Plasma Physics like-A. Dinklage, T. Klinger, G.Marx, L. Schweikhard

Lecture Notes in Physics Editorial Board 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, and Los Angeles, CA, USA S Theisen, Golm, Germany W Weise, Garching, Germany J Wess, München, Germany J Zittartz, Köln, Germany The Editorial Policy for Edited Volumes The series Lecture Notes in Physics (LNP), founded in 1969, reports new developments in physics research and teaching - quickly, informally but with a high degree of quality Manuscripts to be considered for publication are topical volumes consisting of a limited number of contributions, carefully edited and closely related to each other Each contribution should contain at least partly original and previously unpublished material, be written in a clear, pedagogical style and aimed at a broader readership, especially graduate students and nonspecialist researchers wishing to familiarize themselves with the topic concerned For this reason, traditional proceedings cannot be considered for this series though volumes to appear in this series are often based on material presented at conferences, workshops and schools Acceptance A project can only be accepted tentatively for publication, by both the editorial board and the publisher, following thorough examination of the material submitted The book proposal sent to the publisher should consist at least of a preliminary table of contents outlining the structure of the book together with abstracts of all contributions to be included Final acceptance is issued by the series editor in charge, in consultation with the publisher, only after receiving the complete manuscript Final acceptance, possibly requiring minor corrections, usually follows the tentative acceptance unless the final manuscript differs significantly from expectations (project outline) In particular, the series editors are entitled to reject individual contributions if they not meet the high quality standards of this series The final manuscript must be ready to print, and should include both an informative introduction and a sufficiently detailed subject index Contractual Aspects Publication in LNP is free of charge There is no formal contract, no royalties are paid, and no bulk orders are required, although special discounts are offered in this case The volume editors receive jointly 30 free copies for their personal use and are entitled, as are the contributing authors, to purchase Springer books at a reduced rate The publisher secures the copyright for each volume As a rule, no reprints of individual contributions can be supplied Manuscript Submission The manuscript in its final and approved version must be submitted in ready to print form The corresponding electronic source files are also required for the production process, in particular the online version Technical assistance in compiling the final manuscript can be provided by the publisher’s production editor(s), especially with regard to the publisher’s own LATEX macro package which has been specially designed for this series LNP Homepage (springerlink.com) On the LNP homepage you will find: −The LNP online archive It contains the full texts (PDF) of all volumes published since 2000 Abstracts, table of contents and prefaces are accessible free of charge to everyone Information about the availability of printed volumes can be obtained −The subscription information The online archive is free of charge to all subscribers of the printed volumes −The editorial contacts, with respect to both scientific and technical matters −The author’s / editor’s instructions A Dinklage T Klinger G Marx L Schweikhard (Editors) Plasma Physics Confinement, Transport and Collective Effects ABC Editors Priv-Doz Dr Andreas Dinklage Professor Dr Thomas Klinger MPI Plasmaschutz EURATOM Association Wendelsteinstr 17491 Greifswald, Germany andreas.dinklage@ipp.mpg.de thomas.klinger@ipp.mpg.de Dr Gerrit Marx Professor Dr Lutz Schweikhard Ernst-Moritz-Arndt Universität Institut für Physik Domstr 10a 17489 Greifswald, Germany marx @physik.uni-greifswald.de lutz.schweikhard@physik.unigreifswald.de Andreas Dinklage et al., Plasma Physics, Lect Notes Phys 670 (Springer, Berlin Heidelberg 