Ion Kinematic Viscosity Research Articles

Exploring Nonlinear Fractional (2+1)-Dimensional KP–Burgers Model: Derivation and Ion Acoustic Solitary Wave Solution

The purpose of this study is to conduct a complete examination into the fractional (2+1)-dimensional nonlinear KP-Burgers (KP-B) model in the setting of quantum plasma. The main goal is to present a mathematical explanation and derivation for the fractional (2+1)-dimensional nonlinear KP-B model. We used the reductive perturbation technique to obtain the fractional (2+1)-dimensional ion acoustic solitary wave, which leads to the nonlinear KP-B model. To solve the fractional space-time KP-B model, we used the modified sub-equation technique and the extended hyperbolic function methodology. This methodology covers rational, periodic wave, and hyperbolic function solutions. Ion acoustic waves were explored in relation to the effects of ion pressure and an external electric field. The effects of density and fractional order on the properties of a single solution are examined. The plasma system is defined as an unmagnetized epi plasma system composed of relativistic ions, positrons, and nonextensive electrons that can be found in a range of astrophysical and cosmological environments. The solution variables include electron-positron and ion-electron temperature ratios, electron and positron nonextensivity strength, ion kinematic viscosity, positron concentration, and the weakly relativistic streaming factor. The fractional order and associated plasma properties have a considerable influence on the phase velocity of ion acoustic waves. When the fractional order equals one, the obtained results are consistent with known outcomes. This work makes a substantial contribution to our understanding of nonlinear events in quantum plasmas, particularly ion acoustic waves. It provides a solid approach for solution development and analysis, with implications for a variety of astrophysical and cosmological scenarios.

On the oscillations in a nonextensive complex plasma by improved differential transformation method: An application to a damped Duffing equation

In this study, the nonlinear damping oscillations in a complex non-Maxwellian plasma are investigated. For this purpose, the set of fluid equations of the present plasma model is reduced to the Burger-modified Korteweg De Vries equation (BmKdV) equation using a reductive perturbation technique. Using the traveling wave transformation, the BmKdV equation can be reduced to a damped Duffing equation. The numerical solutions to the damped Duffing equation are obtained using multistage differential transformation method (MsDTM). Also, we compared the obtained results to the semi-analytical approximations using the Padé differential transformation (PDTM) method and numerical solution, by the 4th-order Rung Kutta (RK4) method and analytical solution by He’s frequency method. The impact of relevant plasma parameters, namely, negative dust concentrations and ion kinematic viscosity on the profile of dust ion-acoustic oscillations are examined. The suggested mathematical approaches can help many authors for explaining the mystery of their laboratory results. Moreover, the suggested numerical method can be applied for solving higher order nonlinearity oscillations for a long domain.

Evolution of ion-acoustic shock waves in magnetized plasma with hybrid Cairns–Tsallis distributed electrons

Abstract The propagation of nonlinear electrostatic ion-acoustic (IA) shock waves in presence of external magnetic field having Cairns–Tsallis distributed electrons and ion kinematic viscosity is investigated. In the linear regime, the dispersion relation of the ion acoustic shock wave is found to be modified by the external magnetic field. Adopting reductive perturbation approach, it is shown that the dynamics of shocks is modeled by a hybrid Ostrovsky–Burgers’ equation. The influence of relevant physical parameters such as nonthermality and nonextensivity of electrons, magnetic field strength, and ion kinematic viscosity on the time evolution of the shock structure is numerically examined. It is observed the present plasma system supports both compressive and rarefactive shock waves. Furthermore, the analysis is performed through dynamical system approach to elucidate the various aspects of the phase-space shock dynamics.

Nonlinear behaviour of ion acoustic shock waves in a two-electron temperature nonthermal complex plasma

Abstract The nonlinear propagation of dust-ion-acoustic shock waves (DIASWs) in unmagnetized dusty plasma comprising inertial ions, non-Maxwellian electrons with two distinct temperatures, and negatively charged dust is investigated in this article using a different approach based on the Sagdeev pseudopotential theory. The reductive perturbation approach is used to produce the KdVB and mKdVB equations and a comparison of their analytical and numerical solutions is shown. The effects of various parameters consisting of macroscopic non-thermal, ion-kinematic viscosity, etc. that significantly alternate the qualitative properties of DIASW are discussed. Both oscillatory and monotonic natures of the dispersive-diffusive shock wave structures are described in the present study. It has also been concentrated on nonlinear dynamics in such a plasma environment. The findings of this study should aid in understanding the nonlinear dynamics of wave damping and interactions in space and laboratory dusty plasmas, where the most relevant plasma parameters are kinematic viscosity and macroscopic non-thermality.

