Sagdeev Potential Equation Research Articles

Propagation characteristics of nonlinear dust acoustic solitary waves in complex plasma with nonthermal electrons and trapped ions

The propagation characteristics of nonlinear dust acoustic solitary waves in a complex plasma system with nonthermal electrons and trapped ions are investigate in this work. The nonlinear dispersion relation of dust acoustic waves is obtained by using the linear method, and the two-dimensional autonomous system governing the motion of nonlinear dust acoustic waves is derived by using the Sagdeev potential method. At the same time, the specific expression of the Sagdeev potential function is obtained based on the Sagdeev potential equation. The numerical simulations are used to analyze the phase portraits of the two-dimensional autonomous system, revealing the linear periodic wave orbits, nonlinear periodic wave orbits, and homoclinic orbits co-existing in the complex dusty plasma system with nonthermal electrons and trapped ions. Furthermore, from the variations of the Sagdeev potential function with different system parameters it follows that only the compressive solitary waves exist in this complex plasma system. The significant influences of various system parameters on the amplitude, width, and waveform of the nonlinear dust acoustic solitary wave in the complex plasma system are discussed in detail. The results demonstrate that the Mach number, the nonthermal electrons and trapped ions, undisturbed dust particle number density, temperature, and charge have important effects on the propagating characteristics of the nonlinear dust acoustic solitary waves in a complex plasma with nonthermal electrons and trapped ions.

The effects of parameters of Cairns-Tsallis distribution on the properties of ion-acoustic soliton waves in plasma

The specifications of ion-acoustic soliton waves (IASWs) of plasma, including warm fluid ions and Cairns-Tsallis (C-T) distributed electrons and positrons, were investigated. The phase velocity, sagdeev potential, and Korteweg-de Vries (KdV) equation and its solution are obtained using reductive perturbation method (RPM). The results indicated that the parameters α and q have a great effect on phase velocity, nonlinear and dispersive coefficients, Sagdeev potential, maximum amplitude, and width of IASWs.

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.

Effect of Nonthermal Ions on Dust Acoustic Waves in Magnetized Plasma

A fluid model is considered to study the nonlinear dust- acoustic waves (DAW) in magnetized dusty plasma. The model consists of dust articles having negative charge, nonthermal ions, and Boltzmann electrons. Sagdeev Potential equation is derived in the form of an energy integral by applying nonperturbative approach. The pseudopotential (Sagdeev potential) profile is analyzed to study the characteristic of the solitary waves. The study has been made related to the transition of the DAW and the corresponding characters by observing the variation of amplitudes and width of the solitons with Mach number, temperature ratio, density ratio, concentration of nonthermal ions, and the direction cosine. The parametric ranges are estimated numerically to confirm the existence of solitary waves of arbitrary amplitude.

Some studies on transient behaviours of sheath formation in dusty plasma with the effect of adiabatically heated electrons and ions

Based on quasipotential analysis, a plasma sheath is studied through the derivation of the Sagdeev potential equation in dusty plasma coexisting with adiabatically heated electrons and ions. Salient features as to the existence of sheaths are shown by solving the Sagdeev potential equation through the Runge–Kutta method, with appropriate consideration of adiabatically heated electrons and ions in the dynamical system. It has been shown that adiabatic heating of plasma sets a limit to the critical dust speed depending on the densities and Mach number, and it is believed that its role is very important to the sheath. One present problem is the contraction of the sheath region whereby dust grains levitated into the sheath lead to a crystallization similar to the formation of nebulons and are compressed to a larger chunk of the dust cloud by shrinking of the sheath. Our overall observations advance knowledge of sheath formation and are expected to be of interest in astroplasmas.

Rotation as a progenitor of various solitary waves in magnetized plasmas

The main interest is to study the nonlinear acoustic waves in rotating plasma augmented through the derivation of a modified Sagdeev potential equation. Small rotation approximation causes the interaction of Coriolis force in the dynamics, and leads to the complexity in the derivation of the nonlinear wave phenomena. Pseudopotential method has been used to derive the Sagdeev-like wave equation with a view to exhibit the changes in solitary wave propagation. Some special methods have been developed to exhibit the salient features of the nonlinear waves which could be of interest in laboratory as well as in astroplasmas. As a result, findings of the compressive and rarefactive solitons along with the formation of shock waves, double layers, sinh-wave in rotating plasma ought to be of merit. Moreover, studies have expected exciting observations in generating the high energies which, in turns, yields the phenomena of soliton radiation and explosions or bursting of the solitary waves. Further, to support the theoretical investigations, some typical plasma parameters have been taken for the graphical presentation of the waves.