2005), DOI 10.1007/b103882 Library of Congress Control Number: 2005923687 ISSN 0075-8450 ISBN -10 3-540-25274-6 Springer Berlin Heidelberg New York ISBN -13 978-3-540-25274-0 Springer Berlin Heidelberg New York This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Violations are liable for prosecution under the German Copyright Law Springer is a part of Springer Science+Business Media springeronline.com c Springer-Verlag Berlin Heidelberg 2005 Printed in The Netherlands The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Typesetting: by the authors and TechBooks using a Springer LATEX macro package Cover production: design &production GmbH, Heidelberg Printed on acid-free paper SPIN: 11360360 57/3141/jl 543210 Dedicated to Billa, Frauke and Johanna Preface Plasma, sometimes called the fourth state of matter, is a multifaceted substance which poses a variety of challenges Plasma physics deals with the complex interaction of many charged particles with external or self-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 lighting 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 nonlinear dynamics But even though the spatial extension, the density, the ionization degree and the plasma temperature may vary by many orders of magnitude, 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 extended 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 ultimate challenge of many-particle physics: the understanding of 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 variety 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 Beginning with a broad introduction, the book leads graduate students 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 chosen to guide the reader from basic concepts to current research Exercises VIII Preface in computational plasma physics are supplied on a Web site (see Chap 16 in Part III of this book) The contributions are structured in three parts: After a broad introduction to Fundamental Plasma Physics, the focus of this volume on Confinement, 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 supporting the 50th Heraeus Summer School “Plasma Physics: Confinement, Transport and Collective Effects” held in Greifswald during October 2003 We are indebted to those speakers who contributed; this book has benefitted from their encouragement and support We thank Dr Angela Lahee from Springer Heidelberg for her friendly collaboration throughout this project We also appreciate the professional and friendly support from Ms Jaqueline Lenz, Ms Gabriele Hakuba, Ms Elke Sauer and Ms Shanya Rehman during the editorial and technical 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 the technical editorial work Greifswald, April 2005 Andreas Dinklage Thomas Klinger Gerrit Marx Lutz Schweikhard Contents Part I Fundamental Plasma Physics Basics of Plasma Physics U Schumacher 1.1 Definition, Occurrence and Typical Parameters of Plasmas 1.2 Ideal Plasmas 1.3 Important Plasma Properties 1.3.1 Debye Shielding 1.3.2 The Plasma Parameter 1.3.3 Landau Length 1.3.4 Plasma Frequency 1.4 Single Particle Behavior in Plasmas 1.4.1 Coulomb Collisions, Collision Times and Lengths 1.4.2 Electrical Conductivity of Plasmas 1.4.3 Single Charged Particle Motion in Electric and Magnetic Fields 1.5 Kinetic Description References Waves in Plasmas A Piel 2.1 Introduction 2.2 Dispersion Relation for Waves in a Fluid Plasma 2.2.1 Maxwell’s Equations 2.2.2 The Equation of Motion 2.2.3 Normal Modes 2.2.4 The Dielectric Tensor 2.2.5 Phase and Group Velocity 2.3 Waves in Unmagnetized Plasmas 2.3.1 Transverse Waves 2.3.2 Longitudinal Waves 2.3.3 Electron Beam Driven Waves 2.4 Waves in Magnetized Plasmas 2.4.1 Propagation Along the Magnetic Field 3 7 8 10 11 14 15 19 20 21 21 22 22 22 23 23 24 24 25 31 35 37 39 X Contents 2.4.2 Cut-Offs and Resonances 2.4.3 Propagation Across the Magnetic Field 2.5 Concluding Remarks References An Introduction to Magnetohydrodynamics (MHD), or Magnetic Fluid Dynamics B.D Scott 3.1 What MHD Is 3.2 The Ideas of Fluid Dynamics 3.2.1 The Density in a Changing Flow Field – Conservation of Particles 3.2.2 The Advective Derivative and the Co-moving Reference Frame 3.2.3 Forces on the Fluid – How the Velocity Changes 