Electrostatic Shock Structures in a Magnetized Plasma Having Non-Thermal Particles

A rigorous theoretical investigation has been made on the nonlinear propagation of dust-ion-acoustic shock waves in a multi-component magnetized pair-ion plasma (PIP) having inertial warm positive and negative ions, inertialess non-thermal electrons and positrons, and static negatively charged massive dust grains. The Burgers’ equation is derived by employing the reductive perturbation method. The plasma model supports both positive and negative shock structures in the presence of static negatively charged massive dust grains. It is found that the steepness of both positive and negative shock profiles declines with the increase of ion kinematic viscosity without affecting the height, and the increment of negative (positive) ion mass in the PIP system declines (enhances) the amplitude of the shock profile. It is also observed that the increase in oblique angle raises the height of the positive shock profile, and the height of the positive shock wave increases with the number density of positron. The applications of the findings from the present investigation are briefly discussed.

Electrostatic Ion-Acoustic Shock Waves in a Magnetized Degenerate Quantum Plasma

A theoretical investigation has been carried out to examine the ion-acoustic shock waves (IASHWs) in a magnetized degenerate quantum plasma system containing inertialess ultra-relativistically degenerate electrons, and inertial non-relativistic positively charged heavy and light ions. The Burgers equation is derived by employing the reductive perturbation method. It can be seen that under the consideration of non-relativistic positively charged heavy and light ions, the plasma model only supports the positive electrostatic shock structure. It is also observed that the charge state and number density of the non-relativistic heavy and light ions enhance the amplitude of IASHWs, and the steepness of the shock profile is decreased with ion kinematic viscosity. The findings of our present investigation will be helpful in understanding the nonlinear propagation of IASHWs in white dwarfs and neutron stars.

Obliquely propagating ion‐acoustic shock waves in a degenerate quantum plasma

AbstractA theoretical investigation has been carried out on the propagation of non‐linear ion‐acoustic shock waves (IASHWs) in a magnetized degenerate quantum plasma system composed of inertial non‐relativistic positively charged light and heavy ions, inertialess non‐relativistically or ultra‐relativistically degenerate electrons and positrons. The reductive perturbation method has been employed to derive the Burgers' equation. It has been observed that under consideration, our plasma model supports only positive potential shock structure. It is also found that the amplitude and steepness of the IASHWs have been significantly modified by the variation of ion kinematic viscosity, oblique angle, number density, and charge state of the plasma species. The results of our present investigation will be helpful for understanding the propagation of IASHWs in white dwarfs and neutron stars.

Ion-acoustic shock waves in magnetized pair-ion plasma

A theoretical investigation associated with obliquely propagating ion-acoustic shock waves (IASHWs) in a three-component magnetized plasma having inertialess non-extensive electrons, inertial warm positive and negative ions has been performed. A Burgers equation is derived by employing the reductive perturbation method. Our plasma model supports both positive and negative shock structures under the consideration of non-extensive electrons. It is found that the positive and negative shock wave potentials increase with the oblique angle ($\delta$) which arises due to the external magnetic field. It is also observed that the magnitude of the amplitude of positive and negative shock waves is not effected by the variation of the ion kinematic viscosity but the steepness of the positive and negative shock waves decreases with ion kinematic viscosity. The implications of our findings in space and laboratory plasmas are briefly discussed.

Shock waves in magnetized plasmas with superthermal trapped electrons.

