Physics of Space Plasma Activity

This page intentionally left blank Physics of Space Plasma Activity Space plasma is so hot that the atoms break up into charged particles which then become trapped and stored in magnetic fields. When critical conditions are reached the magnetic field breaks up, releasing a large amount of energy and causing dramatic phenomena. A prominent example is the magnetospheric substorm occurring in the Earth’s magnetosphere. It in- volves plasma and magnetic field structures extending from 100 km to tens of Earth radii, and can be seen as strong intensifications of the northern and southern lights. The largest space plasma activity events observed in the Solar System occur on the Sun, when coronal mass ejections expel several billion tons of plasma mass into space. Physics of Space Plasma Activity provides a coherent and detailed treat- ment of the physical background of large plasma eruptions in space. It provides the background necessary for dealing with space plasma activity, and allows the reader to reach a deeper understanding of this fascinating natural event. The book employs both fluid and kinetic models, and discusses the applications to magnetospheric and solar activity. This book will form an interesting reference for graduate students and academic researchers in the fields of astrophysics, space science and plasma physics. karl schindler is an Emeritus Professor with the Faculty of Physics and Astronomy, Ruhr University Bochum, Germany, and a distinguished theorist in the field of space plasma physics. In 2001 he was granted the Orson Anderson Scholarship at Los Alamos National Laboratory by the Institute of Geophysics and Planetary Physics (IGPP). Dr Schindler is also a Fellow of the American Geophysical Union. Physics of Space Plasma Activity Karl Schindler Ruhr-Universität Bochum, Germany CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521858977 © K. Schindler 2007 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2006 ISBN-13 978-0-511-27018-5 eBook (NetLibrary) ISBN-10 0-511-27018-6 eBook (NetLibrary) ISBN-13 978-0-521-85897-7 hardback ISBN-10 0-521-85897-6 hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. To Erika Contents Preface xi 1 Introduction 1 Part I Setting the scene 5 2 Sites of activity 7 2.1 Geospace7 2.2 Solar atmosphere 16 2.3 Other sites 22 3 Plasma models 25 3.1 Single particle motion 26 3.2 Kinetic models 29 3.3 Fluid models 35 3.4 Chew–Goldberger–Low momentum equation 39 3.5 On the validity of MHD models for space plasmas 40 3.6 Electron magnetohydrodynamics, Hall current 41 3.7 Initial and boundary conditions 42 3.8 Conservation laws 42 3.9 Discontinuities 48 Part II Quiescence 55 4 Introduction 57 5 Magnetohydrostatic states 61 5.1 General properties 61 5.2 Symmetric MHS states 76 5.3 Examples of exact solutions 85 5.4 Asymptotic expansions 93 vii viii Contents 6 Particle picture of steady states 107 6.1 General properties 107 6.2 Systems with translational invariance 108 6.3 Adiabatic particle motion 114 6.4 Regular and chaotic particle motion 116 7 A unified theory of steady states 123 7.1 Steady states without gravity 124 7.2 Inclusion of the gravity force 127 7.3 Symmetric states 129 8 Quasi-static evolution and the formation of thin current sheets 133 8.1 Introduction 133 8.2 Perturbed Harris sheet 135 8.3 MHD tail model with flux transfer 140 8.4 TCS from boundary deformation 151 8.5 Vlasov approach to quasi-static evolution 156 8.6 Further aspects 168 Part III Dynamics 181 9 Nonideal effects 185 9.1 Generalized Ohm’s law 185 9.2 Resistivity 187 9.3 Microturbulence 190 9.4 Non-turbulent kinetic effects 200 10 Selected macroinstabilities 203 10.1 Stability concepts 203 10.2 Ideal MHD stability 204 10.3 The resistive tearing instability 235 10.4 Collisionless tearing 249 10.5 Variational principle for 2D collisionless plasmas 254 11 Magnetic reconnection 269 11.1 Introduction 269 11.2 Two-dimensional fluid models 271 11.3 Kinetic reconnection in 2D collisionless plasmas 297 11.4 Inclusion of the third dimension 305 11.5 Kinematics of 3D reconnection 311 11.6 Remark on relativistic covariance 340 Contents ix 12 Aspects of bifurcation and nonlinear dynamics 343 12.1 Bifurcation 343 12.2 A statistical mechanics approach to 2D current sheet bifurcation 355 12.3 Role of perturbations 361 12.4 Self-organized criticality 364 12.5 Low-dimensional modelling 364 Part IV Applications 367 13 Magnetospheric activity 371 13.1 Interaction between the solar wind and the magnetosphere 371 13.2 Convection and pressure crisis 378 13.3 Magnetospheric substorms 385 13.4 Further large-scale processes 