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SuperconductingRadiofrequencyTechnologyforAccelerators
SuperconductingRadiofrequencyTechnology forAccelerators
StateoftheArtandEmergingTrends
HasanPadamsee
Author
Dr.HasanPadamsee
CornellUniversity
NewmanLaboratory
CornellUniversity NY UnitedStates
CoverImage:CourtesyofFermiNational AcceleratorLaboratory
Allbookspublishedby WILEY-VCH arecarefully produced.Nevertheless,authors,editors,and publisherdonotwarranttheinformation containedinthesebooks,includingthisbook, tobefreeoferrors.Readersareadvisedtokeep inmindthatstatements,data,illustrations, proceduraldetailsorotheritemsmay inadvertentlybeinaccurate.
LibraryofCongressCardNo.: appliedfor
BritishLibraryCataloguing-in-PublicationData Acataloguerecordforthisbookisavailable fromtheBritishLibrary.
Bibliographicinformationpublishedby theDeutscheNationalbibliothek TheDeutscheNationalbibliothekliststhis publicationintheDeutscheNationalbibliografie;detailedbibliographicdataareavailable ontheInternetat <http://dnb.d-nb.de>
©2023WILEY-VCHGmbH,Boschstraße12, 69469Weinheim,Germany
Allrightsreserved(includingthoseof translationintootherlanguages).Nopartof thisbookmaybereproducedinanyform–by photoprinting,microfilm,oranyothermeans–nortransmittedortranslatedintoamachine languagewithoutwrittenpermissionfromthe publishers.Registerednames,trademarks,etc. usedinthisbook,evenwhennotspecifically markedassuch,arenottobeconsidered unprotectedbylaw.
PrintISBN: 978-3-527-41409-3
ePDFISBN: 978-3-527-83629-1
ePubISBN: 978-3-527-83630-7
oBookISBN: 978-3-527-83631-4
Typesetting Straive,Chennai,India
1Introduction 3
2SRFFundamentalsReview 7
2.1SRFBasics 7
2.2FabricationandProcessingonNb-BasedSRFStructures 11
2.2.1CavityFabrication 12
2.2.2Preparation 12
2.2.3ADecadeofProgress 15
2.3SRFPhysics 15
2.3.1ZeroDCResistance 15
2.3.2MeissnerEffect 17
2.3.3SurfaceResistanceandSurfaceImpedanceinRFFields 19
2.3.4NonlocalResponseofSupercurrent 22
2.3.5BCS 24
2.3.6ResidualResistance 30
2.3.7SmearingofDensityofStates 31
2.3.8Ginzburg–Landau(GL)Theory 31
2.3.9CriticalFields 34
2.3.10ComparisonBetweenGinzburg–LandauandBCS 39
2.3.11Derivationof Rs and X s 39
PartIIHighQFrontier:PerformanceAdvancesand Understanding 43
3Nitrogen-Doping 45
3.1Introduction 45
3.2N-DopingDiscovery 46
3.3SurfaceNitride 48
3.4InterstitialN 49
3.5ElectronMeanFreePathDependence 52
3.5.1LE-μSRMeasurementsofMeanFreepath 53
3.6Anti-Q-SlopeOriginsfromBCSResistance 55
3.7N-DopingandResidualResistance 58
3.7.1TrappedDCFluxLosses 58
3.7.2ResidualResistancefromHydrideLosses 58
3.7.3TunnelingMeasurements 59
3.8RFFieldDependenceoftheEnergyGap 61
3.9FrequencydependenceofAnti-Q-Slope 63
3.10TheoriesforAnti-Q-Slope 63
3.10.1XiaoTheory 63
3.10.2GurevichTheory 68
3.10.3NonequilibriumSuperconductivity 72
3.10.4Two-FluidModel-BasedonWeakDefects 75
3.11QuenchFieldofN-DopedCavities 77
3.12EvolutionandComparisonofN-dopingRecipes 83
3.13High Q andGradientR&DProgramforLCLS-HE 83
3.14N-DopingatOtherLabs 88
