Warm Adiabatic Ions Research Articles

Head-on collision of ion-acoustic (modified) Korteweg–de Vries solitons in Saturn's magnetosphere plasmas with two temperature superthermal electrons

In view of the recent observations by plasma science-spacecraft-voyager and Cassini plasma spectrometer of Saturn's magnetosphere, the interaction between two counter-propagating ion-acoustic (IA) solitons is studied in an unmagnetized plasma consisting of warm adiabatic ions in addition to hot and cold electrons following kappa distribution. The head-on collision of the IA solitons is investigated using the extended Poincare–Lighthill–Kuo technique. Since this model supports both compressive and rarefactive solitons, therefore, the soliton collisions for both Korteweg–de Vries (KdV) and the modified KdV (mKdV) equations are investigated. The corresponding phase shifts after the collision for both these equations are also derived and examined. Furthermore, the effects of different plasma parameters (corresponding to Saturn's magnetosphere), including superthermality, density, and temperature on the colliding soliton profiles and their phase shifts, are examined. It is concluded that the phase shift is smaller when both hot and cold electrons are Maxwellian by comparison with the superthermal case.

Quantitative and qualitative analyses of the mKdV equation and modeling nonlinear waves in plasma

In this paper, nonlinear electrostatic structures on the ion time scale in plasma consisting of two populations of electrons (cold and hot), positrons, and warm adiabatic ions are investigated. The multiple scale method is used to derive the modified Korteweg–de Vries equation (mKdVE). The Jacobi elliptic function expansion method (JEFEM) is employed to find some exact analytical solutions such as periodic, solitonic, and shock solutions. It is shown that the variation in the plasma parameters of interest, for our model, allows the existence of solitary and periodic structures and no shocks. It is also shown that the most important plasma parameters for the plasma model under consideration are positron concentration, α, and the percentage of cold and hot electrons, represented by the parameters μ and ν, respectively. Additionally, the qualitative behavior of the mKdVE is studied using dynamical system theory. The topological structure of the solution is discussed in the phase plane. In this work, the phase plane analysis, which is restricted to the discrete values of the parameter, is extended to the continuous range of the parameter using a bifurcation diagram. Bifurcation diagrams are drawn to forecast the behavior of the solution for specifically chosen essential plasma parameters. The analytical solution and the qualitative behavior of the solution presented in this paper are shown to be compatible with each other. The results presented here are general and can be gainfully employed to study a variety of nonlinear waves in space, laboratory plasmas, and astrophysical plasmas.

Interaction of ion-acoustic solitons for multi-dimensional Zakharov Kuznetsov equation in Van Allen radiation belts

The propagation of nonlinear ion-acoustic waves (IAWs) in a magnetoplasma having superthermal inertialess electrons and inertial warm adiabatic ions is examined. In this regard, Zakharov Kuznetsov (ZK) equation is derived in order to investigate the characteristics of the ion-acoustic solitons (IASs) in the small but finite amplitude limit. Using the Hirota bilinear method, both single and two-solitons solutions of the two and three-dimensional ZK equations are obtained. According to the parameters of Van Allen radiation belts, the effects of superthermality, magnetic field, ion number density, and the ion temperature on the profile of both single and two-solitons are explored. The estimates of the spatial extent of the interaction of solitons in the outer radiation belts are also given.

Transcritical bifurcation of nonlinear electrostatic waves in a superthermal dusty plasma

The phase portraits and bifurcation properties of nonlinear dust ion-acoustic waves are studied in a complex plasma comprising cold dust particles, warm adiabatic ions, and κ-distributed electrons. A characteristic equation is obtained and solved numerically. The existence domain of fixed points and the stability of traveling wave solutions are discussed in the parameter space of Mach number M and dust concentration δ over a wide range of values of κ and ion temperature σ. It is shown that the motion dynamics of homoclinic orbits and nonlinear periodic orbits undergo a transcritical bifurcation at critical points of and , where two fixed points coalesce, and then switch their stabilities. We observe that at these bifurcation values with half-stable fixed points, the system supports a new analytical solitary wave solutions with much fatter tails than regular solitons. Furthermore, the existence domain of transcritical bifurcation parameters and transition between solitary and nonlinear periodic waves has been determined for different values of M and δ. It is found that the Mach number broadens the region prior to the bifurcation point, and enhances the onset of transition between modes, while the dust concentration has an opposite influence.

