Fundamentals of plasma physics

550 Pages·2006·4.856 MB·English

by  Paul M. Bellan

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September30,2004
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Fundamentals of Plasma Physics
Paul M. Bellan
publisher’sinformationpage(pageiv,butnotnumbered)
Contentsincludes:
PublishedbyCUP
date
LibraryofCongress,
ComposedusingScientificWorkplace,Latex
tomyparents

Contents
Preface xi
1 Basicconcepts 1
1.1 Historyoftheterm“plasma” 1
1.2 Briefhistoryofplasmaphysics 1
1.3 Plasmaparameters 3
1.4 Examplesofplasmas 3
1.5 Logicalframeworkofplasmaphysics 4
1.6 Debyeshielding 7
1.7 Quasi-neutrality 9
1.8 Smallv.largeanglecollisionsinplasmas 11
1.9 Electronandioncollisionfrequencies 14
1.10 Collisionswithneutrals 16
1.11 Simpletransportphenomena 17
1.12 Aquantitativeperspective 20
1.13 Assignments 22
2 Derivationoffluidequations: Vlasov,2-fluid,MHD 30
2.1 Phase-space 30
2.2 DistributionfunctionandVlasovequation 31
2.3 Momentsofthedistributionfunction 33
2.4 Two-fluidequations 36
2.5 Magnetohydrodynamicequations 46
2.6 SummaryofMHDequations 52
2.7 SheathphysicsandLangmuirprobetheory 53
2.8 Assignments 58
3 Motionofasingleplasmaparticle 62
3.1 Motivation 62
3.2 Hamilton-Lagrangeformalismv.Lorentzequation 62
3.3 Adiabaticinvariantofapendulum 66
3.4 ExtensionofWKBmethodtogeneraladiabaticinvariant 68
3.5 Driftequations 73
3.6 RelationofDriftEquationstotheDoubleAdiabaticMHDEquations 91
3.7 Non-adiabaticmotioninsymmetricgeometry 95
3.8 Motioninsmall-amplitudeoscillatoryfields 108
3.9 Wave-particleenergytransfer 110
3.10 Assignments 119
viii
4 Elementaryplasmawaves 123
4.1 Generalmethodforanalyzingsmallamplitudewaves 123
4.2 Two-fluidtheoryofunmagnetizedplasmawaves 124
4.3 Lowfrequencymagnetizedplasma:Alfvénwaves 131
4.4 Two-fluidmodelofAlfvénmodes 138
4.5 Assignments 147
5 StreaminginstabilitiesandtheLandauproblem 149
5.1 Streaminginstabilities 149
5.2 TheLandauproblem 153
5.3 ThePenrosecriterion 172
5.4 Assignments 175
6 Coldplasmawavesinamagnetizedplasma 178
6.1 RedundancyofPoisson’sequationinelectromagneticmodeanalysis 178
6.2 Dielectrictensor 179
6.3 Dispersionrelationexpressedasarelationbetweenn2 andn2 193
x z
6.4 Ajourneythroughparameterspace 195
6.5 Highfrequencywaves: Altar-Appleton-Hartreedispersionrelation 197
6.6 Groupvelocity 201
6.7 Quasi-electrostaticcoldplasmawaves 203
6.8 Resonancecones 204
6.9 Assignments 208
7 Wavesininhomogeneousplasmasandwaveenergyrelations 210
7.1 Wavepropagationininhomogeneousplasmas 210
7.2 Geometricoptics 213
7.3 Surfacewaves-theplasma-filledwaveguide 214
7.4 Plasmawave-energyequation 219
7.5 Cold-plasmawaveenergyequation 221
7.6 Finite-temperatureplasmawaveenergyequation 224
7.7 Negativeenergywaves 225
7.8 Assignments 228
8 Vlasovtheoryofwarmelectrostaticwavesinamagnetizedplasma 229
8.1 Uniformplasma 229
8.2 Analysisofthewarmplasmaelectrostaticdispersionrelation 234