Formation of ion-acoustic shock waves (IAShWs) and their propagation nature in a magnetized plasma in the presence of superthermal trapped electrons are investigated for the first time via the fluid dynamical approach. A magnetized plasma system, comprising of inertial ions and non-inertial electrons following κ-superthermal trapped distribution, is considered to examine the basic features (amplitude, width, phase speed, etc.) of IAShWs in such a plasma. A diffusion effect (due to the ion kinematic viscosity) is taken into account. The reductive perturbation technique is adopted to derive the modified Korteweg de-Vries Burgers’ (mKdVB) equation and the solution of mKdVB equation (derived by adopting the tangent hyperbolic method) is used to investigate the dynamical and structural characteristics (speed, amplitude, width, etc.) of IAShWs. The influence of relevant plasma (configuration) parameters (e.g., the superthermality index κ, concentration of trapped electrons, external magnetic field, and obliquity angle, etc.) on the nature of IAShWs is examined. The applications of the results in space and laboratory plasma environments, where nonthermal trapped electrons are available, are briefly discussed.

Parametric study of cylindrical and spherical dust ion acoustic shock waves with two temperature electrons in dusty plasma relevant to Saturn's E ring

AbstractWe have performed numerical analysis of the one‐dimensional dynamics of the cylindrical/spherical dust ion acoustic shock waves in unmagnetized dusty plasma consisting of positive ions, immobile dust particles, and nonextensive distributed cold and hot electrons. A multiple‐scale expansion method is used to derive Burgers Equation (BE) and modified Burgers equation (MBE) by including higher order nonlinearity. The basic characteristics of the shock waves have been analysed numerically and graphically for different physical parameters relevant to Saturn' E ring through 2D figures. The parametric dependence of dust ion acoustic shock waves on some plasma parameters nonextensive index, density, and temperature of cold and hot electrons, concentration of dust particles, thermal effects and kinematic viscosity of ions is explored. Furthermore, it is found that the nonplanar geometry effects have an important impact on the establishment of shock waves. The amplitude of the wave decreases faster as one departs away from the axis of the cylinder or centre of the sphere. Such decaying behaviour continues as time progresses. It is also found that an increasing dust concentration decreases the amplitude of the dust ion acoustic shock waves.

Nonlinear dust ion acoustic shock wave structures in solar F corona region

Shock wave formation in dusty plasma consisting of mobile positive and negative ions, nonthermal electrons, and negatively charged static dust particles is theoretically studied in the presence of a magnetic field. Using the reductive perturbation technique, the basic set of fluid equations is reduced to the three-dimensional Zakarov–Kuznetsov Burgers nonlinear wave equation. The dissipation generated by ion kinematic viscosity in the system is taken into consideration. Distinct features of the dispersive (oscillatory) shock-like structures are discussed for different plasma parameters such as ion kinematic viscosities, ion density ratio, dust density ratio, nonthermal electrons, and magnetic field effect. It is observed that at large value of ion viscosities, nonthermal electrons, and ion density ratio, the formation of compressive shock strength increases. However, at certain critical values of nonthermal electrons, ion density ratio, the transition in the polarity of shock wave occurs within this range of plasma parameters. The considered parameters are reliable in the Solar F Corona (Dust corona) region. The findings of this work may be helpful in understanding shock formation in the Solar F Corona (Dust corona) region and astrophysical related plasma environments.

Cylindrical and spherical ion acoustic shock waves with two temperature superthermal electrons in dusty plasma

In the present study, the cylindrical/spherical ion acoustic shock waves have been investigated in unmagnetized dusty plasma consisting of positive ions, immobile dust particles and kappa distributed cold and hot electrons. A multiple scale expansion method is employed to derive Burgers equation (BE) and modified Burgers equation (MBE) by including higher order nonlinearity. The basic characeristics of the shock waves have been analyzed numerically and graphically for different physical parameters relevant to space and laboratory dusty plasma environments through 2D figures. We show that the amplitude of the wave decreases faster as one departs away from the axis of the cylinder or centre of the sphere. Such decaying behaviour continues as time progresses. Furthermore, the parametric dependence of wave properties (amplitude, width) on kappa index, density and temperature of cold and hot electrons, concentration of dust particles, thermal effects and kinematic viscosity of ions has been studied in detail and findings obtained here will be beneficial to further astrophysical investigations.

