Dust-acoustic Research Articles

On the propagation of dynamical waves in complex cometary plasma environments with thermal heavy ions and non-extensive light species

A variety of dust acoustic (DA) waves like solitons, shock waves, and double-layer structures can generate and propagate in dusty plasma systems depending on the plasma composition and their particle distributions. In this paper, a refined fluid model is proposed to provide a general description of all possible DA waves that may propagate in complex dusty plasmas with thermally distributed heavy ions and non-extensive light species. The DA waves are characterized using the Further-Burger equation with three newly induced arbitrary parameters, enabling the identification of the different plasma waves. The DA wave's structures are found to be highly sensitive to the thermal parameter σ of the heavy ions and the non-extensive parameter “q” of the light species. Moreover, these two parameters act as key factors that control the polarity of the waves around their critical values, i.e., around σ = 0.11 and “q = 1.146.” The potential relevance of our results in space and astrophysics plasma setups is briefly discussed.

Role of Cairns–Gurevich ion distribution on nonlinear wave propagation in negatively charged dusty plasma

The study of dust-acoustic (DA) nonlinear electrostatic waves in dusty plasma is crucial for understanding plasma behavior in both astrophysical and laboratory environments. Dusty plasmas, characterized by the presence of negatively charged dust particles, exhibit complex dynamics influenced by various factors, including nonthermal electron and ion populations following Cairns–Gurevich distributions. This study addresses the problem of understanding wave propagation under these specific conditions by employing a set of fluid hydrodynamic equations for dust fluid, alongside appropriate electron and Cairns–Gurevich ion distributions, to model the dynamics and propagation of DA nonlinear electrostatic waves under specific plasma conditions with negatively charged dust particles. We derived a nonlinear Zakharov–Kuznetsov (ZK) equation to model the evolution of these waves and further transformed it into the nonlinear Schrödinger (NLS) equation to analyze rogue wave formation and identify unstable and stable zones within the plasma. We focused our analysis on the effects of key parameters, such as the nonthermal index, magnetic field strength, negative dust temperature ratio, polarization force, and density ratio, on the behavior of dust-acoustic waves (DAWs). The results demonstrated that soliton waves, explosive waves, and kink waves exhibit distinct behaviors depending on these parameters and the spatial context of Earth's magnetosphere. These findings provide new insights compared to previous studies into the conditions under which these waveforms emerge and evolve, especially in magnetized environments where earlier models were less effective at accurately characterizing or predicting wave behavior. By applying two different analytical methods, a direct integration approach and a generalized Kudryashov method, we expanded our understanding of nonlinear wave phenomena in dusty plasmas. Our results not only advance theoretical knowledge but also have practical implications for interpreting space plasma observations and guiding experimental design in plasma physics research. This study thus contributes to a more comprehensive understanding of plasma dynamics, with potential applications to astrophysical observation and laboratory plasma experimentation.

تخامد لانداو للأمواج السوليتونية الصوتية الغبارية في بلازما غبارية غير شاملة

تم دراسة الأمواج السوليتونية الصوتية الغبارية تحت تأثير تخامد لانداو للبلازما الغبارية الفضائية تحوي أيونات خاضعة لتوزع سرعة غير شامل. قمنا بالتحقيق في تأثير تخامد لانداو والبارمتر غير الشامل على البنى السوليتونية الصوتية الغبارية من خلال الحل العددي لمعادلة كورديفيك- دي فريس المعدلة بحد تخامد لانداو. باستخدام طريقة الاضطراب الاختزالية قمنا باستنتاج معادلة كورتيفيك – دي فريس مع إضافة حد تخامد لانداو. أظهرت هذه الدراسة أنً كثافة حبيبات الغبار تلعب دوراَ أساسياً في ظهور أو عدم ظهور الأمواج السوليتونية DA في البلازما الغبارية، والتأثير الواضح للخاصية غير الشاملة للأيونات على ظاهرة تخامد لانداو للبنى اللاخطية المتشكلة في البلازما الغبارية. تفيد نتائج هذه الدراسة في محاولة فهم الآلية الفيزيائية للانتشار الأمواج السوليتونية تحت تأثير تخامد لانداو في بيئات البلازما المغبرة غير الشاملة كالمناطق الكوكبية، والأغلفة المغناطيسية، وبيئات البلازما الفضائية.

