Advanced Space Plasma Physics

Advanced Space Plasma Physics Rudolf A. Treumann & Wolfgang Baumjohann Max-Planck-Institut fur¨ extraterrestrische Physik, Garching and Osterreichische¨ Akademie der Wissenschaften Institut fur¨ Weltraumforschung, Graz Revised Edition, Imperial College Press, London, 2001 Preface This book is the second volume of our introductory text on Space Plasma Physics. The first volume is published under the title Basic Space Plasma Physics and covers the more fundamental aspects, i.e., single particle dynamics, fluid equilibria, and waves in space plasmas. This second volume extends the material to the more advanced fields of plasma instabilities and nonlinear effects. Actually, there are already a number of monographs, where the general nonlinear plasma methods are described in considerable detail. But many of these books are quite specialized. The present book selects those methods, which are applied in space plasma physics, and, on the expense of detailedness, tries to make them accessible to the more practically oriented student and researcher by putting the new achievements and methods into the context of general space physics. The first part of the book is concerned with the evolution of linear instabilities in plasmas. Instabilities have turned out to be the most interesting and important phenomena in physics. They arise when free energy has accumulated in a system which the system wants to get rid of. In plasma physics there is a multitude of reasons for the excitation of instabilities. Inhomogeneities may evolve both in real space and in veloc- ity space. These inhomogeneities lead to the generation of instabilities as a first linear and straightforward reaction of the plasma to such deviations from thermal equilibrium. The first chapters cover a representative selection of the many possible macro- and mi- croinstabilities in space plasmas, from the Rayleigh-Taylor and Kelvin-Helmholtz to electrostatic and electromagnetic kinetic instabilities. Their quasilinear stabilization and nonlinear evolution and their application to space physics problems is treated. As a natural extension of the linear evolution, nonlinear effects do inevitably evolve in an unstable plasma, simply because an instability cannot persist forever but will exhaust the available free energy. Therefore all instabilities are followed by nonlinear evolution. The second part of the book, the chapters on nonlinear effects, can only give an overview about the vast field of nonlinearities. These chapters include the nonlinear evolution of single waves, weak turbulence, and strong turbulence, all presented from the view-point of their relevance for space plasma physics. Special topics include soliton formation, caviton collapse, anomalous transport, auroral particle acceleration, and elements of the theory of collisionless shocks. v vi PREFACE Linear theory occupies about half of the book. The second half reviews nonlinear theory as systematically as possible, given the restricted space. The last chapter presents a number of applications. The reader may find our selection a bit unsystematic, but we have chosen to select only those which, in our opinion, demonstrate the currently more important aspects of space physics. There are many other small effects which need to be treated using nonlinear theory, but have been neglected here, since we did not find them fundamental enough to be included in a textbook like the present one. Nevertheless, we hope that the reader will find the book useful as a guide to unstable and nonlinear space plasma physics, giving him a taste of the complexity of the problems. Since space plasma physics has in the past served as a reservoir of ideas and tools also for astrophysics, the present volume will certainly be useful for the needs of a course in non-relativistic plasma astrophysics and for scientists working in this field. With a slight extension to the parameter ranges of astrophysical objects most of the instabilities and nonlinear effects do also apply to astrophysics, as long as high-energy effects and relativistic temperatures are not important. It is a pleasure to thank Rosmarie Mayr-Ihbe for turning our often rough sketches into the figures contained in this book and Thomas Bauer, Anja Czaykowska, Thomas Leutschacher, Reiner Lottermoser, and especially Joachim Vogt for carefully reading the manuscript. We gratefully acknowledge the continuous support of Gerhard Haeren- del, Gregor Morfill and Heinrich Soffel. Last not least, we would like to mention that we have profited from many books and reviews on plasma and space physics. References to most of them have been included into the suggestions for further reading at the end of each chapter. These suggestions, however, do not include the large number of original papers, which we made use of and are indebted to. We have made every effort to make the text error-free in this revised edition; unfor- tunately this is a never ending task. We hope that the readers will kindly inform us about misprints and errors, preferentially by electronic mail to [email protected]. Contents Preface v Contents vii 1. Introduction 1 1.1. Plasma Properties . 