WAVES IN DUSTY SPACE PLASMAS ASTROPHYSICS AND SPACE SCIENCE LIBRARY VOLUME 245 EDITORIAL BOARD Chairman W. B. BURTON, Sterrewacht, Leiden, P.O. Box 9513, 2300 RA Leiden, The Netherlands [email protected] Executive Committee J. M. E. KUIJPERS, Faculty of Science, Nijmegen, The Netherlands E. P. 1. VAN DEN HEUVEL, Astronomical Institute, University of Amsterdam, The Netherlands H. VAN DER LAAN, Astronomical Institute, University of Utrecht, The Netherlands MEMBERS I. APPENZELLER, Landessternwarte Heidelberg-Konigstuhl, Germany 1. N. BAHCALL, The Institute for Advanced Study, Princeton, U.S.A. F. BERTOLA, Universitd di Padova, Italy J. P. CASSINELLI, University of Wisconsin, Madison, U.S.A. C. J. CESARSKY, Centre d'Etudes de Saclay, Gif-sur-Yvette Cedex, France O. ENGVOLD, Institute of Theoretical Astrophysics, University of Oslo, Norway R. McCRAY, University of Colorado, J/LA, Boulder, U.S.A. P. G. MURDIN, Royal Greenwich Observatory, Cambridge, U.K. F. PACINI, Istituto Astronomia Arcetri, Firenze, Italy V. RADHAKRISHNAN, Raman Research Institute, Bangalore, India K. SATO, School of Science, The University of Tokyo, Japan F. H. SHU, University of California, Berkeley, U.S.A. B. V. SOMOV, Astronomical Institute, Moscow State University, Russia R. A. SUNYAEV, Space Research Institute, Moscow, Russia y. TANAKA, Institittel.of..$Paie &.Astrdnautical Science, Kanagawa, Japan S. TREMAINE, CITA, Princeton University, U.S.A. N. O. WEISS, University of Cambridge, U.K. WAVES IN DUSTY SPACE PLASMAS by FRANK VERHEEST Sterrenkundig Observatorium, Universiteit Gent, Gent, Belgium KLUWER ACADEMIC PUBLISHERS DORDRECHT/BOSTON/LONDON A c.I.P. Catalogue record for this book is available from the Library of Congress. ISBN-13: 978-1-4020-0373-8 e-[SBN-13: 978-94-010-9945-5 00[: 10.1007/978-94-010-9945-5 Published by Kluwer Academic Publishers, P.O. Box 17,3300 AA Dordrecht, The Netherlands. 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CONTENTS PREFACE xi 1 PLASMAS AND DUST 1 1.1 Plasmas as the fourth state of matter 1 1.2 Dust ...... 2 1.3 Dusty plasmas . . . . . . 3 1.4 Basic properties . . . . . 5 1.5 Analogies and differences 6 1.6 Reviews and books . 8 1.7 Structure of the book . . 8 2 CHARGING MECHANISMS AND EXPERIMENTS 11 2.1 Grain charging. . . . . . . . . . . . . . . . 11 2.2 Charging mechanisms for isolated grains . 15 2.2.1 Standard model: primary charging 15 2.2.2 Secondary electron emission 22 2.2.3 Photo-emission ..... 25 2.2.4 Electrostatic disruption. 26 2.2.5 Field emission . . . . . . 27 2.2.6 Centrifugal disruption . 27 2.3 Charging model for grain ensembles 28 2.3.1 Havnes model . . . . . . . . 29 2.4 Charging in magnetized plasmas . . 30 2.4.1 Collisionless theory for infinite Debye lengths 31 2.4.2 Combined effects of space charge and collisions 32 2.5 Dusty plasma experiments . . . . . . . . . . . 33 2.5.1 Plasma processing and etching. . . . . 34 2.5.2 Charging experiments and dust modes 34 2.6 Single grain dynamics and planetary rings 36 3 SPACE OBSERVATIONS 41 3.1 Generalities .................. 41 3.2 Noctilucent clouds and magnetospheric dust 43 3.3 Circumsolar dust rings and zodiacal light 44 3.4 Planetary rings ................ 46 v VI CONTENTS 3.4.1 Jupiter 47 3.4.2 Saturn 49 3.4.3 Uranus 55 3.4.4 Neptune 56 3.5 Cometary plasmas . 58 3.6 Interplanetary dust 62 3.7 Interstellar dust clouds 65 4 MULT ISPECIES FORMALISM AND WAVES 67 4.1 General framework ............ 67 4.2 From Liouville to kinetic equations ... 68 4.3 Specific complications for dusty plasmas 70 4.4 Macroscopic fluid equations 72 4.4.1 Macroscopic averages 72 4.4.2 Continuity equations 74 4.4.3 Equations of motion 74 4.4.4 Pressure equations 75 4.4.5 Set of basic fluid equations . 77 4.4.6 Conservation of charge 78 4.5 Maxwell's equations. . . . . . 