Cambridge University Press
0521364833 - Introduction to Plasma Physics - With Space and Laboratory Applications - by D. A. Gurnett and A. Bhattacharjee
Frontmatter/Prelims

INTRODUCTION TO PLASMA PHYSICS

With Space and Laboratory Applications

The emphasis of this text is on basic plasma theory, with applications to both space and laboratory plasmas. All mathematical concepts beyond those normally covered in an advanced calculus course are fully explained.

Topics covered include single particle motions, kinetic theory, magnetohydrodynamics, small amplitude waves in both cold and hot plasmas, non-linear phenomena and collisional effects. Applications include planetary magnetospheres and radiation belts, the confinement and stability of plasmas in fusion devices, the propagation of discontinuities and shock waves in the solar wind, and the analysis of various types of plasma waves and instabilities that can occur in planetary magnetospheres and laboratory plasma devices. This book is structured as a text for a one- or two-semester introductory course in plasma physics at the advanced undergraduate or first-year graduate level. It can also serve as a resource book on the basic principles of plasma physics.

DON GURNETT is a pioneer in the study of waves in space plasmas, and has been the author or co-author of over 470 papers in the field of space plasma physics. He is currently a Carver/James A. Van Allen Professor of Physics at the University of Iowa and has received numerous awards for both his teaching and research. In 1994 he received the Iowa Board of Regents Award for Faculty Excellence, and in 1998 was elected a member of the National Academy of Sciences.

AMITAVA BHATTACHARJEE is a leading theoretical plasma physicist and has published over 170 papers on a wide range of subjects spanning fusion, space, and astrophysical plasma physics. He is currently Paul Professor of Space Science at the Institute for the Study of Earth, Oceans, and Space and the Department of Physics at the University of New Hampshire. He is a Fellow of the American Physical Society and the American Association for the Advancement of Science.

INTRODUCTION TO PLASMA PHYSICS

With Space and Laboratory Applications

D. A. GURNETT and A. BHATTACHARJEE

Department of Physics and Astronomy
The University of Iowa

PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE
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CAMBRIDGE UNIVERSITY PRESS
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This book is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.

First published 2005

Printed in the United Kingdom at the University Press, Cambridge

Typeface Times 11/14 pt. System LATEX 2_e [TB]

A catalogue record for this book is available from the British Library

Library of Congress Cataloguing in Publication data

Gurnett, Donald A.
Introduction to plasma physics : with space and laboratory applications / D.A. Gurnett
and A. Bhattacharjee.
p.   cm.
Includes bibliographical references and index.
ISBN 0 521 36483 3 – ISBN 0 521 36730 1 (paperback)
1. Plasma (Ionized gases). 2. Space plasmas. I. Bhattacharjee, A. (Amitava), 1955. II. Title.
QC718.G87     2004
530.4′4 – dc22         2003069745

