Plasma Physics: Confinement, Transport and Collective Effects PDF
Preview Plasma Physics: Confinement, Transport and Collective Effects
Lecture Notes in Physics EditorialBoard R.Beig,Wien,Austria W.Beiglböck,Heidelberg,Germany W.Domcke,Garching,Germany B.-G.Englert,Singapore U.Frisch,Nice,France P.Hänggi,Augsburg,Germany G.Hasinger,Garching,Germany K.Hepp,Zürich,Switzerland W.Hillebrandt,Garching,Germany D.Imboden,Zürich,Switzerland R.L.Jaffe,Cambridge,MA,USA R.Lipowsky,Golm,Germany H.v.Löhneysen,Karlsruhe,Germany I.Ojima,Kyoto,Japan D.Sornette,Nice,France,andLosAngeles,CA,USA S.Theisen,Golm,Germany W.Weise,Garching,Germany J.Wess,München,Germany J.Zittartz,Köln,Germany TheEditorialPolicy forEditedVolumes TheseriesLectureNotesinPhysics(LNP),foundedin1969,reportsnewdevelopments inphysicsresearchandteaching-quickly,informallybutwithahighdegreeofquality. Manuscriptstobeconsideredforpublicationaretopicalvolumesconsistingofalimited number of contributions, carefully edited and closely related to each other. 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Schweikhard (Editors) Plasma Physics Confinement, Transport and Collective Effects ABC Editors Priv-Doz.Dr.AndreasDinklage Dr.GerritMarx ProfessorDr.ThomasKlinger ProfessorDr.LutzSchweikhard MPIPlasmaschutz Ernst-Moritz-ArndtUniversität EURATOMAssociation InstitutfürPhysik Wendelsteinstr.1 Domstr.10a 17491Greifswald,Germany 17489Greifswald,Germany [email protected] [email protected] [email protected] [email protected] greifswald.de AndreasDinklageetal.,PlasmaPhysics, Lect.NotesPhys.670(Springer,BerlinHeidelberg2005),DOI10.1007/b103882 LibraryofCongressControlNumber:2005923687 ISSN0075-8450 ISBN-10 3-540-25274-6 SpringerBerlinHeidelbergNewYork ISBN-13 978-3-540-25274-0 SpringerBerlinHeidelbergNewYork Thisworkissubjecttocopyright. Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations areliableforprosecutionundertheGermanCopyrightLaw. SpringerisapartofSpringerScience+BusinessMedia springeronline.com (cid:1)c Springer-VerlagBerlinHeidelberg2005 PrintedinTheNetherlands Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelaws andregulationsandthereforefreeforgeneraluse. Typesetting:bytheauthorsandTechBooksusingaSpringerLATEXmacropackage Coverproduction:design&productionGmbH,Heidelberg Printedonacid-freepaper SPIN:11360360 57/3141/jl 543210 Dedicated to Billa, Frauke and Johanna Preface Plasma, sometimes called the fourth state of matter, is a multifaceted sub- stance which poses a variety of challenges. Plasma physics deals with the complexinteractionofmanychargedparticleswithexternalorself-generated electromagnetic fields. It is this unique entanglement which makes plasma physics a fascinating field for basic research. At the same time, plasma plays an essential role in many applications, ranging, e.g., from advanced light- ing devices and surface treatments for semiconductor applications or surface layer generation to the efforts to tame nuclear fusion as an energy source for our future harnessing the nuclear processes which fuel our sun. Modern plasma research is a multidisciplinary endeavor which includes aspects of electrodynamics, many-particle physics, quantum effects and non- lineardynamics.Buteventhoughthespatialextension,thedensity,theioni- zationdegreeandtheplasmatemperaturemayvarybymany ordersofmag- nitude, the physical similarities – or the plasma properties – of, e.g., the solar corona, non-neutral plasmas in ion-traps, the electron gas of metals or planetary interiors lead to similarities of these systems. Plasmas on earth are evanescent. The confinement of plasmas for ex- tended times is a very difficult task and one of the central keys for plasma research and applications. Consequently, transport phenomena which go far beyond classical transport are highly relevant. This also leads to the ulti- mate challenge of many-particle physics:theunderstandingof turbulence.In addition, a variety of “ordered” collective effects can be studied in unique clarity, for example, phase transitions in “dusty” plasmas or the large vari- ety of plasma waves. The corresponding investigations are at the forefront of current research and development. This volume of Springer Lecture Notes in Physics provides an overview of modern plasma research with a special focus on confinement and related issues.Beginningwithabroadintroduction,thebookleadsgraduatestudents and researchers – including those not specialized in plasma research – to the state of the art of modern plasma physics. The book also presents a methodological cross section ranging from plasma applications and plasma diagnostics to numerical simulations, an important link between theory and experiment which is gaining more and more importance. The references are chosentoguidethereaderfrombasicconceptstocurrentresearch.Exercises VIII Preface in computational plasma physics are supplied on aWebsite (see Chap. 16 in Part III of this book). The contributions are structured in three parts: After a broad introduc- tion to Fundamental Plasma Physics, the focus of this volume on Confine- ment, Transport and Collective Effects is covered. Modern plasma physics is also applied science and has many methodological branches as described in the third part on Methods and Applications. The chapters have been written by prominent experts in their respective fields. The book is based on a series of lectures for graduate students in the framework of a W.E.–Heraeus Summer School. We would like to thank the W.E.