Dust–ion acoustic solitary waves in a collisionless magnetized five components plasma

Abstract We have derived a Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation to study the nonlinear behavior of dust–ion acoustic waves in a collisionless magnetized five components dusty plasma consisting of warm adiabatic ions, nonthermal hot electrons, isothermal cold electrons, nonthermal positrons and static negatively charged dust particulates. It is found that the coefficient of the nonlinear term of the KdV-ZK equation vanishes along different family of curves in different compositional parameter planes. In this situation, to describe the nonlinear behavior of dust–ion acoustic waves, we have derived a modified KdV-ZK (MKdV-ZK) equation. When the coefficients of the nonlinear terms of both KdV-ZK and MKdV-ZK equations are simultaneously equal to zero, then we have derived a further modified KdV-ZK (FMKdV-ZK) equation which effectively describes the nonlinear behavior of dust–ion acoustic waves. Analytically and numerically, we have investigated the solitary wave solutions of different evolution equations propagating obliquely to the direction of the external static uniform magnetic field. We have seen that the amplitude of the KdV soliton strictly increases with increasing β e, whereas the amplitude of the MKdV soliton strictly decreases with increasing β e, where β e is the nonthermal parameter associated with the hot electron species. Also, there exists a critical value β r ( c ) ${\beta }_{\text{r}}^{(\text{c})}$ of β e such that the FMKdV soliton exists within the interval β r ( c ) < β e ≤ 4 7 ${\beta }_{\text{r}}^{(\text{c})}< {\beta }_{\text{e}}\le \frac{4}{7}$ , whereas the FMKdV soliton does not exist within the interval 0 < β e < β r ( c ) $0< {\beta }_{\text{e}}< {\beta }_{\text{r}}^{(\text{c})}$ . We have also discussed the effect of different parameters of the system on solitary waves obtained from the different evolution equations.

Spike-Like Traveling Waves at the Critical Point of Bifurcation in a Nonextensive Dusty Plasma With Dust Polarity

This article presents a detailed study on the basic features of bifurcation of dust ion acoustic (DIA) traveling waves in a dusty plasma comprising warm adiabatic ions, nonextensive electrons, and arbitrarily charged dust particles. A reduced dynamical system is obtained for plasma waves’ evolution, and the global dynamics of local bifurcation of waves’ motion are determined on the equilibrium points’ dust concentrations’ plane with respect to all possible plasma parametric combinations. The stability and phase portrait analysis indicate a sudden emergence of nonlinear periodic and solitary waves for critical values of negative (positive) dust concentration. At these critical values, waves’ dynamics exhibit a transcritical bifurcation with half-stable fixed points which support new spike-like traveling waves. The analytical and numerical solutions reveal that the decay rate of this localized structure is much slower than ordinary solitary waves that decay exponentially fast. Furthermore, the existence domain of bifurcation parameters and transitions between modes are found for different values of nonextensive electrons and arbitrarily charged dust concentrations. Our results could be applicable to different space and astrophysical plasma systems, particularly in earth atmosphere.

Effect of dust polarity on transcritical bifurcation of dust ion-acoustic waves in a nonextensive dusty plasma

In this paper, we combine bifurcation techniques and numerical simulations to fully analyze the nonlinear propagation of dust ion-acoustic waves in a complex dusty plasma consisting of warm adiabatic ions, nonextensive electrons, and negatively (positively) charged dust particles. An autonomous dynamical system is derived which captures the main features of traveling wave solutions and transition between nonlinear modes. It is shown that for a range of electron nonextensivity and negative (positive) dust concentration, there are different existence domains of stability regions. At the critical points of nonextensivity parameter and dust concentration, we show that the motion dynamics of low-frequency dust ion-acoustic traveling waves undergoes a transcritical bifurcation, where two equilibrium points coalesce, and then switch their stability. A new kind of solitary structure is also observed which is characterized by the transcritical bifurcation parameters with half-stable equilibrium points. It is found that an increase in negative (positive) dust concentration leads to the appearance of bifurcation points at larger (smaller) values of electron nonextensivity. In accordance with the phase portraits analysis, the coexistence of homoclinic orbits, nonlinear periodic and supernonlinear periodic orbits are also investigated for different conditions. It is shown that the nonextensive parameter and dust polarity play a crucial role in the transition between nonlinear traveling waves.

