Nonlinear Wave Structures Research Articles

Damped electrostatic structures in quantum plasmas

In this work, we study the damped nonlinear solitary wave structures in electron ion dense collisional plasmas in the presence of exchange correlation potential. Due to high density and low temperature, these plasmas are considered as quantum plasmas. The quantum mechanical effects due to quantum statistical pressure, quantum tunnelling, and exchange correlation due to 1/2 spin of Fermions are included in a quantum hydrodynamic model. The collisions of plasmas particles with neutrals are taken into account to derive the Damped Korteweg-de Vries equation. A reductive perturbation technique is performed to study nonlinearities and dispersive effects in the plasma system. The comparative importance of the potential due to the degenerate pressure, exchange correlation potential, and the Bohm potential in the linear and nonlinear dispersion is presented. The effects of variations of different plasma parameters on propagation characteristics of damped oscillations in the context of astrophysical objects like neutron stars/pulsar are discussed.

Higher-Order Corrections to Earthʼs Ionosphere Shocks**Supported by the Deanship of Scientific Research at Prince Sattam Bin Abdulaziz University under the Research Project No. 2015/01/4787

Nonlinear shock wave structures in unmagnetized collisionless viscous plasmas composed fluid of positive (negative) ions and nonthermally electron distribution are examined. For ion shock formation, a reductive perturbation technique applied to derive Burgers equation for lowest-order potential. As the shock amplitude decreasing or enlarging, its steepness and velocity deviate from Burger equation. Burgers type equation with higher order dissipation must be obtained to avoid this deviation. Solution for the compined two equations has been derived using renormalization analysis. Effects of higher-order, positive- negative mass ratio Q, electron nonthermal parameter δ and kinematic viscosities coefficient of positive (negative) ions and on the electrostatic shocks in Earth’s ionosphere are also argued.

Magnetoacoustic nonlinear periodic (cnoidal) waves in plasmas

Magnetoacoustic nonlinear periodic (cnoidal) waves and solitons are studied in magnetized electron-ion plasmas with inertial cold ions and warm electrons. Using the two fluid model, the dispersion relation of the magnetoacoustic waves is obtained in the linear limit and the wave dispersive effects appear through the electron inertial length. The well known reductive perturbation method is employed to derive the Korteweg-de Vries equation for magnetoacoustic waves in plasmas. The Sagdeev potential approach is used, and the cnoidal wave solution of magnetoacoustic waves is obtained under periodic boundary conditions. The analytical solution for magnetoacoustic solitons is also presented. The phase plane portraits are also plotted for magnetoacoustic solitons shown as a separatrix, and the cnoidal wave structure always lies within the separatrix. It is found that plasma beta, which depends on the plasma density, electron temperature, and magnetic field intensity, has a significant effect on the amplitude and phase of the cnoidal waves, while it also affects the width and amplitude of the magnetoacoustic soliton in plasmas. The numerical results are plotted within the plasma parameters for laboratory and space plasmas for illustration. It is found that only compressive magnetoacoustic nonlinear periodic wave and soliton structures are formed in magnetized plasmas.

Coupled drift and ion-acoustic cnoidal waves in an inhomogeneous plasma with field-aligned shear flow

The coupled drift and ion-acoustic cnoidal wave structures in an inhomogeneous plasma with shear flow along the magnetic field lines are investigated. The linear analysis and instability condition of the electrostatic drift and ion acoustic waves with the shear flow is also presented. The Sagdeev potential approach is employed for studying nonlinear periodic wave structures. The analytical solutions of cnoidal wave and soliton structures for coupled drift and ion-acoustic waves in the presence of field-aligned shear flow are obtained. It is found that the shear flow along the magnetic field has a significant effect on the formation of cnoidal waves and solitons in inhomogeneous plasmas. The numerical results in phase plane portraits of cnoidal and soliton structures of coupled drift and ion-acoustic waves are agreed with the satellite observations of F-region ionosphere containing shear field-aligned flows.

Nonlinear propagation of electrostatic travelling waves in degenerate dense magnetoplasmas

The electrostatic travelling wave structures have been investigated in degenerate dense magnetoplasmas consisting of relativistic degenerate inertialess electrons and positrons, as well as nondegenerate inertial cold ions. The well known reductive perturbation method has been applied in obtaining the nonlinear Zakharov-Kuznetsov equation. The formation of the electrostatic solitary waves and periodic travelling waves is carried out by the bifurcation theory of planar dynamical systems. The results demonstrate that the nonlinear electrostatic travelling waves strongly depend on the concentration of positrons, the ion cyclotron frequency, and the direction cosines of the wave vector. The obtained results here may be useful for better understanding of the structure of nonlinear electrostatic travelling wave in dense plasmas, such as the interior of massive white dwarfs.

