Table Of ContentSpringerSerieson
atomic, optical, and plasma physics
39
SpringerSerieson
atomic, optical, and plasma physics
TheSpringerSeriesonAtomic,Optical,andPlasmaPhysicscoversinacompre-
hensivemannertheoryandexperimentintheentirefieldofatomsandmolecules
andtheirinteractionwithelectromagneticradiation.Booksintheseriesprovide
arichsourceofnewideasandtechniqueswithwideapplicationsinfieldssuchas
chemistry,materialsscience,astrophysics,surfacescience,plasmatechnology,ad-
vancedoptics,aeronomy,andengineering.Laserphysicsisaparticularconnecting
themethathasprovidedmuchofthecontinuingimpetusfornewdevelopments
inthefield.Thepurposeoftheseriesistocoverthegapbetweenstandardunder-
graduatetextbooksandtheresearchliteraturewithemphasisonthefundamental
ideas,methods,techniques,andresultsinthefield.
27 QuantumSqueezing
ByP.D.DrumondandZ.Ficek
28 Atom,Molecule,andClusterBeamsI
BasicTheory,ProductionandDetectionofThermalEnergyBeams
ByH.Pauly
29 Polarization,AlignmentandOrientationinAtomicCollisions
ByN.AndersenandK.Bartschat
30 PhysicsofSolid-StateLaserPhysics
ByR.C.Powell
(PublishedintheformerSeriesonAtomic,Molecular,andOpticalPhysics)
31 PlasmaKineticsinAtmosphericGases
ByM.Capitelli,C.M.Ferreira,B.F.Gordiets,A.I.Osipov
32 Atom,Molecule,andClusterBeamsII
ClusterBeams,FastandSlowBeams,AccessoryEquipmentandApplications
ByH.Pauly
33 AtomOptics
ByP.Meystre
34 LaserPhysicsatRelativisticIntensities
ByA.V.Borovsky,A.L.Galkin,O.B.Shiryaev,T.Auguste
35 Many-ParticleQuantumDynamicsinAtomicandMolecularFragmentation
Editors:J.UllrichandV.P.Shevelko
36 AtomTunnelingPhenomenainPhysics,ChemistryandBiology
Editor:T.Miyazaki
37 ChargedParticleTraps
PhysicsandTechniquesofChargedParticleFieldConfinement
ByV.N.Gheorghe,F.G.Major,G.Werth
38 PlasmaPhysicsandControlledNuclearFusion
ByK.Miyamoto
39 Plasma-MaterialInteractioninControlledFusion
ByD.Naujoks
Vols.1–26oftheformerSpringerSeriesonAtomsandPlasmasarelistedattheendofthebook
D. Naujoks
Plasma-Material Interaction
in Controlled Fusion
With54Figures and 11 Tables
123
Dr.DirkNaujoks
Max-Planck-Institutfu¨rPlasmaphysik
TeilinstitutGreifswald
17491Greifswald,Germany
E-mail:[email protected]
ISSN1615-5653
ISBN-103-540-32148-9SpringerBerlinHeidelbergNewYork
ISBN-13978-3-540-32148-4SpringerBerlinHeidelbergNewYork
LibraryofCongressControlNumber:2006927044
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is
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partsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,inits
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toprosecutionundertheGermanCopyrightLaw.
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to Natalie
Preface
Nuclear fusion has the potential to provide a major part of mankind’s energy
needs for many millennia. On the way to controlled thermonuclear fusion on
our planet, the principal goals—from the physical point of view—are firstly
to obtain a sufficiently stable plasma, secondly, to heat this plasma to igni-
tiontemperature,andfinally,toavoidexcessiveinteractionofthehotplasma
with the solid wall of the containing vessel. With respect to the foreseen use
of a fusion reactor as an energy-producing device, an ideal plasma confine-
ment is unattainable nor is it desired. The generated energy together with
the helium particles (fusion “ash”) must be removed from the central region
and conducted to the energy exchanging facilities (blanket), as well as to the
gas exhausting and purifying systems—at the rate they are produced. The
so-called first wall, the border between the hot plasma with sun-like parame-
ters (and beyond) and the “cool earth”, should be able to withstand the high
energy and particle fluxes with little or no maintenance.
