Nonlinear evolution of dust waves driven by cross‐field electron currents

The nonlinear evolution of dust waves generated by a low-frequency Hall current instability in a collisional dusty plasma is investigated with theory and nonlinear numerical simulations. The instability is driven by an electron E × B current and is an analog of the well-known Farley–Buneman instability in the dust acoustic type wave regime. This instability is believed to have broad applications to irregularity production in regions where dust is present in the earth’s ionosphere such as noctilucent clouds and meteor trails. The results indicate that the instability nonlinearly saturates with dust heating and the production of secondary waves that propagate in a direction perpendicular to the primary dust acoustic type waves. Results of the investigation also indicate that dust-neutral collisions increase the amplitude of the unstable dust waves after nonlinear saturation. Possible mechanisms for the production of the secondary waves as well as implications of these waves are described.

The nonlinear features of dust-acoustic waves (DAWs) propagating in a multicomponent, collisional, magnetized dusty plasma whose constituents are negative dust grains, superthermal ions, and electrons are investigated. The hydrodynamic fluid equations are reduced to a damped Zakharov–Kuznetsov (DZK) equation, using the reductive perturbation technique. The DZK equation is solved using both the generalized $$(G^{{\prime }}/G)$$ –expansion method and the Painleve analysis method. Each method gives a class of solutions. This indicates that these methods are sufficient to give all possible solutions of the DZK equation. These solutions successfully describe different kinds of nonlinear waves such as explosive, soliton, shocklike, periodical, and cnoidal waves. Additionally, the effects of different plasma parameters such as relative densities and temperatures as well as superthermality parameters of ions and electrons on the behavior of the obtained diverse waves are investigated. The relevance of the present investigation can be used to understand the cosmic dust-laden plasmas.

Obliquely propagating dust-acoustic solitary waves in cosmic dust-laden plasmas

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

Dynamical properties of dust-ion-acoustic waves (DIAWs) are analysed in a collisional nonextensive dusty plasma composing of mobile ions, q-nonextensive electrons and stationary dust grains with slight collisions between dusts and ions. Reductive perturbation technique (RPT) is practiced to acquire the damped Korteweg-de Vries (DKdV) equation. In absence of collision between dusts and ions, the damping term vanishes and the DKdV equation reduces to the KdV equation. Bifurcation analysis of the dynamical system obtained from the KdV equation is carried out. Analytical solitary wave solution and numerical periodic wave solution of the KdV equation are presented. Approximate analytical DIAW solutions for the DKdV equation are furnished using the novel ( G ′ / G ) -expansion technique. As an outcome, novel approximate analytical solutions of DIAWs are obtained for the DKdV equation. The application of our work is significant to explore nonextensive plasma environment, such as, ionosphere of Earth.

The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the modulational instability for long-crested wave trains, which agrees well with recent large-scale experiments in wave basins, where it was found that narrower directional spectra lead to self-focusing of ocean waves and an enhanced probability of extreme events. We find that the modulational instability is nonlinearly saturated by a broadening of the wave spectrum, which leads to the stabilization of the water-wave system. Applications of our results to other fields of physics, such as nonlinear optics and plasma physics, are discussed.

This research concerns on the influence of higher order solution to nonlinear evolution of bichromatic waves based on Benjamin Bona Mahony (BBM) equation. Asymptotic method was applied to determine the solution expanded to the fifth order. In previous researches, this method was applied on the same equation to find its solution up to the third order and it was obtained that the waves underwent deformation and amplitude amplification affected by the occurrence of a pair of side bands during their propagation. In this study, the effect of the higher order solution on the increasing amplitude was observed. A quantity called as Maximal Temporal Amplitude (MTA) was measured to find the maximum position where the highest amplitude occurred and the Amplitude Amplification Factor (AAF). MTA gives information about the waves’ highest elevation at every spatial position during the observation time. The analysis includes comparison between the third and fifth order solutions in their contribution to the rise of the amplitude and the maximum position.