3.15SummaryofN-doping 88
4High Q via300 ∘ CBake(Mid-T-Bake) 91
4.1ASurpriseDiscovery 91
4.2SimilaritiestoN-Doping 91
4.3Mid-TBakingatOtherLabs 95
4.4TheLow-FieldQ-Slope(LFQS)and340 ∘ CBakingCures 97
4.5LossesatVeryLowFields 100
4.6LossesfromTwo-LevelSystems(TLS) 100
4.7EliminatingTLSLosses 101
5High Q’sfromDCMagneticFluxExpulsion 105
5.1TrappedFluxLosses,Sensitivity 105
5.2TrappedFluxSensitivityModels 106
5.3VortexPhysics 108
5.4CalculationofSensitivitytoTrappedFlux 110
5.5DependenceofSensitivityonRFFieldAmplitude 112
5.6DCMagneticFluxExpulsion 114
5.6.1Fast versus Slow-CoolingDiscovery 114
5.6.2ThermoelectricCurrents 118
5.7CoolingRatesforFluxExpulsion 122
5.8FluxExpulsionPatterns 123
5.9GeometricEffects–FluxHole 127
5.10FluxTrappingWithQuench 127
5.11MaterialQualityVariations 129
5.12ModelingFluxTrappingFromPinningVariations 135
PartIIIHighGradientFrontier:PerformanceAdvancesand Understanding 139
6High-Field Q Slope(HFQS)–UnderstandingandCures 141
6.1HFQSSummary 141
6.2HFQSinLow-�� Cavities 142
6.3Deconvolutionof RBCS and Rres 143
6.4DepthofBakingEffect 145
6.4.1FromAnodization 145
6.4.2FromHFRinsing 145
6.4.3DepthofMagneticFieldPenetrationbyLE-μSR 145
6.5RoleoftheOxideLayerandRoleofN-Infusion 148
6.6SIMSStudiesofO,H,andOHProfiles 151
6.7HydrogenPresenceinHFQS 156
6.8TEMStudiesonHydrides 158
6.9Niobium–hydrogenPhaseDiagram 160
6.10HEnrichmentatSurface 161
6.11 Q-diseaseReview 163
6.12VisualizingNiobiumHydrides 165
6.12.1Cold-stageConfocalMicroscopy 165
6.12.2Cold-stageAtomicForceMicroscopy(AFM) 166
6.13ModelforHFQS–ProximityEffectBreakdownofNano-hydrides 168
6.13.1BakingBenefitandProximityEffectModel 170
6.14PositronAnnihilationStudiesofHFQSandBakingEffect 172
6.15PointContactTunnelingStudiesofHFQSandBakingEffect 173
7QuestforHigherGradients:Two-StepBakingand N-Infusion 175
7.1Two-StepBaking 175
7.2SubtleEffectsofTwo-StepBaking–Bifurcation 175
7.2.1BifurcationReduction 177
7.3N-Infusionat120 ∘ C 181
7.4N-InfusionatMediumTemperatures 184
7.5UnifyingQuenchFields 188
7.6QuenchDetectionbySecondSoundinSuperfluidHelium 190
8ImprovementsinCavityPreparation 193
8.1ComparisonsofColdandWarmElectropolishingMethods 193
8.2ChemicalSoaking 197
8.3OpticalInspectionSystemandDefectsFound 199
8.4RoboticsinCavityPreparation 200
8.5PlasmaProcessingtoReduceFieldEmission 201
9PursuitofHigherPerformancewithAlternateMaterials 207
9.1NbFilmsonCuSubstrates 207
9.1.1DirectCurrentMagnetronSputtering 209
Contents
9.1.2DC-biasDiodeSputteringatHighTemperature(400–600 ∘ C) 209
9.1.3SeamlessCavityCoating 210
9.1.4Nb–CuFilmsbyECR 211
9.1.5Nb–CuFilmsviaHigh-PowerImpulseMagnetronSputtering (HIPIMS) 212
9.2AlternativestoNb 214
9.2.1Nb3 Sn 215
9.2.2MgB2 217
9.2.3NbNandNbTiN 221
9.3Multilayers 222
9.3.1SIS’Structures 222
9.3.2TheoreticalEstimates 223
9.3.3Results 223
9.3.4SS’Structures 225
9.4Summary 227
PartIVApplications 229
10NewCavityDevelopments 231
10.1CrabCavitiesforLHCHighLuminosity 231
10.2Short-PulseX-Rays(SPX)SystemfortheAPSUpgrade 238
