ) increases and the increase is more effective at the higher value of the direction cosine ( L z ). The solitary wave solutions for small amplitude DA waves exhibit distinct behaviors for different values of dust fluid temperature, β and L z .

Theoretical investigation of properties of soliton in hot dusty plasma with non-thermal ions

In this paper, the properties of soliton structures in a hot, unmagnetized dusty plasma which consists of a negatively charged hot dust fluid with variable dust charge, non-thermal distribution of ions and Boltzmann distribution of electrons have been studied. A modified KdV (mKdV) equation which describes the dust acoustic waves in this system is derived by the reductive perturbation method. The effects of dusty plasma parameters on the dust-acoustic solitary waves is studied theoretically. It is found that the soliton structures is determined by the dusty plasma parameters. Furthermore, the soliton only exists in certain regions where these parameters are specially chosen.

Dust-acoustic solitary waves in an inhomogeneous magnetized hot dusty plasma with dust charge fluctuations

Using a standard reductive perturbation theory, a Zakharov-Kuznnetsov (ZK) equation is derived in an inhomogeneous dusty plasma comprised of negatively charged dust grains of equal radii, Boltzmann distributed electrons and positive ions. The effects of dust thermal pressure, dust charge variation, dust-neutral collision, and the external magnetic field are taken into account. Either compressive or rarefective solitons are shown to exist depending on the critical value of the phase velocity which in turn, depends on the dust temperature and pressure. An analytic soliton solution is obtained and discussed. The behaviors of the soliton amplitude, width, and the Mach number are investigated numerically for different plasma parameters.

(2 + 1) dimensional nonlinear waves in a two-ion-temperature warm dusty plasma considering the dust size distribution

For two-ion-temperature dusty plasma with many different dust grains, we derived a Kadomtsev–Petviashvili (KP) equation for unmagnetized, collisionless, hot dusty plasma. We find that in a two-ion-temperature warm dusty plasmas with power law dust size distribution, the velocity of soliton is smaller than that for mono-sized dust plasma which has average dust size. Meanwhile as the temperature of dust plasmas increases, the amplitude of soliton decreases slower than that of mono-sized dust plasma with average dust size, while the width of soliton decreases quicker than that of mono-sized dust plasma with average dust size.

Critical density solitary waves structures in a hot dusty plasma with vortex-like ion distribution in phase space

The nonlinear properties of solitary waves structure in a hot dusty plasma consisting of isothermal hot electrons, non isothermal ions and high negatively charged massive dust grains, are reported. A modified Korteweg-de Vries equation (modified KdV), which admits a solitary waves solution for small but finite amplitude, is derived using a reductive perturbation theory. A nonisothermal ions distribution provides the possibility of coexistence of amplitude rarefactive as well as compressive solitary waves. On the other hand, consideration of a critical ions density gives a stationary solution of solitary waves and the dynamics of small but finite amplitude of solitary waves is governed by Korteweg-de Vries equation (KdV). The properties of solitary waves in the two cases are discussed.

The Kadomtsev–Petviashvili (KP) equation of dust acoustic waves for hot dust plasmas

Kadomtsev–Petviashvili (KP) equation is derived for unmagnetized hot dust plasmas. It suggests that the nonlinear dust acoustic solitary waves in a hot dusty plasma are stable even there are some higher order transverse perturbations. There are only rarefactive solitary waves in hot dust plasmas which has been verified analytically in this paper.

Large amplitude electrostatic solitary structures in a hot non-thermal dusty plasma

A rigorous theoretical investigation has been made of large amplitude compressive and rarefactive dust–acoustic solitary waves in an unmagnetized hot dusty plasma consisting of a negatively charged hot dust fluid and non-thermally distributed ions. The pseudo-potential approach, which is valid for arbitrary amplitude solitary waves, has been employed. It is shown that the presence of the fast or non-thermal ions may allow compressive and rarefactive solitary waves to coexist. It is found that the effect of the dust fluid temperature changes the minimum values of α (a parameter determining the number of fast ions present in our dusty plasma model) and M (the Mach number) for which the compressive and rarefactive solitary waves can coexist. It is also observed that as the dust fluid temperature rises, the amplitude of both the compressive and rarefactive solitary waves decrease, whereas their width increases. The implications of these results to some space and astrophysical dusty plasma situations are briefly discussed.

