The Physics of Plasmas

546 Pages·2003·2.626 MB·English

by  T. J. M. Boyd, J. J. Sanderson

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ThePhysicsofPlasmas
ThePhysicsofPlasmasprovidesacomprehensiveintroductiontothesubjectsuit-
ableforadoptionasaself-containedtextforcoursesatadvancedundergraduateand
graduatelevel.Theextensivecoverageofbasictheoryisillustratedwithexamples
drawnfromfusion,spaceandastrophysicalplasmas.
Aparticularstrengthofthebookisitsdiscussionofthevariousmodelsusedto
describe plasma physics including particle orbit theory, fluid equations, ideal and
resistivemagnetohydrodynamics,waveequationsandkinetictheory.Therelation-
ships between these distinct approaches are carefully explained giving the reader
a firm grounding in the fundamentals, and developing this into an understanding
of some of the more specialized topics. Throughout the text, there is an emphasis
onthephysicalinterpretationofplasmaphenomenaandexercises,designedtotest
thereader’sunderstandingatavarietyoflevels,areprovided.
Students of physics and astronomy, engineering and applied mathematics will
findaclearandrigorousexplanationofthefundamentalpropertiesofplasmaswith
minimal mathematical formality. This book will also serve as a reference source
for physicists and engineers engaged in research on aspects of fusion and space
plasmas.
Beforeretiring,T.J.M. BOYD wasProfessorofPhysicsattheUniversityofEssex.
He has taught graduate students on plasma physics courses in Europe and North
America. His research interests have included atomic collision theory, computa-
tional physics and plasma physics. Professor Boyd has co-authored two previous
books, Plasma Dynamics (1969) with J.J. Sanderson, and Electricity (1979) with
C.A.Coulson.
JEFF SANDERSON is Professor Emeritus at the University of St Andrews. His
research interests are in theoretical plasma physics and specifically plasma insta-
bilities, collisionless shock waves and transport phenomena. Professor Sanderson
hastaughtplasmaphysicsforover30years,principallyatStAndrewsUniversity,
and the UKAEA Culham Summer School, but also by invitation in the USA,
Europe and Pakistan. As well as co-authoring Plasma Dynamics (1969) he was
a contributor to two Culham textbooks and co-editor with R.A. Cairns of Laser
PlasmaInteractions(1980).

The Physics of Plasmas
T.J.M. BOYD
UniversityofEssex
J.J. SANDERSON
UniversityofStAndrews
  