10.3QWRCavityforAcceleration 239
10.4TravelingWaveStructureDevelopment 241
11OngoingApplications 245
11.1Overview 245
11.2Low-BetaAcceleratorsforNuclearScienceandNuclear Astrophysics 246
11.2.1ATLASatArgonne 246
11.2.2ISACandISAC-IIatTRIUMF 247
11.2.3SPIRALIIatGANIL 247
11.2.4HIEISOLDE 248
11.2.5RILACatRIKEN 249
11.2.6SPESUpgradeofALPIatINFN 249
11.2.7FRIBatMSU 250
11.2.8RAON 253
11.2.9SpokeResonatorStructureDevelopmentstoAvoidMultipacting 254
11.2.10JAEAUpgrade 255
11.2.11HELIAC 256
11.2.12SARAF 259
11.2.13HIAFatIMP 259
11.2.14IFMIF 260
11.3High-IntensityProtonAccelerators 260
11.3.1SNS 260
11.3.2ESS 262
11.3.3AcceleratorDrivenSystems(CADS) 262
11.3.4CiADS(ChinaInitiativeAcceleratorDrivenSystem) 265
11.3.5JapanAtomicEnergyAgency(JAEA)–ADS 266
11.3.6High-IntensityProtonAcceleratorDevelopmentinIndia 266
11.3.7PIP-IIandBeyond 267
11.4ElectronsforLightSources–Linacs 269
11.4.1EuropeanX-rayFreeElectronLaser(EXFEL) 269
11.4.2LinacCoherentLightSourceLCLS-IIandLCLS-HE(LCLS-High Energy) 273
11.4.3ShanghaiCoherentLightFacility(SCLF)SHINE 278
11.4.4InstituteofAdvancedScienceFacilities(IASF) 279
11.4.5PolishFree-ElectronLaserPOLFEL 279
11.5ElectronsforStorageRingLightSources 281
11.5.1High-EnergyPhotonSource(HEPS) 281
11.5.2TaiwanPhotonSource(TPS) 281
11.5.3HigherHarmonicCavitiesforStorageRingsChaoenWANG,NSRRC, Taiwan 282
11.5.4BNL 284
11.6ElectronsinEnergyRecoveryLinacs(ERL)forLightSources& Electron–IonColliders 285
11.6.1PrototypingERLTechnologyatCornell 285
11.6.2KEKERLs 287
11.6.3Light-HouseProjectforRadiopharmaceuticals 288
11.6.4PekingERL 288
11.6.5BerlinERL 288
11.6.6MESAERL 289
11.6.7SRFPhoto-injectorsforERLs 289
11.7ElectronsforNuclearPhysics,NuclearAstrophysics,Radio-Isotope Production 290
11.7.1CEBAFatJeffersonLab 290
11.7.2ARIELatTRIUMF 291
11.7.3ERLforLHeCatCERN 291
11.8CrabCavitiesforLHCHighLuminosity 292
11.9OngoingandNear-FutureProjectsSummary 293
12FutureProspectsforLarge-ScaleSRFApplications 295
12.1TheInternationalLinearCollider(ILC)forHigh-EnergyPhysics 295
12.2FutureCircularColliderFCCee 298
12.3ChinaElectron–PositronCollider,CEPC 300
13QuantumComputingwithSRFCavities 303
13.1IntroductiontoQuantumComputing 303
13.2Qubits 303
13.3SuperpositionandCoherence 304
x Contents
13.4Entanglement 304
13.52DSRFQubits 306
13.6JosephsonJunctions 307
13.7DilutionRefrigeratorforMilli-KelvinTemperatures 308
13.8QuantumComputingExamples 310
13.93DSRFQubits 310
13.10CavityQEDQuantumProcessorsandMemories 312
References 315
ListofSymbols 365
ListofAcronyms 369 Index 375
Preface
Ithasbeenmorethan20yearssinceWiley's1998publicationandenthusiastic receptionof RFSuperconductivityforAccelerators [1]andnowmorethan10years sincethesequelin2009: RFSuperconductivity–Science,Technology,andApplications [2].ManyaspectsofsuperconductingRF(SRF)developmentarethoroughly coveredinthesetwobooks,plusmanyreviewpapers[3–6],andmostcompletely intheproceedingsofinternationalSRFconferences(1980–2021)publishedon JACoW.org[7].
