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.
At a glance
- Three theoretical investigations use K-dV, nonlinear Schrödinger and derivative nonlinear Schrödinger models
- Numerical wave analysis uses observed Crab pulsar parameters
- Applies reductive perturbation and W.K.B. approximation to pulsar magnetosphere waves
- 149 sources in the bibliography
- 32 figures
Contents
1 Introduction
1.1 Concept of Plasma
1.1.1 The Evolution of Plasma Physics
1.1.2 Plasma Characteristics
1.1.3 Classification of Plasmas
1.1.4 Occurrences of Plasmas
1.1.5 Applications of Plasmas
1.2 Electron-Positron Plasmas
1.2.1 Occurrences Electron-Positron Plasmas
1.3 Different Plasma Waves Phenomena
1.3.1 Short Notes on Alfvén Waves
1.3.2 Types of Alfvén Waves
1.4 Rotating Astrophysical Objects
1.5 Linearity and Nonlinearity of Waves
1.6 Existing Theoretical Nonlinear Approach
1.7 Nonlinear Wave Phenomena
1.8 Layout of The Book
2 Nonlinear Compressional Alfvén Waves in a Pair Plasma
2.1 Introduction
2.2 Governing Equations
2.3 Derivation of The K-dV Equation
2.4 Solution of The K-dV Equation
2.5 Numerical Analysis
2.6 Discussion
3 Nonlinear Solitary Waves in a Pair Plasma
3.1 Introduction
3.2 Governing Equations
3.3 Derivation of NLSE
3.4 Numerical Analysis
3.5 Modulational Instability
3.6 Discussion
4 Nonlinear Shear Alfvén Waves in a Pair Plasma
4.1 Introduction
4.2 The Mathematical Model
4.3 Derivation of The DNSE
4.4 Solution of The DNSE Equation
4.5 Numerical Analysis and Results
4.6 Conclusion
5 Summary
Objectives and Topics
This dissertation investigates nonlinear electromagnetic waves and solitary structures in relativistic, magnetized electron-positron plasmas in rotating astrophysical environments. It asks how wave properties and modulational stability depend on plasma parameters and rotation, using theoretical models and numerical analysis informed by the Crab pulsar.
- Electron-positron plasma and pulsar magnetospheres
- Compressional and shear Alfvén waves
- Relativistic magnetohydrodynamics in rotating frames
- Nonlinear evolution equations and solitary-wave solutions
- Thermal energy ratios, rotation and modulational instability
Excerpt from the Book
Nonlinear Wave Phenomena
There are various nonlinear waves like Solitary wave (SW), Shock wave, Vortex wave, and Double Layer, etc. As our main concern in this dissertation is to analyze the characteristics of solitary waves, so we will only discuss about solitary waves here.
A SW is a wave which propagates without any temporal evolution in shape or size when viewed in the reference frame moving with the group velocity of the wave. The envelope of the wave has one global peak and decays far away from the peak. A SW is defined as a spatially confined (localized), non-dispersive and nonsingular solution of a non-linear field theory. Therefore, they have been thought impossible because a dispersive and non-linear medium has been expected to alter any shape of any wave over time. Dispersion alone leads to shock fronts of the propagating wave. That the non-linearity can compensate for the dispersion leading to a propagating and stable wave having constant velocity and shape came as a surprise. SWs were firstly discussed in 1845 by J. Scott Russell in the Report of the British Association for the Advancement of Science. He observed a SW traveling along a water channel. The existence and importance was disputed until D. J. Korteweg and G. de Vries gave a complete account of solutions to the non-linear hydro-dynamical equation in 1895 [67].
A soliton is a nonlinear solitary wave with the additional property that the wave retains its permanent structure, even after interacting with another soliton. For example, two solitons propagating in opposite directions effectively pass through each other without breaking. Solitons occur as the undersea internal waves, initiated by seabed topography, that propagate on the oceanic pycnocline. Atmospheric solitons also exist, such as the Morning Glory Cloud of the Gulf of Carpentaria, where pressure solitons travelling in a temperature inversion layer produce vast linear roll clouds.
A single, consensus definition of a soliton is difficult to find. Solitons have the following properties [68]:
(i). They don’t disperse;
(ii). They are of permanent form;
(iii). They are localized within a region;
(iv). They don’t obey the superposition principle;
(v). They can interact with other solitons, and emerge from the collision unchanged, except for a phase shift.
Chapter Summaries
Introduction: Introduces plasma physics, electron-positron plasmas, Alfvén waves, pulsars and nonlinear wave phenomena. It also describes the theoretical approaches used in the research.
Nonlinear Compressional Alfvén Waves in a Pair Plasma: Derives and solves a Korteweg-de Vries equation for compressional solitary waves, followed by a numerical investigation of their properties.
Nonlinear Solitary Waves in a Pair Plasma: Develops a nonlinear Schrödinger equation for electromagnetic waves in a rotating pair plasma and examines numerical behaviour and modulational instability.
Nonlinear Shear Alfvén Waves in a Pair Plasma: Derives a derivative nonlinear Schrödinger equation for shear Alfvén waves and studies its stationary solitary-wave solution numerically.
Summary: Brings together the principal results of the three research chapters.
Keywords
electron-positron plasma, pulsar magnetosphere, Crab pulsar, nonlinear waves, solitary waves, Alfvén waves, relativistic magnetohydrodynamics, rotating reference frame, reductive perturbation method, W.K.B. approximation, Korteweg-de Vries equation, nonlinear Schrödinger equation, modulational instability
Frequently Asked Questions
What is this dissertation about?
It studies nonlinear electromagnetic waves and solitary structures in rotating, relativistic electron-positron plasmas, with particular attention to pulsar magnetospheres.
What are the main topics?
The work addresses pair plasmas, compressional and shear Alfvén waves, solitary-wave models, rotation and modulational instability.
What is the main research objective?
The author aims to understand how nonlinear waves propagate and how their properties depend on plasma conditions and rotation.
What scientific methods are used?
The study combines relativistic magnetohydrodynamic modelling, rotating-frame Maxwell equations, reductive perturbation theory, the W.K.B. approximation and numerical analysis.
What does the main body examine?
Three research chapters examine compressional Alfvén waves, electromagnetic solitary waves and shear Alfvén waves using different nonlinear evolution equations.
Which keywords characterize the work?
Key terms include electron-positron plasma, Alfvén waves, solitary waves, pulsar magnetosphere, Korteweg-de Vries equation and modulational instability.
Why is the Crab pulsar important to the analysis?
The author uses parameters associated with the Crab pulsar for numerical investigations of the theoretical wave models.
How are compressional and shear Alfvén waves modelled?
The compressional-wave chapter derives a Korteweg-de Vries equation, while the shear-wave chapter derives a derivative nonlinear Schrödinger equation.
What role does the positron-to-electron thermal energy ratio play?
It is a parameter used to investigate changes in the speed and solitary-wave profiles of the compressional and shear modes.
- Quote paper
- Tanvir Islam Rajib (Author), 2015, Nonlinear Phenomena in Rotating Astrophysical Objects, Munich, GRIN Verlag, https://www.grin.com/document/418560
