I= ORDER AND CHAOS IN THE TEMPERATURE-GRADIENT-DRIVEN WAVES IN SHEARED FLOW PLASMA
Pakistan Research Repository Home
 

Title of Thesis
ORDER AND CHAOS IN THE TEMPERATURE-GRADIENT-DRIVEN WAVES IN SHEARED FLOW PLASMA

Author(s)
ANISA QAMAR
Institute/University/Department Details
Department of Physics/ Quaid-i-Azam University Islamabad, Pakistan
Session
2003
Subject
Physics
Number of Pages
109
Keywords (Extracted from title, table of contents and abstract of thesis)
temperature-gradient-driven waves, sheared flow plasma, electrostatic waves, ion-temperature-gradient, nondissipative plasma, electron-temperature-gradient, nonthermal electromagnetic fluctuations, plasma vortices, dipolar vortices, quadrupolar vortices

Abstract
By using Braginskii's transport equations for ions and Boltzmann distribution for electrons, a system of nonlinear equations governing the dynamics of low-frequency, short-wavelength electrostatic waves in the presence of equilibrium density, temperature, magnetic field and electrostatic potential gradients has been derived. New ion-temperature-gradient (ITG) driven drift-dissipative modes are shown to exist. An expression for anomalous ion energy transport caused by nonthermal electrostatic fluctuations is also derived. Furthermore, possible stationary solutions of the nonlinear system are obtained in the form of double vortex. For some specific profiles of the equilibrium flow velocity, number density, temperature, and magnetic field, new type of solutions in the form of quadrupole are found to exist for a nondissipative plasma. When the plasma beta exceeds the electron to ion mass ratio, incorporation of electromagnetic effects on the ITG modes become necessary. We examined the linear and nonlinear properties of electrostatic and electromagnetic waves in the presence of ion-temperature, magnetic-field, density and velocity gradients. In the linear limit, a dispersion relation is obtained that admits new instabilities of drift waves. It is found that parallel velocity shear couples the electrostatic and magnetostatic modes and can cause an instability. An estimate of anomalous ion energy transport and particle flux on the basis of mixing length hypothesis is made and the results are discussed for some interesting limiting cases. The stationary solutions of the nonlinear equations without dissipation are also presented. We re-examined nonlinear mode coupling equations for finite amplitude low-frequency electromagnetic waves in the presence of nonuniform, resistive, magnetized electron-ion plasma with sheared flows. The temporal behavior of the nonlinear mode coupling equations is found to be governed by eight coupled equations, which are the generalization of the Lorenz and Stenflo equations, admitting chaotic trajectories. The linear stability of the generalized Lorenz-Stenflo system of equations is also presented under different approximations. By employing Braginskii's transport equations for electrons, we derive a system of nonlinear equations which govern the dynamics of low-frequency short wavelength electromagnetic waves in the presence of equilibrium density, temperature, and magnetic field gradients. In the linear limit, a dispersion relation is derived and analysed. New electron-temperature-gradient (ETG) driven electromagnetic drift-wave instabilities are also shown to exist. Anomalous electron energy transport caused by nonthermal electromagnetic fluctuations is derived. Possible stationary solutions of the nonlinear system are obtained in the form of spatially bounded dipolar as well as chain of vortices. In the nonlinear case, the chaotic behavior of a nonlinear dissipative system can be written in the form of well known Lorenz and Stenflo type equations. The results of our investigation should be helpful for understanding the wave phenomena in space and to kamak plasmas.

Download Full Thesis
1004.06 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents
78.83 KB
2 1 Introduction 4
95.44 KB
  1.1 Layout of the Thesis 10
3 2 Linear Study of ITG and ETG Modes 11
333.97 KB
  2.1 Introduction 11
  2.2 Fluid Motion Across the Magnetic Field 12
  2.3 Derivation of Electrostatic ITG Mode 13
  2.4 Derivation of ITG Driven Drift-Dissipative Acoustic Waves 17
  2.5 Electromagnetic ITG Mode 25
  2.6 Electrostatic ETG Mode 35
  2.7 Summery 46
4 3 Plasma Vortices 47
317.42 KB
  3.1 Introduction 47
  3.2 Stationary Solutions of Electrostatic ITG Mode 50
  3.3 Quadrupolar Vortices in Electrostatic ITG Mode 57
  3.4 Derivation of Dipolar Vortices in Electromagnetic ITG Mode 67
  3.5 Vortex Street Type Solution for Electromagnetic ETG Mode 75
  3.6 Summery 78
5 4 Chaos in ITG and ETG Modes 80
206.83 KB
  4.1 Introduction 80
  4.2 Lorenz model 80
  4.3 Summery 100
6 5 Summary and Conclusions 101
110.84 KB
  5.1 Future work 103