I= Self-Organized and Chaotic States in Electron-Positron-Ion Magnetoplasma
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Title of Thesis
Self-Organized and Chaotic States in Electron-Positron-Ion Magnetoplasma

Muhammad Azeem
Institute/University/Department Details
Department of Physics/ Quaid-i-Azam University
Number of Pages
Keywords (Extracted from title, table of contents and abstract of thesis)
electron-positron-ion magnetoplasma, nonlinear dynamics, ion dynamics, monopolar vortex, quadrupolar vortices, ion-temperature-gradient, tripolar vortices, astrophysical plasmas, ambient magnetic field, electromagnetic nonlinear equations, electrostatic nonlinear equations

In this thesis, we have investigated the nonlinear dynamics of low-frequency electrostatic/electromagnetic waves in a nonuniform electron-positron-ion (e-p-i) magnetoplasma with sheared ion flows. The ion dynamics is governed by the ion continuity and momentum balance equations, whereas the electrons and positrons are assumed to follow Boltzmann distributions, for electrostatic case. It is shown that the low-frequency ion-acoustic and electrostatic-drift waves can become unstable due to the ion sheared flow. In a collisional case a drift-dissipative instability can also take place. For the nonlinear case, it is shown that a quasi-stationary solution of the mode coupling equations can be represented in the form of monopolar vortex. We have also generalized the said work by considering non uniform strongly magnetized electron-positron plasma with finite ion-temperature effect and in the presence of sheared ion flows. In the linear limit, a dispersion relation is obtained that admits new instability of drift-waves. Whereas, the nonlinear interaction between the finite amplitude short-wavelength waves give rise to quadrupolar vortices.

We have extended our earlier studies to the ion-temperature-gradient (lTO) driven electrostatic waves in a collisionless e-p-i magnetoplasma that contain equilibrium density, temperature, magnetic field, velocity and electrostatic potential gradients. We thus use hydrodynamic equations under drift-approximation and derive a set of non linear equations composed of ion continuity, the ion equation of motion and ion energy balance equations. In the linear limit, it is shown that non-zero equilibrium ion-temperature-gradient and the presence of positrons modify the basic drift modes. On the other hand, in the nonlinear case, it is shown that under certain conditions possible stationary solutions of the same set of nonlinear equations are reduced in the form of various types of vortex patterns. We have also incorporated the self-gravitational effect of ions in this work and have shown that possible stationary solutions of the nonlinear equations can be represented in the form of dipolar and tripolar vortices of gravitational potential.

Furthermore, we have also extended our study of electrostatic ITO modes to the electromagnetic case and derived a new set of coupled nonlinear equations which governs the dynamics of low-frequency electromagnetic ITO-driven modes in a nonuniform electronpositron-ion magnetoplasma with non-zero ion-temperature-gradients.

We reexamined nonlinear mode coupling equations under various approximations. In the linear limit, a local dispersion relation has been derived and analyzed in several interesting limiting cases. On the other hand, a quasi-stationary solution of the mode coupling equations in the absence of collisions can be represented in the form of dipolar and vortex-chain solutions.

Finally, we have studied the temporal behavior of electrostatic/electromagnetic ITG modes in e-p-i magnetoplasma and showed that the mode coupling equations can be represented in the form of well-known Lorenz and Stenflo type equations that admit chaotic trajectories. The results of our investigations are helpful to understand the wave phenomena in laboratory and astrophysical plasmas.

Download Full Thesis
4254.06 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents
166.98 KB
2 1 Introduction 5
738.42 KB
  1.1 Existence of Electron-Positron-Ion Plasma 5
  1.2 Self-organized Structures in Plasma 8
  1.3 Chaotic Behavior 13
  1.4 Layout of the Thesis 15
3 2 Derivation of Nonlinear Equations 17
520.41 KB
  2.1 Introduction 17
  2.2 Drift-Motion Across the Ambient Magnetic Field 19
  2.3 Derivation of Electromagnetic Nonlinear Equations 22
  2.4 Derivation of Electrostatic Nonlinear Equations 26
4 3 Nonlinear Dynamics in Cold and Hot Ions Limits 28
546.65 KB
  3.1 Introduction 28
  3.2 Cold Ions 29
  3.3 Hot Ions 34
5 4 Nonlinear Dynamics of ITG-driven Electrostatic Waves 42
761.16 KB
  4.1 Introduction 42
  4.2 Electrostatic ITG Modes 44
  4.3 Self-Gravitation Effect of Ions 54
  4.4 Summary 62
6 5 Nonlinear Dynamics of ITG-driven Electromagnetic Waves 64
520.28 KB
  5.1 Introduction 64
  5.2 Electromagnetic ITG Modes 65
  5.3 Summary 78
7 6 Chaotic States in Electron-Positron-Ion Magnetoplasma 79
809.67 KB
  6.1 Introduction 79
  6.2 Chaotic Behavior of Electrostatic Waves in Cold Ions Limit 89
  6.3 Chaotic Behavior of ITG-driven Electrostatic Waves 92
  6.4 Chaotic Behavior of ITG-driven Electromagnetic Waves 97
  6.5 Summery 102
8 7 Summary and Conclusions 103
337.42 KB