Nonlinear ion acoustic waves in dissipative and dispersive magneto‐rotating relativistic plasmas with two temperature superthermal electrons

AbstractA study has been presented for the nonlinear features of ion‐acoustic (IA) shock waves in a magnetorotating plasma consisting of warm viscous streaming ions along with kappa‐distributed electrons having two different temperatures. In this regard, we have employed the reductive perturbation technique to derive the Zakharov‐Kuznetsov‐Burgers (ZKB) equation that governs the dynamics of IA shock waves. The solution obtained by the hyperbolic tangent method has been shown to depend on various plasma parameters such as spectral index (κc), density fraction (f), effective rotation frequency (Ωc), ion kinematic viscosity (ηo), and temperature ratio (σ). In the limiting case when dissipative coefficient D → 0, we have also examined the solitary potential distributions, which are the solutions of Zakharov Kuznetsov (ZK) equation. It is found that both rarefactive and compressive structures exist for the system under consideration. The transition in the nature of such profiles is due to the enhancement in the density of cold electrons. The importance of present theoretical investigations has been carried out with regard to Saturn's magnetosphere, where two temperature superthermal electron populations have been observed by various satellite missions.

Head-on collision of nonlinear electrostatic shock waves in a relativistically degenerate plasma

We present here theoretical investigation of colliding electrostatic shocks in an electron–ion plasma with relativistically degenerate electrons. A set of Korteweg–de Vries Burgers equations has been derived by employing a modified Poincaré–Lighthill–Kuo method for dissipative nonlinear ion acoustic structures. It has been found that relativistically degenerate plasma allows the formation of only compressional shocks. Moreover, the shocks are found to be sub-acoustic for the non-relativistic regime and super-acoustic for ultra-relativistic regime for a certain range of values of the ion kinematic viscosity. We have estimated the spatio–temporal scales, using the parameters generally found in white dwarf stars, for which the shock waves are theoretically anticipated to collide with each other in the relativistically degenerate plasma. The electric field across the shock has also been plotted numerically. The phase shifts of the shock waves resulting from the head-on collision have been estimated. The results may be helpful to understand the collision and dynamics of shock waves in astrophysical objects, such as hydrogen-rich white dwarf stars, and laboratory experiments, such as inertial confinement fusion.

On the Characteristics of Solitary Waves and Shocks in Nonextensive Plasmas: Collisionality and Kinematic Viscosity Effects

In this article, a comprehensive investigation of the linear and nonlinear waves’ structure in an unmagnetized plasma consisting of nonextensive electrons, considering collisionality and kinematic viscosity effects, is studied. Using a reductive perturbation technique, we have derived a hybrid Korteweg–de Vries–Burgers equation for ion-acoustic (IA) waves. Analytical solutions for solitary waves and shock structures are obtained. We have also solved this equation numerically in order to investigate the basic properties of solitary/shock waves in such a plasma system. The presence of nonextensive electrons with $q$ -distribution influences significantly the solitary and shock wave structures. In other words, the compressive and rarefactive-type solitons or shock waves can also be seen in this plasma model depending on the strength of nonextensivity. On the other hand, the effects of ion-neutral collision and ion kinematic viscosity on the characteristics of IA solitary/shock waves are discussed. It is found that these parameters modify the basic features of the solitonic and shock excitations.

Excitation and Formation Conditions of Monotonic Shock Waves in Magnetized Plasmas with Superthermality Distributed Electrons

Nonlinear excitation and the properties of ion-acoustic shock waves (IASWs) in a magnetoplasma model composed of viscous ions with two-temperature superthermality distributed electrons are studied by employing the well-known reductive perturbation analysis to obtain a nonlinear Zakharov-Kuznetsov-Burgers equation (ZKBE), which admits the excitation of nonlinear IASWs in superthermal plasmas. Applying the tanh method, we discuss the solutions of the ZKBE. The asymptotic behavior and the stability of the analytical shock wave solution are studied. In general, nonlinear ion-acoustic disturbances are found analytically to exhibit only monotonic shock structures in the proposed model. For different situations, the effects of the dispersion and the dissipation coefficients on the profiles of the shock structures are discussed. The findings here demonstrate that the effective features of nonlinear IASWs depend strongly on the dispersion and the dissipation coefficients, which include physical parameters such as the superthermality of cold electrons, the cold superthermal electron-to-ion number density ratio, the ion kinematic viscosity and the ion cyclotron frequency. The current work may be helpful for an advanced comprehension of the physical nature of shock waves in astrophysical plasma situations.

