MHD Waves in the Solar Atmosphere

530 Pages·2019·5.227 MB·English

by  Bernard Roberts

MHDWavesintheSolarAtmosphere
This volume presents a full mathematical exposition of the growing field of coronal seis-
mologywhichwillproveinvaluableforgraduatestudentsandresearchersalike.Roberts’
detailed and original research draws upon the principles of fluid mechanics and electro-
magnetism, as well as observations from the TRACE and SDO spacecraft and key results
insolarwavetheory.TheuniquechallengesposedbytheextremeconditionsoftheSun’s
atmosphere,whichoftenfrustrateattemptstodevelopacomprehensivetheory,aretackled
withrigourandprecision;complexmodelsofsunspots,coronalloopsandprominencesare
presented, based on a magnetohydrodynamic (MHD) view of the solar atmosphere, and
makinguseofFaraday’sconceptofmagneticfluxtubestoanalyseoscillatoryphenomena.
The rapid rate of progress in coronal seismology makes this essential reading for those
hopingtogainadeeperunderstandingofthefield.
bernard roberts isEmeritusProfessorofSolarMagnetohydrodynamicsattheUni-
versity of St Andrews. His important contributions to the field over the past forty years
havebeenrecognizedwithanelectiontotheRoyalSocietyofEdinburghin1997,aSaltire
Scottish Science Award in 1998, and, in 2010, the Royal Astronomical Society’s presti-
giousChapmanMedal,awardedfor‘investigationsofoutstandingmeritinsolar-terrestrial
physics’.

MHD Waves in the Solar Atmosphere
BernardRoberts
UniversityofStAndrews,Scotland
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Informationonthistitle:www.cambridge.org/9781108427661
DOI:10.1017/9781108613774
©BernardRoberts2019
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Firstpublished2019
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LibraryofCongressCataloging-in-PublicationData
Names:Roberts,Bernard,1946-author.
Title:MHDwavesinthesolaratmosphere/BernardRoberts
(UniversityofStAndrews,Scotland).
Othertitles:Magnetohydrodynamicwavesinthesolaratmosphere
Description:Cambridge;NewYork,NY:CambridgeUniversityPress,2019.|
Includesbibliographicalreferencesandindex.
Identifiers:LCCN2019002497|ISBN9781108427661(hardback:alk.paper)
Subjects:LCSH:Helioseismology.|Magnetohydrodynamicwaves.|Fluid
dynamics.|Solaratmosphere.|Electromagnetism.
Classification:LCCQB539.I5R632019|DDC523.7/6–dc23
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ISBN978-1-108-42766-1Hardback
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Contents
Preface pagexvii
1 GeneralPrinciples 1
1.1 Introduction 1
1.2 AVarietyofPlasmas 3
1.2.1 TheSun 4
1.3 TheMagnetohydrodynamicEquations 7
1.4 SomePropertiesoftheMHDEquations 9
1.4.1 FundamentalSpeeds 10
1.4.2 MagneticFluxTubes 13
1.4.3 TheInductionEquation 14
1.4.4 DiffusionofMagneticField (R (cid:2)1) 17
m
1.4.5 AdvectionofMagneticField(R (cid:3)1) 18
m
1.4.6 Thej×BForce 19
1.4.7 Energetics 21
1.5 AspectsofWavePropagation 22
1.5.1 Linearization 22
1.5.2 FourierRepresentation 23
1.5.3 DispersionRelations,PhaseSpeedandGroupVelocity 24
2 WavesinaUniformMedium 27
2.1 Introduction 27
2.2 WaveEquations 29
2.3 PlaneWaves 33
2.4 SoundWaves 35
2.5 MagnetohydrodynamicWaves 37
2.6 Alfve´nWaves 38
2.6.1 PhaseSpeedandGroupVelocity 38
2.6.2 PerturbationsinanAlfve´nWave 40
2.7 MagnetoacousticWaves 42
2.7.1 DispersionRelation 42
2.7.2 PhaseSpeedDiagrams 45
vii
viii Contents
2.7.3 GroupVelocityofMagnetoacousticWaves 46
2.7.4 PerturbationsintheMagnetoacousticWaves 50
2.8 MagnetoacousticWaves:TheSpecialCasec =c 57
A s
2.9 TwoPhysicalExtremes 58
2.9.1 TheIncompressibleFluid 60
2.9.2 Theβ =0Plasma 63
3 MagneticallyStructuredAtmospheres 66
3.1 Introduction 66
3.1.1 WaveEquations 67
3.1.2 SoundWaves 70
3.1.3 TheAlfve´nWave 71
3.2 MagnetohydrodynamicWaves:CartesianSystem 71
3.2.1 UniformMedium 73
3.2.2 TheCasek =0 74
y
3.3 MagnetohydrodynamicWaves:CylindricalGeometrySystem 75
3.4 Singularities 77
3.5 PhaseMixingoftheAlfve´nWave 78
3.6 TwoSpecialCases 79
3.6.1 TheIncompressiblePlasma 80
3.6.2 Theβ =0Plasma 80
4 SurfaceWaves 83
4.1 Introduction 83
4.2 ParallelPropagation 85
4.2.1 BoundaryConditionsatanInterface 86
4.3 TheSurfaceWaveDispersionRelation 87
4.3.1 The Hydromagnetic Surface Wave of an Incompressible
Medium 89
4.3.2 SurfaceWavesonaMagnetic–Non-MagneticInterface 89
4.3.3 Theβ =0Medium 93
4.3.4 PropertiesofSurfaceWaves 94
4.4 Non-ParallelPropagation 95
4.4.1 TheIncompressibleCase 97
4.4.2 Theβ =0Plasma 98
4.5 ResonantAbsorptionataSingleInterface:TheIncompressibleCase 99
5 MagneticSlabs 102
5.1 Introduction 102
5.2 TheIncompressibleCase:HydromagneticSurfaceWavesinaSlab 103
5.2.1 SausageandKinkModes 106
5.2.2 DispersionRelations 107
5.2.3 PressureandLongitudinalMotion 110
5.3 CompressibleEffects 113
5.4 TheIsolatedMagneticSlab 119