Fusion Plasma Physics, Second Edition

647 Pages·2012·6.959 MB·English

by  Prof. Weston M. Stacey(auth.)

Weston M. Stacey
Fusion Plasma Physics
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Weston M. Stacey
Fusion Plasma Physics
Second, Revised and Enlarged Edition
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Georgia Institute of Technology these books, including this book, to be free of errors.
Fusion Research Center Readers are advised to keep in mind that statements,
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USA may inadvertently be inaccurate.
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Preface for 2nd Edition
There have been significant developmentsin magnetic fusion plasma physics (and sup-
portingtechnology)sincethefirsteditionofthisbookwaspublishedalmostsevenyears
ago.TheformationoftheITERproject,inwhichEurope,Japan,Russia,theUSA,China,
India and South Korea are collaborating on the construction and subsequent operation
in the 2020s of the first experimentalfusion power reactor, has done much to focus the
world’sfusionresearcheffortsonresolvingthe resolvablephysicsissuesthatremainfor
thisperhapspenultimatesteponthepathtofusionpower.Thisfocusedattentionhasstim-
ulated substantial progress in better understanding the physics of burning plasmas, the
transportofparticlesandenergyfromthecentralplasmacoretotheedge,thephysicsof
theedgeplasmawheretheinteractionwiththesurroundingmaterialwalltakesplace,and
otherareasimportanttothesuccessofITER.
Itistheintentionofthissecondeditiontoincorporatetheseadvancesinunderstanding
oftokamakplasmaphysicsintoa comprehensivetextbookandreferenceonthestate-of-
the-artin fusion plasma physics. Major additionshave been made to the sections on the
physicsoftheplasmaedge,onthedivertor,ontherecyclingofneutralatomstorefuelthe
plasma, on the physicsmodelsfor the transportof energyand particlesfromthe plasma
coreintoandacrosstheplasmaedge,ontheevolvingfirst-principlesphysicscalculations
of the turbulent processes thought to govern transport of energy from the core and on
severalotherphysicsissuesimportanttoITER.Othersectionscontainingmaterialthathas
beensupplantedorfoundtobenotasrelevantasthenewermaterialhavebeenreducedor
eliminated.
Aswiththe1st edition,this2nd editionisintendedasatextbookforadvancedunder-
graduateandgraduatestudentsinphysics,nuclearengineeringandotherdisciplinesoffer-
ing courses in fusion plasma physics. It is also intended as a reference for practicing
physicistsandengineersinthefieldoffusionplasmaphysics,andasacombinationtext-
book and referencefor those who are enteringthat field. The bookshould be accessible
to anyone with the backgroundin math and physics of a university senior in physics or
aphysics-basedbranchofengineering.Thematerialwasdevelopedforgraduatecourses
in nuclear engineering at Georgia Tech (an asterisk denotes the material that we defer
untilthesecondgraduatecourse),butthefirstgraduatecourseisroutinelytakenbyafew
seniors.
Asalways,theproductionofabooklikethisinvolvesalotmorepeoplethantheauthor.
Iamgratefultoafewgenerationsofstudentswhohavehelpedmehonethematerialinto
a formthey foundmoreunderstandable,to my administrativeassistants at GeorgiaTech
who have helped with the assembling of figures, permissions, etc., and of course to the
very good team under Anja Tschoertner at Wiley-VCH who pulled it all together. I am
VI Prefacefor2ndEdition
alsogratefultomywife,Penelope,fortoleratingwithreasonablygoodgracethenumerous
holidayandweekendhoursthatIputintothiseffort,whichshenodoubtcorrectlypredicts
“willnevermakeyouahouseholdname”.
