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A. Dinklage T. Klinger G. Marx L. 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
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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