Propagation of Solitary Waves in Warm Magnetized Plasma with Two Temperature Electrons

Nonlinear wave structure of ion acoustic disturbances is investigated in magnetized plasma consisting of warm ions and two electron components, namely hot and cold. The basic set of fluid equations for the flow variables is reduced to a single equation known as Sagdeev Potential (SP) equation using non perturbative approach. The properties of solitary wave structures are studied by pseudo potential method, which is valid for arbitrary amplitude. The amplitude of the solitary waves and the depth of the potential well are found to decrease with the increase of the direction-cosine of the wave propagation. The ranges of temperature ratios (ion to electrons) for the existence of solitary waves and their effects on the plasma medium are studied in detail and presented graphically fordifferent sets of plasma parameters.

Dynamical behavior of size-graded dust grains levitated in rotating magnetized astroplasmas

Our purpose is to examine the formation of different sheaths in rotating astroplasmas embedded in an ambient magnetic field. Sequel to our recent work (Das and Chakraborty in Astrophys. Space Sci., 2011) we remodeled our present study with the view to finding of robust sheath over the Earth’s Moon along with the formation of dust clouds therein. Based on using the pseudopotential analysis, a modified Sagdeev potential equation has been derived, which, in turns, quantifies the interaction of Coriolis force and magnetic field and to derive the different natures of sheath and dust atmosphere. The application of this result to the input numeric data of the lunar environment and dynamical behaviors of dust levitation has been studied. Our study finds that the dust particles having a spatial segregation within the sheath region form dust clouds in spaces.

Arbitrary amplitude double layers in warm dust kinetic Alfvén wave plasmas

Large amplitude electrostatic structures associated with low-frequency dust kinetic Alfvénic waves are investigated under the pressure (temperature) gradient indicative of dust dynamics. The set of equations governing the dust dynamics, Boltzmann electrons, ions and Maxwell’s equation have been reduced to a single equation known as the Sagdeev potential equation. Parameter ranges for the existence of arbitrary amplitude double layers are observed. Exact analytical expressions for the energy integral is obtained and computed numerically through which sub-Alfvénic arbitrary amplitude rarefactive double layers are found to exist.

Propagation of ion-acoustic waves in a dusty plasma with non-isothermal electrons

For an unmagnetised collisionless plasma consisting of warm ions, nonisothermal electrons and cold, massive and charged dust grains, the Sagdeev potential equation, considering both ion dynamics and dust dynamics has been derived. It has been observed that the Sagdeev potential V(ϕ) exists only for ϕ > 0 up to an upper limit (ϕ ≃ 1.2). This implies the possibility of existence of compressive solitary wave in the plasma. Exhaustive numerics done for both the large-amplitude and small-amplitude ion-acoustic waves have revealed that various parameters, namely, ion temperature, non-isothermality of electrons, Mach numbers etc. have considerable impact on the amplitude as well as the width of the solitary waves. Dependence of soliton profiles on the ion temperature and the Mach number has also been graphically displayed. Moreover, incorporating dust-charge fluctuation and non-isothermality of electrons, a non-linear equation relating the grain surface potential to the electrostatic potential has been derived. It has been solved numerically and interdependence of the two potentials for various ion temperatures and orders of non-isothermality has been shown graphically.

Salient features of solitary waves in dusty plasma under the influence of Coriolis force

The main interest is to study the nonlinear acoustic wave in rotating dusty plasma augmented through the derivation of a modified Sagdeev potential equation. Small rotation causes the interaction of Coriolis force in the dynamical system, and leads to the complexity in the derivation of the nonlinear wave equation. As a result, the finding of solitary wave propagation in dusty plasma ought to be of merit. However, the nonlinear wave equation has been successfully solved by the use of the hyperbolic method. Main emphasis has been given to the changes on the evolution and propagation of soliton, and the variation caused by the dusty plasma constituents as well as by the Coriolis force have been highlighted. Some interesting nonlinear wave behavior has been found which can be elaborately studied for the interest of laboratory and space plasmas. Further, to support the theoretical investigations, numeric plasma parameters have been taken for finding the inherent features of solitons.

