Waves And Wave Interactions In Plasmas

"This book is written in a lucid and systematic way for advanced postgraduates and researchers studying applied mathematics, plasma physics, nonlinear differential equations, nonlinear optics, and other engineering branches where nonlinear wave phenomena is essential. In sequential order of the book's development, readers will understand basic plasmas with elementary definitions of magnetized and unmagnetized plasmas, plasma modeling, dusty plasma and quantum plasma. Following which, the book describes linear and nonlinear waves, solitons, shocks and other wave phenomena, while solutions to common nonlinear wave equations are derived via standard techniques. Readers are introduced to elementary perturbation and non-perturbation methods. They will discover several evolution equations in different plasma situations as well as the properties of solitons in those environments. Pertaining to those equations, readers will learn about their higher order corrections, as well as their different forms and solutions in non-planar geometry. The book offers further studies on different types of collisions between solitons in plasma environment, phenomena of soliton turbulence as a consequence of multi-soliton interactions, properties of large amplitude solitary waves which are discovered via non-perturbative Sagdeev's Pseudopotential Approach, as well as the speed and shape of solitons. Finally, the book reveals possible future developments of research in this rich field"-- Provided by publisher Contents Preface Acknowledgments Chapter 1. Introduction to Plasmas 1.1 Introduction 1.2 Saha Equation and Plasma Temperature 1.3 Basic Concepts of Plasma 1.3.1 Basic dimensionless parameters 1.3.2 Debye length and Debye shielding 1.3.3 Quasineutrality 1.3.4 Response time 1.3.5 Plasma frequency 1.3.6 Collisions and coupling limit 1.4 Criteria for Plasma 1.5 High-Temperature Plasmas 1.6 Mathematical Description 1.7 Magnetized Plasmas 1.8 Single Particle Motion in Uniform Electric and Magnetic Field 1.9 Fluid Approach 1.10 Maxwell’s Equations 1.11 Electromagnetic Wave Equation in Free Space 1.12 Plasma Kinetic Theory 1.12.1 Distribution function 1.12.2 Macroscopic variables 1.12.3 Maxwellian distribution function 1.12.4 Non-Maxwellian distribution in plasmas 1.12.5 Nonthermal distribution 1.12.6 Superthermal distribution 1.12.7 q-nonextensive distribution 1.13 Closure Form of Moment Equation 1.13.1 Equation of continuity 1.13.2 Equation of motion 1.13.3 Equation of energy 1.14 Dusty Plasma 1.15 Quantum Plasma 1.16 Quantum Plasma Models References Chapter 2. Introduction to Waves in Plasma 2.1 Introduction 2.2 Mathematical Description of Waves 2.3 Dispersion Relation 2.4 Linear Waves in Plasmas 2.5 Plasma Oscillation 2.6 Electromagnetic Waves 2.7 Upper Hybrid Frequency 2.8 Electrostatic Ion Cyclotron Waves 2.9 Lower Hybrid Frequency 2.10 Electromagnetic Waves with B0 = 0 2.11 Electromagnetic Waves Perpendicular to B0 2.11.1 Ordinary wave 2.11.2 Extraordinary wave 2.12 Electromagnetic Waves Parallel to B0 2.13 Hydromagnetic Waves 2.13.1 Alfven wave 2.13.2 Magnetosonic wave 2.14 Some Acoustic Type of Waves in Plasmas 2.14.1 Electron plasma waves 2.14.2 Ion acoustic waves 2.14.3 Dust acoustic waves 2.14.4 Dust ion acoustic waves 2.15 Nonlinear Wave 2.16 Solitary Waves and Solitons 2.16.1 History of solitary waves and solitons 2.17 Properties of Solitons References Chapter 3. Solution of Nonlinear Wave Equations 3.1 Nonlinear Waves 3.2 Direct Method 3.2.1 Korteweg–de Vries (KdV) equation 3.2.2 Cnoidal waves 3.2.3 Modified KdV (MKdV) equation 3.2.4 Schamel-type KdV (S-KdV) equation 3.2.5 Burgers’ equation 3.2.6 KP equation 3.2.7 Modified KP equation 3.3 Hyperbolic Tangent