Bifurcation types and dynamic control of dust ion‐acoustic waves propagation in dusty plasmas with non‐thermal electrons

AbstractThe bifurcation types and phase portraits of non‐linear dust ion‐acoustic travelling waves are studied in a dusty plasma comprising warm adiabatic ions, non‐thermal electrons and stationary cold dust species. A dynamical system is derived for the plasma waves evolution, and then the bifurcation response is determined on the equilibrium points‐non‐thermal parameter plane. It is shown that the motion dynamics of travelling waves undergoes a transcritical as well as saddle‐node bifurcations for the critical values of energetic electrons. We indicate that a sudden emergence and transition between solitary waves and non‐linear periodic waves occur at the critical point of transcritical bifurcation. For the saddle‐node bifurcation, we show that both solitary and super‐nonlinear periodic waves disappear, and only a large amplitude periodic wave can propagate in plasma. Further, the coexistence of solitary waves, non‐linear and super‐nonlinear waves are investigated for different values of plasma parameters. The results obtained here could be applicable to different space and astrophysical plasma systems, particularly in Saturn's E‐ring.

Propagation of dust-acoustic nonlinear waves in a homogeneous collisional dusty plasma

Nonlinear propagation of dust-acoustic waves DAWs in a weakly collisional dusty plasma comprising warm adiabatic fluid dust particles, isothermal electrons, and ions is investigated. We used the reductive perturbation theory to reduce the basic set of fluid equations to one evolution equation, namely damped Kadomtsev–Petviashivili (DKP). The analytical stationary solutions of the DKP equation are numerically analyzed, and the effect of various dusty plasma parameters on DAWs wave propagation is taken into account. We obtained, blast, anti-kink, periodic cnoidal and cnoidal waves. It is well known that explosive waves are a double edged sword. They can be seen, for example, in the atmosphere, or in engineering applications in metal coating.

Ion-acoustic solitary structures at the acoustic speed in a collisionless magnetized nonthermal dusty plasma

Abstract At the acoustic speed, we have investigated the existence of ion-acoustic solitary structures including double layers and supersolitons in a collisionless magnetized plasma consisting of negatively charged static dust grains, adiabatic warm ions, and nonthermal electrons. At the acoustic speed, for negative polarity, the system supports solitons, double layers, supersoliton structures after the formation of double layer, supersoliton structures without the formation of double layer, solitons after the formation of double layer whereas the system supports solitons and supersolitons without the formation of double layer for the case of positive polarity. But it is not possible to get the coexistence of solitary structures (including double layers and supersolitons) of opposite polarities. For negative polarity, we have observed an important transformation viz., soliton before the formation of double layer → double layer → supersoliton → soliton after the formation of double layer whereas for both positive and negative polarities, we have observed the transformation from solitons to supersolitons without the formation of double layer. There does not exist any negative (positive) potential solitary structures within 0 < μ < μ c (μ c < μ < 1) and the amplitude of the positive (negative) potential solitary structure decreases for increasing (decreasing) μ and the solitary structures of both polarities collapse at μ = μ c, where μ c is a critical value of μ, the ratio of the unperturbed number density of electrons to that of ions. Similarly there exists a critical value β e2 of the nonthermal parameter β e such that the solitons of both polarities collapse at β e = β e2.

Arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless magnetized plasma consisting of non-thermal and isothermal electrons

Abstract Using Sagdeev pseudo-potential technique, we have studied the arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless plasma consisting of adiabatic warm ions, non-thermal hot electrons and isothermal cold electrons immersed in an external uniform static magnetic field. We have used the phase portraits of the dynamical system describing the non-linear behaviour of ion acoustic waves to confirm the existence of different solitary structures. We have found that the system supports (a) positive potential solitons, (b) negative potential solitons, (c) coexistence of both positive and negative potential solitons, (d) negative potential double layers, (e) negative potential supersolitons and (f) positive potential supersolitons. Again, we have seen that the amplitude of the positive potential solitons decreases or increases with increasing n ch according to whether 0 < n c h < n c h ( c ) $0{< }{n}_{ch}{< }{n}_{ch}^{\left(c\right)}$ or n c h ( c ) < n c h ≤ 1 ${n}_{ch}^{\left(c\right)}{< }{n}_{ch}\le 1$ , where n c h ${n}_{ch}$ is the ratio of isothermal cold and non-thermal hot electron number densities, and n c h ( c ) ${n}_{ch}^{\left(c\right)}$ is a critical value of n ch . Also, we have seen that the amplitude of the positive potential solitons decreases with increasing β e , where β e is the non-thermal parameter. We have also investigated the transition of different negative potential solitary structures: negative potential soliton (before the formation of negative potential double layer) → negative potential double layer → negative potential supersoliton → negative potential soliton (after the formation of negative potential double layer) by considering the variation of θ only, where θ is angle between the direction of the external uniform static magnetic field and the direction of propagation of the ion acoustic wave.

Nonlinear Dynamics of Dust-Ion-Acoustic Waves in Magnetized Collisional Opposite Polarity Dusty Plasmas

A four-component magnetized collisional superthermal opposite polarity dusty plasma (OPDP), containing stationary dust grains of opposite charges, inertial ion fluid, and non-inertial superthermal electrons, has been considered to study different modes of dust-ion-acoustic waves (DIAWs) theoretically and numerically. In addition, the collisional effect between ion and neutral particles and the temperature effect of adiabatic warm ions have been taken into account to draw a more generalized picture of DIAWs. To investigate the growth, evaluation, propagation, and fundamental features (e.g., speed, amplitude, energy, width, etc.) of DIAWs, the reductive perturbation theory has been employed to derive the damped Zakharov-Kuznetsov-Burgers (dZKB) equation, and the hyperbolic tangent method is adopted to find the solution of dZKB equation. The fundamental attributes of DIAWs are seen to be affected significantly due to the variation of basic plasma parameters (e.g., adiabaticity, superthermality, viscosity, ion temperature, obliquity angle, magnetic field intensity, the amount of charge residing onto the dust grains, ion-neutral collision frequency, etc.). In addition, the coexistence of oppositely charged dust grains has a notable effect on the dynamics of linear and nonlinear DIAWs, which has been established in the bifurcation analysis. The polarity of the DIAWs changes if the amount of positive charge on dust is excessively greater than that of negative charge and vice versa. The findings of this research work may be apply to examine the properties of DIAWs in experimental and space dusty plasmas, where the opposite polarity dust grains are present, adiabatic thermal pressure of warm ion and damping due to ion-neutral collision are accountable.

Combined effect of Kappa and Cairns distributed electrons on ion acoustic solitary structures in a collisionless magnetized dusty plasma

Starting from one dimensional Kappa distribution for electrons, we have systematically developed the combined Kappa-Cairns distribution. We have found the effective bounds of both nonthermal parameters $\kappa $ and $\beta _{e}$ for the combined Kappa-Cairns distribution. This distribution can generate more highly energetic particles in comparison with both Kappa and Cairns distributions. We have investigated ion acoustic solitary structures in a collisionless magnetized plasma composed of negatively charged static dust grains, adiabatic warm ions and a population of highly energetic electrons generated from the combined Kappa-Cairns distribution. Sagdeev pseudo-potential technique has been considered to investigate the arbitrary amplitude steady state solitary structures including double layers and supersolitons. We have developed a computational scheme to draw the existence domains showing the nature of existence of different solitary structures. Different solitary structures of both positive and negative polarities have been observed for different values of $\kappa $ and $\beta _{e}$. We have seen two important transitions of solitary structures for negative polarity, viz., soliton before the formation of double layer → double layer → supersoliton → soliton after the formation of double layer, and soliton before the formation of supersoliton → supersoliton → soliton. For the second case, we have a supersoliton structure without the formation of double layer and this case is completely new one for magnetized plasma. Different solitary structures supported by the system have been investigated with the help of compositional parameter spaces and the phase portraits of the dynamical systems describing different solitary structures.