Overtheperiod2010–2022therehasbeenspectacularprogressintermsofthe performanceofSRFstructures,scientificunderstandingoftheimprovements, innovativecavitydesignsfornewapplications,andwideexplorationofnewmaterialavenuestotakeusbeyondthecapabilitiesofthepopularstandardofniobium, aswellasthelargescale,worldwideimplementationofthematuretechnologyto manynewaccelerators.Excitingnewprospectsareonthehorizon.
ItistimeforanewvolumeonRFSuperconductivitytoprovideacomprehensive updateformorethanadecadeofadvancescarriedoutbyenthusiasticresearchersall overtheworld.AlargefractionoftheprogressinSRFperformancereportedhereisa testamenttothecreativityandsuccessofimaginativeresearcherswhohaveworked oninnovativetreatments,pursuedeffortstogainunderstanding,andopenedthe doortonewapplications.OurreviewofthefieldcoversprogresstillJanuary2022. NodoubttherewillbemuchadditionalprogressreportedinupcomingcomingmeetingssuchasTeslaTechnologyCollaboration(TTC)Meetings,aswellasThinFilm SRFConferences.WelookforwardtomanynewresultsbythetimeofthenextSRF Conferencein2023.
Expertsaswellasnewcomerstothefield,includingstudents,willbenefitfromthe discussionofprogress,aswellasrecentandforthcomingapplications.Researchers inacceleratorphysicsmayalsofindmuchthatisrelevanttotheirdiscipline.There arenowmorethanathousandpractitionersoftheSRFfieldatmorethan150institutionsandindustriesworldwide.
Thebookhasfourparts.PartIistheintroductionandupdateofSRFfundamentals.ManyoftheSRFbasicscoveredinthefirsttwobookswillonlybebriefly touched,althoughessentialswillbesummarizedforthesakeofcompleteness. PartIIcoversperformanceadvancesandunderstandingatthe highQfrontier .Part IIIcoversperformanceadvancesandunderstandingatthe highgradient frontier.
PartIVcoversnewcavityandnewtreatmentdevelopments,aswellasongoing applicationsandfutureprospects.
AnexcitingnewdevelopmentdiscussedbrieflyinPartIVistheuseofSRFcavities forquantumcomputing.Nbcavitiesofferatransformativevehicleforincreasingthe coherencetimesofqubitsfromsub-millisecondstoseconds,promisingtobringthe quantumcomputingfieldtoquantumadvantageoverclassicalcomputers.
October26,2022
References
HasanPadamsee
1 Padamsee,H.,Knobloch,J.,andHays,T.(1998). RFSuperconductivityfor Accelerators,2e,2008Wiley.
2 Padamsee,H.(2009).RFSuperconductivity:Science,Technology,and Applications,2e2008.Wiley.
3 Kelly,M.(2012).Superconductingradio-frequencycavitiesforlow-betaparticle accelerators. Rev.Accel.Sci.Technol. 5:185–203.https://doi.org/10.1142/ 9789814449953_0007.
4 Belomestnykh,S.(2012).Superconductingradio-frequencysystemsforhigh-ß particleaccelerators.In: ReviewsofAcceleratorScienceandTechnology: ApplicationsofSuperconductingTechnologytoAccelerators (eds.A.Choa andW.Chou)vol.5,147–184.WorldScientific.https://doi.org/10.1142/ S179362681230006X.
5 Reece,C.E.andCiovati,G.(2012).Superconductingradio-frequencytechnology R&Dforfutureacceleratorapplications.In: ReviewsofAcceleratorScienceand Technology:ApplicationsofSuperconductingTechnologytoAccelerators,vol.5 (ed.A.ChaoandW.Chou),285–312.WorldScientific.https://doi.org/10.1142/ S1793626812300113.
