High Temperature Plasmas E-Book

Karl-Heinz Spatschek

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 748

Veröffentlichungsjahr: 2012

Beschreibung

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.

Leseprobe

Contents

Cover

Half Title page

Title page

Copyright page

Preface

Chapter 1: Introduction

1.1 Quasineutrality and Debye Shielding

1.2 Degree of Ionization

1.3 Characteristic Parameters

1.4 Individual and Collective Effects

1.5 Fusion Processes

Chapter 2: Single Particle Motion

2.1 Heuristic Approaches to Guiding Center Motion

2.2 Systematic Averaging

2.3 Motion of a Single Particle (Electron) in an Electromagnetic Wave

2.4 Lagevin Approach

Chapter 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

Chapter 4: Kinetic Description of Nonequilibrium Plasmas

4.1 Historical Remarks on Well-Known Kinetic Equations

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

Chapter 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

5.3 General Outline and Models for Plasmas

5.4 MHD Model

5.5 Simple MHD Applications

Chapter 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

6.5 Simple Models in Stochastic Transport Theory

6.6 Basic Statistics for Magnetic Field Lines and Perpendicular Particle Diffusion

6.7 Phenomenology of Stochastic Particle Diffusion Theory in Perpendicular Direction

6.8 Stochastic Theory of the Parallel Test Particle Diffusion Coefficient

Chapter 7: Linear Waves and Instabilities

7.1 Waves and Instabilities in the Homogeneous Vlasov Description

7.2 Waves and Instabilities in Inhomogeneous Vlasov Systems

7.3 Waves and Instabilities in the Magnetohydrodynamic Description

Chapter 8: General Theory of Nonlinear Waves and Solitons

8.1 Historical Remarks

8.2 The Generalized KdV Equation for Ion-Acoustic Solitons

8.3 Envelope Solitons

8.4 Nonlinear Langmuir Waves

8.5 Longitudinal Stability of Generalized Langmuir Solitons

8.6 Transverse Instabilities

8.7 The Collapse Phenomenon and the Existence of Stable 3D Solitons

Chapter 9: Nonlinear Wave Aspects in Laser–Matter Interaction

9.1 History and Perspectives of Laser–Plasma Interaction

9.2 Time- and Space-Dependent Maxwell Fluid Models

9.3 Stationary Wave Solutions and Their Stability

9.4 Parametric Instabilities in the Relativistic Regime

9.5 Solitary Envelope Solutions and Their Stability

9.6 Wake Field Excitation

9.7 Breaking of Wake Fields

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 f Appearing in Hydromagnetic Variational Principles

References

Index

Karl-Heinz Spatschek

High Temperature Plasmas

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The Author

Prof. K.-H. SpatschekInstitut für Theoretische Physik IUniversität Dü[email protected]

Cover pictureTemperature distribution pattern on the divertor target plates of TEXTOR during DED operation, measured by an infrared camera. Photograph by Marcin Jakubowski

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Preface

High-temperature plasma physics is a rapidly growing field of physics. In the areas of magnetic confinement, laser-plasma interaction, and plasma astrophysics, the scientific progress is enormous. During the last decades, the record value of fusion power reached in magnetic confinement experiments has significantly increased (even faster than the memory capacity of semiconductor chips). Large tokamaks in USA, Europe, and Japan, came close to the energy break even point while operating without tritium. The international test reactor ITER, being built in Cadarache (France), should demonstrate within the next 15 years reactor capability of ignition, producing net power. A new area or laser-plasma interaction started approx. 40 years ago when laser fields became strong enough to directly ionize matter. Meanwhile, since the invention of the Chirped Pulse Amplification (CPA) technique (approx. 20 years ago), short pulse laser-matter interaction lead to an entirely new area of research, namely what is called relativistic optics. Intensities of more than 1019W/cm2 are now available in terawatt tabletop laser systems to study matter under extreme conditions. In the future, in the ultra-relativistic regime with socalled ultra-high intensities, short-pulse lasers may permit the test of nonlinear quantum-electrodynamics (QED). The development of modern ionospheric, magnetospheric and solar physics relies to a large extent on our understanding of plasma physics. Main topics of astrophysics, such as, star formation, emission of electromagnetic radiation from astronomical objects, theory of cosmic rays, and cosmological models, benefit to a large extent from plasma physics.

The present book concentrates on high-temperature plasma physics, with applications to fusion and laser plasmas and perspectives for plasma astrophysics. It discusses the fundamentals and provides mathematical tools for handling problems of high-temperature plasma theory. The transferability of ideas between the different and important areas is one of the peculiarities characterizing high-temperature plasma physics.Theoretical plasma physics is being taught in physics departments as graduate and advanced undergraduate courses following the theory courses on mechanics, electrodynamics, quantum theory, and statistical physics. The present book is laid out for the basic plasma physics contribution in a theoretical physics curriculum. Of course, it should be supplemented by other, more detailed presentations, such as, “Strongly coupled plasmas”, “Non-neutral plasmas”, “Low temperature plasmas”, “Plasma astrophysics”, “Fusion plasmas”, “Laser produced plasmas”, and so on.

There are two persons who indirectly influenced the choice of topics (fusion and laser plasmas) of this book and whom I want to thank (although they are not responsible for the presentation at all). The personal contacts with Radu Balescu (a statistical physicists who tremendously advanced the field of transport in magnetically confined plasmas; much to our regret he passed away June 1st, 2006) and Akira Hasegawa (who is one of the leading contributors to nonlinear plasma physics, and the “father of the optical soliton”) certainly influenced my scientific understanding and choice of research topics. I also want to thank the many students, collaborators, and colleagues with whom I had the privilege to work. Just to mention a few of them, lately I collaborated with Sadrilla Abdullaev, Wolfgang Laedke, Götz Lehmann, and Andreas Wingen; part of their work has been included into the present monograph. Unfortunately, I cannot refer to all the individuals who have contributed during the last years. The same is true for the huge amount of literature being available in the wide range of material being reviewed here. I only tried to reference to those papers and books which probably could lead readers to other related work. I apologize to those who were not adequately mentioned.

SI units are used throughout the text (unless otherwise so specified), following general recommendations of international societies and publishers. Theoreticians and plasma physicists very often prefer the Gaussian system. Therefore, a simple translation table is presented in Appendix A. In the majority of cases, temperatures are given in energy equivalents eV (as mostly done in high-temperature plasma physics). However, at some places, when the main emphasis is on the statistical methods, the Boltzmann constant is maintained and temperature is measured in Kelvin, as usually being done in statistical physics. I hope this ambiguity will satisfy both communities, and not lead to confusion. Finally, the transliteration of names, for example with Cyrillic letters, has not been standardized (see, for example, Lyapunov, Liapunov, or Ljapunov) to retain the custom in literature.

The technical help of my collaborators for many years, Elvira Gröters and Eckhard Zügge, is gratefully acknowledged. I would like to express my deepest gratitude to Wiley-VCH, in particular Christoph von Friedeburg, who initiated the project, and Ulrike Werner, who took on the role afterwards and became a judicious advisor. During the production process, the team of le-tex publishing services GmbH was extremely helpful in solving technical problems. The book never would have been completed in time without the unfailing encouragement and patience of my wife Tuta to whom I am most thankful.

Düsseldorf, August 2011

Karl-Heinz Spatschek