The effect of magnetic field quantization on the propagation of shock waves in quantum plasmas

Nonlinear ion acoustic shock structures are investigated in the presence of trapping effects and Landau quantization in quantum plasmas. Ion electron plasma is under consideration in which ions are classical and quantum mechanical effects of electrons are taken into account. We assume that the orbital motion of electrons is quantized such that the condition kBT≪ℏωce is satisfied. To study the energy transfer mechanism in such conditions, the reductive perturbation technique has been employed to derive the nonlinear differential equation. In the presence of dissipation, which appears through kinematic viscosity of ions, the Korteweg-de Vries Burgers (KdVB) equation is obtained. The different solutions of KdVB are presented, and excitation from KdV oscillations to shock solution is explained in the presence of orbital motion of electrons which are discussed. The devastating effect of Landau quantization on the height (strength) of the nonlinear shock structure is pointed out.

Radially ingoing and outgoing dispersive and dissipative structures in electron‐ion plasmas in the presence of electron trapping

In this article, non‐linear propagation of ingoing and outgoing electrostatic waves on the ion time scale in an unmagnetized, non‐relativistic electron‐ion (ei) plasma in the presence of warm ions, ion kinematic viscosity, and trapped Maxwellian electrons was examined in a non‐planar geometry. In the weak non‐linearity limit, modified soliton and shock equations were derived with the inclusion of electron trapping in cylindrical and spherical geometries. The finite difference method was used to solve all these equations in the non‐planar geometries using the planar versions of these equations as an initial input. The results were compared with their counterparts with quadratic non‐linearity and the main differences were expounded. It was shown that the spatio‐temporal scales over which the shocks form for the non‐planar trapped Burgers equation are much shorter by comparison with the shocks admitted by the non‐planar trapped Korteweg de Vries Burgers equation. It was also found that unlike their non‐linear shock counterparts, the solitary structures admitted by the non‐planar trapped Korteweg de Vries equation exhibit a phase shift.

Dust Ion-Acoustic Shock Waves in a Multicomponent Magnetorotating Plasma

Abstract The nonlinear properties of dust ion-acoustic (DIA) shock waves in a magnetorotating plasma consisting of inertial ions, nonextensive electrons and positrons, and immobile negatively charged dust are examined. The effects of dust charge fluctuations are not included in the present investigation, but the ion kinematic viscosity (collisions) is a source of dissipation, leading to the formation of stable shock structures. The Zakharov–Kuznetsov–Burgers (ZKB) equation is derived using the reductive perturbation technique, and from its solution the effects of different physical parameters, i.e. nonextensivity of electrons and positrons, kinematic viscosity, rotational frequency, and positron and dust concentrations, on the characteristics of shock waves are examined. It is observed that physical parameters play a very crucial role in the formation of DIA shocks. This study could be useful in understanding the electrostatic excitations in dusty plasmas in space (e.g. interstellar medium).

Nonlinear quantum ion acoustic shock wave dynamics with exchange-correlation effects

The dynamics of linear and nonlinear electrostatic shock excitations is studied in homogeneous, unmagnetized, unbounded and dissipative quantum plasma consisting of electrons and ions. The dissipation in the system is taken into account by incorporating the ion kinematic viscosity. The system is modelled using the quantum hydrodynamic equations in which the electrons are significantly affected by the quantum forces, viz., the quantum statistical pressure, the quantum Bohm potential and electron exchange-correlations due to electron spin. In the weakly nonlinear limit, using reductive perturbation method deformed Korteweg-de Vries Burgers’s (KdVB) equation, which elegantly combines the effects of nonlinearity, dispersion and dissipation is derived. It is found that the present model predicts the existence of both nonlinear oscillatory and monotonic shock structures. The temporal evolution, stability and phase-space dynamics of nonlinear ion acoustic shocks are investigated numerically to elucidate the effects of quantum diffraction, electron exchange correlation and ion kinematic viscosity.