6 Gurevich,A.(2012).Superconductingradio-frequencyfundamentalsforparticleaccelerators. Rev.Accel.Sci.Technol. 5:119–146.https://doi.org/10.1142/ S1793626812300058.
7 SRFConferenceProceedings.
UpdateofSRFFundamentals
Introduction
Discoveredin1911,superconductivityisafascinatingphenomenaofmodern physicswithmarvelousscientificandtechnologicalapplications,suchaspowerful magnetsformedicalimaging(magneticresonanceimaging[MRI]),forhighenergy physics,inparticular,thelargehadroncollider(LHC),fornuclearfusion,anda widerangeofmodernapplications.
Thefirstmajormilestoneinthehistoryofsuperconductivitywasthediscovery byKamerlinghOnnes[1,2]thattheelectricalresistanceofvariousmetals,such asmercury,lead,andtindisappearswhenthetemperatureisloweredbelowsome criticaltemperaturevalue, T c .Zeroelectricalresistanceallowspersistentcurrentsin superconductingrings.Thesecurrentsflowwithoutanymeasurabledecreaseupto oneyear,allowingalowerboundof105 yearsontheirdecaytime.Comparedtogood conductors,suchascopper,whichhavearesidualresistivityatlowtemperatureof theorderof10 6 Ω-cm,theresistivityofasuperconductorislowerthan10 23 Ω-cm.
Subsequently,MeissnerandOchsenfeld[3]discoveredperfectdiamagnetismin superconductors.Magneticfieldsareexcludedfromsuperconductors.Anyfieldoriginallypresentinthemetalisexpelledfromthemetalwhenloweringthetemperature belowitscriticalvalue.Expulsionofmagneticfieldfromwallsofsuperconducting cavitiesviatheMeissnereffectwillbeanimportanttopicinChapter4.
Startingwithpioneeringeffortsinthe1960's,RFsuperconductivity(SRF)finally catapultedtoanenablingtechnologysincethe1980's.SRFhassinceequippedfrontieracceleratorsinhighenergyphysics,nuclearastrophysics,nuclearphysics,as wellaslightsourcesandneutronsourcesformaterialsandlifesciences.Newapplicationsarecomingonlinetointenseprotonsourcesforneutrinobeams,andtransmutationofnuclearwaste,aswellasfordeflectingcavitiesforbeamtiltsforhigher luminosityatLHC.
TheprimaryadvantagesoftheSRFtechnologyhavebeendiscussedinthetwo previousbooks[4,5].ThemostattractivefeaturesofapplyingSRFtoparticleacceleratorslieinthehighacceleratinggradient, Eacc ,possibleincontinuouswave(cw)and long-pulseoperatingmodes,alongwithextremelylowRFlossesinthecavitywalls atcryogenictemperatures.Thereisanotherimportantadvantage.Thepresenceof acceleratingstructureshasadisruptiveeffectonthebeam,limitingthequalityofthe beaminaspectssuchasenergyspread,beamhalo,orthemaximumcurrent.SRF systemscanbeshorter,andtherebyimposelessdisruptiontothebeam.Byvirtueof SuperconductingRadiofrequencyTechnologyforAccelerators:StateoftheArtandEmergingTrends, FirstEdition.HasanPadamsee.
©2023WILEY-VCHGmbH.Published2023byWILEY-VCHGmbH.
Figure1.1 Superconductingcavitiesspanningthefullrangeofparticlevelocities.
Source:[6]/M.Kelly,ArgonneNationalLab/withpermissionfromWorldScientificPublishing.
lowwalllosses,SRFcavitiescanbedesignedwithlargebeamholes(apertures)to furtherreducebeamdisruptionandallowhigherbeamcurrentsdesirable.
