Electrodynamics of Conducting Dispersive Media PDF
Preview Electrodynamics of Conducting Dispersive Media
Springer Series on Atomic, Optical, and Plasma Physics 111 Babak Shokri Anri A. Rukhadze Electrodynamics of Conducting Dispersive Media Springer Series on Atomic, Optical, and Plasma Physics Editor-in-Chief GordonW.F.Drake,DepartmentofPhysics,UniversityofWindsor,Windsor,ON, Canada SeriesEditors JamesBabb,Harvard-SmithsonianCenterforAstrophysics,Cambridge,MA,USA Andre D. Bandrauk, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, QC,Canada Klaus Bartschat, Department of Physics and Astronomy, Drake University, DesMoines,IA,USA Charles J. Joachain, Faculty of Science, Université Libre Bruxelles, Bruxelles, Belgium Michael Keidar, School of Engineering and Applied Science, George Washington University,Washington,DC,USA PeterLambropoulos,FORTH,UniversityofCrete,Iraklion,Crete,Greece Gerd Leuchs, Institut für Theoretische Physik I, Universität Erlangen-Nürnberg, Erlangen,Germany Alexander Velikovich, Plasma Physics Division, United States Naval Research Laboratory,Washington,DC,USA The Springer Series on Atomic, Optical, and Plasma Physics covers in a compre- hensivemannertheoryandexperimentintheentirefieldofatomsandmoleculesand their interaction with electromagnetic radiation. Books in the series provide a rich source of new ideas and techniques with wide applications in fields such as chem- istry,materialsscience,astrophysics,surfacescience,plasmatechnology,advanced optics, aeronomy, and engineering. Laser physics is a particular connecting theme thathasprovidedmuchofthecontinuingimpetusfornewdevelopmentsinthefield, suchasquantum computation andBose-Einsteincondensation.Thepurposeofthe seriesistocoverthegapbetweenstandardundergraduatetextbooksandtheresearch literaturewithemphasisonthefundamentalideas,methods,techniques,andresults inthefield. Moreinformationaboutthisseriesathttp://www.springer.com/series/411 (cid:129) Babak Shokri Anri A. Rukhadze Electrodynamics of Conducting Dispersive Media BabakShokri AnriA.Rukhadze PhysicsDepartment Fizikaplazmy ShahidBeheshtiUniversity ProkhorovGeneralPhysicsInstitute Tehran,Iran Moscow,Russia ISSN1615-5653 ISSN2197-6791 (electronic) SpringerSeriesonAtomic,Optical,andPlasmaPhysics ISBN978-3-030-28967-6 ISBN978-3-030-28968-3 (eBook) https://doi.org/10.1007/978-3-030-28968-3 ©SpringerNatureSwitzerlandAG2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartofthe materialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors, and the editorsare safeto assume that the adviceand informationin this bookarebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Ithasbeenmorethan55yearssincetheRussianeditionofthebookElectromagnetic PropertiesofPlasmaandPlasma-likeMediabyV.SilinandA.Rukhadzeappeared. At that time, this book was one of the world’s first book publications on the electrodynamics of plasma and was the first in which both the electrodynamics of plasmaandplasma-likemediasuchasgaseousplasma,metals,semiconductors,and molecularcrystalswereexpoundedinacommonapproach.Itwasimpossibletobe confined only to the classical approach and so the authors presented the quantum descriptionforthefirsttimeinmonographform. Despitethegreatpopularityofthebookinmanycountries,thebookhasnotyet beentranslatedtoanyotherlanguageandsoonlytheRussianeditionisused.There appearsanewopportunitytogatherthisbookwithasignificantexpansiontomakeit morepopularforstudentsandresearchers. Overtheyears,electrodynamicsofplasma-likemediaachievedsignificantdevel- opments, particularly in respect of the applications. The methods and applications outlined in the present monograph of electrodynamic properties have generally foundtheirrelevanceandcanrightfullybecomethetablebookfortheoristsworking inthisfieldofscience,especiallyforyoungphysicists. The authors have written this book using the books Electrodynamics of Plasma and Plasma-like Media (by Silin and Rukhadze in the Russian language) and Principles of Plasma Electrodynamics (by Alexandrov, Bogdankevich, and Rukhadze in the English language) supplemented by new subjects. Furthermore, eachchapterhasitsownproblemsintroducingsomeconceptsandmodels.Someof