Nonlinear Phenomena in Rotating Astrophysical Objects

Inhaltsverzeichnis (Table of Contents)

• Abstract
• Chapter 1: Introduction
  • 1.1. General Introduction
  • 1.2. Nonlinear Phenomena in Plasmas
  • 1.3. Pair Plasmas
  • 1.4. Astrophysical Pair Plasmas
  • 1.5. Outline of the Thesis
• Chapter 2: Basic Concepts and Equations
  • 2.1. Basic Equations for Plasma Physics
  • 2.2. Fluid Model of Plasma
  • 2.3. Electromagnetic Waves in Plasma
  • 2.4. Nonlinearity in Plasma
  • 2.5. Nonlinear Wave Equations
• Chapter 3: Nonlinear Waves in Pair Plasmas
  • 3.1. The Propagation of Electromagnetic Waves in Pair Plasmas
  • 3.2. Derivation of Korteweg-de Vries (K-dV) Equation
  • 3.3. Derivation of Derivative Nonlinear Schrödinger Equation (DNSE)
  • 3.4. Derivation of Nonlinear Schrödinger Equation (NLSE) via W.K.B Method
  • 3.5. Solitary Wave (SW) Solutions of K-dV and DNSE Equations
  • 3.6. Solitary Wave (SW) Solutions of NLSE Equation
  • 3.7. Numerical Results and Discussion
• Chapter 4: Conclusion

Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)

This dissertation explores the nonlinear propagation of electromagnetic (EM) waves in a pair plasma, specifically focusing on electron-positron (e-p) plasmas present in rotating astrophysical objects like pulsar magnetospheres. The primary objective is to investigate the influence of rotation and thermal energy ratio on the characteristics of nonlinear waves in these plasmas.

• Nonlinear wave propagation in pair plasmas
• The role of rotation in shaping wave characteristics
• The impact of thermal energy ratio on wave properties
• Derivation and analysis of nonlinear wave equations (K-dV, DNSE, NLSE)
• Exploration of solitary wave solutions and their dependence on plasma parameters

Zusammenfassung der Kapitel (Chapter Summaries)

• Chapter 1 provides an introduction to the topic, outlining the general context of nonlinear phenomena in plasmas and specifically addressing pair plasmas found in astrophysical environments like pulsar magnetospheres.
• Chapter 2 delves into the fundamental concepts and equations relevant to plasma physics, focusing on fluid models, electromagnetic wave propagation in plasmas, and the introduction of nonlinearity in plasma systems.
• Chapter 3 is the core of the dissertation, investigating the propagation of electromagnetic waves in pair plasmas. It covers the derivation of Korteweg-de Vries (K-dV), derivative nonlinear Schrödinger (DNSE), and nonlinear Schrödinger (NLSE) equations. The chapter also analyzes the solitary wave solutions obtained from these equations, examining their properties and dependence on parameters like rotational frequency and thermal energy ratio.

Schlüsselwörter (Keywords)

The primary focus of this dissertation revolves around the nonlinear propagation of electromagnetic waves in pair plasmas, particularly electron-positron plasmas. Key terms include: pair plasma, pulsar magnetosphere, rotational frequency, thermal energy ratio, Korteweg-de Vries equation (K-dV), derivative nonlinear Schrödinger equation (DNSE), nonlinear Schrödinger equation (NLSE), solitary waves, and Wentzel, Kramers, and Brillouin (W.K.B) approximation.