1 1.2. Particle Motions . 3 1.3. Basic Kinetic Equations . 5 1.4. Plasma Waves . 7 2. Concept of Instability 11 2.1. Linear Instability . 12 2.2. Electron Stream Modes . 16 2.3. Buneman-Instability . 22 2.4. Ion Beam Instability . 27 3. Macroinstabilities 31 3.1. Rayleigh-Taylor Instability . 31 3.2. Farley-Buneman Instability . 41 3.3. Kelvin-Helmholtz Instability . 43 3.4. Firehose Instability . 51 3.5. Mirror Instability . 55 3.6. Flux Tube Instabilities . 60 4. Electrostatic Instabilities 69 4.1. Gentle Beam Instability . 70 4.2. Ion-Acoustic Instabilities . 75 4.3. Electron-Acoustic Instability . 82 4.4. Current-Driven Cyclotron Modes . 84 4.5. Loss Cone Instabilities . 90 4.6. Electrostatic Cyclotron Waves . 98 vii viii CONTENTS 5. Electromagnetic Instabilities 103 5.1. Weibel Instability . 103 5.2. Anisotropy-Driven Instabilities . 105 5.3. Ion Beam Instabilities . 114 5.4. Upstream Ion Beam Modes . 118 5.5. Maser Instability . 120 6. Drift Instabilities 129 6.1. Drift Waves . 129 6.2. Kinetic Drift Wave Theory . 133 6.3. Drift Modes . 136 7. Reconnection 143 7.1. Reconnection Rates . 144 7.2. Steady Collisionless Reconnection . 150 7.3. Resistive Tearing Mode . 155 7.4. Collisionless Tearing Mode . 160 7.5. Percolation . 168 8. Wave-Particle Interaction 175 8.1. Trapping in Single Waves . 176 8.2. Exact Nonlinear Waves . 181 8.3. Weak Particle Turbulence . 184 8.4. Resonance Broadening . 199 8.5. Pitch Angle Diffusion . 203 8.6. Weak Macro-Turbulence . 211 9. Weak Wave Turbulence 219 9.1. Coherent Wave Turbulence . 220 9.2. Incoherent Wave Turbulence . 227 9.3. Weak Drift Wave Turbulence . 231 9.4. Nonthermal Radio Bursts . 238 10. Nonlinear Waves 243 10.1. Single Nonlinear Waves . 244 10.2. Nonlinear Wave Evolution . 250 10.3. Inverse-Scattering Method . 255 10.4. Acoustic Solitons . 260 10.5. Alfven´ Solitons . 268 10.6. Drift Wave Turbulence . 277 CONTENTS ix 11. Strong Turbulence 283 11.1. Ponderomotive Force . 284 11.2. Nonlinear Wave Equation . 287 11.3. Modulational Instability . 293 11.4. Langmuir Turbulence . 298 11.5. Lower-Hybrid Turbulence . 305 11.6. Particle Effects . 307 12. Collective Effects 317 12.1. Anomalous Resistivity . 318 12.2. Anomalous Diffusion . 329 12.3. Collisionless Shock Waves . 334 12.4. Shock Wave Structure . 341 12.5. Particle Acceleration . 353 12.6. Acceleration in Wave Fields . 362 Epilogue 375 Index 377 x CONTENTS 1. Introduction Space physics is to a large part plasma physics. This was realized already in the first half of this century, when plasma physics started as an own field of research and when one began to understand geomagnetic phenomena as effects caused by processes in the uppermost atmosphere, the ionosphere and the interplanetary space. Magnetic storms, bay disturbances, substorms, pulsations and so on were found to have their sources in the ionized matter surrounding the Earth. In our companion volume, Basic Space Plasma Physics, we have presented its concepts, the basic processes and the basic observations. The present volume builds on the level achieved therein and proceeds into the domain of instabilities and nonlinear effects in collisionless space plasmas. In this introduction we review some of the very basics from the companion volume. 1.1. Plasma Properties Classical non-relativistic plasmas are defined as quasineutral, i.e., in a global sense non- charged mixtures of gases of negatively charged electrons and positive ions, containing very large numbers of particles such that it is possible to define quantities like number densities, ns, thermal velocities, vths, bulk velocities, vs, pressures, ps, temperatures, Ts, and so on. Viewed from kinetic theory, it must be possible to define a distribution function, fs(x; v; t), for each species s = e; i (electrons, ions) in the plasma such that it gives the probability of finding a certain number of particles in the phase space interval [x; v; x + dx; v + dv]. If this is the case, any microscopic electric fields of a test charge in the plasma, i.e., of every point charge or every particle in the plasma, will be screened out by the Coulomb fields of the many other charges over the distance of a Debye length given in Eq. (I.1.3) of our companion book (equation numbers from that volume are prefixed by the roman numeral). Here it is written for the particle species s µ ¶1=2 ²0kBTs ¸Ds = 2 (1.1) nee 1 2 1. INTRODUCTION where kB is the Boltzmann constant. The Debye length of electrons is abbreviated as ΛD = ΛDe throughout this book. The condition for considering a group of particles to constitute a plasma is then that the number of particles in the Debye sphere is large, or after Eq. (I.1.5) that the plasma parameter 3 Λ = ne¸D À 1 (1.2) In this book we deal mainly with collisionless plasmas.

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