3.2.4 Thermodynamics of an Ideal Fluid – How the Temperature Changes 3.2.5 The Composite Fluid Plasma System 3.3 From Many to One – the MHD System 3.3.1 The MHD Force Equation 3.3.2 Treating Several Ion Species 3.3.3 The MHD Kinematic Equation 3.3.4 MHD at a Glance 3.4 The Flux Conservation Theorem of Ideal MHD 3.4.1 Proving Flux Conservation 3.4.2 Magnetic Flux Tubes 3.5 Dynamics, or the Wires-in-Molasses Picture of MHD 3.5.1 Magnetic Pressure Waves 3.5.2 Alfv´en Waves: Magnetic Tension Waves 3.6 The Validity of MHD 3.6.1 Characteristic Time Scales of MHD 3.6.2 Checking the Assumptions 3.6.3 A Comment on the Plasma Beta 3.7 Parallel Dynamics and Resistivity, or Relaxing the Ideal Assumption 3.8 Towards Multi-Fluid MHD 3.9 Further Reading References Physics of “Hot” Plasmas H Zohm 4.1 What is a Hot Plasma? 4.2 Kinetic Description of Plasmas 4.2.1 The Kinetic Equation 40 43 47 48 51 51 52 52 54 55 57 58 59 60 60 61 62 62 62 64 64 65 67 68 68 69 70 71 73 73 74 75 75 77 77 482 T Hamacher 22 R S´ aez: 1999 Socio-economic Research in Fusion SERF 1997-98: Externalities of the Fusion Fuel Cycle Final Report (Coleccion Documentos CIEMAT, Madrid 1999) 473 23 S Barabaschi, C Berke, F Fuster Jaume et al: Fusion programme evaluation 1996, EUR 17521 (Office for Official Publications of the European Communities, Luxembourg 1997) 473 24 P Lako, J.R Ybema, A.J Seebregts et al: Long term scenarios and the role of fusion power, Report ECN BS: ECN-C–98-095 (ECN Policy Studies, Petten 1998) 474, 475, 476, 478 25 T.C Hender, P.J Knight, I Cook: Fusion Technol 30, 1605 (1996) 474 26 P.J Knight, S.C Donovan: Calculations with SUPERCODE for SERF Task E1, Progress Report (UKAEA Fusion, Culham 1998) 474, 475 27 J Edmonds, H.M Pitcher, D Barns et al: Modelling Future Greenhouse gas emissions: The second generation model description, in Modeling global Change (United Nations University Press, Tokyo 1993); J Edmonds, J.A Reilly: Ener Econ 5, 74 (1983) 474 28 F Najmabadi, R.W Conn, P.I.H Cooke et al: The ARIES-I Tokamak Fusion Reactor Study – The Final Report, UCLA report UCLA-PPG-1323 (UCLA, San Diego 1991); J.G Delene: Fusion Technol 26, 1105 (1994) 474 29 J.H Ausubel, A Gr¨ ubler, N Nakicenovic et al: Climate Change 12, 245 (1988) 475 30 N Nakicenovic, A Gr¨ ubler, A McDonald: Global Energy Perspectives (Cambridge University Press, Cambridge 1998) 476 31 P Lako, J.R Ybema, A.J Seebregts: The Long-Term Potential of Fusion Power in Western Europe, Report ECN BS: ECN-C–98-071 (ECN Policy Studies, Petten 1998) 476 32 P Lako, A.J Seebregts: Characterisation of Power Generation Options for the 21st Century, Report ECN BS: ECN-C–98-085 (ECN Policy Studies, Petten 1998) 477 33 K Tokimatsu, J Fujino, Y Asaoka et al: Studies of Nuclear Fusion Energy Potential Based on Long-term World Energy and Environment Model In: Proceedings of the 18th IAEA Fusion Energy Conference, Sorrento, Italy, 4.–10 October 2000, paper IAEA-CN-77/SEP/03 (IAEA, Vienna 2001) 477 34 J Edmonds: private communication (2004) 477 35 Der Fischer Weltalmanach (Fischer Taschenbuch Verlag GmbH, Frankfurt am Main 1996) 479 36 http://www.eia.doe.gov/emeu/iea/table62.html 479 Abbreviations ACTEX APGL ASDEX Upgrade AU B2 B2-Eirene bbc BBGKY BES BESI BoRiS CARS CCD CCP CFL CHS CME COE COREX CR CRPP DALF3 DAW DBD DEMO activity expansion atmospheric pressure glow discharge Axial Symmetric Divertor EXperiment Upgrade astronomical unit Braams (developer) B2 and Eirene body centered cubic Born, Boguljubov, Green, Kirkwood, Yvon-theory beam emission spectroscopy beam emission spectroscopy imaging Borchardt Riemann Schneider (developers) coherent anti-Stokes Raman scattering charge coupled device capacitively coupled plasmas compact f luorescent lamp Compact Helical System fusion device (IPP) 2D Fluid code 2D Fluid code 3D fluid code fusion device (NIFS) coronal mass ejection cost of electricity Cooperative Resonance Cone Experiment collisional-radiative (model) Centre de Recherches en Physique des EPFL Plasmas drift Alf v´en turbulence code 3D dust-acoustic wave dielectric barrier discharge demonstration electricity-generating power plant 484 Abbreviations DEOS DESY DFT DIAW DiG DIII-D DKES DNS DOS DLW ECE ECR ECRH EEDF