# Instability saturation by the oscillating two-stream instability in a weakly relativistic plasma

TL;DR: In this article, a truncation of the nonlinear Schrodinger equation to three modes is considered and the equilibrium points of the model are determined and their stability natures are discussed.

Abstract: The two-stream instability has wide range of astrophysical applications starting from gamma-ray bursts and pulsar glitches to cosmology. We consider one dimensional weakly relativistic Zakharov equations and describe nonlinear saturation of the oscillating two-stream instability using a three dimensional dynamical system resulting form a truncation of the nonlinear Schrodinger equation to three modes. The equilibrium points of the model are determined and their stability natures are discussed. Using the tools of nonlinear dynamics such as the bifurcation diagram, Poincare maps, and Lyapunav exponents, existence of periodic, quasi-periodic, and chaotic solutions are established in the dynamical system. Interestingly, we observe the multistable behavior in this plasma model. The system has multiple attractors depending on the initial conditions. We also notice that the relativistic parameter plays the role of control parameter in the model. The theoretical results presented in this paper may be helpful for better understanding of space and astrophysical plasmas.

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TL;DR: In this article, the dynamics of ion acoustic waves in Thomas-Fermi plasmas with source term consisting of electrons, positrons and positive ions, where electrons and positrons follow zero-temperature Fermi-gas statistics, but ions behave as classical fluid.

Abstract: Dynamics of ion acoustic waves are studied in Thomas-Fermi plasmas with source term consisting of electrons, positrons and positive ions, where electrons and positrons follow zero-temperature Fermi-gas statistics, but ions behave as classical fluid. Using RPT (reductive perturbation technique) the forced KdV and modified KdV equations are obtained. Employing the concept of planar dynamical systems, periodic, quasiperiodic and chaotic features of ion-acoustic waves are studied in Thomas-Fermi plasmas with space debris depending on positron concentration ( α ), speed ( v d ) of the space debris and strength ( f 0 ) of source perturbation. The results of this work may have relevance in the Thomas-Fermi plasma environments with space debris.

26 citations

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TL;DR: In this article, a bifurcation analysis of ion-acoustic (IA) superperiodic waves is studied in dense plasmas composed of electrons, positrons, and positive ions.

Abstract: Bifurcation analysis of ion-acoustic (IA) superperiodic waves is studied in dense plasmas composed of electrons, positrons, and positive ions. Employing bifurcation analysis of dynamical systems, all feasible phase plots including superperiodic trajectory and superhomoclinic trajectory are obtained based on positron concentration (α) and velocity (v) of IA traveling wave. Using symbolic computation, superperiodic wave solutions are obtained for ultra-relativistic environment as well as non-relativistic environment. It is discerned that positron concentration (α) affects the bifurcation of IA superperiodic waves. The results of this work may be applied to understand superperiodic wave features in cold neutron star.

18 citations

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TL;DR: In this article, a forced and damped Zakharov-Kuznetsov equation for a magnetized electron-positron-ion plasma affected by an external force is studied via the Hirota method.

Abstract: A forced and damped Zakharov–Kuznetsov equation for a magnetized electron–positron–ion plasma affected by an external force is studied in this paper. Via the Hirota method, the soliton-like solutions are given. The soliton’s amplitude gets enhanced with the phase velocity decreasing or ion-to-electron density ratio increasing. With the damped coefficient increasing, when the external force is periodic, the two solitons are always parallel during the propagation and background of the two solitons drops on the plane, and amplitudes of the two solitons increase on the and planes, with as the coordinates of the propagation plane and as the time. When is exponentially decreasing, the two solitons merge into a single one and the background rises on the plane, and amplitudes of the two solitons decrease on the and planes. Further, associated chaotic motions are obtained when is periodic. Using the phase projections and Poincare sections, we find that the chaotic motions can be weakened with , the amplitude of , decreasing. With , the frequency of , decreasing, a three-dimensional attractor with stretching-and-folding structure is found, indicating that the weak chaos is transformed into the developed chaos. Chaotic motions can also be weakened with , the phase velocity, decreasing, but strengthened with , the ion-to-electron density ratio, and decreasing.

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TL;DR: In this paper, the authors revisited the analytical formulism of oscillating two-stream instability of a plasma wave by incorporating the effect of a relativistic electron-beam and found that the growth of interacting waves during the instability is seriously affected by the relative motion between the beam electrons and the background plasma particles.