398 13.5 Statistical and nonlinear dynamics aspects 400 13.6 Discussion 403 14 Models of solar activity 407 14.1 General aspects 407 14.2 Model constraints and boundary conditions 412 14.3 Arcade models of solar flares 416 14.4 Coronal mass ejections 424 14.5 Further aspects 431 15 Discussion 433 15.1 The reconnection problem 433 15.2 A general eruption scheme 438 Appendix 1 Unified theory: details and derivations 441 Appendix 2 Variational principle for collisionless plasmas 451 Appendix 3 Symbols and fundamental constants 465 References 469 Index 503 Preface A major motivation for writing this book is the strong fascination that visible signatures of plasma activity are able to generate. This goes along with considerable professional research interest in this area. Also, those who have admired spectacular pictures or video presentations on the internet displaying spacecraft observations of auroral activity or of solar eruptions, are often motivated to learn more about their physical background. In the early days of spacecraft observations, the understanding of dynami- cal phenomena such as geomagnetic storms and solar flares was considered as poor and high up on the list of particularly challenging problems. Re- markably, this is still true today. The observational database has increased dramatically and important new phenomena were discovered, such as coronal mass ejections and manifestations of the global nature of magnetospheric substorms involving large regions of the magnetosphere. There are many more aspects than envisaged originally, and today we have good reasons to use the comprehensive notions of solar and magnetospheric activity,which in this book are combined under the working term space plasma activity. The desire to understand these complex phenomena has mobilized considerable research efforts, but due to the overwhelming complexity that one encounters, our present understanding is still far from being satisfactory. One might ask, whether in this situation it is appropriate to write a book that concentrates on space plasma activity. Would it not be more reasonable to wait until our understanding of the underlying physical processes has settled down more solidly? The main reason for writing this book at this time is the fact that during past decades a substantial wealth of theoretical tools has been developed, which can be expected to remain useful, even if many of the final answers are still to be found. In fact, good knowledge and further development of those tools could well help to accelerate progress in this field. The situation xii Preface appears to be similar to that of the Earth’s lower atmosphere, where several phenomena associated with atmospheric disturbances are still not well understood; on the other hand, there is little doubt that gas-dynamics methods play an important role in present and future investigations in that area. Regarding that the electrodynamic interactions make plasma dynamics con- siderably more complicated than gas dynamics, it is obvious that there is a strong need for reviewing and, where possible, for improving the exist- ing tools and for developing new ways of approach. Therefore, after the phenomenological survey given in Part I, the relevant methods and plasma properties are addressed in Parts II and III, starting from basic plasma models. In this way an updated (although necessarily incomplete) toolbox for the study of space plasma activity arises. I hope that this will be found useful for research in space plasma activity. A further aim is to meet the needs of scientists or graduate students trying to enter the field of large-scale space plasma phenomena. They often ask for coherent descriptions of the theoretical methods that would allow them to discriminate between conclusions that can safely be drawn and concepts that are more of a speculative nature. There are also indications suggesting that the occupation with topics re- lated to space plasma activity have enjoyed increasing attractiveness since it became clear that such phenomena have aspects falling under notions of modern theoretical physics, such as nonlinear dynamics, spontaneous processes or catastrophe theory. The separation between the theoretical tools (Parts II and III) and the applications (Part IV) was chosen for several reasons. First, this separation allows a systematic and coherent presentation of the theory. Further, it makes it possible to present the applications of Part IV in such a way that, to some extent, they can be understood without detailed knowledge of Parts II and III.

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