Therearetwodistincttypesofsuperconductingcavities.Thefirsttype,TM-mode cavities,isforacceleratingchargedparticlesthatmoveatnearlythespeedoflight, suchaselectronsinahigh-energylinearaccelerator(linac)orastoragering.The secondtype,TEM-modecavities,isforparticlesthatmoveatasmallfraction (e.g.0.01–0.5)ofthespeedoflight,suchastheheavyions.Structuresforthese applicationsarethequarterwaveresonator(QWR),thehalfwaveresonator(HWR) andthesinglespokeresonator(SSR),oronewithmultiplespokes.Atintermediate velocities,bothTMandTEMtypescouldbeused,dependingontheapplication. Figure1.1[6]showspracticalgeometrysketches,andtypicalRFfrequenciesfor eachcavitytype,dependingonthevelocityoftheparticlesspanningthefullvelocity rangeofparticles.
TheQWRisthecompactchoiceforlow-�� applications(��< 0.15)requiring ∼50% lessstructurewithlessoverallRFdissipationcomparedtotheHWRforthesamefrequencyand �� .(Here �� = v/c, where v isthespeedoftheparticleunderacceleration, and c isthespeedoflight.)Buttheasymmetricfieldpatternintheacceleratinggaps producesverticalsteeringthatincreaseswithvelocity.TheQWRislessmechanicallystablethantheHWRduetotheunsupportedendatthebottominFigure1.1. HencetheHWRismoresuitableinthemid-velocityrange(��> 0.15)orwheresteeringmustbeeliminated(i.e.forhighintensity).Ithasasymmetricfieldpatternand provideshighermechanicalrigidity.ButtheHWRislarger,requiresalargercryomodule(CM),andhasroughlytwicethedissipationforthesame �� andfrequency. TheSSRisamorecompactvariantoftheHWR.Itopensapathtoextensiontoseveralacceleratinggapsalongthebeaminasingleresonator,usingmultiplespokes. Itprovidesahighereffectivevoltage,butwithanarrowertransittimeacceptance.
1Introduction 5
Thisbookwillmostlyfocusonareviewforthenearvelocity-of-light,orhigh-�� acceleratingcavities,andtoparticleacceleratorsthatusethesestructures.Weonly brieflycoversomeofthelatestapplicationsoflow-�� structurestomajorfacilities. Forin-depthcoverageoflow-�� cavities,wereferthereadertoexcellentarticles[6], andtutorialsatInternationalSRFconferences[7,8].
ThisbookwillnotcovermanyimportanttopicsinSRF,suchasinputcouplers, higher-order-modecouplers,tuners,andcryomodules.Forlatestdevelopmentsin theseareas,wereferthereadertomanypaperspublishedintheProceedingsof theInternationalSRFConferences.TheproceedingsareavailableontheJACoW website[9].
SRFFundamentalsReview
2.1SRFBasics
Webrieflyreviewthekeyfiguresofmeritthatcharacterizetheperformanceofan SRFcavityorstructure,referringthereaderto[4,5]forin-depthcoverage.The firstimportantparameter–the acceleratingvoltageV c – istheratioofthemaximumenergygainthataparticlemovingalongthecavityaxiscanachieve,tothe chargeofthatparticle.Asallexistinghigh-�� multicellSRFstructuresoperateina �� standing-wavemode,theoptimallength(activelength)ofthecavitycellsis ����/2. Here �� istherfwavelength.Next,the acceleratinggradient istheratiooftheacceleratingvoltagepercelltothecelllength,or Eacc = V c /(����/2).Thecavity quality factorQ0 determinesthenumberofrfcycles(multipliedby2�� )requiredtodissipate theenergystoredinthecavity.ThekeyperformancefactorofanSRFcavityistypicallygivenbythe Q0 versus E curve,showinghowrflosseschangeasthegradient (Eacc )rises.Thequalityfactor(Q0 )isderivedasaratiooftwovaluesvia Rs = G/Q0 , where G isthegeometryfactor,and Rs isthesurfaceresistivity.Asthenamesuggests, thegeometryfactorisdeterminedonlybytheshapeofthecavity.Surfaceresistivity(oftenreferredtoassurfaceresistance, Rs )dependsonlyonmaterialproperties andtherffrequency.Thephysicsofsurfaceresistanceisdominatedbythephysics ofsuperconductors,andsowillbeamajortopicofthebook.Thecavity’sshunt impedance, Rsh ,determineshowmuchaccelerationaparticlecanderivefromacavityforagivenpowerdissipation, Pc inthecavitywalls.Hence Rsh = V c 2 /Pc .Arelated quantityisthegeometricshuntimpedance Rsh /Q0 ,orsimply R/Q,whichdepends onlyonthecavityshape.Twootherimportantfiguresofmeritaretheratios Epk /Eacc and Bpk /Eacc ofthepeaksurfaceelectricfield Epk andmagneticfield Bpk totheacceleratinggradient Eacc .Thetypicaldistributionsoftheelectricandmagneticfield inasinglecell �� = 1cavityareshowninFigure2.1a,b,aswellasforalow-�� QWR inFigure2.1c.Notethatforthesinglecell �� = 1 cavity,themagneticfieldismaximumneartheequator,whereastheelectricfieldisatapeakneartheiris.Maximum electricfieldlocationsfortheQWRareshowninred. Foragivenacceleratingfield,both Epk and H pk needtobeminimizedforagood design.Ahighsurfaceelectricfieldcancausefieldemissionofelectrons,which
Note: Q0 and Q willbeusedinterchangeablythroughoutthebook.