ISBN 0 521 36483 3 hardback
ISBN 0 521 36730 1 paperback

	Preface	page ix
1	Introduction	1
2	Characteristic parameters of a plasma	5
	2.1 Number density and temperature	5
	2.2 Debye length	7
	2.3 Plasma frequency	10
	2.4 Cyclotron frequency	12
	2.5 Collision frequency	13
	2.6 Number of electrons per Debye cube	15
	2.7 The de Broglie wavelength and quantum effects	17
	2.8 Representative plasma parameters	18
3	Single particle motions	23
	3.1 Motion in a static uniform magnetic field	23
	3.2 Motion in perpendicular electric and magnetic fields	26
	3.3 Gradient and curvature drifts	32
	3.4 Motion in a magnetic mirror field	39
	3.5 Motion in a time varying magnetic field	45
	3.6 Adiabatic invariants	48
	3.7 The Hamiltonian method	60
	3.8 Chaotic orbits	68
4	Waves in a cold plasma	75
	4.1 Fourier representation of waves	75
	4.2 General form of the dispersion relation	84
	4.3 Waves in a cold uniform unmagnetized plasma	87
	4.4 Waves in a cold uniform magnetized plasma	94
	4.5 Ray paths in inhomogeneous plasmas	127
5	Kinetic theory and the moment equations	137
	5.1 The distribution function	137
	5.2 The Boltzmann and Vlasov equations	140
	5.3 Solutions based on constants of the motion	144
	5.4 The moment equations	146
	5.5 Electron and ion pressure waves	155
	5.6 Collisional drag force	162
	5.7 Ambipolar diffusion	166
6	Magnetohydrodynamics	175
	6.1 The basic equations of MHD	175
	6.2 Magnetic pressure	183
	6.3 Magnetic field convection and diffusion	185
	6.4 The energy equation	192
	6.5 Magnetohydrodynamic waves	195
	6.6 Static MHD equilibrium	204
	6.7 MHD stability	219
	6.8 Magnetic reconnection	240
7	Discontinuities and shock waves	251
	7.1 The MHD jump conditions	252
	7.2 Classification of discontinuities	255
	7.3 Shock waves	258
8	Electrostatic waves in a hot unmagnetized plasma	281
	8.1 The Vlasov approach	281
	8.2 The Landau approach	290
	8.3 The plasma dispersion function	308
	8.4 The dispersion relation for a multi-component plasma	311
	8.5 Stability	318
9	Waves in a hot magnetized plasma	341
	9.1 Linearization of the Vlasov equation	342
	9.2 Electrostatic waves	345
	9.3 Electromagnetic waves	367
10	Non-linear effects	391
	10.1 Quasi-linear theory	391
	10.2 Stationary non-linear electrostatic potentials	406
11	Collisional processes	415
	11.1 Binary Coulomb collisions	416
	11.2 Importance of small-angle collisions	417
	11.3 The Fokker–Planck equation	420
	11.4 Conductivity of a fully ionized plasma	427
	11.5 Collision operator for Maxwellian distributions of electrons and ions	431
	Appendix A Symbols	435
	Appendix B Vector differential operators	441
	Appendix C Vector calculus identities	443
	Index	445

Preface

This textbook is intended for a full year introductory course in plasma physics at the senior undergraduate or first-year graduate level. It is based on lecture notes from courses taught by the authors for more than three decades in the Department of Physics and Astronomy at the University of Iowa and the Department of Applied Physics at Columbia University. During these years, plasma physics has grown increasingly interdisciplinary, and there is a growing realization that diverse applications in laboratory, space, and astrophysical plasmas can be viewed from a common perspective. Since the students who take a course in plasma physics often have a wide range of interests, typically involving some combination of laboratory, space, and astrophysical plasmas, a special effort has been made to discuss applications from these areas of research. The emphasis of the book is on physical principles, less so on mathematical sophistication. An effort has been made to show all relevant steps in the derivations, and to match the level of presentation to the knowledge of students at the advanced undergraduate and early graduate level. The main requirements for students taking this course are that they have taken an advanced undergraduate course in electricity and magnetism and that they are knowledgeable about using the basic principles of vector calculus, i.e., gradient, divergence and curl, and the various identities involving these vector operators. Although extensive use is made of complex variables, no special background is required in this subject beyond what is covered in an advanced calculus course. Relatively advanced mathematical concepts that are not typically covered in an undergraduate sequence, such as Fourier transforms, Laplace transforms, the Cauchy integral theorem, and the residue theorem, are discussed in sufficient detail that no additional preparation is required. Although this approach has undoubtedly added to the length of the book, we believe that the material covered provides an effective and self-contained textbook for teaching plasma physics. MKS units are used throughout.

For the preparation of this text we would especially like to thank Kathy Kurth who did the typing and steadfastly stuck with us through the many revisions and additions that occurred over the years. We would also like to thank Joyce Chrisinger and Ann Persoon for their outstanding work preparing the illustrations and proofreading, and Dr. C.-S. Ng and Dr. Z. Ma for checking the accuracy of the equations. Don Gurnett would like to acknowledge the salary support provided by the Carver Foundation during the preparation of this manuscript, and Amitava Bhattacharjee would like to acknowledge the generous support of the Faculty Scholar Program at the University of Iowa and the Peter Paul Chair at the University of New Hampshire.