78 4.6 Waves in multispecies plasmas 79 4.6.1 Introductory remarks . 79 4.6.2 Equilibrium discussions . 81 4.6.3 Linearization procedure. 82 4.7 Linear parallel modes and equilibrium streaming. 84 4.8 Arbitrary angles of wave propagation without streaming 86 4.8.1 General expressions . . . . . 86 4.8.2 Oblique electrostatic modes 87 4.8.3 Perpendicular propagation 88 5 ELECTROSTATIC MODES 89 5.1 Introduction................. 89 5.2 Linear parallel modes in ordinary plasmas 90 5.2.1 Langmuir waves. . . . 90 5.2.2 Buneman instabilities . 91 5.2.3 Ion-acoustic modes . . 92 5.3 Dusty plasma modes ..... 95 5.3.1 Pioneering work on dust modified modes 95 5.3.2 Dust-ion-acoustic waves ......... 97 5.3.3 Dust-acoustic waves ........... ". 98 5.3.4 Two-stream and Buneman instabilities 99 5.4 General nonlinear wave theory . . . . . . . . . . 102 5.4.1 Arbitrary amplitudes and Sagdeev potential 102 5.4.2 Reductive perturbation theory . . . . . . . . 109 CONTENTS Vll 5.4.3 Korteweg-de Vries-type expansions . . . . . 111 5.4.4 Modified Korteweg-de Vries-type expansions 112 5.4.5 Higher-order expansions . . . . . . 113 5.4.6 Expansion of the Sagdeev potential 114 5.5 Nonlinear dusty plasma modes. 116 5.5.1 Solitons ... 116 5.5.2 Double layers . . . . . . 119 5.6 Oblique propagation ...... 121 5.6.1 Upper and lower hybrid modes 121 5.6.2 Dust hybrid modes . . . 122 5.6.3 Nonlinear developments 124 5.7 Collisional and kinetic effects. 124 6 ELECTROMAGNETIC MODES 127 6.1 Parallel electromagnetic waves . . . . . . . . . . . . . .. 127 6.1.1 Dispersion law, resonances and cut-off frequencies 127 6.1.2 Whistler waves ... 129 6.1.3 Alfven waves. . . . . 129 6.1.4 Cometary turbulence 131 6.2 Dusty plasmas. . . . . . . . 133 6.2.1 Dust whistler waves. 134 6.2.2 Charged dust in cometary plasmas 135 6.3 Magnetosonic modes .... 139 6.3.1 Multispecies plasmas . . . . . . . . 139 6.3.2 Dusty plasmas. . . . . . . . . . . . 140 6.4 Reductive perturbation for nonlinear waves. 142 6.4.1 Parallel propagation ....... 142 6.4.2 Oblique and perpendicular modes 147 7 FLUCTUATING DUST CHARGES 151 7.1 Charge fluctuations . . . . . . . . . . . . . . . . . . . .. 151 7.1.1 History........................ 151 7.1.2 Continuity equations and attachment frequencies 154 7.1.3 Momentum equations. . . . . . . . . . . . . . . 156 7.1.4 Charging frequencies . . . . . . . . . . . . . . . 156 7.2 Parallel electrostatic waves with variable dust charges. 159 7.2.1 Dispersion law in general. 159 7.2.2 No dust dynamics. . . . 163 7.2.3 Langmuir modes .... 163 7.2.4 Dust-ion-acoustic modes 166 7.2.5 Dust-acoustic modes . . 167 7.2.6 Zero-frequency modes. . 170 7.2.7 Case studies: Rings of Saturn 170 7.2.8 Implications for other electrostatic modes 172 V111 CONTENTS 7.3 Kinetic theory and nonlinear developments 173 7.3.1 Kinetic treatments .. . . . . . . . 173 7.3.2 Electrostatic solitons . . . . . . . . 174 7.4 Electromagnetic waves with variable dust charges 174 7.5 Nonlinear electromagnetic waves with variable dust charges 179 7.6 Oblique and perpendicular modes . . . . . . . . . . . . .. 183 8 SELF-GRAVITATION 185 8.1 Janus faces of Jeans instabilities . . . . . . . . 185 8.1.1 Jeans {in)stabilities . . . . . . . . . . . 185 8.1.2 Physics of the classic Jeans instability 186 8.2 Revisiting the Jeans swindle 187 8.2.1 Basic stationary state. . . . . . . . . . 188 8.2.2 Linear perturbations . . . . . . . . . . 190 8.2.3 Standard assumption of a uniform basic state 192 8.2.4 Local solutions 193 8.2.5 Global solutions . . . . . . 194 8.2.6 Caveat........... 195 8.3 Self-gravitation of dusty plasmas. 196 8.3.1 Different aspects of gravitation 196 8.3.2 Other factors 197 8.3.3 Chronology .. 