Collisionless Plasmas in Astrophysics

427 Pages·2013·5.925 MB·English

by  Gérard Belmont, Roland Grappin, Fabrice Mottez, Filippo Pantellini, Guy Pelletier

Gérard Belmont, Roland Grappin, Fabrice Mottez,
Filippo Pantellini, Guy Pelletier
Collisionless
Plasmas in
Astrophysics

GérardBelmont
RolandGrappin
FabriceMottez
FilippoPantellini
GuyPelletier
CollisionlessPlasmas
inAstrophysics
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Gérard Belmont
Roland Grappin
Fabrice Mottez
Filippo Pantellini
Guy Pelletier
Collisionless Plasmas in Astrophysics
TheAuthors AllbookspublishedbyWiley-VCHarecarefully
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V
Contents
AbouttheAuthors XI
1 Introduction 1
1.1 GoalsoftheBook 1
1.2 PlasmasinAstrophysics 5
1.2.1 PlasmasAreUbiquitous 5
1.2.2 TheMagnetosphereofStars 6
1.2.3 ShockWaves 6
1.2.4 PlanetaryMagnetospheres 7
1.3 UpstreamofPlasmaPhysics:ElectromagneticFieldsandWaves 9
1.3.1 ElectromagneticFields 9
1.3.2 TransverseandLongitudinalElectromagneticField 16
1.3.3 ElectromagneticFieldsinVacuum 17
1.3.4 PlaneWavesinaPlasma 24
1.3.5 ElectromagneticComponentsofPlanePlasmaWaves 25
1.3.6 SomeGeneralPropertiesofPlaneWavePolarizationandDispersion 26
1.3.7 ElectrostaticWaves 27
1.3.8 WavePacketsandGroupVelocity 28
1.3.9 PropagationofPlaneWavesinaWeaklyInhomogeneousMedium 28
1.3.10 UsefulApproximationsoftheMaxwellEquationsinPlasmaPhysics 30
1.4 UpstreamofPlasmaPhysics:TheMotionofChargedParticles 35
1.4.1 TheMotionoftheGuidingCenter 35
1.4.2 AdiabaticInvariants 39
1.4.3 TheMotionofaParticleinaWave 42
2 PlasmaDescriptionsandPlasmaModels 47
2.1 DistributionFunctionandMoments 47
2.1.1 FromIndividualParticlestoKineticDescription 47
2.1.2 KineticDescriptionandFirstOrderMoments 50
2.1.3 Higher-OrderMoments 53
2.1.4 MomentsforaMixtureofPopulations 54
2.1.5 NontrivialGeneralizationoftheFluidConcepts 55
2.1.6 Fluidvs.KineticDescription:AnExample 57
2.2 FromKinetictoFluidEquations 58
VI Contents
2.2.1 MomentEquations 58
2.2.2 LagrangianFormoftheMomentEquations 62
2.2.3 FluidEquations:NecessityofaClosureEquation 63
2.2.4 CollisionalLimit:FluidDynamicsandThermodynamics 65
2.3 NumericalMethods 67
2.3.1 VlasovCodes 67
2.3.2 ParticleinCellCodes(PIC) 69
2.3.3 PerturbativePICCodes 73
2.4 FluidCodes 74
2.5 HybridCodes 75
3 TheMagnetizedPlasmas 77
3.1 IdealMHD 77
3.1.1 TheIdealMHDSystem 77
3.1.2 TheIdealOhm’sLaw 79
3.2 EstablishingtheMHDModel 82
3.2.1 Large-ScaleConditionsofValidity 85
3.2.2 DeparturesfromMHD:Multi-FluidandKineticEffects 86
3.3 DimensionalAnalysisandPlasmaCharacteristicScales 88
3.3.1 DimensionalAnalysis:TheGeneralMethods 88
3.3.2 TemporalandSpatialScales,AdimensionalNumbers 92
3.3.3 DispersiveandDissipativeEffects 102
3.3.4 PhysicalImportanceoftheDimensionlessParameters 103
4 Collisional–Collisionless 105
4.1 NotionofCollisionsinPlasmaPhysics 105
4.1.1 CoulombInteraction:ALongRangeInteraction 105
4.1.2 MeanFreePath 109
4.1.3 TheDebyeLengthandtheNotionofDebye“Screening” 113
4.1.4 KnudsenNumber 115
4.1.5 PlasmaRegimes 117
4.2 NotionofDissipation 119
4.2.1 TransfersofEnergyandDissipation 119
4.2.2 TheConceptofDissipationinCollisionalFluids 120
4.2.3 Reversibility 123
4.2.4 IrreversibilityandDamping 125
4.2.5 TheNotionofReversibilityDependsontheDescription 127
4.2.6 Entropy 132
5 WavesinPlasmas 135
5.1 MHDWaves 136
5.1.1 PolarizationoftheMHDWaves 137
5.1.2 Application:AlfvénandMHDWavesintheEarth’sMagnetosphere 139
5.2 TransportInducedbyWaves 140
5.2.1 AlfvénWavePressure 141
5.3 High-FrequencyWaves 146
Contents VII
5.3.1 ColdPlasmaModel 146
5.3.2 ParallelPropagation 148
5.3.3 PerpendicularPropagation:OrdinaryandExtraordinaryWaves 150