Electrostatic baryonic solitary waves in ambiplasma with nonextensive leptons

The nonlinear wave structures of baryon acoustic waves in ambiplasma consisting of baryons (positive and negative ions), and nonextensive leptons (electrons and positrons) are theoretically investigated by employing a pseudo-potential approach, which is valid for arbitrary amplitude structures. The propagation of small but finite amplitude solitary structures is also examined by using the reductive perturbation method. The presence of nonextensive q-distributed electrons and positrons has shown to influence the soliton structure quite significantly. From the analysis of our results it is shown that the present plasma model supports the coexistence of both the compressive and rarefactive solitons. Our present analysis should be useful for understanding the collective interactions in astronomical, space and laboratory plasmas such as capsule implosion, shock tube, star formation and supernova explosion.

Deterministic drift instability and stochastic thermal perturbations of magnetic dissipative droplet solitons

The magnetic dissipative droplet is a strongly nonlinear wave structure that can be stabilized in a thin film ferromagnet exhibiting perpendicular magnetic anisotropy by use of spin transfer torque. These structures have been observed experimentally at room temperature, showcasing their robustness against noise. Here, we quantify the effects of thermal noise by deriving the stochastic equations of motion for a droplet based on soliton perturbation theory. First, it is found that deterministic droplets are linearly unstable at large bias currents, subject to a drift instability. When the droplet is linearly stable, our framework allows us to analytically compute the droplet's generation linewidth and center variance. Additionally, we study the influence of non-local and Oersted fields with micromagnetic simulations, providing insight into their effect on the generation linewidth. These results motivate detailed experiments on the current and temperature-dependent linewidth as well as drift instability statistics of droplets, which are important figures-of-merit in the prospect of droplet-based applications.

Higher-order corrections to broadband electrostatic shock noise in auroral zone

Nonlinear shock wave structures in collisionless unmagnetized viscous plasma comprised of fluid of cold electron and nonisothermal hot electrons obeying superthermal electron distribution and ions in stationary state are examined. For nonlinear electron acoustic shock waves, a reductive perturbation method was applied to deduce the Burger equation in terms of first order potential. When the shock wave amplitude was enlarged, the steepness and the velocity of the wave sidetrack from Burger equation. We have to resume our calculations to obtain the Burger-type equation with higher order dissipation. The collective solution for the resulting equations has been given by the renormalization method. The effects of spectral index κ, the ratio of the initial equilibrium density of cold electron to hot electrons β, and the kinematic viscosity coefficient η on the broadband electrostatic shock noise in aurora are also argued.

Zakharov–Kuznestov–Burger Equation for Ion-Acoustic Waves in Cylindrical Geometry

The nonlinear wave structures of ion acoustic waves in magnetized plasma comprising ions, non-extensive distributed electrons and kinematic viscosity are investigated through dynamical study. In a bounded cylindrical geometry Zakharov–Kuznestov–Burger (ZKB) equation is derived, for the first time, using reductive perturbation technic. System of coupled nonlinear ordinary differential equations is derived from ZKB equation and is solved numerically using fourth order Runge–kutta method. Equilibrium points are obtained and the features are studied dynamically in the neighbourhood of these points. With the variation of the non-extensive parameter and the kinematic viscosity parameter some important features in the nonlinear waves like oscillatory shocks to steady state propagation and vis-a-vis steady state propagation to oscillatory shocks emerge. When the values of the non-extensive parameter decrease, the phase portrait of the system shows that the change from stable spiral to stable closed and stable to unstable equilibrium happens . When the effect of dissipative term i.e. kinematic viscosity is considered some other significant features also evolve .The reduction of the value of kinematic viscosity results the change in nature of the waves from oscillatory shocks to periodic one.