Effect of nonthermal electron distributions on dust acoustic solitons in cometary plasmas

We investigate the effect of nonthermal electrons modeled by two non-Maxwellian distribution functions, i.e., the (r, q) and Cairn’s distributions on the formation of dust acoustic (DA) solitons in an un-magnetized dusty plasma by incorporating the effect of dust streaming. We adopt the pseudopotential technique to obtain solitary wave solutions from fluid equations. It is seen that only rarefactive soliton can be obtained in such plasmas where ions are considered Boltzmannian and electrons non-Maxwellian. We find that soliton characteristics are strongly dependent on the nonthermal spectral indices r, q, and α and dust temperature Td. For (r, q) distribution, it is found that soliton amplitude increases but width decreases when the positive (negative) value of r decreases (increases). For Cairn’s distribution, we find that with the increase in α, soliton amplitude decreases. In space environments, such as cometary tails, solar wind, and Earth’s magnetosphere, where non-Maxwellian populations of electrons are present, our theoretical results show that the amplitude of soliton remains smaller than the Maxwellian case. Thus, Maxwellian distribution overestimates the soliton amplitude in such space environments. Therefore, we feel that our results will better interpret the results of observations, from cometary tails, and other space plasmas where nonlinear DA structures are likely to be observed.

Propagation of Arbitrary Amplitude Dust Acoustic (DA) Waves in a Magnetized Plasma with Non-thermal Electrons and Ions

Propagation of Arbitrary Amplitude Dust Acoustic (DA) Waves in a Magnetized Plasma with Non-thermal Electrons and Ions

Solitary wave solution of (3+1)-dimensional cylindrical Kadomstev–Petviashvili equation in warm opposite polarity dusty plasma

A theoretical investigation is done to study the propagation of dust-acoustic (DA) solitary waves in a dusty plasma system containing dynamic positively as well as negatively charged warm dust species and nonthermally distributed ion and electron species. The standard reductive perturbation method is employed to derive the (3+1)-dimensional cylindrical Kadomstev–Petviashvili (KP) equation (also known as cylindrical Korteweg–de Vries equation), which admits solitary wave solution for small but finite amplitudes. The parametric regimes for the existence of DA solitary waves are obtained. Two modes, namely, slow and fast are observed corresponding to different phase velocities. The slow mode has negative solitary pulses, whereas the fast mode contains both positive and negative DA solitary waves. It is shown that the ratio of positively charged dust to negatively charged dust number density significantly modifies the basic features of the DA solitary waves. The noteworthy effects of other parameters (viz. the nonthermal parameter and ion-to-electron temperature ratio) on the basic properties (namely, phase speed, polarity, amplitude, and width) of the DA solitary waves are also mentioned. The fundamental features and the underlying physics of the electrostatic solitary structures that are relevant to cometary tails, upper mesosphere, Jupiter’s magnetosphere, etc., are briefly discussed.

Three-Dimensional Cylindrical Dust-Acoustic Solitary Pulses in Warm Nonthermal Plasma

The nonlinear propagation of 3-D cylindrical dust-acoustic (DA) solitary waves in an unmagnetized dusty plasma system consisting of mobile adiabatic positively charged dust (PCD) grains, nonthermal ions, and electrons is investigated. The basic properties of nonlinear DA solitary structures, which exist in such a warm dusty plasma medium, are studied. The ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3+1$</tex-math> </inline-formula> )-dimensional cylindrical Kadomstev–Petviashvili equation (cKPE) (also known as cylindrical Korteweg-de Vries (KdV) equation) is derived by using the reductive perturbation method (RPM). The possible region of the formation of solitons is shown. The effects of different plasma parameters (viz., the nonthermal parameter, the dust-to-ion temperature ratio, the ion-to-dust number density ratio, etc.) on the characteristics of the DA solitary waves are studied, and also the graphical representation of the cylindrical DA solitary structures is presented. The polarity of DA solitary waves changes with different plasma parameters (viz., the ion-to-electron temperature ratio, the nonthermality of ions and electrons, the ion-to-dust number density, etc.). These results may improve our understanding of DA solitary structures in space and laboratory plasma devices where nonthermal dusty plasma occurs.

