High Temperature Plasmas 2nd edition: Theory & Mathematical Tools for Laser & Fusion Plasmas

1 Introduction

• 1.1 Quasineutrality and Debye Shielding
• 1.2 Degree of Ionization
• 1.2.1 The Saha Equation
• 1.2.2 Thomson Cross Section and Rate Equation
• 1.2.3 The Corona Formula
• 1.3 Characteristic Parameters
• 1.3.1 Typical Parameters of (Magnetic) Fusion Plasmas
• 1.3.2 Parameters of the Sun
• 1.4 Individual and Collective Effects
• 1.4.1 The Plasma Frequency
• 1.4.2 General Remark on Individual Collisions
• 1.4.3 Collision Frequencies for Momentum and Energy Transfer
• 1.4.4 Friction Force in Thermal Plasmas
• 1.5 Fusion Processes
• 1.5.1 Fusion Processes in Burning Stars

2 Single Particle Motion

• 2.1 Heuristic Approaches to Guiding Center Motion
• 2.2 Systematic Averaging
• 2.2.1 Systematic Averaging over Fast Gyro-Motion
• 2.2.2 Pseudocanonical Transformations
• 2.2.3 Magnetic Moment as the First Adiabatic Invariant
• 2.2.4 On the Second Adiabatic Invariant
• 2.2.5 On the Third Adiabatic Invariant
• 2.2.6 Selected Applications
• 2.3 Motion of a Single Particle (Electron) in an ElectromagneticWave
• 2.4 Lagevin Approach

3 Plasma in Thermodynamic Equilibrium

• 3.1 Basic Approach
• 3.2 A Heuristic Derivation of the Modified Equation of State
• 3.3 The Holtsmark Distribution for Electric Microfields

4 Kinetic Description of Nonequilibrium Plasmas

• 4.1 Historical Remarks on Well-Known Kinetic Equations
• 4.1.1 The Fokker–Planck Equation
• 4.1.2 The Boltzmann Equation
• 4.1.3 The Boltzmann H-Theorem
• 4.1.4 The Boltzmann Entropy
• 4.1.5 Transition to Equilibrium and Maxwellian
• 4.2 BBGKY Hierarchy
• 4.3 Vlasov Equation and Landau Damping
• 4.4 Z-Function and Dispersive Properties of a Collisionless and Unmagnetized Plasma
• 4.5 Landau–Fokker–Planck Equation
• 4.6 Kinetic Description of Strongly Magnetized Plasmas
• 4.6.1 The Drift-Kinetic Equation
• 4.6.2 The Gyrokinetic Approach

5 Fluid Description

• 5.1 Moments and Hierarchy of Moment Equations
• 5.2 Truncation of the Corresponding Hierarchy in the Case of the Boltzmann Equation
• 5.2.1 Hierarchical Form of the First Moment Equations for the Boltzmann Equation
• 5.2.2 Truncation of the Hierarchy, Transport Coefficients, and the Euler Equation
• 5.2.3 Equation of State
• 5.2.4 Sound Wave Dispersion from the Euler Equations
• 5.2.5 Next Order Approximation and Navier–Stokes Equations
• 5.2.6 Simplified Solution with a Krook Collision Term
• 5.3 General Outline and Models for Plasmas
• 5.3.1 General Starting Point
• 5.3.2 Simple Two-Fluid Model in Unmagnetized Plasma
• 5.3.3 Drift Model
• 5.3.4 Braginskii Equations
• 5.4 MHD Model
• 5.4.1 MHD Ordering
• 5.5 Simple MHD Applications
• 5.5.1 Frozen-in Magnetic Field Lines
• 5.5.2 MHD Equilibria
• 5.5.3 Alfvén Waves
• 5.5.4 Energy Conservation in Ideal MHD

6 Principles of Linear and Stochastic Transport

• 6.1 Moments in Linear Transport Theory
• 6.2 The Hydrodynamic Regime in Linear Transport Theory
• 6.3 Summary of Linear Transport Coefficients
• 6.4 Nonlinear Transport Phenomenology
• 6.4.1 Fluctuation Spectra and Transport
• 6.5 Simple Models in Stochastic Transport Theory
• 6.5.1 Description of Stochastic (Magnetic) Fields
• 6.5.2 Symplectic Mappings
• 6.5.3 The Standard Map as a Simple Example for Stochastic Field Line Dynamics
• 6.5.4 Tokamap as a Twist Map with Polar Axis
• 6.6 Basic Statistics for Magnetic Field Lines and Perpendicular Particle Diffusion
• 6.6.1 Correlation Functions for Magnetic Field Fluctuations
• 6.6.2 Elementary Estimates of the Kolmogorov Length LK
• 6.7 Phenomenology of Stochastic Particle Diffusion Theory in Perpendicular Direction
• 6.7.1 Perpendicular Particle Diffusion
• 6.7.2 Test of the Diffusion Predictions with the Standard Map
• 6.7.3 Trapping and Percolation (K > 1)
• 6.8 Stochastic Theory of the Parallel Test Particle Diffusion Coefficient
• 6.8.1 Fundamental Relations for the Parallel Diffusion Coefficient
• 6.8.2 Pitch Angle Diffusion

7 Linear Waves and Instabilities

• 7.1 Waves and Instabilities in the Homogeneous Vlasov Description
• 7.1.1 The Penrose Criterion and Its Cognate Formulations
• 7.1.2 Dispersion in Homogeneous, Magnetized Vlasov Systems
• 7.1.3 Instabilities in Homogeneous Vlasov Systems
• 7.2 Waves and Instabilities in Inhomogeneous Vlasov Systems
• 7.2.1 Stationary Solutions and a Liapunov Stability Criterion
• 7.2.2 Instabilities in Inhomogeneous Vlasov Systems
• 7.3 Waves and Instabilities in the Magnetohydrodynamic Description
• 7.3.1 Hydromagnetic Variational Principle
• 7.3.2 Kink and Sausage Instability
• 7.3.3 Interchange Instability