Atlanta,Georgia WestonM.Stacey
January2012
Preface
The developmentof mankind’s ultimate energy source, thermonuclearfusion, is a com-
pellingintellectualchallengeforthoseinvolvedandamatterofenormousimportancefor
all.Progresstodatehasbeenhardwon,butsubstantial.Wehavecomealongwayfromthe
beginningofthisquestinthemiddleofthepastcenturyandnowstandonthethresholdof
significantpowerproduction.Thetemperaturesoflaboratoryplasmas(theworkinggasof
fusion)havebeenincreasedfromthetensofthousandsofdegreesoftheearlyfusionexper-
imentstoabovesolartemperaturesandthentothehundredsofmillionsofdegreesrequired
forterrestrialfusion.Theproximitytothe conditionsatwhichthistemperaturecouldbe
maintainedindefinitelybytheself-heatingofthefusioneventhasbeenreducedfromthe
factor of hundreds of thousands that characterized the early experiments to within less
thanafactoroften.Tensofkilowattsoffusionpowerhavebeenproduced.Theengineer-
ingdesignandR&DfortheInternationalThermonuclearExperimentalReactor(ITER),
whichwillproducehundredsofmillionsofwatts,hasbeencompleted.Theconstruction
ofITERinFrancewilllbegininthenearfuture.
This progress in fusion energy development has been based on an ever-expanding
understandingofthephysicsofmagneticallyconfinedplasmasandonimprovementsinthe
technologyusedfortheirheatingandconfinement.Mostoftheadvancescitedabovehave
been realized in a toroidal confinement concept known as the “tokamak,” and there are
“advanced”variantsofthetokamakwhichpromisecertainadvantagesrelativetothe“con-
ventional”tokamak.Moreover,thereareanumberofother,lessdevelopedmagneticcon-
finementconceptsthatmayalsoleadtoimprovedperformance.Thenextquartercentury
willsurelywitnessstepsonthepathtofusionpowerequallyasexcitingasthoseofthepast.
Ihaveworkedonthedevelopmentoffusionpowerforabout30yearsandhavetaught
graduate and advanced undergraduatecourses in fusion plasma physics at GeorgiaTech
foralmostthatlong.Overthisperiod,boththedetailsandthescopeofthematerialthatI
feltwasappropriatetoincludeinacourseonfusionplasmaphysicshaschangedsignifi-
cantly,sothattheavailabletextbooks(includingoneofmyown)graduallybecameifnot
outofdateatleastsomewhatdated,asmorecompletedevelopmentsofthe“conventional”
topicsofplasmaphysics(e.g.individualparticlemotioninelectromagneticfields,kinetic
andfluidtheory,MHDequilibrium,plasmainstabilities,classicaltransport,neutralbeam
and wave heating) became available and as the portfolio of plasma physics was broad-
enedtoincludenewtopics(e.g.non–inductivecurrent-drive,fluctuation-driventransport,
rotation,plasma–materialsinteractions,H-modeedgetransportbarriers,thermalinstabili-
ties,neutralatomtransport,divertors,operationaldensityandpressurelimits,futurefusion
reactorandneutronsourceconcepts).Asmylecturenotesevolvedovertheyears,thenew
materialcametodominatetheconventionalmaterialfoundintheavailabletextbookson
plasmaphysics;hencemydecisiontopublishanewbookbasedontheselecturenotes.
VIII Preface
Thisbookisintendedasatextbookforstudentswithlittleornoknowledgeofplasma
physicsbutwiththebackgroundinmathandphysicsthatwouldbeexpectedofthegrad-
uate of a good undergraduatephysics or nuclear engineeringdepartment. Essentially all
ofthematerialcanbecoveredinatwo-semestercourse.Thesectionsthatarenotmarked
withanasteriskcontainmaterialthatcanbecoveredinaone-semestercourseforstudents
at the senior or first year graduate level. The sections marked with an asterisk contain
materialthatIwouldomitfromaone-semestercourseeitherbecauseitisoflowerpriority
oratamoreadvancedlevel.Thebookshouldalsoserveasaself-studyguideforadvanced
studentsandprofessionalsonthe newermaterialnotfoundin othertextbooks.Since the
bookprovidesmanypracticalcomputationalformulas,itshouldfurtherserveasauseful
referenceforpracticingprofessionals,andithasadetailedindexforthatpurpose.