ELM EOS EPFL ETG FactSage fcc FEL FIDAP FIDF FL FLOP FOM FVT FWHM GA GHG GtC GWe HFS HIBP HID HMDSO HP IAW ICCD ICP Department of Earth Observation and Space Systems Deutsches Elektronen Synchrotron density f unctional theory dust-ion-acoustic waves diffusion in Graphite Doublet III-D fusion device (GA) drift kinetic equation solver numerical code direct numerical simulations density of states dust lattice wave electron cyclotron emission spectroscopy electron cyclotron resonance electron cyclotron resonance heating electron energy distribution f unction edge localized mode equation of state Ecole Polytechnique Federale de Lausanne (Switzerland) electron temperature gradient combines FACT-Win and Chemsage code, commercial tool f ace-centered cubic f ree electron laser Fluid Dynamics Analysis Package software package f ull ion distribution f unction f luorescent lamp floating point operation Fundamenteel Onderzoek der Materie Netherlands f luid variational theory f ull width half maximum General Atomics San Diego (USA) greenhouse gas Gigatonnes of carbon GW electric high f ield side heavy ion beam probe high intensity discharge hexamethyldisiloxane high pressure ion-acoustic waves intensified charge coupled device inductively coupled plasmas Abbreviations ICRH IIASA IMS IPP ISS95 ITER ITG JET KAM theorem KEMS KMC LASNEX LED LES LFS LHD LIDAR LIF LP LLNL LTE MAGPIE MARKAL MC MCC MD MF MHD NBI NIF NIFS NIST 485 ion cyclotron resonance heating International Institute of Applied System Analysis Intelligent Maintenance Systems Max–Planck–Institut f¨ ur Plasmaphysik Garching, Greifswald (Germany) International Sterallator Scaling 95 formerly interpreted to stand for projected fusion International Thermonuclear device, latin: the Experimental Reactor way ion temperature gradient Joint European Torus fusion device, Culham, GB theorem of Kolmogorov, Arnold and Moser Knudsen Effusion Mass Spectrometry kinetic Monte Carlo Los Alamos ICF design code light emitting diode large eddy simulation low f ield side Large Helical Device fusion device (NIFS) light detection and ranging laser-induced f luorescence low pressure Lawrence Livermore National Laboratory local thermodynamic equilibrium mega-ampere generator for plasma implosion experiments MARKet Allocation linear programming model Monte-Carlo method numerical method Monte Carlo collisions molecular dynamics melamine f ormaldehyde magnetohydrodynamics neutral beam injection National Ignition Facility LLNL, USA National Institute for Fusion Science Toki (Japan) National Institute of Standards and Gaithersburg, USA Technology 486 Abbreviations OCP ODE OH OML PCA PDE PDF pe PIC one component plasma ordinary differential equation ohmic heating orbital motion limit poly-crystalline alumina partial differential equation probability density f unction polyethylene particle-in-cell PIMC path-integral Monte Carlo PIP PLTE PPT P.S ps PTE PWR QEOS QMD RABER R&D rf partially ionized plasmas partial local thermodynamic equilibrium plasma phase transition Pfirsch-Schl¨ uter polystrene partial thermodynamic equilibrium pressurised water reactor quotidian EOS quantum molecular dynamics Radio Beacon on Rocket research and development radio f requency RPA RTP random phase approximation Rijnhuizen Tokamak Project SEAFP Safety and Environmental Assessment of Fusion Power scanning electron microscopy Socio-Economic Research on Fusion scrape-off layer standard temperature and pressure tight-binding molecular dynamics total electron content trapped particle modes Tokamak Experiment for Technology fusion device, Oriented Research Forschungszentrum J¨ ulich, Germany TEXTOR - dynamic ergodic divertor SEM SERF SOL STP TB-MD TEC TEM TEXTOR TEXTORDED simulation technique simulation technique electromagnetic waves fusion device (FOM) Abbreviations 487 TEXT-U TEXas Tokamak-Upgrade TF TJ-II toroidal f ield second upgrade of Torus JEN (former fusion device, name of Spanish energy agency; now Madrid, Spain CIEMAT) theta-pinch orbit code gyro-kinetic global nonlinear code universal Edge code 2D fluid transport code ultraviolet vacuum ultraviolet Wendelstein7-Advanced Stellarators fusion device (IPP) Wendelstein7-X fusion device (IPP) (under