Introduction to Plasma Physics and Controlled Fusion

Transcription

1 Introduction to Plasma Physics and Controlled Fusion

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3 Francis F. Chen Introduction to Plasma Physics and Controlled Fusion Third Edition

4 Francis F. Chen Electrical Engineering University of California at Los Angeles Los Angeles, CA, USA ISBN ISBN (ebook) DOI / Library of Congress Control Number: Springer Cham Heidelberg New York Dordrecht London Springer International Publishing Switzerland 2016, corrected publication 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (

5 Preface It has been 30 years since the Second Edition. Plasma physics has grown so much that the temptation is to include all that s new, but I haven t done that. This is a book for those learning plasma physics for the first time and could care less about the fine points. The basics remain the same, but new areas have arisen: dusty plasmas and plasma accelerators, for instance, and these subjects had to be added. The semiconductor industry has sprouted since the 1980s, affecting all our lives. Computer chips cannot be made without plasmas, but these are partially ionized, radiofrequency ones, which are new. I ve spent 25 years helping to make these industrial plasmas into an interesting subject, one that was previously avoided because it was too messy. Meanwhile, Al Gore has warned us about global warming. The best solution to this, and to energy shortage, is of course hydrogen fusion. With the ITER (International Thermonuclear Experimental Reactor) project going swimmingly in southern France, we are on schedule to get a fusion reactor by In laser fusion, the NIF (National Ignition Facility) at Livermore can focus the entire energy output of the United States onto a pinpoint for a fraction of a nanosecond to get inertial fusion. It is a technical achievement without peer, but so far we don t have a laser that can pulse rapidly enough. Fusion plasma physics was planned to be Vol. 2 of this textbook; and, in answer to so many questions, it is still in future plans. The job will be easier now that I have written An Indispensable Truth, How Fusion Power Can Save the Planet, which includes a chapter on fusion physics. On the personal side, you will remember from the second edition that the poet (my father, who used to recite Chinese poetry from memory) had passed away, and that the eternal scholar (my mother) had finally gotten her Ph.D. at 72. She lived to 99 and died with a smile on her face. I myself am now 85, happily married for 49 years to artist Ande (Edna backwards), and we have two daughters and a son: Sheryl, a Cistercian nun in Norway; Patricia, a dancer and English teacher in France; and Bob, a chemical oceanography professor and education expert at UMass Boston, as well as an active soccer coach. We have four granddaughters, v

6 vi Preface the three Boston ones being third-generation soccer players, and the French one a four-language linguist and former equestrian. Finally, I would like to thank all the instructors and students who have used the second edition and have pointed out errors and made suggestions for improvement. Los Angeles, CA 2015 Francis F. Chen

7 Contents 1 Introduction Occurrence of Plasmas in Nature Definition of Plasma Concept of Temperature Debye Shielding The Plasma Parameter Criteria for Plasmas Applications of Plasma Physics Gas Discharges (Gaseous Electronics) Controlled Thermonuclear Fusion Space Physics Modern Astrophysics MHD Energy Conversion and Ion Propulsion Solid State Plasmas Gas Lasers Particle Accelerators Industrial Plasmas Atmospheric Plasmas Single-Particle Motions Introduction Uniform E and B Fields E ¼ Finite E Gravitational Field Nonuniform B Field B B: Grad-B Drift Curved B: Curvature Drift BjjB: Magnetic Mirrors vii

8 viii Contents 2.4 Nonuniform E Field Time-Varying E Field Time-Varying B Field Summary of Guiding Center Drifts Adiabatic Invariants The First Adiabatic Invariant, μ The Second Adiabatic Invariant, J The Third Adiabatic Invariant, Ф Plasmas as Fluids Introduction Relation of Plasma Physics to Ordinary Electromagnetics Maxwell s Equations Classical Treatment of Magnetic Materials Classical Treatment of Dielectrics The Dielectric Constant of a Plasma The Fluid Equation of Motion The Convective Derivative The Stress Tensor Collisions Comparison with Ordinary Hydrodynamics Equation of Continuity Equation of State The Complete Set of Fluid Equations Fluid Drifts Perpendicular to B Fluid Drifts Parallel to B The Plasma Approximation Waves in Plasmas Representation of Waves Group Velocity Plasma Oscillations Electron Plasma Waves Sound Waves Ion Waves Validity of the Plasma Approximation Comparison of Ion and Electron Waves Electrostatic Electron Oscillations Perpendicular to B Electrostatic Ion Waves Perpendicular to B The Lower Hybrid Frequency Electromagnetic Waves with B 0 ¼ Experimental Applications Electromagnetic Waves Perpendicular to B Ordinary Wave, E 1 B Extraordinary Wave, E 1 B