Higher-order shock wave structures and phase plane analysis in multicomponent dusty plasma

In this investigation, dust acoustic (DA) shocks and dressed shocks formed due to the contribution of higher-order effects in a non-Maxwellian plasma have been examined. The reductive perturbation method is employed to derive the nonlinear Burgers and Burgers-type inhomogeneous equations with the contribution of higher-order effects of nonlinearity and dissipation. The properties of dust acoustic shocks and higher order (dressed shocks) are examined from the solutions of these nonlinear equations under the effect of various plasma parameters. Furthermore, the travelling wave analysis is used to obtain the dynamical system for the Burgers equation using bifurcation theory. The characteristic properties of DA periodic waves have also been analysed under the influence of various plasma parameters.

Localized Dust Acoustic Solitons in Electron-Depleted Dusty Plasmas With κ-Gurevich Distributed Ions

A first theoretical attempt is made to investigate the adiabatically trapped suprathermal ions effect on dust acoustic (DA) solitons in electron-depleted dusty plasmas. Our investigation is motivated by space and laboratory plasma observations of plasmas containing suprathermal particles, resulting from long-tailed distributions, combined with trapped particles in a finite region of phase space. For this goal, the 1-D <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula> -Gurevich distribution, which describes the adiabatic trapping of suprathermal ions, is constructed, and the associated density expression is derived. The reductive perturbation method (RPM) has been adopted to establish a modified Kortweg-de-Vries (mK-dV)-like equation, and analyze its comportment. The numerical investigation revealed that the main properties (phase velocity, amplitude, and width) of small DA solitons are significantly affected by adiabatically trapped suprathermal ions. In particular, we have found that as the suprathermality of the ions increases, the DA soliton amplitude decreases while its width increases. The significant changes induced by the presence of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula> -Gurevich distributed ions on the transported energy and electrical field of DA solitons are also analyzed. We have shown that when the ions evolve far from their Maxwellian trapping (i.e., as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula> decreases), the DA soliton energy quantity (bipolar electric field) associated with electronically depleted dusty plasma becomes smaller (stronger). The results of the present study provide new insight into established findings on this issue.

Dynamics and head-on collisions of multidimensional dust acoustic shock waves in a self-gravitating magnetized electron-depleted dusty plasma

The dynamics and collisions of dust acoustic (DA) shock excitations traveling in opposite directions are theoretically investigated in a three-dimensional self-gravitating magnetized electron-depleted dusty plasma whose ingredients are extremely warm positively and negatively charged massive dust grains as well as ions that follow the q-nonextensive distribution. A linear analysis and the extended Poincare–Lighthill–Kuo method are used to derive the dispersion relation, the two-sided Korteweg–de Vries Burgers equations, and the phase shift that occurs due to the wave interaction. It is found that gravitation introduces Jeans-like instability, reduces the wave damping rate, decays the aperiodic oscillatory structure of DA excitations, and strongly affects the amplitude, steepness, and occurrence of monotonic compressive and rarefactive shocks. Numerical simulations also highlighted the stabilizing role of the magnetic field and the singularities of the collision process of monotonic shock fronts as well as the undeniable influence of viscosity, ion nonextensivity, and obliqueness between counter-traveling waves on the phase shift and collision profiles. The present results may be useful to better understand interactions of dust acoustic shock waves in the laboratory and astrophysical scenarios, such as dust clouds in the galactic disk, photo-association regions separating H II regions from dense molecular clouds, Saturn's planetary ring, and Halley Comet.

The attributes of the dust-acoustic solitary and periodic structures in the Saturn's inner magnetosphere

Nonlinear characteristics of dust-acoustic (DA) structures including the localized and periodic waves in a plasma having Maxwellian ions and superthermal two-temperature electrons are investigated. The wave equations, including both Kadomtsev–Petviashvili (KP) and modified KP (mKP) equations, are derived using the reductive perturbation technique (RPT). The quantitative and qualitative characteristics of both compressive and rarefactive structures are studied. The Jacobi elliptic function expansion method (JEFEM) is employed for the purpose of quantitative analysis, while the qualitative behavior is studied by the dint of the dynamical system approach. The solutions to the mKP equation hold under a critical condition where the quadratic nonlinearity ceases to exist. It is noticed that the KP equation admits only rarefactive solitary waves (SWs), whereas the mKP equation admits both compressive and rarefactive SWs. It is found that the profile (amplitude and width) of both DA solitary and periodic structures are different at different radii of Saturn's inner magnetosphere. The effect of the kappa spectral index is studied, and it is found that when the population of energetic cold electrons is decreased, the solitary structure gets energized. Our study is applied to Saturn's inner magnetosphere where kappa distributed two-temperature electrons and dust grains with negative charge are observed by various satellite missions.