198 8.4 Jeans-Buneman modes 199 8.4.1 Global results 199 8.4.2 Cold and massive dust 200 8.4.3 Boltzmann electrons 201 8.4.4 Boltzmann electrons and ions 202 8.4.5 Oblique electrostatic modes 203 8.5 Magnetosonic Jeans modes. . . . . . 204 8.5.1 Inertialess electrons and ions. 204 8.5.2 Alfven-Jeans modes in the absence of neutral gas 205 8.5.3 Charged and neutral dust 208 8.5.4 Interstellar dust 210 8.5.5 Summing up . . . . . . . . 211 8.6 Nonlinear modes. . . . . . . . . . 212 9 MASS AND SIZE DISTRIBUTIONS 215 9.1 Dust mass distributions. . . . . . 215 9.2 Parallel modes in a fluid description . 216 9.2.1 Dust-acoustic modes . . . . . 216 9.2.2 Continuous mass distribution 220 9.2.3 Circularly polarized electromagnetic modes. 224 9.2.4 Nonlinear dust-acoustic modes. 225 9.3 Kinetic equations for dust distributions . . . . . . . 226 CONTENTS IX 10 OTHER MODES 227 10.1 Inhomogeneous plasmas and mode coupling ........ 227 10.2 Rayleigh-Taylor, Kelvin-Helmholtz instabilities and vortices 228 10.2.1 Rayleigh-Taylor instabilities . 228 10.2.2 Kelvin-Helmholtz instabilities 229 10.2.3 Vortex formation 23] 10.3 Surface waves . . . . . 233 10.4 Self-similar expansions . 234 10.5 Lattice waves ...... 235 11 CONCLUSIONS AND OUTLOOK 239 11.1 Comparison with observations 239 11.1.1 Spokes in Saturn's Bring 239 11.1.2 Planetary rings 240 11.1.3 Comets. . . . . 241 11.1.4 Interstellar dust 242 11.2 Summing up 243 11.3 Outlook ........ 244 BIBLIOGRAPHY 245 INDEX 261 PREFACE Dusty plasmas Plasmas and dust are both ubiquitous ingredients of the universe. The interplay between both has opened up a new and fascinating research do main, that of dusty plasmas, containing charged dust grains besides the usual plasma constituents. The original impetus was given by the Voyager observations in the early 1980s, that showed phenomena in the rings of Saturn which could not really be explained on purely gravitational grounds alone. Telltale were the spokes in the B ring and the braids in the F ring, the latter ring itself being discovered by these missions. Other examples in the solar system are circumsolar dust rings, noctilucent clouds in the arc tic troposphere as the closest natural dusty plasmas, or even the flame of a humble candle. Other dusty plasmas occur in the asteroid belt, in cometary comae and tails, in the rings of all the Jovian planets and in interstellar dust clouds, to name but a few. Charging of typical micron-sized grains can lead to several thousand electron charges, for masses of million to billion proton masses. The ensu ing, extremely small charge-to-mass ratios lead to new plasma eigenmodes at the very low-frequency end of the spectrum, the full implications of which have not been completely digested yet. A truly self-consistent study of various types of modes in dusty plasmas is, however, still in its infancy, the many papers published during the last decade notwithstanding. Many obstacles prevent analogies with standard plasmas to be fully exploited, since grain charges are determined by the plasma potentials and can fluc tuate, and dust comes in all sizes, in an almost continuous range from macromolecules to rock fragments. The daunting task to describe such a variety of sizes, masses and of course also charges by any form of tractable distribution has so far deterred all but preliminary efforts. Naturally, most efforts have gone in modelling the dust grains as if they were an additional, heavy ion species. Even within these severe limitations, however, the study of dusty plasmas, and of the wave modes possible therein, have yielded a great many interesting and new results. The scarcity of adequate space missions and observations in the plane tary realm had caused theory to surge far ahead of observations. Luckily, the thread has been picked up by experimentalists, who have produced an Xl