theseproblemshavebeenselectedfromthebooksPrinciplesofPlasmaElectrody- namics (by Alexandrov, Bogdankevich, and Rukhadze) and Electromagnetic Phe- nomenainMatter:StatisticalandQuantumApproaches(byI.N.Toptygin). In this book, a sequential representation of the electrodynamics of conducting ! ! ! mediawithdispersioninthreevectorrepresentations(E,B,D)isgiven.Inaddition to the general formalism of such a representation, specific media such as classical nondegenerateplasma,degeneratemetalplasma,magnetoactiveanisotropicplasma, v vi Preface atomichydrogengas,semiconductors,andmolecular crystalsareconsidered. Each chapter is equipped with a sufficient number of problems with solutions that have academicandappliedimportance. This book is designed for post-graduate students, as well as scientific profes- sionalsinvolvedinrelevantfieldsofscience. Wehopethatthecontentofthisbooksignificantlyexpandsthecircleofreadersof the book, which is designed not only for plasma physicist but also for the pro- fessionals in material media with temporal and spatial dispersions, senior and graduatestudents,andpostdocresearchers. Here it is worthy to respect the memory of Professor Anri A. Rukhadze, who passedawayinMarch2018andleftmealoneinthefinalpreparationofthisbook. Hewasanoutstandingscientistandteacher.Mayhismemorybeeternal. Tehran,Iran BabakShokri Moscow,Russia AnriA.Rukhadze Contents 1 PrinciplesofElectrodynamicsofMediawithSpatial andTemporalDispersion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 EquationsofElectromagneticFields. . . . . . . . . . . . . . . . . . .. . . 1 1.2 TensorofComplexDielectricPermittivity. . . . . . . . . . . . . . . . . 7 1.3 DispersionofDielectricPermittivity. .. . . . .. . . . .. . . .. . . . .. 15 1.4 EnergyoftheElectromagneticFieldinaMedium. . . . . . . . . . . . 21 1.5 ElectromagneticWaveinaMedium. . . . . . . . . . . . . . . . . . . . . . 28 1.6 PlaneMonochromaticWavesinaMedium. . . . . . . . . . . . . . . . . 34 1.7 ElectromagneticWave’sPropagationinaWeakly SpatiallyDispersiveMedium. . . . . . . . . . . . . . . . . . . . . . . . . . . 41 1.8 EnergyLossofFastMovingElectronsintheMedium. . . . . . . . . 51 1.9 ElectromagneticFieldFluctuations. . . . . . . . . . . . . . . . . . . . . . . 60 1.9.1 CorrelationFunctionsandGeneralAnalysis. . . . . . . . . . 60 1.9.2 ElectromagneticFieldFluctuationsin HomogenousIsotropicNon-gyrotropicMedia. . . . . . . . 68 1.9.3 CausalityPrincipleandGeneralizationof Kramers–KronigRelations. . . . . . . . . . . . . . . . . . . . . . 73 1.10 ElectromagneticPropertiesofInhomogeneousMedia. . . . . . . . . 75 1.10.1 InhomogeneousMediaWithoutSpatialDispersion. ApproximationofGeometricalOptics. . . . . . . . . . . . . . 76 1.10.2 ApproximationofGeometricalOpticsfor InhomogeneousMediawithSpatialDispersion. . . . . . . 84 1.11 Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 2 IsotropicPlasma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 2.1 KineticEquationwithSelf-consistentFields. . . . . . . . . . . . . . . . 111 2.2 DielectricPermittivityofCollisionlessIsotropicPlasma. . . . . . . 116 2.3 DielectricPermittivityandElectromagneticOscillations ofIsotropicCollisionlessNon-relativisticElectronPlasma. . . . . . 126 vii viii Contents 2.4 DielectricPermittivityandElectromagneticOscillations ofRelativisticCollisionlessElectronPlasma. . . . . . . . . . . . . . . . 135 2.5 OscillationsofIsotropicElectron–IonPlasma. . . . . . . . . . . . . . . 140 2.6 HydrodynamicsofCollisionlessPlasma. . . . . . . . . . . . . . . . . . . 144 2.7 DielectricPermittivityofPlasma;Takingaccountof ParticleCollisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 2.8 BoundaryProblemofFieldsinPlasma. . . . . . . . . . . . . . . . . . . . 160 2.9 ReflectionandAbsorptionofElectromagneticWavesin Semi-boundedPlasma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 2.10 LinearElectromagneticPhenomenainBoundedPlasmas. . . . . . . 180 2.10.1 SurfaceElectromagneticWavesin Semi-BoundedPlasmas. . . . . . . . . . . . . . . . . . . . . . . . 181 2.10.2 SurfaceWavesonPlasmaLayers. . . . . . . . . . . . . . . . . 192 2.11 Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 3 AnisotropicPlasma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 3.1 DielectricPermittivityofCollisionlessPlasmaina ConstantMagneticField. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 3.2 ElectromagneticOscillationsofNon-relativisticPlasma inaConstantMagneticField. . . . . . . . . . . . . . . . . . . . . . . . . . . 233 3.3 RelativisticElectronPlasmaintheMagneticField. . . . . . . . . . . 245 3.4 Electron-IonPlasmaintheExternalMagneticField. . . . . . . . . . 253 3.5 ParticleCollisionsinMagneto-ActivePlasma. . . . . . . . . . . . . . . 259 3.6 MagnetohydrodynamicsofCollisionlessPlasma. . . . . . . . . . . . . 267 3.7 InteractionofStraightNeutralizedBeamsofCharged ParticleswithPlasma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 3.7.1 InteractionofaStraightMonoenergeticElectron BeamwithColdPlasma:CherenkovInstability. . . . . . . 280 3.7.2 EffectofThermalMotionontheCherenkov Instability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 3.7.3 Current-DrivenInstabilitiesinPlasma:Bunemann Instability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 3.7.4 Current-DrivenInstabilitiesinPlasma:Ion-Acoustic Instability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 3.8 DielectricTensorofWeaklyInhomogeneousMagnetized PlasmasintheApproximationofGeometricalOptics. . . . . . . . . 292 3.8.1 DistributionFunctionofEquilibrium InhomogeneousPlasma. . . . . . . . . . . . . . . . . . . . . . . . 292 3.8.2 MagneticConfinementofInhomogeneousPlasma. . . . . 294 3.8.3 DielectricTensorofWeaklyInhomogeneous MagnetizedPlasma. . . . . . . . . . . . . . . . . . . . . . . . . . . 295 3.8.4 LarmorDriftFrequency. . . . . . . . . . . . . . . . . . . . . . . . 298 3.9 SpectraofHFandLarmorOscillationsinWeakly InhomogeneousPlasmas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Contents ix 3.9.1 TransverseOscillationsofWeaklyInhomogeneous IsotropicPlasma. . . .. . . .. . . .. . . .. . . . .. . . .. . . .. 299 3.9.2 LangmuirOscillations.Tonks-DattnerResonances. . . . . 301 3.9.3 Ion-AcousticOscillationsofInhomogeneous IsotropicPlasma. . . .. . . .. . . .. . . .. . . . .. . . .. . . .. 302 3.9.4 OscillationsofWeaklyInhomogeneous Magneto-ActivePlasma. . . . . . . . . . . . . . . . . . . . . . . . 303 3.9.5 DriftOscillationsofWeaklyInhomogeneous CollisionlessPlasma. . . . . . . . . . . . . . . . . . . . . . . . . . . 305 3.10 InstabilityofBoundaryofMagneticallyConfinedPlasma. . . . . . 312 3.10.1 Poisson’sEquationforMagneticallyConfined InhomogeneousPlasma. . . . . . . . . . . . . . . . . . . . . . . . 313 3.10.2 SurfaceOscillationsofColdMagneto-Active PlasmawithaSharpBoundary. . . . . . . . . . . . . . . . . . . 315 3.10.3 InstabilityoftheSurfaceofMagnetically ConfinedPlasma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 3.11 Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 4 QuantumPlasma:InfluenceofSpatialDispersionon SomePhenomenainMetals. . . . .. . . . .. . . . . .. . . . .. . . . .. . . . .. 341 4.1 QuantumKineticEquationwithSelf-consistentFields andMagneticPermittivityofanElectronGas. . . . . . . . . . . . . . . 341 4.2 LongitudinalOscillationsofaDegenerateElectron GasandCharacteristicEnergyLossoftheFast MovingElectrons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 4.3 AnomalousSkin-EffectinMetals.. . . . . . . . . . .. . . . . . . . . .. . 352 4.4 ParamagneticResonanceAbsorptionofMetalsby ConductionElectrons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 4.5 CollisionlessAbsorptionandExcitationofSound WavesinCondensedMatters. . . . . . . . . . . . . . . . . . . . . . . . . . . 366 4.5.1 AcousticWaveAbsorptionandExcitationin Piezo-Semiconductors. . . . . . . . . . . . . . . . . . . . . . . . . 371 4.5.2 ExcitationofCoupledQuasiElasto-Electromagnetic SurfaceWaves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 4.6 Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 5 SpatialDispersioninMolecularCrystals.. . . . .. . . . .. . . . .. . . . .. 409 5.1 DielectricPermittivityofMolecularCrystals. . . . . .. . . . . . . . .. 409 5.2 ThePermittivityofaMonatomicGaswithSpatial Dispersion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 5.3 Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454
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