Chao-Hai Du · Pu-Kun Liu Millimeter- Wave Gyrotron Traveling-Wave Tube Amplifi ers Millimeter-Wave Gyrotron Traveling-Wave Tube Amplifiers Chao-Hai Du • Pu-Kun Liu Millimeter-Wave Gyrotron Traveling-Wave Tube Amplifiers 123 Chao-HaiDu Pu-KunLiu SchoolofElectronicsEngineering andComputerScience PekingUniversity Beijing,China ISBN978-3-642-54727-0 ISBN978-3-642-54728-7(eBook) DOI10.1007/978-3-642-54728-7 SpringerHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2014940850 ©Springer-VerlagBerlinHeidelberg2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface Agyrotrontraveling-wavetube(gyro-TWT)amplifieriscapableofgeneratinghigh- powerandbroadbandcoherentelectromagneticradiationonthelevelofhundredsof kilowatts in the millimeter-wave range. It is one of the most promising candidates of the electromagnetic-wave power amplifier for the next generation of imaging radars and long-range high-data-rate wireless communications. It would play an important role in many fields, such as national security, small objects tracking in the outer space, accurate atmosphere and weather monitoring, and so on. A gyro- TWT amplifies the driving power based on the convective instability principle of the relativistic electron cyclotron maser (ECM). The amplification simultaneously suffersfromcompetingabsoluteinstabilities,whichleadtocomplicatedself-excited oscillations.Asaresult,theinstabilitycompetitionnotonlystopsthesystemfrom efficientoperationbutalsohinderspracticalapplications.Investigatingthephysics oftheinstabilitycompetitionandexploringsolutionstosuppressself-excitedoscil- lationsturnintoprimaryfactorsessentiallyrelatedtothegyro-TWTdevelopment. Hence, it is of important academic value and engineering application to study the beam-waveinteractionmechanismandtorevealtheinstabilitycompetitionphysics in depth, as a way to further enhance the amplifier performance and promote its applicationinhigh-powermillimeter-waveradarsandcommunicationsystems. This book focuses on the beam-wave interaction mechanisms and the compe- tition relations between the convective instability and the absolute instability in gyro-TWT amplifiers. The book starts with a technical review of the gyro-TWT development in past decades in Chap. 1. Chapter 2 presents a comprehensive presentation of the linear theory and nonlinear theory of ECM interaction. The main content of the book is conveyed in Chaps. 3, 4, and 5, including detailed investigation of the lossy dielectric-loaded (DL) waveguide, ultrahigh gain gyro- TWT amplifier, and lossy DL gyro-TWT amplifier. Chapter 6 is arranged as an exploratorysection.Threenovelconceptsrelatedtoamplifierinteractioncircuitare introducedhere.Chapter7presentssomekeytechnologiesrelatedtodevelopinga gyrotronamplifier. Thecontentsofthebookoriginatefromrecentyearstheoreticalandengineering works on developing gyrotron amplifiers in our group. We try to present them in v vi Preface a comprehensive way, especially a lot of vivid figures are conceived to illustrate the complicated physics. The millimeter-wave gyrotron amplifier has experienced a tremendous advance in the past decade. We hope this book would be helpful to promoteitsfurtherdevelopment. Beijing,China Chao-HaiDu Pu-KunLiu Contents 1 ReviewofGyrotronTraveling-WaveTubeAmplifiers................... 1 1.1 MicrowaveElectronics.................................................. 1 1.2 ElectronsCyclotronMaserandGyrotron.............................. 4 1.2.1 ThePrincipleofECM.......................................... 4 1.2.2 TheCharacteristicsofaGyrotron.............................. 6 1.2.3 TheCategoryofGyrotronTubes............................... 7 1.3 GyrotronTraveling-Wave-TubeAmplifiers............................ 10 1.3.1 TheDevelopmentofGyro-TWTs.............................. 10 1.3.2 CommentsonTechnologies.................................... 14 1.3.3 ProblemsandProspects ........................................ 19 References..................................................................... 21 2 FundamentalTheoryoftheElectronCyclotronMaser ................. 27 2.1 Introduction ............................................................. 27 2.2 TheoryoftheWaveguides.............................................. 29 2.2.1 TheoryofUniformDielectric-LoadedWaveguide............ 30 2.2.2 TheoryofPeriodicDielectric-LoadedWaveguide............ 34 2.3 TheoryoftheElectronCyclotronMaserinWaveguideSystem...... 39 2.3.1 PartitioningtheTransversePlaneofanECMSystem ........ 40 2.3.2 TheLinearTheoryofDielectric-LinedECMSystem ........ 42 2.3.3 TheNonlinearTheoryofDielectric-LoadedECMSystem... 45 2.3.4 BasicConcepts.................................................. 47 2.4 Summary ................................................................ 50 Appendix I: Derivation of the Linear Theory inDielectric-LinedWaveguide......................................... 50 1.TheFieldExpressioninGCC ....................................... 51 2.TheTransversePerturbedBeamCurrent............................ 52 3.TheLaplaceTransformation......................................... 55 References..................................................................... 58 vii viii Contents 3 Novel Propagation Characteristics of Lossy Dielectric-LoadedWaveguides ............................................. 