Dynamical Systems and Nonlinear Waves in Plasmas

Cover
Title Page
Copyright Page
Dedication
Preface
Table of Contents
1. Introduction
	1.1 Plasma as a state
	1.2 Plasmas exist in nature
		1.2.1 Ionosphere
		1.2.2 Van Allen belts
		1.2.3 Aurorae
		1.2.4 Solar corona
		1.2.5 Core of the sun
		1.2.6 HII regions
	1.3 Concept of temperature
		1.3.1 Existence of several temperatures
		1.3.2 Electron and ion temperatures
		1.3.3 Quasineutrality in plasma
	1.4 Debye length and Debye sphere
	1.5 Criteria for plasma
	1.6 Plasma frequency
	1.7 Applications of plasma
		1.7.1 Space physics
		1.7.2 Astrophysics
		1.7.3 Gas lasers
		1.7.4 Industrial application
	1.8 Fluid description of plasma
		1.8.1 Maxwell’s equation
		1.8.2 Equation of motion
		1.8.3 Equation of continuity
		1.8.4 Equation of state of plasma
		1.8.5 Poisson equation
	References
2. Dynamical Systems
	2.1 Introduction to dynamical systems
		2.1.1 One-dimensional system
			2.1.1.1 Equilibrium point and its stability
			2.1.1.2 Trajectory and phase portrait
			2.1.1.3 Example
		2.1.2 Linear stability analysis
			2.1.2.1 Example
		2.1.3 Potentials
			2.1.3.1 Example
			2.1.3.2 Example
		2.1.4 Bifurcations
		2.1.5 Linear system in two-dimension
			2.1.5.1 Example
		2.1.6 Phase plane analysis
			2.1.6.1 Nonlinear system in two-dimension
			2.1.6.2 Conservative system
			2.1.6.3 Example
			2.1.6.4 Example
			2.1.6.5 Hamiltonian system
			2.1.6.6 Example
	References
3. Waves in Plasmas
	3.1 Introduction to wave modes
		3.1.1 Ion-acoustic (IA) waves
		3.1.2 Dust-acoustic (DA) waves
		3.1.3 Dust-ion-acoustic (DIA) waves
		3.1.4 Upper hybrid wave
		3.1.5 Electrostatic cyclotron waves
		3.1.6 Lower hybrid wave
	3.2 Reductive perturbation technique and evolution equations
		3.2.1 The KdV equation
		3.2.2 The Burgers equation
		3.2.3 The KP equation
		3.2.4 The ZK and mZK equations
	3.3 Analytical wave solutions of evolution equations
		3.3.1 Analytical wave solution of the KdV equation
		3.3.2 Analytical wave solution of the mKdV equation
		3.3.3 Analytical wave solution of the KP equation
		3.3.4 Analytical wave solution of the mKP equation
		3.3.5 Analytical wave solution of the ZK equation
		3.3.6 Analytical wave solution of the mZK equation
		3.3.7 Analytical wave solution of the Burgers equation
	References
4. Bifurcation of Small Amplitude Waves in Plasmas
	4.1 Introduction
	4.2 Bifurcation of ion-acoustic waves with small amplitude
		4.2.1 Basic equations
		4.2.2 Derivation of the KdV equation
		4.2.3 Formation of dynamical system
		4.2.4 Phase plane analysis
		4.2.5 Wave solutions
	4.3 Bifurcation of dust-ion-acoustic waves with small amplitude
		4.3.1 Governing equations
		4.3.2 Derivation of the KP equation
		4.3.3 Formation of dynamical system and phase portraits
		4.3.4 Wave solutions
	4.4 Bifurcation of dust-acoustic waves with small amplitude
		4.4.1 Basic equations
		4.4.2 Derivation of the Burgers equation
		4.4.3 Formation of dynamical system and phase portraits
		4.4.4 Wave solutions
	4.5 Bifurcation of electron-acoustic waves with small amplitude
		4.5.1 Basic equations
		4.5.2 Derivation of the KdV equation
		4.5.3 Formation of dynamical system and phase portraits
		4.5.4 Wave solutions
	References
5. Bifurcation of Arbitrary Amplitude Waves in Plasmas
	5.1 Introduction
	5.2 Bifurcation of ion-acoustic waves with arbitrary amplitude
		5.2.1 Basic equations
		5.2.2 Formation of dynamical system and phase portraits
		5.2.3 Wave solutions
	5.3 Bifurcation of dust-ion-acoustic waves with arbitrary amplitude
		5.3.1 Basic equations
		5.3.2 Formation of dynamical system and phase portraits
		5.3.3 Wave solutions
	5.4 Bifurcation of dust-acoustic waves with arbitrary amplitude
		5.4.1 Basic equations
		5.4.2 Formation of dynamical system and phase portraits
		5.4.3 Wave solutions
	5.5 Bifurcation of electron-acoustic waves with arbitrary amplitude
		5.5.1 Basic equations
		5.5.2 Formation of dynamical system and phase portraits
		5.5.3 Wave solutions
	References
6. Bifurcation Analysis of Supernonlinear Waves
	6.1 Introduction: supernonlinear waves
		6.1.1 Different kind of trajectories
	6.2 Bifurcation of supernonlinear ion-acoustic waves
		6.2.1 Basic equations
		6.2.2 Modified KdV equation
		6.2.3 Formation of dynamical system and phase portraits
		6.2.4 Wave solutions
	6.3 Bifurcation of supernonlinear dust-acoustic waves
		6.3.1 Basic equations
		6.3.2 Formation of dynamical system and phase portraits
		6.3.3 Wave solutions
	6.4 Bifurcation of supernonlinear electron-acoustic waves (EAWs)
		6.4.1 Basic equations
		6.4.2 The evolution equation and dynamical system
		6.4.3 Wave solutions
	References
7. Chaos, Multistability and Stable Oscillation in Plasmas
	7.1 Chaos in a conservative dusty plasma
		7.1.1 Basic equations
		7.1.2 Multiperiodic, quasiperiodic and chaotic oscillations
	7.2 Multistability of electron-acoustic waves
		7.2.1 Basic equations
		7.2.2 Multistability
	7.3 Stable oscillation in a dissipative plasma
		7.3.1 Model equations
		7.3.2 The KdV-Burgers equation
		7.3.3 Stability analysis of DAWs
	References
Index