8.3 Bernsteinwaves 236
8.4 Warm,magnetized,electrostaticdispersionwithsmall,butfinitek 239
(cid:1)
8.5 Analysisoflinearmodeconversion 241
8.6 Driftwaves 249
8.7 Assignments 263
9 MHDequilibria 264
9.1 WhyuseMHD? 264
9.2 Vacuummagneticfields 265
ix
9.3 Force-freefields 268
9.4 Magneticpressureandtension 268
9.5 Magneticstresstensor 271
9.6 Fluxpreservation,energyminimization,andinductance 272
9.7 Staticversusdynamicequilibria 274
9.8 Staticequilibria 275
9.9 Dynamicequilibria:flows 286
9.10 Assignments 295
10 StabilityofstaticMHDequilibria 298
10.1 TheRayleigh-Taylorinstabilityofhydrodynamics 299
10.2 MHDRayleigh-Taylorinstability 302
10.3 TheMHDenergyprinciple 306
10.4 Discussionoftheenergyprinciple 319
10.5 Current-driveninstabilitiesandhelicity 319
10.6 Magnetichelicity 320
10.7 Qualitativedescriptionoffree-boundaryinstabilities 323
10.8 Analysisoffree-boundaryinstabilities 326
10.9 Assignments 334
11 MagnetichelicityinterpretedandWoltjer-Taylorrelaxation 336
11.1 Introduction 336
11.2 Topologicalinterpretationofmagnetichelicity 336
11.3 Woltjer-Taylorrelaxation 341
11.4 Kinkingandmagnetichelicity 345
11.5 Assignments 357
12 Magneticreconnection 360
12.1 Introduction 360
12.2 Water-beading:ananalogytomagnetictearingandreconnection 361
12.3 Qualitativedescriptionofsheetcurrentinstability 362
12.4 Semi-quantitativeestimateofthetearingprocess 364
12.5 Generalizationoftearingtoshearedmagneticfields 371
12.6 Magneticislands 376
12.7 Assignments 378
13 Fokker-Plancktheoryofcollisions 382
13.1 Introduction 382
13.2 StatisticalargumentforthedevelopmentoftheFokker-Planckequation 384
13.3 Electricalresistivity 393
13.4 Runawayelectricfield 395
13.5 Assignments 395
14 Wave-particlenonlinearities 398
14.1 Introduction 398
14.2 Vlasovnon-linearityandquasi-linearvelocityspacediffusion 399
x
14.3 Echoes 412
14.4 Assignments 426
15 Wave-wavenonlinearities 428
15.1 Introduction 428
15.2 Manley-Rowerelations 430
15.3 Applicationtowaves 435
15.4 Non-lineardispersionformulationandinstabilitythreshold 444
15.5 Diggingaholeintheplasmaviaponderomotiveforce 448
15.6 Ionacousticwavesoliton 454
15.7 Assignments 457
16 Non-neutralplasmas 460
16.1 Introduction 460
16.2 Brillouinflow 460
16.3 Isomorphismtoincompressible2Dhydrodynamics 463
16.4 Nearperfectconfinement 464
16.5 Diocotronmodes 465
16.6 Assignments 476
17 Dustyplasmas 483
17.1 Introduction 483
17.2 Electronandioncurrentflowtoadustgrain 484
17.3 Dustcharge 486
17.4 Dustyplasmaparameterspace 490
17.5 LargeP limit:dustacousticwaves 491
17.6 Dustionacousticwaves 494
17.7 Thestronglycoupledregime: crystallizationofadustyplasma 495
17.8 Assignments 504
Bibliographyandsuggestedreading 507
References 509
AppendixA: Intuitivemethodforvectorcalculusidentities 515
AppendixB: Vectorcalculusinorthogonalcurvilinearcoordinates 518
AppendixC: Frequentlyusedphysicalconstantsandformulae 524
Index 528