Effect of Tsallis–Gurevich distributed ions on nonlinear dust‐acoustic oscillations in collisionless nonextensive plasma

AbstractBoth linear and weakly nonlinear dust‐acoustic (DA) solitons propagation are revisited in the presence of adiabatically trapped‐nonextensive ions. A physically relevant distribution (called Tsallis‐Gurevich ions distribution) is outlined here for the first time. The effect of particle trapping has been taken into account, resulting in a new expression for the ion density. The role a background ion nonextensivity may play on the main proprieties (viz., dispersion relation and soliton's profile) of DA mode, inherent to space dusty plasma, is then analysed. In the q &gt; 1 case, we have shown that as the nonextensive character of trapped ions increases in the plasma, the potential pulse amplitude increases while its width is narrowed. The modifications prompted by the presence of adiabatically trapped‐nonextensive ions on both DA energy and solitary wave's electric field are also analysed. Interestingly, we have found that DA soliton energy increases as the ions evolve far away from their Maxwellian extensive trapping. Also, it is found that, for q &gt; 1, the stronger the inter‐ions correlation, the stronger the electric field. Our investigation, motivated by space and laboratory plasma observations of plasmas containing non‐Maxwellian particles alongside trapped particles, may complement and provide new insight into previously published works dealing with solitary waves in plasma.

The Compressive and Rarefactive Dust Acoustic Solitary Waves with Two Different Temperatures for Both Electrons and Ions

The Compressive and Rarefactive Dust Acoustic Solitary Waves with Two Different Temperatures for Both Electrons and Ions

Effect of Gurevich Polarization Force on Arbitrary Amplitude Dust-Acoustic Waves and Double-Layer Structures in a Collisionless Complex Plasma

In this article, we have investigated the effect of the Gurevich polarization force on both large-amplitude dust-acoustic (DA) solitary waves and double-layer (DL) structures in a collisionless complex plasma. To do this, we have redefined the 3-D Gurevich distribution, which describes the evolution of the adiabatically trapped ions in the plasma potential well and derived the associated density and polarization force expressions. As an application, we have reviewed, using the pseudo-potential approach, the nonlinear DA solitons in an unmagnetized polarized complex plasma containing inertial dust grains, Maxwellian electrons, and adiabatically trapped ions. We have shown that the spatial profile of DA solitary waves is drastically affected by the Gurevich polarization force. In particular, we have found that due to the presence of this polarization force, the potential pulse amplitude increases while its width decreases, thus making the DA structure more spiky. For the sake of completeness, we have also analyzed the effect of the polarization force on DA-DL structures. Our numerical results have shown that both amplitude and width of rarefactive (compressive) DL DA structure decrease (increase) in the presence of polarization force.

Propagation and energy of the dressed solitons in the Thomas–Fermi magnetoplasma

A theoretical investigation is presented for dust-acoustic (DA) waves in a collisionless Thomas–Fermi magnetoplasma. The plasma system consists of electrons, ions, and negatively charged dust grains, all existing in a quantizing magnetic field. The Korteweg–de Vries (KdV) and KdV type equations are derived by using the reductive perturbation method. The solutions of these evolved equations are obtained. The contribution of higher-order corrections to the DA is investigated. The electric field and the soliton energy were also derived. The K-dV and dressed soliton energies are depleted as the dust temperature and magnetic field increase. But they magnify as obliqueness increases. The present results are beneficial in understanding the waves propagating in Thomas–Fermi magnetoplasma that are applicable for high-intensity laser–solid matter interaction experiments and astrophysical compact objects such as white dwarfs.

Study of cylindrical and spherical dust acoustic solitons and quasiperiodic structures in a quantum dusty plasma

The solitonic and quasiperiodic structures of dust acoustic (DA) waves are investigated in a three components quantum dusty plasma composed of mobile negative dust grains, ions, and inertialess electrons. The reductive perturbation method is employed to derive A deformed Korteweg–de Vries (dKdV) equation in planar and nonplanar geometries, and its numerical solutions are obtained using the two level finite difference approximation method. The influence of geometries on DA solitons is discussed. It is observed that in nonplanar geometries, DA solitons travel at different speeds in comparison to one-dimensional planar ones. Furthermore, in the planar geometry, the bifurcation of DA traveling waves has been analyzed on the framework of the dKdV equation. By adding an external periodic force to the derived dKdV equation, the quasiperiodic behaviors of DA waves are presented.