Method 3.3.1 KdV equation 3.3.2 Modified KdV equation 3.3.3 Burgers’ equation 3.3.4 KdV Burgers’ equation 3.3.5 KP equation 3.4 Tanh–Coth Method 3.4.1 KdV equation 3.4.2 Burgers’ equation 3.5 Solution of KP Burger Equation 3.6 Conservation Laws and Integrals of the Motions 3.6.1 Conserved quantity of KdV equation 3.7 Approximate Analytical Solutions 3.7.1 Damped KdV equation 3.7.2 Force KdV equation 3.7.3 Damped-force KdV equation 3.8 Multisoliton and Hirota’s Direct Method 3.8.1 Hirota’s method 3.8.2 Multisoliton solution of the KdV equation 3.8.3 Multisoliton solution of the KP equation References Chapter 4. RPT and Some Evolution Equations 4.1 Perturbation Technique 4.2 Reductive Perturbation Technique 4.3 Korteweg–de Vries (KdV) Equation 4.4 Modified KdV (MKdV) Equation 4.5 Gardner’s Equation 4.6 Gardner and Modified Gardner’s (MG) Equation 4.7 Damped Forced KdV (DFKdV) Equation 4.8 Damped Forced MKdV (DFMKdV) Equation 4.9 Forced Schamel KdV (SKdV) Equation 4.10 Burgers’ Equation 4.11 Modified Burgers’ Equation 4.12 KdV Burgers’ (KdVB) Equation 4.13 Damped KdVB Equation 4.14 Kadomtsev–Petviashvili (KP) Equation 4.15 Modified KP (MKP) Equation 4.16 Further MKP (FMKP) Equation 4.17 KP Burgers’ (KPB) Equation 4.18 Damped KP (DKP) Equation 4.19 Zakharov–Kuznetsov (ZK) Equation 4.20 ZK Burgers’ (ZKB) Equation 4.21 Damped ZK (DZK) Equation References Chapter 5. Dressed Soliton and Envelope Soliton 5.1 Dressed Soliton 5.2 Dressed Soliton in a Classical Plasma 5.3 Dressed Soliton in a Dusty Plasma 5.4 Dressed Soliton in Quantum Plasma 5.5 Dressed Soliton of ZK Equation 5.6 Envelope Soliton 5.7 Nonlinear Schrodinger Equation (NLSE) References Chapter 6. Evolution Equations in Nonplanar Geometry 6.1 Introduction 6.2 Basic Equations of Motion in Nonplanar Geometry 6.3 Nonplanar KdV Equation in Classical Plasma 6.4 Nonplanar KdV Equation in Quantum Plasma 6.5 Nonplanar Gardner’s or Modified Gardner’s Equation 6.6 Nonplanar KP and KP Burgers’ Equation 6.7 Nonplanar ZK Equation 6.8 Nonplanar ZKB Equation References Chapter 7. Collision of Solitons 7.1 Introduction 7.2 Head-on Collision 7.2.1 Head-on collision of solitary waves in planar geometry 7.2.2 Head-on collision of solitons in a Magnetized Quantum Plasma 7.2.3 Head-on collision of magneto-acoustic solitons in spin-1/2 fermionic quantum plasma 7.2.4 Interaction of DIASWs in nonplanar geometry 7.3 Oblique Collision 7.3.1 Oblique collision of DIASWs in quantum plasmas 7.4 Overtaking Collision 7.4.1 Overtaking interaction of two solitons and three solitons of EAWs in quantum plasma 7.5 Soliton Interaction and Soliton Turbulence 7.6 Statistical Characteristics of the Wavefield 7.7 Plasma Parameters on Soliton Turbulence References Chapter 8. Sagdeev’s Pseudopotential Approach 8.1 Nonperturbative Approach 8.2 Sagdeev’s Pseudopotential Approach 8.2.1 Physical interpretation of Sagdeev’s potential 8.2.2 Determination of the range of Mach number 8.2.3 Shape of the solitary waves 8.2.4 Physical interpretation of double layers 8.2.5 Small amplitude approximation 8.3 Effect of Finite Ion Temperature 8.4 Large-amplitude DASWs 8.5 Large-amplitude Double Layers 8.6 Effect of Ion Kinematic Viscosity 8.7 DIASWs in Magnetized Plasma 8.8 Solitary Kinetic Alfven Waves 8.9 Collapse of EA Solitary Waves 8.10 Collapse of DASWs in Presence of Trapped Ions References Chapter 9. Conclusion and Future Scopes Index Waves are essential phenomena in most scientific and engineering disciplines, such as electromagnetism and optics, and different mechanics including fluid, solid, structural, quantum, etc. They appear in linear and nonlinear systems. Some can be observed directly and others are not. The features of the waves are usually described by solutions to