construction) World Energy Council X-ray diffraction TORB UEDGE UV VUV W7-AS W7-X WEC XRD fusion device, U-Texas at Austin (USA) Index 1/ν regime 239, 242 absorption coefficient 410 adiabatic electrons 194 invariant 18, 19, 144, 145 response 191, 194 advective derivative 55 Alfv´en velocity 66, 84 Alfv´en waves see waves ambipolar diffusion 101, 104, 233, 303 ambipolarity 241, 242 Ampere’s law 62 amplitude histogram 378 anomalous transport see transport ASDEX Upgrade 75, 76, 153, 154, 431, 457 aspect ratio 152 atomic relaxation times 367 B-spline 438 banana orbit 167, 227, 228, 237 BBGKY-hierarchy see kinetic equation BES see plasma diagnostics β see plasma beta Bethe–Weizs¨ acker cycle see CNO cycle Blackman–Tukey method 380 Bohm criterion 106, 107 diffusion coefficient 169, 199 velocity 106, 319 Boltzmann distribution 368 equation 19, 78, 96, 128, 222 relation 251, 257, 385 bootstrap current 156, 169, 222 bounce motion 18, 227, 228, 238 breathing mode 280 bremsstrahlung 130, 215, 356, 363, 455 Brillouin density 279 Brownian motion 165, 320, 325 canonical momentum 144 capacitively coupled plasmas 105 CCP see capacitively coupled plasmas center-of-mass mode 280 charge state distribution 364 Child-Langmuir law 107 CHS 42, 244, 263 circulation 247 Clebsch coordinates 433 cluster decomposition 122 clusters 124, 125, 324 CNO cycle 331, 450 CO2 emission 465, 475, 480 COE see cost of electricity collision time see also collisions 10, 12, 13 collisional radiative model 367, 393 collisionality 238 collisions charge transfer 96 Coulomb 8, 10, 11, 78, 138, 148, 304 electron–electron 13 electron–ion 13 ion–electron 13 ion–ion 13 conduction–convection problems 426 conductivity 127, 343 confinement 213 H-mode 169, 216 L-mode 169, 216 scaling laws 169, 216 continuity equation 54, 62 490 Index Corona model 369 coronal loop 88 correlation 250 cost of electricity 474 Coulomb barrier 448 cross section 12 crystal 269, 294 Coulomb logarithm 12, 232 coupling parameter 6, 117, 276, 309 cross section differential 357 Thomson 353 cross-correlation function 250 curvature drift see drifts cut-off 40 density 26, 391 frequency 26 wavelength 30 cyclotron frequency 16, 140, 273 cyclotron heating see heating D-T reaction see fusion DAW see waves Debye length 7, 77, 278, 355 degeneracy parameter 117 Delaunay triangulation 434 DEMO 458, 474 diamagnetism 16, 140, 162, 233 DIAW see waves dielectric tensor 23 diffusion 223 banana 227, 238 classical 165 neoclassical 166 random walk diffusion coefficient 224 diocotron waves see waves discharge arc 95, 97, 102 corona 97, 102 dc 97, 104, 107 dielectric barrier 103 glow 95, 99–101, 104 atomospheric pressure 103 micro 102, 103 microwave 110 mircowave 97, 104, 105 overview 97 rf 97, 104, 105, 107–110, 113, 115, 305, 429 Townsend 100 dispersion relation see corresponding waves disruptions 91 divertor 162, 467, 474 DLW see waves Doppler cooling 276, 277 Doppler shift 354 drift ordering 198 drift parameter 70 drift surface 149, 237 drift waves see waves drifts ∇B 17, 142, 149, 150, 436 E × B 16, 141, 249, 250 curvature 17, 143, 230, 235, 436 diamagnetic 233, 241 general force 16, 141 gravitational 17 Druyvesteyn method 112 dual cascade 248 dust charge 301, 307 dust charging 298, 300, 302 dust plasma frequency 313 dust resonance 306, 308 dynamic form factor 357 dynamical screening 123 dynamo effect 70, 189 E × B velocity 61 ECE see plasma diagnostics ECR see electron cyclotron resonance ECRH see plasma heating eddy mitosis 174 edge localised mode 91 EEDF see electron energy distribution function Ehrenfest theorem 269 Einstein’s energy-mass relation 445 electric breakdown 98, 99, 102–104 electric probes see plasma diagnostics electrical conductivity 15, 23, 51, 82, 85, 117, 118, 122, 127, 130, 233, 235, 333, 345, 403, 408 electron attachment 96 electron cyclotron frequency 40 Index electron energy distribution function 96 electron root 243 electron volt (eV) electron–diamagnetic direction 253 elementary processe excitation 96 elementary processes 96 charge exchange 367 excitation 367, 369 recombination 367 self-absorption 367 ELM see edge localised mode Els¨ asser variables 188 emissive probes 386 energy consumption 461 resources 464 energy