Nonlinear propagation of dust-acoustic modes in a dusty plasma with the Kappa-Cairns polarization force effects

In this paper, the influence of Kappa-Cairns polarization force on solitary and periodic dust-acoustic (DA) waves is studied in a non-uniform dusty plasma containing negatively charged dust grains, Maxwellian electrons, and the Kappa-Cairns distributed ions. It is observed that in the presence of Kappa-Cairns distributed ions, the magnitude of the polarization force first increases as the spectral index increases and then decreases. The nonlinear Korteweg-de-Vries (K-dV) equation is obtained employing the reductive perturbation technique. The effects of polarization parameter (), Kappa-Cairns distribution parameters ( and ), and different ratios of ion to electron number densities () are investigated on the characteristics of DA solitary waves. We observed that the variations in the phase speed, amplitude, and width of DA solitons in the presence of the Kappa-Cairns polarization force are considerably different for case with respect to . The bifurcation theory of planar dynamical systems is also applied to investigate the existence of the solitary/periodic traveling wave in this plasma model. The phase portrait topology is illustrated for the K-dV equation. It is found that polarization force and other plasma parameters have a vital role in the traveling wave structures.

Formation of electrostatic solitary and periodic waves in dusty plasmas in the light of Voyager 1 and 2 spacecraft and Freja satellite observations

Motivated by the observations of Voyager 1 and 2 spacecraft and Freja satellite observations in Saturn’s magnetosphere, the formation of dust-acoustic (DA) localized and periodic waves in a complex plasma having superthermal electrons and ions are reported. In this regard, a modified Kadomtsev–Petviashvili (mKP) equation is derived by employing the weak turbulence theory for studying the characteristics of the nonlinear dust-acoustic waves (DAWs) in the model under consideration. The localized and periodic wave solutions to the mKP equation are derived using ansatz method in terms of Jacobi elliptic functions (JEFs). It is reported that the phase velocity of the DAWs in the Saturn’s magnetosphere is lower for kappa distributed ions and electrons by comparison with regions of space plasmas where the electrons and ions follow the Maxwellian distribution. The conditions for the existence of both localized and periodic waves are also presented. Estimates are also given of the spatial scales over which the dust-acoustic solitary/periodic structures form in Saturn’s magnetosphere.

Dust-acoustic solitary and periodic waves in magnetized self-gravito-electrostatic opposite polarity dusty plasmas

Dust-acoustic (DA) solitary and periodic waves investigations were performed in a magnetized self-gravitating dusty plasma consisting of negatively and positively charged dust grains in the presence of inertialess ions and electrons. The Korteweg–de Vries–Burger (KdVB) equation has been derived. The numerical investigations revealed the compressive or rarefactive DA solitons depending on the plasma parameters. The nonlinear homoclinic and periodic trajectories from the KdVB equation were obtained for the phase portrait profiles when employing the phase plane theory of dynamical systems. The periodic wave solution depends also on the system parameters. The present results are considered to be beneficial in understanding the nonlinear structures in experimental devices and different astrophysical environments such as the Earth’s mesosphere, cometary tails, and Jupiter’s magnetosphere.

Effects of trapped ions concentration on the dynamics of dust‐acoustic periodic travelling waves in dusty plasmas

AbstractThis study is essentially an attempt to investigate the effects of trapped ions concentration on the dynamics of dust‐acoustic (DA) periodic travelling waves in dusty plasmas, which consist of dust fluid, trapped ions, and Maxwellian electrons. The physical nature of DA solitary and periodic travelling waves in the plasma model at hand is governed by a Korteweg‐de Vries (KdV) type equation. Bifurcation analysis of the Hamiltonian system is applied to demonstrate the probability of the presence of DA solitary and periodic travelling waves for the KdV type equation. A careful discussion illustrates that non‐linear phenomena of DA solitary and periodic travelling waves are modified due to the presence of the trapped ions concentration. It is found numerically that the negative amplitude of DA periodic travelling waves is amplified, as the trapping parameter that determines the number of the trapped ions is increased. The numerical simulation gives rise to significant highlights on the dynamics of solitary and periodic travelling waves in astrophysical environments such as Saturn's moon Enceladus.