Effect of Landau damping on ion acoustic solitary waves in a collisionless unmagnetized plasma consisting of nonthermal and isothermal electrons

We have used the Sagdeev pseudo-potential technique to investigate the arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless magnetized plasma consisting of adiabatic warm ions, isothermal cold electrons and nonthermal hot electrons immersed in an external uniform static magnetic field. We have used the phase portraits of the dynamical system describing the nonlinear behaviour of ion acoustic waves to confirm the existence of different solitary structures. We have also investigated the transition of different solitary structures: soliton (before the formation of double layer) $\rightarrow$ double layer $\rightarrow$ supersoliton $\rightarrow$ soliton (soliton after the formation of double layer) by considering the variation of $\theta$ only, where $\theta$ is the angle between the direction of the external uniform static magnetic field and the direction of propagation of the wave.

New insights on fast ion-acoustic soliton stopbands and extension to dusty plasmas

Large amplitude fast ion-acoustic solitons are revisited in a three-component plasma composed of cold ions, warm (adiabatic) ions, and hot Boltzmann electrons to determine where the limits occur in the ranges of the warm ion-to-electron temperature ratio τ and the charge-to-mass ratio of the cold ions relative to the warm ions μ for the existence of stopbands. The warm (adiabatic) ion limiting curve evolves in a similar fashion for increasing values of τ or decreasing values of μ in supporting the existence of stopbands when the warm ion limiting curve is double-valued in the Mach number over part of a range of cold ion densities, to the disappearance of the stopbands when the warm ion limiting curve is single-valued over the complete range of cold ion densities. The bifurcation of the warm ion limiting curve into an upper and lower branch indicates the transition region in parameter space, which is between the region where stopbands are supported and the region where stopbands do not occur. The stopbands are found to have an infinite extent over the range of cold ion densities in the transition region. The widening (or narrowing) of the stopbands over the range of cold ion densities associated with a kappa (or Cairns) distribution of hot ions in a four-component plasma is found to be much weaker than non-thermal electron effects on the stopbands as reported by Maharaj and Bharuthram [Phys. Plasmas 24, 022305 (2017)].

Modulation instability of obliquely propagating ion acoustic waves in a collisionless magnetized plasma consisting of nonthermal and isothermal electrons

We have studied the modulation instability of obliquely propagating ion acoustic waves in a collisionless magnetized warm plasma consisting of warm adiabatic ions and two different species of electrons at different temperatures. We have derived a nonlinear Schr{\"o}dinger equation using the standard reductive perturbation method to describe the nonlinear amplitude modulation of ion acoustic wave satisfying the dispersion relation of ion acoustic wave propagating at an arbitrary angle to the direction of the external uniform static magnetic field. We have investigated the correspondence between two nonlinear Schr{\"o}dinger equations $-$ one describes the amplitude modulation of ion acoustic waves propagating along any arbitrary direction to the direction of the magnetic field and other describes the amplitude modulation of ion acoustic waves propagating along the direction of the magnetic field. We have derived the instability condition and the maximum growth rate of instability of the modulated ion acoustic wave. We have seen that the region of existence of maximum growth rate of instability decreases with increasing values of the magnetic field intensity whereas the region of existence of the maximum growth rate of instability increases with increasing $\cos \theta$, where $\theta$ is the angle of propagation of the ion acoustic wave with the external uniform static magnetic field. Again, the maximum growth rate of instability increases with increasing $\cos \theta$ and also this maximum growth rate of instability increases with increasing $\beta_{e}$ upto a critical value of the wave number, where $\beta_{e}$ is the parameter associated with the nonthermal distribution of hotter electron species.