confinement time 137, 214, 215 enstrophy 175, 183, 247 EOS see equation of state Epstein friction coefficient 304 equation of motion 15, 22 equation of state 118, 125, 127, 128, 331, 333, 337, 338, 339, 341, 342 equilibrium corona 365 in toroidal geometries 149 local thermodynamic 57, 58, 102 local thermodynamic (LTE) 95, 368, 404 partial local thermodynamic (PLTE) 369 partial thermodynamic (PTE) 95 Saha 366 thermodynamic 51, 57, 79, 139 ergodic magnetic fields 90, 150, 427, 432 ETG see instability eV extrasolar planets 334 F-layer 40, 46 Faraday effect 41, 352 Fermi distribution 124 Fermi energy 6, 117 Feynman diagram 119 Fick’s law 165, 215 field line tension 68, 82, 83 491 finite clusters 324–326 floating point operations 425 floating potential 300 FLOP see floating point operations fluctuations 19, 32, 164, 195, 245, 249, 251, 254 fluid equations see MHD equations fluid variational theory 338 Fokker–Planck equation 78, 166 forces on dust particles 302 electric force 302 gravity 302 ion drag 303 neutral drag 304 nonreciprocal attraction 311 theromophoresis 304 Fourier notation 31 free energy 338 fusion 445 D-T reaction 450, 451, 454 impurity radiation 364 inertial 360, 445, 456 muon-catalyzed 458 power balance 455, 456 power plant 458, 467, 469–471 economic considerations 473 safety 470 reactions 448, 450, 454 reactor 138, 156, 428, 449, 452, 458 resources 469 socio-economic stuides 476 triple product 137 FVT see fluid variational theory FWHM see spectral lines Gibbs free energy 412 Gibbs phenomenon 379 Gibbs–Bogolyubov inequality 338 Green’s function 119 group velocity 24 guiding centre 140, 150, 166, 229 gyro radius 16, see Larmor radius gyro-averaging 436 gyro-Bohm scaling 169 gyro-kinetic ordering 198 gyro-kinetic theory 435, 437 gyro-motion 140 H-mode see confinement 492 Index Hall sensors 390 Hall term 193 Hartree–Fock approximation 120 heavy ion beam probe see plasma diagnostics helical magnetic field lines 156 helically trapped particles 229–231, 239 heliotron see also stellarator 41, 217 Helmholtz equation 436, 438 HIBP see plasma diagnostics HID see high intensity discharge lamps high intensity discharge lamps 399, 400, 403–405, 408 chemical modelling 413 corrosion analysis 418, 419 modelling 407 radiation transport 409 spectral intensity 406 high-field side (HFS) 225 Hugoniot curve 127, 341, 343 ICP see inductively coupled plasmas ICRH see plasma heating ideal plasma see plasma ideal two fluid model 51 impedance probe see plasma diagnostics inductively coupled plasmas 105, 110 inertial confinement 456 infrared absorption 114 instability beam–plasma 35, 36 electron-temperature gradient (ETG) 254 interchange 87, 253 ion-temperature gradient (ITG) 168, 254, 434, 435, 437, 439 MHD 86 Rayleigh–Taylor 46 trapped electron modes (TEM) 254 interferometry see plasma diagnostics inverse cascade 175 inward pinch 221 ion acoustic velocity 33 ion cyclotron frequency 40 ion energy distribution function 107 ion root 243 ion trap 269 cooling 278 Paul trap 270, 271, 271, 278, 287, 289 ion clouds 275 potential 270, 271 stability 272 Penning trap 270, 273, 274, 279, 282 collective effects 284 ion crystals 291 loading 275 plasma 280 potential 270 ionisation 95 associative 96 collsional 96 Penning effect 96 photo 96 ionosondes see plasma diagnostics ionosphere 40, 46 island see magnetic islands ITER 42, 154, 361, 458, 470, 473, 474 ITG see instability JET 153, 154, 351, 357, 361, 457 Jupiter 117, 297, 331–333, 335, 336 K41 theory 176, 247 KEMS see Knudsen effusion mass spectrometry kinetic equation 19, 78, 80, 96, 166, 431 BBGKY-hierarchy 78 drift-kinetic equation 166 kink instability 87 Knudsen effusion mass spectrometry 404, 413–415, 422 Kolmogorov length 433 kurtosis 379 L-mode see confinement L-wave see waves L¨ ust-Schl¨ uter-Grad-Shafranov-equation 154 Landau damping 78, 79, 87, 253, 360 Landau length Langmuir oscillations Index Langmuir probe see plasma diagnostics Laplacian pressure method 188 Larmor radius 16, 138 laser manipulation of dust 307, 311, 319–321 Lawson parameter 137 LHD 41, 170, 217, 457 LIDAR 357 LIF see plasma diagnostics linear response theory 127 local thermal equilibrium 404 Lorentz force 144 Lorenz number 343 loss cone 