It is always necessary to be selective in choosing what to include and what to omit
in a textbook. Most importantly, I have chosen to describe fusion plasma physics from
a theoretical viewpoint, although the field is predominantly experimental, because this
seemsthe bestway to conveyan understandingofthe basic principles.I have attempted
to be comprehensivein the treatment of plasma physics topics that are importantto the
developmentoffusionpower,buthaveomittedotherplasmaphysicstopics.Ihaveusually
chosena tokamakapplicationto illustrate these topicsbecausethe tokamakapplications
are the most highly developed. I have tried both to develop the basic principles and to
provide formulas that can be used in analyzing experimentalresults or designing future
reactors,butIhavestoppedshortofdescribingthecalculationalproceduresusedinthebig
codesof the field. I have includedsome discussionof experimentalresults, in particular
forareasofcurrentresearch,buthaveomittedanydiscussionofplasmadiagnostics.
The person who masters the material in this book should be able to understand the
work that is going on in fusion research laboratories and should be able to understand
the research reported in the major fusion plasma physics research journals. He or she
shouldhavethebackgroundnecessarytoacquirethedetailedexpertiserequiredfororigi-
nalresearchinanyareaofcurrentinterestinfusionplasmaphysics.
The author of a textbook such as this is always indebted to the many people who
developedthesubjectmatterandtothemanyotherpeoplewhoproducedthelecturenotes
and finally the book. The subject matter of this book is based on material from many
sources–thearchivalliteratureofthefield,specializedmonographsandreferencebooks,
earliertextbooks,laboratoryreports,etc.,onlyafractionofwhicharecitedinthesection
onfurtherreading.JohnMandrekasandEdwardThomaswereinvolvedintheassembling
ofmaterialonplasmaedgephysicsandplasma-materialsinteractionsforanearlyversion
of the lecture notes. Several versions of the lecture notes and the final manuscript were
preparedbyShaunaBennett-BoydandCandaceSalim.Agenerationofstudentscalledmy
attentiontotyposandworseinthelecturenotes,andZachFriis,DingkangZhangandRob
Johnson helped with the proofreadingfinal. Finally, the team at Wiley-VCH – Cornelia
Wanka,ClaudiaGrössl,PlamenTanovskiandothers–expertlyhandledtheconversionof
thelecturenotesintoabook.ToallofthesepeopleIamgrateful.
Atlanta,Georgia WestonM.Stacey
August2005
Contents
1 BasicPhysics 1
1.1 Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 CoulombCollisions . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4 ElectromagneticTheory . . . . . . . . . . . . . . . . . . . . . . . . . 17
2 MotionofChargedParticles 23
2.1 GyromotionandDrifts . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.1 Gyromotion . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.2 E (cid:1)B Drift . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.1.3 Grad-B Drift . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.1.4 PolarizationDrift . . . . . . . . . . . . . . . . . . . . . . . 29
2.1.5 CurvatureDrift . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 ConstantsoftheMotion . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2.1 MagneticMoment . . . . . . . . . . . . . . . . . . . . . . . 33
2.2.2 SecondAdiabaticInvariant* . . . . . . . . . . . . . . . . . 34
2.2.3 CanonicalAngularMomentum . . . . . . . . . . . . . . . . 36
2.3 Diamagnetism* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 MagneticConfinement 43
3.1 ConfinementinMirrorFields . . . . . . . . . . . . . . . . . . . . . . 43