8 General Theory of Nonlinear Waves and Solitons

• 8.1 Historical Remarks
• 8.1.1 The Water-Wave Paradigm
• 8.2 The Generalized KdV Equation for Ion-Acoustic Solitons
• 8.3 Envelope Solitons
• 8.3.1 Modulational Instability
• 8.3.2 Historical Remark on Envelope Water Solitons
• 8.3.3 Nonlinear Dispersion Relation and Schrödinger Equation
• 8.4 Nonlinear LangmuirWaves
• 8.5 Longitudinal Stability of Generalized Langmuir Solitons
• 8.6 Transverse Instabilities
• 8.6.1 Transverse Instabilities of KdV Solitons
• 8.6.2 Transverse Instability of Envelope Solitons (NLS)
• 8.7 The Collapse Phenomenon and the Existence of Stable 3D Solitons
• 8.7.1 The Collapse Phenomenon
• 8.7.2 Stable Three-Dimensional Envelope Solitons

9 Nonlinear Wave Aspects in Laser–Matter Interaction

• 9.1 History and Perspectives of Laser–Plasma Interaction
• 9.1.1 Areas of Relativistic Optics
• 9.2 Time- and Space-Dependent Maxwell Fluid Models
• 9.2.1 Fully Relativistic Maxwell Electron Fluid Model
• 9.2.2 Fully Relativistic Maxwell Two-Fluid Model
• 9.2.3 1D Propagation in Space-Direction x
• 9.2.4 The Weakly Relativistic Limit
• 9.2.5 The Weakly Relativistic 1D Maxwell Two-Fluid Model
• 9.2.6 The Nonrelativistic Limit
• 9.2.7 One-Field Models
• 9.3 StationaryWave Solutions and Their Stability
• 9.3.1 Fully Relativistic Maxwell Fluid Systems
• 9.3.2 Hamiltonian Formulation for Linearly Polarized Waves
• 9.3.3 Plasma Motion in Linearly PolarizedWaves
• 9.3.4 Influence of Mobile Ions on Stationary Wave Solutions
• 9.3.5 Electron–Positron Plasmas
• 9.3.6 Wave Solutions in Weakly Relativistic Two-Field Models
• 9.3.7 Instability of Stationary Wave Solutions
• 9.4 Parametric Instabilities in the Relativistic Regime
• 9.4.1 Stimulated Raman and Brillouin Scattering in the Classical Regime
• 9.4.2 Stimulated Scattering Instabilities in the Relativistic Regime
• 9.5 Solitary Envelope Solutions and Their Stability
• 9.5.1 The Farina–BulanovModel for Circularly Polarized Solitons
• 9.5.2 Linearly Polarized Solitons of the Maxwell Fluid System
• 9.5.3 Longitudinal Stability of Solitary Envelope Solutions
• 9.5.4 Solitary Envelope Solutions in Higher Dimensions
• 9.6 Wake Field Excitation
• 9.6.1 Excitation of QuasistationaryWake Fields
• 9.6.2 Strongly Relativistic Nonlinear Electrostatic Wake Fields
• 9.7 Breaking of Wake Fields
• 9.7.1 Classical, NonrelativisticWave-Breaking Analysis
• 9.7.2 Relativistic Wave-Breaking Analysis
• 9.7.3 Numerical Results for Wave-Breaking

Appendices

• Appendix A Units
• Appendix B Fourier and Laplace Transforms for Pedestrians
• Appendix C The Inverse Scattering Transform (IST) for Nonlinear Waves
• Appendix D Lie Transform Techniques for Eliminating Fast Variations
• Appendix E Choices of Low-Dimensional Basis Systems
• E.1 Galerkin Approximation
• E.2 Karhunen–Loève Expansion
• E.3 Determination of the Basis Functions in Practice
• Appendix F Center Manifold Theory
• Appendix G Newell–Whitehead Procedure
• Appendix H Liapunov Stability
• Appendix I Variational Principles
• Appendix J Self-Adjointness of the Operator

Appearing in Hydromagnetic Variational Principles

References

Index

 

Filling the gap for a treatment of the subject as an advanced course in theoretical physics with a huge potential for future applications, this monograph discusses aspects of these applications and provides theoretical methods and tools for their investigation. Throughout this coherent and up-to-date work the main emphasis is on classical plasmas at high-temperatures, drawing on the experienced author's specialist background. As such, it covers the key areas of magnetic fusion plasma, laser-plasma-interaction and astrophysical plasmas, while also including nonlinear waves and phenomena.

For master and PhD students as well as researchers interested in the theoretical foundations of plasma models.

About the Author

• Karl-Heinz Spatschek is professor at the University of Düsseldorf, Germany. After obtaining his PhD from University of Bochum, his research visits included stays at the University of Kyoto (Japan), Oxford (UK) and Maryland (USA). He has been playing a key role in research projects funded by the German Research Foundation. His research concentrates on high temperature plasma physics, nonlinear dynamics and waves, and laser plasma interaction.

Book Details

• Hardcover: 642 pages
• Publisher: Wiley-VCH; 2 edition (January 18, 2012)
• Language: English
• ISBN-10: 3527410414
• ISBN-13: 978-3527410415
• Product Dimensions: 9.4 x 6.7 x 1.3 inches

List Price: $165.00 

 

Tags: Mathematics, Physics, Wiley