During the last few decades a large number of dedicated experimental
results as well as theoretical and simulation studies have been performed—
thankstotheeffortofscientistsfrommanycountriesparticipatinginthistruly
international project of controlled fusion. Several aspects of plasma–surface
interaction have been reviewed in various publications [1–5] as well as in pro-
ceedings of conferences such as the series of Plasma Surface Interaction and
FusionReactorMaterials conferences.Acomprehensive“DataCompendium”
related to atomic processes taking place in plasma–surface interactions and
material questions is given in special supplements issued by the journal Nu-
clear Fusion [6–9].
Itriedtoprovideanin-depthlookatthemulti-facetedaspectsofplasma–
surface interaction in controlled fusion, to give a comprehensive analysis of
the main processes and the main parameters ruling them, together with an
assessmentofthemostcriticalquestionsandopenpointsthatdemandfurther
investigation.Ihopethiscanassistthereaderbyperformingtheirownestima-
tionsandassessmentsofrelevantphysicalprocessesandproblems.Forfurther
VIII Preface
studies,referencestoselectedpapersaregiven.Acomprehensivereviewofthe
enormousexperimentalworkdoneinthisfieldisoutofthescopeofthisbook,
but can be found in the references given above. A more detailed quantitative
analysis can be acquired by applying simulation techniques, which are pre-
sented shortly, used together with special data compilations.
Sincetheinvolvedprocessesareidentical,thebookmightalsobeofinterest
in the fast-paced field of surface modification by means of plasma technology.
Whetherthinlayersaredepositedonmaterialsinordertoimprovethesurface
characteristics or whether plasma ions are implanted into the depth using
biased targets, the underlying physics is the same as in fusion experiments.
IwouldliketothankProf.V.N.Afanas’evforconductingmyinitialsteps
into scientific work in the field of particle interaction with solids, who has
encouraged me to combine experimental, theoretical, and simulation studies
wherever it seems possible. He suffered, but dealt gracefully with my poor
Russian during my stay in Moscow.
IammuchobligedtoDr.R.Behrisch,whohasintroducedmetotheworld
of plasma–surface interaction. He allowed me to benefit from his wide expe-
rience and pushed me to make things clear and simple without unessential
elaborating—not always with success I am afraid. I have also learned from
him to fight for each discharge against the persistent fear of the operators of
how a rather small surface probe would harm the device by exposing it into
the plasma. Iam thankful to Prof. G. Fussmann, who surprisedme with ana-
lytical descriptions of effects, which I thought were studied only by computer
simulation, and who showed me, in detail, that the complexity of particle–
surface interaction is quite negligible compared to the situation in another
topic—in plasma physics. The suggestions and corrections made by both of
themareveryappreciatedandhelpedtoimprovethemanuscriptsignificantly.
Thanks to all colleagues I worked with in the inspiring and challenging
atmosphere of the international fusion community.
IamgratefultoDr.Ascheronforhisencouragementandsupporttopublish
this book with Springer, and in particular, to Ms. Blanck for her excellent
technical assistance. Many thanks to Ms. Dewitz for most of the drawings
and illustrations.
Greifswald, May 2006 Dirk Naujoks
Contents
1 Introduction............................................... 1
Part I Fusion as Energy Source
2 Energy Problem and Related Safety Aspects .............. 5
3 Fusion Fuel ................................................ 9
3.1 Fusion Reactions ........................................ 9
3.2 Ignition and Burn Criteria................................ 12
4 Fusion Concepts ........................................... 19
4.1 Inertial Plasma Confinement.............................. 19
4.2 Magnetic Plasma Confinement ............................ 20
4.3 Stellarator Concept...................................... 20
4.4 Tokamak Concept ....................................... 22
4.5 Design of the First Wall.................................. 23
4.5.1 Limiter .......................................... 25
4.5.2 Divertor.......................................... 26
Part II The Plasma-Material Interface
5 The Plasma State.......................................... 31
5.1 Ionization Degree and Coupling Constant................... 32
5.2 Debye Length........................................... 34
5.3 Plasma Frequency ....................................... 35
5.4 Collisions in Plasmas .................................... 36
5.5 Transport Processes in Plasmas ........................... 41
5.5.1 Transport by Binary Collisions...................... 42
5.5.2 Neoclassical Diffusion .............................. 43
5.5.3 Anomalous Transport.............................. 44
X Contents
5.6 The Vlasov Equation .................................... 45