3.1.1 SimpleMirror . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.2 TandemMirrors* . . . . . . . . . . . . . . . . . . . . . . . 48
3.2 ClosedToroidalConfinementSystems . . . . . . . . . . . . . . . . . 51
3.2.1 Confinement . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2.2 FluxSurfaces . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.3 TrappedParticles . . . . . . . . . . . . . . . . . . . . . . . 57
3.2.4 TransportLosses . . . . . . . . . . . . . . . . . . . . . . . 61
4 KineticTheory 67
4.1 BoltzmannandVlasovEquations . . . . . . . . . . . . . . . . . . . . 68
4.2 DriftKineticApproximation. . . . . . . . . . . . . . . . . . . . . . . 68
4.3 Fokker–PlanckTheoryofCollisions . . . . . . . . . . . . . . . . . . 71
4.4 PlasmaResistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.5 CoulombCollisionalEnergyTransfer . . . . . . . . . . . . . . . . . . 80
4.6 KrookCollisionOperators* . . . . . . . . . . . . . . . . . . . . . . . 84
X Contents
5 FluidTheory 87
5.1 MomentsEquations . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2 One-FluidModel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.3 MagnetohydrodynamicModel. . . . . . . . . . . . . . . . . . . . . . 95
5.4 AnisotropicPressureTensorModel* . . . . . . . . . . . . . . . . . . 98
5.5 StrongField,TransportTimeScaleOrdering . . . . . . . . . . . . . . 100
6 PlasmaEquilibria 105
6.1 GeneralProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.2 AxisymmetricToroidalEquilibria . . . . . . . . . . . . . . . . . . . . 107
6.3 LargeAspectRatioTokamakEquilibria. . . . . . . . . . . . . . . . . 113
6.4 SafetyFactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.5 ShafranovShift* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.6 Beta* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.7 MagneticFieldDiffusionandFluxSurfaceEvolution* . . . . . . . . . 127
6.8 AnisotropicPressureEquilibria* . . . . . . . . . . . . . . . . . . . . 130
6.9 ElongatedEquilibria* . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.9.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.9.2 Fluxsurfaceaverage . . . . . . . . . . . . . . . . . . . . . 134
6.9.3 Equivalenttoroidalmodels . . . . . . . . . . . . . . . . . . 134
6.9.4 Interpretationofthermaldiffusivitiesfrommeasured
temperaturegradients . . . . . . . . . . . . . . . . . . . . . 136
6.9.5 Predictionofpoloidaldistributionofconductiveheatflux . . 137
6.9.6 Mappingradialgradientstodifferentpoloidallocations . . . 138
7 Waves 141
7.1 WavesinanUnmagnetizedPlasma . . . . . . . . . . . . . . . . . . . 141
7.1.1 ElectromagneticWaves . . . . . . . . . . . . . . . . . . . . 141
7.1.2 IonSoundWaves . . . . . . . . . . . . . . . . . . . . . . . 143
7.2 WavesinaUniformlyMagnetizedPlasma . . . . . . . . . . . . . . . 144
7.2.1 ElectromagneticWaves . . . . . . . . . . . . . . . . . . . . 144
7.2.2 ShearAlfvenWave . . . . . . . . . . . . . . . . . . . . . . 147
7.3 LangmuirWavesandLandauDamping . . . . . . . . . . . . . . . . . 149
7.4 VlasovTheoryofPlasmaWaves* . . . . . . . . . . . . . . . . . . . . 152
7.5 ElectrostaticWaves* . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
8 Instabilities 165
8.1 HydromagneticInstabilities . . . . . . . . . . . . . . . . . . . . . . . 168
8.1.1 MHDTheory . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.1.2 Chew–Goldberger–LowTheory . . . . . . . . . . . . . . . 170
8.1.3 GuidingCenterTheory . . . . . . . . . . . . . . . . . . . . 172
8.2 EnergyPrinciple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
8.3 PinchandKinkInstabilities . . . . . . . . . . . . . . . . . . . . . . . 179
8.4 Interchange(Flute)Instabilities . . . . . . . . . . . . . . . . . . . . . 183