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge  , United Kingdom
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521452908
© Cambridge University Press 2003
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without the written permission of Cambridge University Press.
First published in print format 2003
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Contents
Preface pagexi
1 Introduction 1
1.1 Introduction 1
1.2 Thermonuclearfusion 2
1.2.1 TheLawsoncriterion 3
1.2.2 Plasmacontainment 4
1.3 Plasmasinspace 6
1.4 Plasmacharacteristics 7
1.4.1 Collisionsandtheplasmaparameter 10
2 Particleorbittheory 12
2.1 Introduction 12
2.2 Constanthomogeneousmagneticfield 14
2.2.1 Magneticmomentandplasmadiamagnetism 16
2.3 Constanthomogeneouselectricandmagneticfields 16
2.3.1 Constantnon-electromagneticforces 18
2.4 Inhomogeneousmagneticfield 19
2.4.1 Gradientdrift 19
2.4.2 Curvaturedrift 21
2.5 Particledriftsandplasmacurrents 22
2.6 Time-varyingmagneticfieldandadiabaticinvariance 24
2.6.1 Invariance of the magnetic moment in an inhomogeneous
field 25
2.7 Magneticmirrors 26
2.8 Thelongitudinaladiabaticinvariant 28
2.8.1 Mirrortraps 30
2.9 Magneticfluxasanadiabaticinvariant 31
v
vi Contents
2.10 Particleorbitsintokamaks 33
2.11 Adiabaticinvarianceandparticleacceleration 35
2.12 Polarizationdrift 37
2.13 Particlemotionatrelativisticenergies 38
2.13.1 Motioninamonochromaticplane-polarized
electromagneticwave 38
2.14 Theponderomotiveforce 40
2.15 Theguidingcentreapproximation:apostscript 41
Exercises 43
3 Macroscopicequations 48
3.1 Introduction 48
3.2 Fluiddescriptionofaplasma 49
3.3 TheMHDequations 58
3.3.1 ResistiveMHD 59
3.3.2 IdealMHD 60
3.4 ApplicabilityoftheMHDequations 61
3.4.1 Anisotropicplasmas 67
3.4.2 CollisionlessMHD 69
3.5 Plasmawaveequations 71
3.5.1 GeneralizedOhm’slaw 73
3.6 Boundaryconditions 74
Exercises 76
4 Idealmagnetohydrodynamics 77
4.1 Introduction 77
4.2 Conservationrelations 78
4.3 Staticequilibria 82
4.3.1 Cylindricalconfigurations 85
4.3.2 Toroidalconfigurations 89
4.3.3 NumericalsolutionoftheGrad–Shafranovequation 100
4.3.4 Force-freefieldsandmagnetichelicity 102
4.4 SolarMHDequilibria 105
4.4.1 Magneticbuoyancy 106
4.5 StabilityofidealMHDequilibria 108
4.5.1 Stabilityofacylindricalplasmacolumn 111
4.6 Theenergyprinciple 119
4.6.1 FiniteelementanalysisofidealMHDstability 123
4.7 Interchangeinstabilities 124
4.7.1 Rayleigh–Taylorinstability 124
4.7.2 Pressure-driveninstabilities 128
Contents vii
4.8 IdealMHDwaves 130
Exercises 133
5 Resistivemagnetohydrodynamics 140
5.1 Introduction 140
5.2 Magneticrelaxationandreconnection 142
5.2.1 Drivenreconnection 145
5.3 Resistiveinstabilities 148
5.3.1 Tearinginstability 151
5.3.2 Drivenresistiveinstabilities 155
5.3.3 Tokamakinstabilities 157
5.4 Magneticfieldgeneration 162
5.4.1 Thekinematicdynamo 163
5.5 Thesolarwind 169
5.5.1 Interactionwiththegeomagneticfield 177
5.6 MHDshocks 179
5.6.1 Shockequations 182
5.6.2 Parallelshocks 186
5.6.3 Perpendicularshocks 188
5.6.4 Obliqueshocks 189
5.6.5 Shockthickness 190
Exercises 193
6 Wavesinunboundedhomogeneousplasmas 197
6.1 Introduction 197
6.2 Somebasicwaveconcepts 198
6.2.1 Energyflux 200
6.2.2 Dispersivemedia 200
6.3 Wavesincoldplasmas 202
6.3.1 Field-freeplasma(B = 0) 209
0
6.3.2 Parallelpropagation(k (cid:2) B ) 210
0
6.3.3 Perpendicularpropagation(k ⊥ B ) 214
0
6.3.4 Wavenormalsurfaces 217
6.3.5 Dispersionrelationsforobliquepropagation 222
6.4 Wavesinwarmplasmas 227
6.4.1 Longitudinalwaves 228
6.4.2 Generaldispersionrelation 230
6.5 Instabilitiesinbeam–plasmasystems 238
6.5.1 Two-streaminstability 240
6.5.2 Beam–plasmainstability 241
6.6 Absoluteandconvectiveinstabilities 244
viii Contents
6.6.1 Absolute and convective instabilities in systems with
weaklycoupledmodes 245
Exercises 248
7 Collisionlesskinetictheory 252
7.1 Introduction 252
7.2 Vlasovequation 254
7.3 Landaudamping 256
7.3.1 ExperimentalverificationofLandaudamping 263
7.3.2 Landaudampingofionacousticwaves 265
7.4 Micro-instabilities 268
7.4.1 Kineticbeam–plasmaandbump-on-tailinstabilities 273
7.4.2 Ionacousticinstabilityinacurrent-carryingplasma 274
7.5 Amplifyingwaves 276
7.6 TheBernsteinmodes 277
7.7 Inhomogeneousplasma 283
7.8 TestparticleinaVlasovplasma 287
7.8.1 Fluctuationsinthermalequilibrium 288
Exercises 289
8 Collisionalkinetictheory 296
8.1 Introduction 296
8.2 Simpletransportcoefficients 297
8.2.1 Ambipolardiffusion 300
8.2.2 Diffusioninamagneticfield 301
8.3 Neoclassicaltransport 304
8.4 Fokker–Planckequation 307
8.5 Collisionalparameters 313
8.6 Collisionalrelaxation 317
Exercises 321
9 Plasmaradiation 324
9.1 Introduction 324
9.2 Electrodynamicsofradiationfields 325
9.2.1 Powerradiatedbyanacceleratedcharge 326
9.2.2 Frequencyspectrumofradiationfromanacceleratedcharge 328
9.3 Radiationtransportinaplasma 330
9.4 Plasmabremsstrahlung 334
9.4.1 Plasmabremsstrahlungspectrum:classicalpicture 336
9.4.2 Plasma bremsstrahlung spectrum: quantum mechanical
picture 338