61 3.1 Introduction ............................................................. 61 3.2 DielectricLoss-InducedModalTransition............................. 63 3.2.1 EigenvalueandModeIdentification ........................... 63 3.2.2 ModalTransition................................................ 66 3.2.3 ModalDegeneration............................................ 69 3.2.4 ModalSelection................................................. 71 3.3 PeriodicDLWaveguidewithSuppressedPropertyofPeriodicity.... 74 3.3.1 EigenvalueandModeIdentification ........................... 75 3.3.2 InfluenceofDielectricSlotRatio.............................. 75 3.3.3 ModalTransitioninaPeriodicDielectric WaveguideSystem.............................................. 78 3.3.4 Suppressing the System Periodicity Using DielectricLoss.................................................. 81 3.4 ModeMapping.......................................................... 82 3.5 Conclusion .............................................................. 87 References..................................................................... 88 4 InstabilityCompetitioninanUltrahighGainGyro-TWTAmplifier.. 91 4.1 Introduction ............................................................. 91 4.1.1 AnalysisMethodoftheInstabilityCompetition .............. 92 4.1.2 TheKeyFactorsofInstabilityCompetition................... 93 4.2 BalanceBetweentheBackwardWaveandForwardWave inanAbsoluteInstability............................................... 94 4.2.1 InternalFeedbackDynamicsofanAbsoluteInstability...... 96 4.2.2 MagneticTuning................................................ 98 4.2.3 High-OrderAxialMode........................................ 101 4.2.4 WaveguideWallLoss........................................... 104 4.2.5 AMultistageInteractionGyro-TWTCircuit.................. 106 4.3 OscillationwithMulti-steadyStates ................................... 109 4.3.1 Self-ConsistentNonlinearInstabilityStudy................... 109 4.3.2 AttenuationStrengthoftheLossyLinearStage............... 110 4.3.3 Multi-steadyStatesofAbsoluteInstabilityOscillation....... 111 4.3.4 ApplyingMagneticFieldTaperingtoEnhance NonlinearStageStability....................................... 114 4.3.5 InfluenceoftheDownstreamPortReflection ................. 116 4.3.6 Pre-bunchedECMRadiation................................... 117 4.4 Summary ................................................................ 118 References..................................................................... 119 Contents ix 5 ALossyCeramic-LoadedMillimeter-WaveGyro-TWTAmplifier .... 121 5.1 Introduction ............................................................. 121 5.2 PropagationCharacteristicsApproximation........................... 123 5.2.1 The Propagation Characteristics oftheDielectric-LoadedWaveguide........................... 123 5.2.2 LinearandNonlinearInstabilityStudy........................ 126 5.3 Linear Study of Full-Wave Interaction inDielectric-LoadedWaveguide ....................................... 132 5.3.1 LinearInstabilityCompetitionStudy.......................... 133 5.3.2 LinearGrowthRateStudy...................................... 135 5.4 Nonlinear Study of Full-Wave Interaction inDielectric-LoadedWaveguide ....................................... 137 5.4.1 NonlinearInstabilityCompetitionStudy...................... 138 5.4.2 AmplificationCharacteristics .................................. 140 5.5 Beam-WaveCouplingStrength......................................... 143 5.6 Summary ................................................................ 149 References..................................................................... 149 6 Exploring New Mechanisms for High Power Millimeter-WaveGyrotronAmplifiers .................................... 151 6.1 Introduction ............................................................. 151 6.2 AnECM-CascadedAmplifier.......................................... 153 6.2.1 TheConceptofECM-CascadedAmplifier.................... 154 6.2.2 Beam-WaveInteractioninanECM-CascadedAmplifier..... 155 6.2.3 Discussion....................................................... 157 6.3 High-OrderModeDriftTube........................................... 158 6.3.1 TheConceptofHigh-OrderModeDriftTube ................ 158 6.3.2 Beam-WaveInteractioninOvermodedDriftTube............ 159 6.3.3 Discussion....................................................... 161 6.4 High-PowerGyrotronAmplifierBasedonBi-modesOperation ..... 161 6.4.1 TheConceptofBi-modesOperation .......................... 161 6.4.2 ThePrincipleofBi-modesOperation.......................... 163 6.5 High-PowerGyrotronAmplifierBasedonECM-Cascade andPre-bunchingScheme(Gyro-CPA)................................ 164 6.5.1 KeyTechnologiesRelatedtoaGyro-CPA..................... 164 6.5.2 PrincipleofAmplifierBasedonECMCascade andPre-bunchingExcitation................................... 165 6.5.3 Discussion....................................................... 171 6.6 Conclusion .............................................................. 171 References..................................................................... 172