5.7 The Poisson Equation.................................... 46
6 Particle Coupling.......................................... 51
6.1 Binary Collisions ........................................ 52
6.1.1 Scattering Angle α ................................ 55
6.1.2 Scattering in the Coulomb Field, U(r)=C/r ......... 57
6.1.3 Cross-Section ..................................... 57
6.1.4 Interaction Potential U(r) .......................... 59
6.1.5 Binary Collision: General Case ...................... 62
6.2 Particle Transport in Matter.............................. 65
6.2.1 Definitions and Main Parameters.................... 66
6.2.2 Elastic Energy Loss................................ 68
6.2.3 Inelastic Energy Loss .............................. 70
6.3 Material Modification by Ion Beams ....................... 74
6.4 Retention and Tritium Inventory Control ................... 77
6.5 Impurity Generation ..................................... 78
6.5.1 Physical Sputtering................................ 79
6.5.2 Chemical Erosion.................................. 85
6.5.3 Radiation-Enhanced Sublimation.................... 87
6.5.4 Thermal Evaporation .............................. 88
6.5.5 Blistering ........................................ 89
6.6 Charge Effects .......................................... 90
6.7 Diffusion-Controlled Sputtering ........................... 91
6.8 Backscattering .......................................... 93
6.8.1 One-Collision Model ............................... 95
6.8.2 The Diffusion Model............................... 96
6.8.3 Approximations ................................... 97
6.9 Electron Emission ....................................... 98
6.9.1 Secondary Electron Emission (SEE) ................. 99
6.9.2 Thermionic Electron Emission ......................100
6.9.3 Electron Emission by the Application of an Electric
Field ............................................101
6.10 Modeling of Particle–Solid Interaction......................102
6.10.1 Molecular Dynamics ...............................102
6.10.2 Monte Carlo Methods..............................103
7 Electrical Coupling ........................................109
7.1 Electron Flux Density....................................110
7.2 Ion Flux Density ........................................111
7.3 Bohm Criterion with the “=” Sign.........................112
7.4 Space Charge Limited Currents ...........................116
7.5 Effect of Magnetic Field Geometry.........................118
Contents XI
7.6 Modeling of the Electric Sheath ...........................120
7.6.1 Principles of PIC Simulations .......................120
7.6.2 Boundary Conditions ..............................123
7.6.3 Choice of Time Step and Spatial Resolution ..........124
8 Power Coupling ...........................................127
8.1 Heat Flux Densities......................................127
8.2 Change of Surface Temperature ...........................129
8.2.1 Heat Conduction in a Half-Infinite Medium...........130
8.2.2 Point-like Heat Load...............................131
8.2.3 Heat Conduction and Diffusion......................131
8.3 Power Removal..........................................132
8.4 Thermal Stress..........................................133
9 Impurity Problems in Fusion Experiments .................135
9.1 Impurity Radiation ......................................135
9.1.1 Line Radiation....................................136
9.1.2 Bremsstrahlung ...................................136
9.1.3 Cyclotron Radiation ...............................138
9.1.4 Radiation Phenomena..............................138
9.1.5 Benefits of Radiation ..............................139
9.2 Erosion Phenomena in Fusion Experiments .................141
9.2.1 Plasma Disruption.................................142
9.2.2 Edge Localized Modes (ELMs)......................143
9.2.3 Runaway Electrons ................................144
9.2.4 Erosion by Energetic Alpha Particles ................145
9.2.5 Hot Spots or Carbon “Blooming” ...................146
9.2.6 Flake and Dust Production .........................147
9.2.7 Erosion by Charge-Exchange Neutrals................147
9.2.8 Erosion by Arcing .................................148
9.2.9 Non-Linear Erosion due to Impurities ................149
9.3 Impurity Transport ......................................154
9.3.1 Spatial Distributions of Neutrals ....................156
9.3.2 Atomic Processes in Impure Plasmas.................161
9.3.3 Prompt Redeposition ..............................163
9.3.4 SOL Screening Efficiency ...........................166
9.3.5 Accumulation of High-Z Impurities ..................167
9.3.6 Transport Barriers.................................167
9.3.7 Sawteeth as Plasma Cleaner ........................168
9.3.8 Deposition of Impurities............................169
9.3.9 Modeling of Erosion and Redeposition ...............172
9.4 Critical Impurity Concentration ...........................176