9 Contents ix 4.15 Cutoffs and Resonances Electromagnetic Waves Parallel to B Experimental Consequences The Whistler Mode Faraday Rotation Hydromagnetic Waves Magnetosonic Waves Summary of Elementary Plasma Waves The CMA Diagram Diffusion and Resistivity Diffusion and Mobility in Weakly Ionized Gases Collision Parameters Diffusion Parameters Decay of a Plasma by Diffusion Ambipolar Diffusion Diffusion in a Slab Diffusion in a Cylinder Steady State Solutions Constant Ionization Function Plane Source Line Source Recombination Diffusion Across a Magnetic Field Ambipolar Diffusion Across B Experimental Checks Collisions in Fully Ionized Plasmas Plasma Resistivity Mechanics of Coulomb Collisions Physical Meaning of η Numerical Values of η Pulsed Currents The Single-Fluid MHD Equations Diffusion of Fully Ionized Plasmas Solutions of the Diffusion Equation Time Dependence Time-Independent Solutions Bohm Diffusion and Neoclassical Diffusion Equilibrium and Stability Introduction Hydromagnetic Equilibrium The Concept of β

10 x Contents 6.4 Diffusion of Magnetic Field into a Plasma Classification of Instabilities Streaming instabilities Rayleigh Taylor instabilities Universal instabilities Kinetic instabilities Two-Stream Instability The Gravitational Instability Resistive Drift Waves The Weibel Instability Kinetic Theory The Meaning of f(v) Equations of Kinetic Theory Derivation of the Fluid Equations Plasma Oscillations and Landau Damping The Meaning of Landau Damping The Kinetic Energy of a Beam of Electrons The Effect of Initial Conditions A Physical Derivation of Landau Damping The Resonant Particles Two Paradoxes Resolved BGK and Van Kampen Modes Experimental Verification Ion Landau Damping The Plasma Dispersion Function Ion Waves and Their Damping Kinetic Effects in a Magnetic Field The Hot Plasma Dielectric Tensor Cyclotron Damping Bernstein Waves Nonlinear Effects Introduction Sheaths The Necessity for Sheaths The Planar Sheath Equation The Bohm Sheath Criterion The Child Langmuir Law Electrostatic Probes Ion Acoustic Shock Waves The Sagdeev Potential The Critical Mach Numbers

11 Contents xi Wave Steepening Experimental Observations Double Layers The Ponderomotive Force Parametric Instabilities Coupled Oscillators Frequency Matching Instability Threshold Physical Mechanism The Oscillating Two-Stream Instability The Parametric Decay Instability Plasma Echoes Nonlinear Landau Damping Equations of Nonlinear Plasma Physics The Korteweg de Vries Equation The Nonlinear Schr odinger Equation Reconnection Turbulence Sheath Boundaries Special Plasmas Non-Neutral Plasmas Pure Electron Plasmas Experiments Solid, Ultra-Cold Plasmas Pair-ion Plasmas Dusty Plasmas Dust Acoustic Waves Dust Ion-acoustic Waves Helicon Plasmas Plasmas in Space Atmospheric-Pressure Plasmas Dielectric Barrier Discharges RF Pencil Discharges Plasma Applications Introduction Fusion Energy Magnetic Fusion Plasma Accelerators Free-Electron Lasers Inertial Fusion Glass Lasers KrF Lasers

12 xii Contents 10.5 Semiconductor Etching Spacecraft Propulsion General Principles Types of Thrusters Plasmas in Everyday Life Erratum to: Introduction to Plasma Physics and Controlled Fusion... E1 Appendix A: Units, Constants and Formulas, Vector Relations Appendix B: Theory of Waves in a Cold Uniform Plasma Appendix C: Sample Three-Hour Final Exam Appendix D: Answers to Some Problems Index The original version of this book was revised. An erratum to this book can be found at org/ / _11