147, 150, 168 low-field side (LFS) 225 lower hybrid resonance 44 LTE see equilibrium Lundquist number 73, 88 Mach cone compressional 320 in Saturn’s rings 322 shear 322 Mach probe see plasma diagnostics Mach-Zehnder interferometer 27 magnetic axis 150 magnetic flux tube 64 magnetic islands 89, 90, 150 magnetic mirror 143, 225 magnetic moment 18, 145 gyrating particles 140 magnetic pressure 65, 82 magnetic pressure waves 66 magnetic pumping 240 magnetic surface 150 magnetic tension 65 magnetohydrodynamics see also MHD 51 adiabatic pressure 62 flux conservation 62 force equation 62 force free equilibrium 65 kinematic equation 62 time scales 68 validity 69 magnetron frequency 284 Maxwell’s equations 22 MD see modelling 493 mean free path 10 at magnetic fusion conditions 138 MHD see also magnetohydrodynamics equations 82 equilibrium 82, 160, 193 force equation 60 kinematic equation 61 microgravity 305 mirror machine 147 mixing length 251 modelling 2D fluid 431 3D fluid 431 discharge lamps 407 kinetic Monte Carlo 429 kinetic PIC 429 molecular dynamics (MD) 279, 426–428 Monte Carlo methods 119, 409, 427, 429–432, 434 particle–in–cell (PIC) 427, 430, 437 plasma edge 427 radiation transport 409 thermochemical 412 turbulence 434 Mott effect 122, 345 Navier–Stokes equation 246, 248, 432 NBI see plasma heating neoclassical transport see transport Noether’s theorem 144 ν regime 244 nuclear binding energy 446 Nyquist limit 378 Ohmic heating see plasma heating OML see orbital motion limit orbital motion limit 111, 112, 298 particle confinement time 215 particle–in–cell see modelling partition function 124, 366, 368, 410 Paschen law 100 passing particles 226, 234, 236, 237 passive scalar 175, 192 Paul trap see ion trap PCA see poly-crystalline alumina PDF see probability density function 494 Index Penning effect 96 Penning trap see ion trap Pfirsch–Schl¨ uter current 161, 165, 235, 236 Pfirsch–Schl¨ uter transport see transport phase velocity 24 PIC see modelling plasma beta 70, 77, 162, 170 low–β 70, 175, 187, 190 crystal 279, 287, 289, 291, 294, 310, 430 phase transition 312 degenerated diagnostics see plasma diagnostics edge 91, 169, 219, 257, 426, 427, 431–433 frequency 9, 10, 25, 32, 279, 313, 318 heating 356 electron cyclotron resonance heating (ECRH) 105, 215 ion cyclotron resonance heating (ICRH) 215 neutral beam injection (NBI) 215 Ohmic 105, 215 ideal 5, 6, 117, 161, 164 low temperature 95 non-thermal 95 oscillations parameter polarisation 141 quasi-neutrality 7, 9, 10, 13, 14, 33, 60, 69, 81, 235 reactive 114 relativistic sheath 105, 106, 107–110, 114 surface interaction 427 waves see waves plasma diagnostics beam emission spectroscopy (BES) 393 density measurements for dense plasmas 30 double probes 112 electric probes 110–112 electron cyclotron emission 41, 384, 392 electron cyclotron emission (ECE) 41, 90 emissive probe 386 emissive probes 387 Hall probe 390 heavy ion beam probe (HIBP) 244, 259, 384, 394 impedance probe 46 induction coil 388 interferometry 26–29, 352 ionosondes 44 Langmuir probe 110, 384, 387 electron saturation current 385 floating potential 385 ion saturation current 384 laser aided diagnostics 352 laser induced fluorescence (LIF) 33, 279, 395 Mach probe 388 plasma oscillation method 37 probe arrays 382 radio beacon technique 29 reflectometry 391 resonance cone 46, 48 Thomson scattering 118, 126, 220, 352, 353 collective 357 incoherent 353 LIDAR 357 plasma phase transition 341 plasma surface interaction 96, 114 transition 95, 106 plateau regime 238 Poisson’s equation 7, 32, 78, 107, 313 poloidal coordinate 151 poloidal Larmor radius 226 poly-crystalline alumina 404–406, 420 power spectral density 379 PPT see plasma phase transition pressure dissociation 339 probability density function 179, 224, 258, 378, 379 PTE see equilibrium quasi-neutrality see plasma radial electric field 229 radiation transport 410 Index radio beacon technique see plasma diagnostics Raman scattering 356 random walk 223 rate coefficient 454 rate equations 365 Rayleigh scattering 356 recombination 96, 356 reconnection 73, 85, 86, 88, 89, 190 reflectometry see plasma diagnostics resistive decay time 73 resistive MHD 72 resonance cone see plasma diagnostics