Abstract: Analytical formulism of oscillating two-stream instability of a plasma wave has been revisited by incorporating the effect of a relativistic electron-beam. A large-amplitude plasma wave may be susceptible to oscillating two-stream instability by decaying in a low-frequency mode and the sideband waves. The relativistic electron-beam may contribute in decaying the energy associated with the pump wave. In consequence, the growth of instability is enhanced. The findings of our calculations show that the growth of instability may be reached to a crucial level in the presence of a relativistic electron-beam. The growth of interacting waves during the instability is seriously affected by the relative motion between the beam electrons and the background plasma particles. This work may be important to understand the behavior of space and astrophysical plasmas.

1 citations

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TL;DR: The theory of homogeneous four-wave interactions, extended to include effects of nonresonant transfer, compares favorably with the ensemble-averaged results of the Monte Carlo simulations as discussed by the authors.

Abstract: Four-wave interactions are shown to play an important role in the evolution of the spectrum of surface gravity waves. This fact follows from direct simulations of an ensemble of ocean waves using the Zakharov equation. The theory of homogeneous four-wave interactions, extended to include effects of nonresonant transfer, compares favorably with the ensemble-averaged results of the Monte Carlo simulations. In particular, there is good agreement regarding spectral shape. Also, the kurtosis of the surface elevation probability distribution is determined well by theory even for waves with a narrow spectrum and large steepness. These extreme conditions are favorable for the occurrence of freak waves.

627 citations

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Kyoto University

^{1}TL;DR: In this paper, the coupling of two waves due to the presence of a third wave with large amplitude is studied on the basis of simple model equations, and the conditions for excitation of the first two waves are discussed for the following three cases: i) ω 1, ω 2 are large compared with their frequency shift.

Abstract: The coupling of two waves due to the presence of a third wave with large amplitude is studied. On the basis of simple model equations, the conditions for excitation of the first two waves are discussed for the following three cases: i) \(\omega_{1}+\omega_{2}{\risingdotseq}\omega_{0}\) and ω 1 , ω 2 are large compared with their frequency shift, ii) \(\omega_{1}{\ll}\omega_{2}{\lesssim}\omega_{0}\) and iii) \(\omega_{1}{\ll}\omega_{0}{\lesssim}\omega_{2}\), where ω 1 , ω 2 are the unperturbed frequencies of the two waves under consideration and ω 0 is the frequency of the incident large amplitude wave. In the first two cases, the excited wave is found oscillatory, while in the third it is found non-oscillatory. The threshold power of the incident wave for the onset of excitation, the frequency shift at the threshold and the growth rate above threshold are calculated in each case.

368 citations

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TL;DR: Based on a weakly non-Gaussian theory, the occurrence probability of freak waves is formulated in terms of the number of waves in a time series and the surface elevation kurtosis.

Abstract: Based on a weakly non-Gaussian theory, the occurrence probability of freak waves is formulated in terms of the number of waves in a time series and the surface elevation kurtosis. Finite kurtosis gives rise to a significant enhancement of freak wave generation in comparison with the linear narrowbanded wave theory. For a fixed number of waves, the estimated amplification ratio of freak wave occurrence due to the deviation from the Gaussian theory is 50%–300%. The results of the theory are compared with laboratory and field data.

229 citations

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Kyoto University

^{1}TL;DR: In this paper, the general theory of the parametric excitation of coupled waves developed in the preceding paper is applied to the parameterized interaction of the electrostatic waves in a plasma with radiation whose frequency is close to the electron plasma frequency.

Abstract: The general theory of the parametric excitation of coupled waves developed in the preceding paper is applied to the parametric interaction of the electrostatic waves in a plasma with radiation whose frequency is close to the electron plasma frequency. On the basis of the hydrodynamic equations, the coupled equations for the electron plasma wave and ion acoustic wave are derived. The effect of the Landau damping is also considered phenomenologically. Using the coupled wave equations, the expressions for the threshold radiation intensity, the frequency shift at the threshold and the growth rate above threshold are obtained. In particular, the dependence of these quantities on the wave-length of the electrostatic waves is discussed in detail. The results are compared with experiment of Stern and Tzoar.

213 citations

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