5.3.4 Application:PlasmaCut-offsandLimitstotheRadioAstronomy 151
5.3.5 Application:TheDispersionofRadioWavesfromPulsars 152
5.3.6 Application:FaradayRotationintheInterstellarMedium 153
5.4 WhistlerMode 154
5.5 CollisionalDampinginFluidTheories 158
5.5.1 DissipativeEffectsandEntropy 158
5.5.2 DissipationandCollisions 161
5.5.3 StronglyCollisionalSystems 163
5.5.4 HeatConduction:FromCollisionaltoCollisionless 164
5.5.5 TheThermoelectricField:AnotherConsequenceofCollisionsbetween
IonsandElectrons 167
5.6 CollisionlessDamping 168
5.6.1 NumberofEigenmodes:Fluidvs.Kinetic 168
5.6.2 ASimpleExample:TheLangmuirWave,fromFluidtoKinetic 169
5.6.3 FluidTreatmentoftheLangmuirWave:ChoiceofaClosure 170
5.6.4 KineticTreatmentoftheLangmuirWave:LandauDamping 176
5.6.5 OtherTypesofKineticDamping 192
5.7 Instabilities 193
5.7.1 RealSpaceInstabilities:FluidTreatment 193
5.7.2 VelocitySpaceInstabilities:KineticTreatment 193
5.7.3 WeakKineticEffects 194
5.7.4 AnExample:TheTwo-StreamInstability 196
6 NonlinearEffects,Shocks,andTurbulence 199
6.1 CollisionlessShocksandDiscontinuities 199
6.1.1 NonlinearPropagation,Discontinuities,Jumps 199
6.1.2 ShocksandOtherDiscontinuitiesinaMagnetizedPlasma 205
6.1.3 TheUnmagnetizedShockWave 208
6.1.4 AParticularCase:TheTangentialDiscontinuity 208
6.1.5 Example:TheTerrestrialBowShock,theForeshocks 211
6.2 Turbulence(MainlyMHD) 213
6.2.1 Hydrodynamics:Equations,Shocks 216
6.2.2 Hydrodynamics:3DIncompressibleTurbulence 220
6.2.3 MHDTurbulence–Introduction 225
6.2.4 WeakIsotropic(IK)Regime 230
6.2.5 AnisotropicRegimes 235
6.2.6 Discussion 250
6.3 NonlinearKineticPhysics 253
6.3.1 NonlinearElectrostaticWaves 254
6.3.2 ParticleTrapping 255
6.3.3 The Nonlinear Interaction of Many Electrostatic Waves of Low
Amplitude 263
VIII Contents
6.3.4 Quasi-LinearTheory 265
6.3.5 TrappingversusQuasi-LinearDiffusion 269
7 FlowandParticleAccelerationProcesses 275
7.1 FlowAccelerationandHeatinginaCollisionalFluid 275
7.1.1 BasicEquations 275
7.1.2 ExpressionsforthePolytropicFluids 279
7.1.3 Bernoulli’sPrinciple 281
7.1.4 VenturiEffect 281
7.1.5 DeLavalNozzle 283
7.1.6 StellarWinds 284
7.1.7 PossibleRoutestoTurbulenceinStellarWinds 291
7.1.8 Accretion 293
7.2 MagneticReconnection 294
7.2.1 ConservationofConnectionsvs.Reconnection 294
7.2.2 DeparturefromtheIdealOhm’sLaw:MicroscopicMechanismsand
MacroscopicConsequences 296
7.2.3 FlowAccelerationbyReconnection 297
7.2.4 TearingInstability 302
7.2.5 3DReconnection 304
7.3 KineticAccelerationProcessesinMagnetospheres 305
7.3.1 SubstormsandAurorasintheEarth’sMagnetosphere 305
7.3.2 FermiAccelerationintheMagnetosphere 307
7.3.3 AccelerationbyaForcedCurrentForcedalongConvergentMagnetic
FieldLines 307
7.3.4 AccelerationbyanElectricCurrentForcedbyaWave 311
7.3.5 AccelerationbyanAlfvénWave(NonMHD)ParallelElectricField 312
7.3.6 ResonantAccelerationbyaWave 315
7.3.7 AccelerationbyaWaveofShortLength 316
7.3.8 Application:AccelerationintheEarth’sMagnetosphere 317
8 TransportandAccelerationofCosmicRays 319
8.1 TheProblemofTransport 320
8.1.1 TheMagneticField:ObstructiontoTransport 320
8.1.2 MagneticIrregularities:TransportAgent 322
8.1.3 OtherDiffusionCoefficients 327
8.1.4 TransportEquationofCosmicRays 330
8.1.5 DistributionofSuprathermalParticlesCrossingaShock 334
8.1.6 FromTransporttoAcceleration 336
8.2 FermiAccelerationofCosmicRays 336
8.2.1 TheBasicFermiProcess 338
8.2.2 FermiProcessataNonrelativisticShock 346
8.2.3 AstrophysicalApplication:CosmicRaysandSupernovae 350
8.2.4 AstrophysicalApplication:SynchrotronSources 351
8.2.5 GenerationofMagneticTurbulence 353
8.2.6 WhyAreFermiProcessesFavoredatShocks? 354