either linear or nonlinear partial differential equations, which are fundamental to the students and researchers. Generic equations, describing wave and pulse propagation in linear and nonlinear systems, are introduced and analyzed as initial/boundary value problems. These systems cover the general properties of non-dispersive and dispersive, uniform and non-uniform, with/without dissipations. Methods of analyses are introduced and illustrated with analytical solutions. Wave-wave and wave-particle interactions ascribed to the nonlinearity of media (such as plasma) are discussed in the final chapter. This interdisciplinary textbook is essential reading for anyone in above mentioned disciplines. It was prepared to provide students with an understanding of waves and methods of solving wave propagation problems. The presentation is self-contained and should be read without difficulty by those who have adequate preparation in classic mechanics. The selection of topics and the focus given to each provide essential materials for a lecturer to cover the bases in a linear/nonlinear wave course "The beauty of the theoretical science is that quite different physical, biological, etc. phenomena can often be described as similar mathematical objects, by similar differential (or other) equations. In the 20th century, the notion of 'theory of oscillations' and later 'theory of waves' as unifying concepts, meaning the application of similar methods and equations to quite different physical problems, came into being. In the variety of applications (quite possibly in most of them), the oscillatory process is characterized by a slow (as compared with the characteristic period) variation of its parameters, such as the amplitude and frequency. The same is true for the wave processes. This book describes a variety of problems associated with oscillations and waves with slowly varying parameters. Among them the nonlinear and parametric resonances, self-synchronization, attenuated and amplified solitons, self-focusing and self-modulation, and reaction-diffusion systems. For oscillators, the physical examples include the van der Pol oscillator and a pendulum, models of a laser. For waves, examples are taken from oceanography, nonlinear optics, acoustics, and biophysics. The last chapter of the book describes more formal asymptotic perturbation schemes for the classes of oscillators and waves considered in all preceding chapters."-- Provided by publisher The interaction of electromagnetic waves with matter has always been a fascinating subject of study. As matter in the universe is mostly in the plasma state, the study of electromagnetic waves in plasmas is of importance to astrophysics, space physics and ionospheric physics. The physics of electromagnetic wave interacting with electron beams and plasmas also serves as a basis for coherent radiation generation such as free electron laser and gyrotron and advanced accelerators. This monograph aims at reviewing the physical processes of linear and nonlinear collective interactions of electromagnetic waves with electron beams and unmagnetized plasmas. Ch. I. General properties of electromagnetic waves in dielectric media -- ch. II. Linear waves and instabilities in uniform unmagnetized plasmas -- ch. III. Linear waves and instabilities in uniform magnetized plasmas -- ch. IV. Linear waves and instabilities in nonuniform plasmas -- ch. V. Topics in nonlinear plasma theory The topics covered in these notes are selective and tend to emphasize more on kinetic-theory approaches to waves and instabilities in both uniform and non-uniform plasmas, students are assumed to have some basic knowledge of plasma dynamics in terms of single-particle and fluid descriptions.