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

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 dimens...

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Bibliographic Details
Published in:Physics of plasmas 2015-04, Vol.22 (4)
Main Authors: Pal, Barnali, Poria, Swarup, Sahu, Biswajit
Format: Article
Language:English
Subjects:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ASTROPHYSICS
ASTROPHYSICS, COSMOLOGY AND ASTRONOMY
ATTRACTORS
BIFURCATION
Bifurcations
COSMIC GAMMA BURSTS
COSMOLOGY
Dynamic stability
Dynamical systems
Gamma ray bursts
Gamma rays
Initial conditions
LYAPUNOV METHOD
Mathematical models
MATHEMATICAL SOLUTIONS
Nonlinear dynamics
Nonlinear equations
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
Parameters
Plasma physics
Poincare maps
PULSARS
Relativism
Relativistic effects
RELATIVISTIC PLASMA
Relativistic plasmas
RELATIVISTIC RANGE
Saturation
Schrodinger equation
SCHROEDINGER EQUATION
THREE-DIMENSIONAL CALCULATIONS
TWO-STREAM INSTABILITY
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Summary: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, Poincaré 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.
ISSN:1070-664X
1089-7674
DOI:10.1063/1.4917333