Ion-acoustic cnoidal waves in a quantum plasma

Nonlinear ion-acoustic cnoidal wave structures are studied in an unmagnetized quantum plasma. Using the reductive perturbation method, a Korteweg-de Vries equation is derived for appropriate boundary conditions and nonlinear periodic wave solutions are obtained. The corresponding analytical solution and numerical plots of the ion-acoustic cnoidal waves and solitons in the phase plane are presented using the Sagdeev pseudo-potential approach. The variations in the nonlinear potential of the ion-acoustic cnoidal waves are studied at different values of quantum parameter He which is the ratio of electron plasmon energy to electron Fermi energy defined for degenerate electrons. It is found that both compressive and rarefactive ion-acoustic cnoidal wave structures are formed depending on the value of the quantum parameter. The dependence of the wavelength and frequency on nonlinear wave amplitude is also presented.

A wave equation model for retrograde media with a bubble structure

A nonlinear wave equation is obtained for liquid-vapor mixtures with regard to arbitrary change of equilibrium sound speed in a mixture with growth and condensation of vapor bubbles, which has a limit transition to a wave equation for pure liquid at full collapse of vapor cavities. A particular case of a collapsing wave equation (CWE) of retrograde media is considered, e.g., liquid-vapor media with low vaporization heat and low dissipation, observed near the critical liquid-vapor point, where the main effect is variable sound speed. Based on the CWE numerical solutions it is shown that in such liquid-vapor media, one can observe previously unknown nonlinear wave structures with depression waves.

Compressive and rarefactive ion acoustic solitons in a magnetized two-ion component plasma

The formation of compressive (hump) and rarefactive (dip) ion acoustic solitons is studied in magnetized O+- H+- e and O+- H−- e plasmas. The hydrodynamics equations are described for cold heavy (oxygen) ions, warm light (hydrogen) ions and isothermal Boltzmann distributed electrons along with Poisson equations in the presence of a magnetic field. The reductive perturbation method is used to derive the nonlinear Zakharov–Kuznetsov (ZK) equation for an ion acoustic wave in magnetized two-ion component plasma. It is found that two modes of ion acoustic waves with fast and slow speeds can propagate in the linear limit in such a plasma. It is noticed that, in the case of positively charged light hydrogen ions O+- H+- e plasmas, the slow ion acoustic wave solitons formed both potential hump as well as dip structures, while fast ion acoustic wave solitons give only hump structures. However in the case of negatively charged light hydrogen ions O+- H−- e plasmas, the slow ion acoustic wave solitons formed potential hump structures while fast ion acoustic wave solitons produce dip structures. The variations in the amplitude and width of the nonlinear slow and fast ion acoustic wave structures with density, temperature of light ions and magnetic field intensity are obtained in magnetized two-ion component plasmas. The magnetic field has its effect only on the width of the nonlinear ion acoustic wave structures in two-ion component plasmas.

Ion acoustic traveling waves

AbstractModels for traveling waves in multi-fluid plasmas give essential insight into fully nonlinear wave structures in plasmas, not readily available from either numerical simulations or from weakly nonlinear wave theories. We illustrate these ideas using one of the simplest models of an electron–proton multi-fluid plasma for the case where there is no magnetic field or a constant normal magnetic field present. We show that the traveling waves can be reduced to a single first-order differential equation governing the dynamics. We also show that the equations admit a multi-symplectic Hamiltonian formulation in which both the space and time variables can act as the evolution variable. An integral equation useful for calculating adiabatic, electrostatic solitary wave signatures for multi-fluid plasmas with arbitrary mass ratios is presented. The integral equation arises naturally from a fluid dynamics approach for a two fluid plasma, with a given mass ratio of the two species (e.g. the plasma could be an electron–proton or an electron–positron plasma). Besides its intrinsic interest, the integral equation solution provides a useful analytical test for numerical codes that include a proton–electron mass ratio as a fundamental constant, such as for particle in cell (PIC) codes. The integral equation is used to delineate the physical characteristics of ion acoustic traveling waves consisting of hot electron and cold proton fluids.

Obliquely propagating solitary wave structures in nonextensive magneto-rotating plasmas

The propagation of the nonlinear electrostatic ion acoustic solitary wave structures in two component, non relativistic, homogenous, magneto rotating plasma are studied. The inertialess electrons are assumed to follow nonextensive q velocity distribution. Small amplitude reductive perturbation technique is applied to derive Korteweg de Vries (KdV) equation and its analytical solution is presented. The effects of variation of different plasma parameters on propagation characteristics of solitary wave structure in the presence of the Coriolis force are discussed. It is observed that nonextensive parameter q modifies the structure of solitary wave structures in rotating plasmas.

Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation

AbstractTranscritical flow of a stratified fluid past a broad localised topographic obstacle is studied analytically in the framework of the forced extended Korteweg–de Vries, or Gardner, equation. We consider both possible signs for the cubic nonlinear term in the Gardner equation corresponding to different fluid density stratification profiles. We identify the range of the input parameters: the oncoming flow speed (the Froude number) and the topographic amplitude, for which the obstacle supports a stationary localised hydraulic transition from the subcritical flow upstream to the supercritical flow downstream. Such a localised transcritical flow is resolved back into the equilibrium flow state away from the obstacle with the aid of unsteady coherent nonlinear wave structures propagating upstream and downstream. Along with the regular, cnoidal undular bores occurring in the analogous problem for the single-layer flow modelled by the forced Korteweg–de Vries equation, the transcritical internal wave flows support a diverse family of upstream and downstream wave structures, including kinks, rarefaction waves, classical undular bores, reversed and trigonometric undular bores, which we describe using the recent development of the nonlinear modulation theory for the (unforced) Gardner equation. The predictions of the developed analytic construction are confirmed by direct numerical simulations of the forced Gardner equation for a broad range of input parameters.

Ion acoustic solitary waves in electron-positron-ion magneto-rotating Lorentzian plasmas

Nonlinear ion acoustic solitary wave structures in electron-positron-ion (e-p-i) magnetized rotating plasmas is studied. The electron and positron species are assumed to be nonthermal and follow the kappa distribution function. The Korteweg de Vries (kdV) equation is derived by employing the reductive perturbation technique for solitary wave in the nonlinear regime. The variation in the amplitude and width of the solitary wave are discussed with the effects of positron concentration, temperature ratio of kappa distributed electrons to positrons, spectral index of the positrons, direction of propagation of the wave with magnetic field and effective gyrofrequency of the rotating nonthermal plasmas. The numerical results are also presented for illustration.

Arbitrary Amplitude Ion Acoustic Solitary Waves in An Unmagnetized Two Electron Population Ultra-Relativistic Dense Plasmas

The nonlinear wave structure of arbitrary amplitude ion acoustic solitary waves (IASWs) are studied in the Sagdeev’s pseudopotential framework for an ultra-relativistic degenerate dense plasma comprising cold and hot electrons and inertial ultra-cold ions. By employing standard normal-mode analysis the dispersion relation for linear waves is studied. The numerical results are presented to understand the features of ion acoustic solitary wave structures. It is shown that the present plasma model supports IASWs having positive potential well. Also, it is found that the small amplitude rarefactive double layer solution can exist in such a plasma system in some parametric region. It is shown that solitary structures and double layers are affected by relevant plasma parameters.

Rogue wave impact on a tension leg platform: The effect of wave incidence angle and mooring line tension

An understanding of the interaction between extreme ocean conditions and floating offshore platforms is required for their design and safe operation. Rogue wave impacts cannot easily be handled by traditional analytic or computational techniques. Here we use Smoothed Particle Hydrodynamics (SPH) to simulate the fully non-linear dynamics of a large breaking wave on a semi-submersible tension leg platform. We consider the effect of wave impact angle and mooring line pre-tension on the subsequent motion of the platform, and predict the maximum tension in each mooring line. The primary effect of wave impact angle is to determine the peak mooring line tension and line “slackness” during wave impact. A 45° impact results in the maximum tension on the leading line. The maximum heave, surge and pitch vary only slightly with wave angle. As mooring line pre-tension is increased, the duration of heave and pitch excursions is reduced. Peak mooring tension increases only slightly, but the incidence of mooring line “slack” decreases significantly for higher pre-tension. Properly applied, SPH has a wide application in predicting non-linear wave–structure interactions. Genuine opportunity exists for using SPH in the design of structures and mooring systems exposed to extreme ocean events such as rogue wave impact.

Two-soliton solution of ion acoustic solitary waves in nonplanar geometry

The nonlinear wave structures of ion acoustic waves (IAWs) in an unmagnetized plasma consisting of superthermal electrons and warm ions are studied in bounded nonplanar geometry. Using reductive perturbation technique we have derived cylindrical and spherical Korteweg-de Vries (KdV) equations for IAWs to study the propagation of two-solitons. The presence of superthermally distributed electrons is shown to influence the propagation of two-solitons in nonplanar geometry.

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.