Reynolds number 175, 177, 178, 246 Reynolds stress 189, 263 rf discharge see discharge rotational transform 149, 150, 156 safety factor see rotational transform Saha’s equation 5, 126, 368, 369 Salpeter approximation 357 shape function 358 scaling laws 168 scanning electron microscopy 420 scattering 352 cross-section 355 parameter 355 vector 354 X-ray 361 scrape-off layer 388, 427 secondary electron emission 96, 98, 99, 101, 102, 104, 106 self-energy 119, 120 SEM see scanning electron microscopy Shafranov shift 154, 161, 162, 165 shock waves 337, 341 skewness 379 SOL see scrape-off layer solar system 332 Sonin plot 111 space-time data 382 spectral emission coefficient 364 spectral function 120 spectral lines Doppler broadening 370 Doppler line shape function 370 495 full width half maximum (FWHM) 355, 370, 410 Gaussian 371 Lorentzian line shape function 370, 410 natural broadening 370 pressure broadening 371 Stark broadening 371, 410 van-der-Waals broadening 410 Voigt line shape function 372 spectral radiance 364 Spitzer resistivity 164, 300 Stark broadening see spectral lines stellarator 156, 158 modular 159 optimisation 161 Stix parameter 39 stray light 356 streamer 102, 103, 253 strongly coupled plasmas 117 strongly coupled systems one component plasma (OCP) 310 Yukawa systems 310 sustainable development 462 τE see energy confinement time tearing mode 90 TEC see total electron content TEM see instability thermal limit 369 thermodynamic equilibrium see equilibrium θ–pinch 440 Thomas–Fermi model 118 Thomson scattering see plasma diagnostics three-body collision 96 three-wave coupling 173, 174, 176, 181, 182, 186, 189, 192, 207 tokamak 75, 76, 90, 91, 151 coil system 152 equilibrium 153 Tore Supra 152, 457 toroidal confinement 148 toroidal coordinate 151 toroidal resonance 230, 236, 242 torsatron see also stellarator 158, 159, 228, 244, 259 total electron content 30 496 Index Townsend mechanism 98, 102 first coefficient α 98, 99 second Townsend coefficient β 98 third Townsend coefficient γ 98 Townsend discharge see discharge transport 164, 213 anomalous 168, 213, 245, 377, 381, 434, 435 coefficient in partially ionized plasmas 127 heat flux 218 ITG see instability matrix 221 neoclassical 166, 231, 238, 242 particle flux 220 Pfirsch–Schl¨ uter 234, 238 timescale 91 timescales 92 trapped particles 226 tunnelling probability 451 turbulence drift wave 191 electromagnetic 245 electrostatic 245, 257 entropy 192 helicity conservation 189 high Reynolds number regime 175, 178, 191, 194, 199, 200, 203, 206 inertial range 177 Kolmogorov spectrum 177 polarization current 196 saturated state 179 turbulence modelling 434 two-point spectral analysis 381 upper hybrid resonance 44 Virial theorem 151 Vlasov equation 19, 78 void 305 vortex tube stretching 184 vorticity 175, 176, 183, 192, 195, 196, 199–201, 247, 248, 256 warm dense matter 331 waves 21 Alfv´en 67, 83, 189, 395 fast 69 slow 69 diocotron wave 280 drift 191, 194, 210, 252, 253 dust acoustic (DAW) 313 dust ion-acoustic (DIAW) 33, 34, 316 dust lattice (DLW) 313, 318–320, 323 dust-acoustic (DAW) 313–315 electron beam driven 35 electron plasma 359 electrostatic 32 ion-acoustic 31–33, 359 L-wave 39, 40 longitudinal 31 magnetic pressure 65 magnetized plasma 37 normal modes 23 O-mode 43, 46 R-wave 39–42, 105 transverse 25 unmagnetized plasma 24 whistler 42 X-mode 43, 46 Welch’s method 380 Wendelstein 7-A 158 Wendelstein 7-AS 160, 171, 242 Wendelstein 7-X (W7-X) 162, 163, 217, 435, 439, 459 Wiener–Khintchine theorem 250 Wigner–Seitz radius 6, 117, 277 X-ray diffraction 420 XRD see X-ray diffraction ... Gerrit Marx Professor Dr Lutz Schweikhard Ernst-Moritz-Arndt Universität Institut für Physik Domstr 10a 17489 Greifswald, Germany marx @physik.uni-greifswald.de lutz .schweikhard@ physik.unigreifswald.de... scientific and technical matters −The author’s / editor’s instructions A Dinklage T Klinger G Marx L Schweikhard (Editors) Plasma Physics Confinement, Transport and Collective Effects ABC Editors Priv-Doz... Germany marx @physik.uni-greifswald.de lutz .schweikhard@ physik.unigreifswald.de Andreas Dinklage et al., Plasma Physics, Lect Notes Phys 670 (Springer, Berlin Heidelberg 2005), DOI 10.1007/b103882