Characteristic behaviour of dust grains in a magnetized plasma sheath

Based on quasipotential analysis, the Sagdeev potential equation has been derived to study the sheath characteristics in magnetized plasma. Theoretical studies have tried to determine if there are new features in the sheath region. Because of the ubiquitous presence of dust in every plasma environment, our motivation is to estimate the interaction of charged dust grains levitated into the magnetized plasma sheath. We have calculated the size of dust grains, the generation of surface potential and the net forces acting on it inside the sheath, for some chosen laboratory plasma parameters. The estimation of dust dynamics in the sheath should take into account that it is controlled by its properties like size, surface potential and the force acting on it, besides the ambient plasma properties. The overall observations of the forces on different dust sizes enable us to obtain information about the formation of dust atmosphere.

Effect of dust-charge variation on dust acoustic solitary waves in a dusty plasma with trapped electrons

The effect of variable dust charge, dust temperature and trapped electrons on small-amplitude dust acoustic waves is investigated. It is found that both compressive and rarefractive solitons as well as double layers exist depending on the non-isothermality parameter. A modified Korteweg de Vries (MKdV) equation is derived. Critical cases, at which the nonlinear coefficient is approximately zero, are derived. In the vicinity of the critical values, KdV and further MKdV (FMKdV) equations are obtained. Employing quasipotential analysis, the Sagdeev potential equation has been derived. Because of the presence of free and trapped electrons, the plasma acoustic wave exhibits different features of various solitary waves. The Sagdeev potential equation, at a small amplitude, shows that the ordering of non-isothermality in the dusty plasma plays a unique role. In the case of a plasma with first-order non-isothermality, the Sagdeev potential equation shows the compressive solitary-wave propagation while, for a plasma with higher-order non-isothermality, the solution of this equation reveals the coexistence of compressive and farefractive solitary waves. In addition, for certain plasma parameters, the solitary wave disappears and a double layer is expected. Again, with the better approximation in the Sagdeev potential equation, more features of solitary waves, known as spiky and explosive, along with the double layers, are also highlighted. The findings of this investigation may be useful in understanding laboratory plasma phenomena and astropbysical situations.

Characteristic behaviour of dust grains in a sheath formed in plasma with negative ions

The motivation of this paper is to study the formation of a sheath in plasma contaminated with additional negative ions. Sheath formation has been analysed through the solution of the Sagdeev potential equation derived in a plasma by using the pseudopotential method. Because of the negative ions, it has been shown that the sheath formation, in contrast to that in a simple plasma, faces difficulties. A potential barrier from which modes are reflected is introduced and the potential variation beyond it is complex which, in turn, shows new findings. It is also revealed that the potential variation should be estimated in the plasma sheath in the presence of low as well as high negative-ion concentrations. The levitation of a dust grain into the sheath and its characteristic behaviour have also been investigated. Furthermore, the dust size in the ideal plasma sheath along with the causes of formation of the dust atmosphere have been studied.

Dust acoustic solitary waves and double layers in a dusty plasma with trapped electrons

The effect of variable dust charge, dust temperature, and trapped electrons on small amplitude dust acoustic waves is investigated. It is found that both compressive and rarefactive solitons as well as double layers exist depending on the nonisothermality parameter. A modified Korteweg–de Vries is derived. At critical density, the Korteweg–de Vries equation is obtained. Employing quasipotential analysis, the Sagdeev potential equation with the inclusion of different new effects has been derived. Because of the presence of free and trapped electrons, the plasma acoustic wave has gained features of various solitary waves. The Sagdeev potential equation, at a small amplitude, shows that the ordering of nonisothermality plays a unique role. In the case of a plasma with first-order nonisothermality, the Sagdeev potential equation shows the compressive solitary wave propagation, while for plasma with higher-order nonisothermality, the solution of this equation reveals the coexistence of both compressive and rarefactive solitary waves. In addition, for certain plasma parameters, the solitary wave disappears and a double layer is expected. Again, with the better approximation in the Sagdeev potential equation, more features of solitary waves, e.g., spiky and explosive, along with the double layers, are also highlighted. The findings of this investigation may be useful in understanding laboratory plasma phenomena and astrophysical situations.