Modulational Instability of Ion Acoustic Waves in a Magnetized Plasma Consisting of Isothermally Distributed Hot and Cold Electrons

Using the standard Reductive Perturbation Method a nonlinear Schr¨odinger equation is derived to study the modulational instability of small amplitude ion acoustic waves in a collisionless magnetized plasma composed of adiabatic warm ions, Maxwell-Boltzmann distribution of hot electrons as well as Maxwell-Boltzmann distribution of cold electrons, and the plasma system immersed in an external uniform static magnetic field (B0 = B0ˆz) propagating along the z-axis.The instability condition and the maximum growth rate of instability have been investigated analytically as well as numerically. We have studied the effect of each parameter of the present plasma system on the maximum growth rate of instability. In particular, it is found that the maximum growth rate of instability decreases with the increasing value of the ion cyclotron frequency with some set of values of the parameters associated with the present plasma system. Again, we have seen that the instability region decreases with the increasing value of the ion cyclotron frequency.

Dust Ion Acoustic Solitary Structures at the Acoustic Speed in the Presence of Nonthermal Electrons and Isothermal Positrons

The Sagdeev pseudo-potential technique and the analytic theory developed by Das et al. [J. Plasma Phys. 78, 565 (2012)] have been used to investigate the dust ion acoustic solitary structures at the acoustic speed in a collisionless unmagnetized dusty plasma consisting of negatively charged static dust grains, adiabatic warm ions, nonthermal electrons and isothermal positrons. The present system supports both positive and negative potential solitary waves at the acoustic speed, but the system does not support the coexistence of solitary structures of opposite polarity at the acoustic speed. The system also supports negative potential double layer at the acoustic speed, but does not support positive potential double layer. Although the system supports positive potential supersoliton at the supersonic speed, but there does not exist supersoliton of any polarity at the acoustic speed. Solitary structures have been investigated with the help of compositional parameter spaces and the phase portraits of the dynamical system describing the nonlinear behaviour of the dust ion acoustic waves at the acoustic speed. For the case, when there is no positron in the system, there exist negative potential double layer and negative potential supersoliton at the acoustic speed and for such case, the mechanism of transition of supersoliton to soliton after the formation of double layer at the acoustic speed has been discussed with the help of phase portraits. The differences between the solitary structures at the acoustic speed and the solitary structures at the supersonic speed have been analysed with the help of phase portraits.

The effects of cool ion temperature on fast ion-acoustic soliton stopbands in a plasma with two positive ion species

The existence of stopbands was reported for the very first time in a study of fast ion-acoustic solitons by Nsengiyumva et al. [Phys. Plasmas 21, 102301 (2014)] in a plasma with cold ions, warm (adiabatic) ions, and Boltzmann electrons. We recall that a stopband is a range of speeds (Mach numbers) for which solitons cannot propagate. In this paper, we investigate the effect of the temperature of the cooler ions on stopbands. It is found that the Mach number range for the stopbands and the range of cool ion densities over which the stopbands occur become narrower with increasing temperature of the cooler ions, until the stopbands vanish at an upper limiting value. The extension of the model to include nonthermal effects for the electrons reveals that the range of cool ion temperatures which favors the existence of stopbands becomes wider for a kappa electron distribution, but narrower when the electrons are Cairns distributed for increasing strength of the nonthermal coefficient.

Modulational Instability, Ion-Acoustic Envelope Solitons, and Rogue Waves in Four-Component Plasmas

Modulational instability (MI) of ion-acoustic waves (IAWs) has been theoretically investigated in a plasma system which is composed of inertial warm adiabatic ions, isothermal positrons, and two-temperature super-thermal electrons (cool and hot). A nonlinear Schrodinger equation (NLSE) is derived by using reductive perturbation method that governs the MI of the IAWs. The numerical analysis of the solution of NLSE shows the existence of both stable (dark envelope solitons) and unstable (bright envelope solitons and rogue waves) regimes of IAWs. It is observed that the basic features (viz., stability of the wave profile and MI growth rate) of the IAWs are significantly modified by the superthermality of electrons and related plasma parameters. The results of our present investigation should be useful for understanding different nonlinear phenomena in both space (viz., Saturn’s magnetosphere and interplanetary medium) and laboratory plasmas (viz., hot-cathode discharge and high-intensity laser irradiation).