Numerical investigation on the generation and evolution of nonlinear internal waves in the southern Strait of Georgia

Influence of superthermal plasma particles on the Jeans instability in self-gravitating dusty plasmas with dust charge variations

We have studied the instability of electrostatic ion-cyclotron waves in collisional magnetized two-ion component plasma (light positive K + ions and heavy positive Cs + ions). An ion beam propagating through collisional magnetized plasma containing electrons and two positive ion components drives electrostatic ion cyclotron (EIC) waves to instability via Cerenkov interaction. Analytical expressions & numerical calculations have been carried out for the frequency and growth rate of ion cyclotron waves for two EIC wave modes for existing experimental parameters, and it is found that the unstable mode frequency does not depend on electron collision frequency, while the growth rate is increased linearly with the electron collision frequency. Moreover, as the light ion concentration is increased, the frequency of the heavy ion mode moves closer to its gyrofrequency. Similarly, the frequency of the light ion mode approaches the light ion cyclotron frequency as the heavy ion concentration is increased. It is also found that the normalized unstable mode frequencies remains unchanged with electron collision frequencies, while the growth rate is increased linearly with the electron collision frequencies. In addition, the unstable mode frequencies are found to be dependent on the magnetic field strengths.

Modulational instability, rogue waves, and envelope solitons in opposite polarity dusty plasmas

The propagation characteristics of small-amplitude electrostatics solitary wave in magnetized dusty plasma in the presence of relativistic thermal ion with non-thermal electron and positron are investigated. Here, Zakharov–Kuznetsov (Z–K) equation is studied to observe the evolution of dust ion acoustic solitary waves with the help of perturbative procedures. In the present plasma system, the Mach number (phase velocity) is found to be in the supersonic range and it decreases (increases) with normalized positron density (thermal ion parameter). On the other hand, the plasma system behaves in the least nonlinear way when the non-thermal parameter of electrons and positrons has the lowest value allowing the solitary wave potential to propagate with maximum value. It is found that the non-thermal parameters of electrons and positrons, relativistic factor and dust density, can effectively control the variation of Mach number. The solitary wave potential has the least value when the thermal ion parameter increases, whereas it is the highest when the positron density has the highest.

The nonlinear evolution of ion-acoustic waves in a multi-component plasma with negative ions has been studied experimentally using a double-plasma device. At a critical concentration of negative ions the phase velocity of the ion- acoustic waves increases with the wave amplitude, and the wave has negative dispersion, which show that the wave satisfies Lighthill's condition. The initial small modulation in amplitude is found to grow spatially. The observed phenomena are compared with the relevant theory using the nonlinear Schrödinger equation. The fluid equations are integrated to confirm the validity of the nonlinear Schrödinger equation.

The effect of an external magnetic field on an ion-dust two-stream instability in a collisional dusty plasma is investigated. We consider the parameter regime in which the ions and electrons are strongly magnetized, while the charged dust is unmagnetized. The presence of a magnetic field tends to hinder the growth of the instability. The implications for laboratory dusty plasmas such as 'plasma crystals' are discussed.

Although great advances have been made over the last five decades in modelling the nonlinear wave-wave interactions, the topic is far from being exhausted. Despite considerable progress, many open questions remain. This paper gives a brief summary of problems in the understanding and modelling of nonlinear wave-wave interactions. Recent developments together with suggestions for further research are also discussed. The discussion is confined to a few outstanding issues: (a) Although nonlinear energy transfer can be predicted with rigorous theories such as that of resonant weakly nonlinear interaction between sets of four waves (i.e. the kinetic or Boltzmann equation by Hasselmann) or directly from the hydrodynamic equations based on first principles with no assumptions involved, it is not yet completely clear whether the solutions converge to the same universal solution. Despite a few results available in literature there are still unresolved controversies, discrepancies and challenges that we aim discussing in this paper along with some recent developments. (b) To date, there is no clear view on the role of near-resonant interactions in the evolution of nonlinear waves. Recent works point out to expectations that near-resonant interactions, rather than the exact resonance, dominate the temporal nonlinear evolution. Even though one can in principle account for near-resonant interaction in the spatio-temporal domain, its practical use in an operational wave prediction model is far from being established. This paper will discuss the latest development within the framework of a novel wave-action transfer model that would cover near-resonant interactions and Stokes corrections, as well as the associated computational challenges and the open questions that must be addressed. (b) Currently, quite a few exact, quasi-exact and approximate methods exist to compute the nonlinear fourwave interaction. However, usually only one approximate method is in use to compute the non-linear quadruplet wave-wave interactions for a discrete wind wave spectrum usually in third-generation wave prediction models. Up untill now no comprehensive and more importantly objective comparison has been performed to determine the best (both in terms of performance and accuracy) method for computing the nonlinear four-wave interactions in a discrete spectral model. A good understanding of these methods is crucial for the interpretation of the results of the numerical aspects. In this paper we outline and discuss the foundation of an inter-comparison study that should provide answers to a range of basic questions as well as provide a systematic analysis of the characteristics of these methods.