Speed and shape of dust acoustic solitary waves

Parametric conditions for the existence of dust acoustic solitary waves are investigated without dust charge variation, as well as with dust charge variation. The Sagdeev potential equation is derived in terms of the dust velocity ud0 in both cases. It is found that there exists, in both cases, a critical value of ud0(≠0), the value of ud at which (ud′)2=0, beyond which the soliton solution ceases to exist. This is demonstrated clearly in the plots given for ud against the traveling wave coordinate ξ=x−Vt.

Characteristic behavior of the sheath formation in thermal plasma

The plasma sheath equation, based on the quasipotential analysis, has been derived in a plasma taking finite ion temperature into account with a view to showing the characteristic behavior of the sheath formation in front of the electron absorbing wall. The derived Sagdeev potential equation, under small amplitude approximation, describes the Bohm sheath criterion, which enables one to find the required condition for the formation of sheath in plasmas. Later, the sheath equation is completely solved numerically by using the fourth-order Runge–Kutta method to yield the characteristic features of the potential variation in the sheath region. The main goal is to determine the sheath thickness and the potential variation in the sheath region and to compare the variation with those in cold ion plasma. Again, in the higher potential region, an improved Child’s law has been derived and the potential variation has been estimated numerically, which shows that the improved Child’s law improves the results as compared to that by Child’s law.

Quasipotential analysis for deriving the multidimensional Sagdeev potential equation in multicomponent plasma

The exact multidimensional Sagdeev potential is derived in a multicomponent plasma consisting of negative ions wherein a fraction of electrons is trapped in the potential well developed in the plasma. More precisely, the Sagdeev potential equation revisits the results stemming from the Kadomtsev–Petviashvili (K–P) equation deduceable by applying the reductive perturbation technique in plasma-acoustic wave dynamics. In the study we show that the multidimensional Sagdeev potential derived here yields the formation and propagation of solitons, as well as double layers in plasma, by using a new approach known as the tanh-method to solve out the soliton phenomena. It is seen that different ordering in φ, the electrical potential, yields different solitary wave solutions that agree with earlier observations.

Quasipotential analysis for ion-acoustic solitary waves and double layers in plasmas

By using the quasipotential analysis, we first derive the Sagdeev potential equation with an aim to highlight the existence of various solitary waves and double layers as well as some other progressive modes in plasma, that includes some trapping of electrons in the potential well. The study advances to describe the spiky and explosive solitary waves along with the possible existence of double layers causeway from the interaction of trapped electrons which are to be expected as common features in space plasmas. Moreover the approach, under certain conditions, derives the intermediate integral form of the Korteweg-deVries (K-dV) equation and the K-dV equation derived with mixed nonlinearity ultimately highlights various new features of solitions in plasmas. The present theoretical observations sieved many nonlinear waves which could meet the eyes of researchers to relate the results in space plasma and expects it could be of interest to enhance the understanding of the solitary waves in laboratory and space plasmas.

Dynamical aspects of various solitary waves and double layers in dusty plasmas

Employing quasipotential analysis, the Sagdeev potential equation has been derived in a multicomponent plasma consisting of free and trapped electrons and contaminated by the dust charged grains forming therein by the attachment of electrons to finite-size dust particles. Because of the free and trapped electrons in the dusty plasma, the plasma-acoustic wave exhibits the different features of various solitary waves. The Sagdeev potential equation, at a small-amplitude approximation, leads to the evaluation, by a proposed new formalism of a simple wave solution technique, of the new scenario of solitary wave propagation in a dusty plasma. It has been shown that the ordering of the nonisothermality in the dusty plasma also plays a unique role. In the case of a plasma with first-order nonisothermality, the Sagdeev potential equation derives the compressive solitary wave propagation, while for plasma with higher-order nonisothermality the method might fail to solve the Sagdeev potential equation and, thus, an alternate method is used to reveal the coexistence of compressive and rarefactive solitary waves. In addition, for certain plasma parameters, the solitary waves disappear and a double layer is expected. Again, with the better approximation in the Sagdeev potential, more features of solitary waves, known as spiky and explosive, along with the double layers, are also highlighted. The observations made of the solitary waves could be of further interest in the understanding of laboratory and space plasmas.