Effects of dust temperature and fast ions on gravitational instability in a self-gravitating magnetized dusty plasma

A theoretical investigation has been made of effects of dust temperature, fast (nonthermal) ions, and external magnetic field on gravitational instability in a self-gravitating magnetized hot dusty plasma, which consists of extremely massive, negatively charged hot dust fluid, nonthermally distributed ions, and Boltzmann distributed electrons, where the gravitational force is comparable to or greater than the electrostatic force. The effects of dust temperature, fast ions, and external magnetic field have been found to modify the criterion for this gravitational instability. It has been shown that the growth rate of this gravitational instability decreases with dust temperature, fast ions, and external magnetic field, but increases with the number of free electrons, with the ratio of ion temperature to electron temperature, and with the ratio of dust mass to dust charge. The implications of this result in some astrophysical situations are briefly discussed.

Nonlinear scattering of Alfvén waves off low-frequency dust modes in a magnetized dusty plasma

The three-wave nonlinear scattering of an electromagnetic Alfven wave off a low-frequency dust mode,viz. dust-Bernstein mode in a homogeneous, magnetized, hot and collisionless dusty plasma, has been analytically investigated. The Vlasov equation in terms of gyrokinetic variables has been employed to find the nonlinear response of the plasma particles including the finite-Larmor-radius thermal kinetic effects. An approximate expression for the comparative growth rates of the three-wave parametric instability has been obtained. It is noted that for the usual dusty plasma parameters the parametric scattering of the electromagnetic Alfven waves through the dust-Bernstein modes in the low-density limit is more efficient than that in the high-density limit.

Obliquely propagating electrostatic solitary structures in a magnetized hot dusty plasma with trapped ions

A theoretical investigation has been made of obliquely propagating electrostatic solitary structures in a hot magnetized three-component dusty plasma, which consists of a negatively charged hot dust fluid, Blotzmann distributed electrons, and free and trapped ions. It has been found that owing to the departure from the Boltzmann ion distribution to a trapped ion one, the dynamics of small but finite-amplitude electrostatic waves in a magnetized hot dusty plasma is governed by the modified Korteweg–de Vries (KdV) equation. The latter admits a stationary solitary wave solution that has a larger amplitude, a smaller width, and higher propagation velocity, than that involving Boltzmann distributed ions. It has been shown that the effects of obliqueness, external magnetic field, trapped ions, and free electrons change the behavior of these electrostatic solitary structures that have been found to exist with only negative potential in this dusty plasma model.

Modulational instability of an electron plasma wave in a dusty plasma

The modulational instability of an electron plasma wave in a homogeneous, unmagnetized, hot, and collisionless dusty plasma has been investigated analytically. The Vlasov equation has been solved perturbatively to find the nonlinear response of the plasma particles with random static distribution of massive and charged dust grains having certain correlation. It is noticed that the growth rate of the modulational instability of the electron plasma wave through a new ultra-low-frequency dust mode is more efficient than that through the usual ion-acoustic mode in the dusty plasma.

Modification and damping of magnetosonic waves in a dusty plasma

A rigorous investigation has been made on the modification of the dispersion properties of electromagnetic waves in a hot dusty plasma in the presence of a homogeneous external magnetic field. The Vlasov equation has been employed to find the response of the magnetized plasma particles where the dust grains form a static background of highly charged and massive centers having certain correlation. As an example, we derive the modified dispersion relation of the low frequency electromagnetic wave propagating perpendicular to the external magnetic field, i.e., the magnetosonic wave in the dusty plasma. We find important modifications in the dispersion relation and a finite damping of the usually undamped magnetosonic wave due to the presence of the dust. The modification of the dispersion properties and the new source of damping depend upon dust perturbation parameters, temperature, external magnetic field and the dust correlation length.