–Heraeus Foundation for funding and the International Max Planck Research School “Bounded Plasmas” for sup- porting the 50th Heraeus Summer School “Plasma Physics: Confinement, Transport and Collective Effects” held in Greifswald during October 2003. Weareindebted tothose speakerswhocontributed; this bookhas benefitted from their encouragement and support. We thank Dr. Angela Lahee from Springer Heidelberg for her friendly collaborationthroughoutthisproject.Wealsoappreciatetheprofessionaland friendly support from Ms. Jaqueline Lenz, Ms. Gabriele Hakuba, Ms. Elke SauerandMs.Shanya Rehman duringthe editorial andtechnical realization of this book. And last – but certainly not least – we are deeply grateful to Ms. Andrea Pulss, for whom it must have been much more than a “challenging effort” to do the technical editorial work. Greifswald, Andreas Dinklage April 2005 Thomas Klinger Gerrit Marx Lutz Schweikhard Contents Part I Fundamental Plasma Physics 1 Basics of Plasma Physics U. Schumacher ................................................. 3 1.1 Definition, Occurrence and Typical Parameters of Plasmas ................................................ 3 1.2 Ideal Plasmas.............................................. 5 1.3 Important Plasma Properties ................................ 7 1.3.1 Debye Shielding...................................... 7 1.3.2 The Plasma Parameter ............................... 8 1.3.3 Landau Length ...................................... 8 1.3.4 Plasma Frequency.................................... 9 1.4 Single Particle Behavior in Plasmas .......................... 10 1.4.1 Coulomb Collisions, Collision Times and Lengths......... 11 1.4.2 Electrical Conductivity of Plasmas ..................... 14 1.4.3 Single Charged Particle Motion in Electric and Magnetic Fields .................................. 15 1.5 Kinetic Description......................................... 19 References ..................................................... 20 2 Waves in Plasmas A. Piel ........................................................ 21 2.1 Introduction............................................... 21 2.2 Dispersion Relation for Waves in a Fluid Plasma ............... 22 2.2.1 Maxwell’s Equations.................................. 22 2.2.2 The Equation of Motion .............................. 22 2.2.3 Normal Modes....................................... 23 2.2.4 The Dielectric Tensor................................. 23 2.2.5 Phase and Group Velocity............................. 24 2.3 Waves in Unmagnetized Plasmas............................. 24 2.3.1 Transverse Waves .................................... 25 2.3.2 Longitudinal Waves .................................. 31 2.3.3 Electron Beam Driven Waves .......................... 35 2.4 Waves in Magnetized Plasmas ............................... 37 2.4.1 Propagation Along the Magnetic Field .................. 39 X Contents 2.4.2 Cut-Offs and Resonances.............................. 40 2.4.3 Propagation Across the Magnetic Field ................. 43 2.5 Concluding Remarks ....................................... 47 References ..................................................... 48 3 An Introduction to Magnetohydrodynamics (MHD), or Magnetic Fluid Dynamics B.D. Scott ..................................................... 51 3.1 What MHD Is ............................................. 51 3.2 The Ideas of Fluid Dynamics ................................ 52 3.2.1 The Density in a Changing Flow Field – Conservation of Particles .......................................... 52 3.2.2 The Advective Derivative and the Co-moving Reference Frame.................... 54 3.2.3 Forces on the Fluid – How the Velocity Changes ......... 55 3.2.4 Thermodynamics of an Ideal Fluid – How the Temperature Changes ............................. 57 3.2.5 The Composite Fluid Plasma System ................... 58 3.3 From Many to One – the MHD System ....................... 59 3.3.1 The MHD Force Equation............................. 60 3.3.2 Treating Several Ion Species ........................... 60 3.3.3 The MHD Kinematic Equation ........................ 61 3.3.4 MHD at a Glance .................................... 62 3.4 The Flux Conservation Theorem of Ideal MHD ................ 62 3.4.1 Proving Flux Conservation ............................ 62 3.4.2 Magnetic Flux Tubes ................................. 64 3.5 Dynamics, or the Wires-in-Molasses Picture of MHD................................................... 64 3.5.1 Magnetic Pressure Waves ............................. 65 3.5.2 Alfv´en Waves: Magnetic Tension Waves ................. 67 3.6 The Validity of MHD ....................................... 68 3.6.1 Characteristic Time Scales of MHD..................... 68 3.6.2 Checking the Assumptions ............................ 69 3.6.3 A Comment on the Plasma Beta ....................... 70 3.7 Parallel Dynamics and Resistivity, or Relaxing the Ideal Assumption ....................................... 71 3.8 Towards Multi-Fluid MHD .................................. 73 3.9 Further Reading ........................................... 73 References ..................................................... 74 4 Physics of “Hot” Plasmas H. Zohm....................................................... 75 4.1 What is a Hot Plasma? ..................................... 75 4.2 Kinetic Description of Plasmas............................... 77 4.2.1 The Kinetic Equation................................. 77
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