Nonlinear Phenomena in Rotating Astrophysical Objects

Master's Thesis , 2015 , 105 Pages , Grade: A+ (4.00 on a scale of 4.00)

Physics - Other

The nonlinear propagation of electromagnetic (EM) waves in a pair plasma consisting of electron-positron (e-p) has been rigorously investigated in rotating astrophysical objects (e.g. pulsar magnetosphere). Two nonlinear approaches have been used to analyze the nonlinear wave phenomena in pulsar magnetosphere. The reductive perturbation method has been employed in order to derive the Korteweg-de Vries (K-dV) and derivative nonlinear Schrodinger equation (DNSE) as well as Wentzel, Kramers, and Brillouin (W.K.B) approximation technique has also been used to derive nonlinear Schrodinger equation (NLSE). The steady-state solutions of these nonlinear equations have been obtained and analyzed theoretically and numerically. The existence of solitary waves (SWs) in e-p plasma is found depending on the basic plasma parameters of considered e-p plasma. It has been seen that the basic features of SWs are significantly modified by the effects of rotational frequency (RF) and positron-to-electron thermal energy ratio (ER). The results, which have been found in this dissertation are summarized as follows: (i). e-p plasma medium supports low phase speed, high frequency, compressional e-p Alfven (CEPA) waves, and shear e-p Alfven (SEPA) waves; (ii). Both the amplitude and the width of CEPA, and SEPA SWs are seen to increase with the increase of ER. It is investigated that the RF does not have any influence on the amplitude and width of the K-dV and DNSE SWs observed in the e-p plasma of crab pulsar but the RF has a significant effect on the basic properties of SWs obtained via NLSE; (iii). The frequency of EM waves propagated in the crab pulsar lies in the range of radio waves. It is also observed that the phase speed of the EM waves increases with the decreasing values of the angle between the magnetic moment and the rotational axis, and waves are modulationally unstable when W.K.B technique has been used. The findings of these investigations may use to understand the nonlinear EM waves phenomena in rotating astrophysical and laboratory plasmas.

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.

• College: Jahangirnagar University
• Course: Plasma Physics
• Grade: A+ (4.00 on a scale of 4.00)
• Author: Tanvir Islam Rajib (Author)
• Publication Year: 2015
• Pages: 105
• Catalog Number: V418560
• ISBN (eBook): 9783668683723
• ISBN (Book): 9783668683730
• Language: English
• Tags: nonlinear, phenomena, rotating, astrophysical, objects