SuperconductingRadiofrequencyTechnologyforAccelerators:StateoftheArtandEmergingTrends, FirstEdition.HasanPadamsee. ©2023WILEY-VCHGmbH.Published2023byWILEY-VCHGmbH.
Figure2.1 (a)Electricandmagneticfielddistributionsforasingle-cellTM010 cavity. Source:[10]CourtesyofJ.Knobloch,CornellUniversity.(b)MicrowaveStudio® [11] simulationsoftheelectricfield(left)andmagneticfield(right)inaTM010 mode[12] CourtesyofD.Bafia,IllinoisInstituteofTechnology.Thephaseofthemagneticfieldis90∘ shiftedrelativetothephaseoftheelectricfield.(c)Electricfield(left)andmagneticfield (right)simulationfortheQWR[13].ZhangandVenturiniDelsolaro/JACoW/CCBY3.0.
(a)
Beam tube
(b)
Cell Beam tube
(c)
Figure2.2 Typical Q versus E curvesobtainedforcavitiesexhibitingvariousperformance limitingphenomenasuchas:hydrogen-Q-disease,multipacting,thermalinstability(or quench),fieldemission,orhighfield Q-slope(HFQS).Theflatcurvedepictingideal performanceisrarely(ornever)achieved.TheX-axisforgradientisnottoscale[14].
impactandheatthecavitywall,oftenleadingtoaprematurebreakdownofsuperconductivity(called“quench”).Fieldemissionelectronsalsogenerateundesirable “darkcurrent”intheaccelerator.Ahighsurfacemagneticfieldmaylimitthecavity’sperformanceathighgradientsifrfheatingfromahighresistanceregion(such asadefect)triggersaquenchofsuperconductivity,orifthelocalfieldapproaches thecriticalrfmagneticfield,discussedinmoredetailinlaterchapters.
ThekeyperformanceofanSRFcavityisexpressedbymeasuringthe Q0 versus Eacc curve.AsshowninFigure2.2,the Q0 departsfromtheidealflatcurvedue tolimitationsarisingfromvariousphenomenasuchasthehydrogen-related Q-disease,multipacting,breakdownfromadefect,fieldemission,highfield Q-slope (HFQS),andmediumfield Q-slope(MFQS).Eachofthesephenomenahasbeen extensivelystudiedwithgreatprogressinunderstandingthefundamentalcauses. Remedieshavebeendevelopedtoovercomethelimitationsandtoreturncavity behaviortowardtheideal,flat Q0 versus Eacc curve.
Temperaturemappingoftheouterwallofthecavityhasplayedacrucialrole inunderstandingandcuringmanyoftheselimitations.Figures2.3and2.4show theearliestsystem[15]for rapid mappingtheouter-walltemperaturebelow thelambdapointofliquidHe(2.2K).Figure2.4alsoshowsatemperaturemap whenthereisheatingatadefectthateventuallyleadstoaquenchatahigherfield. Thethermometrysystemshownherehasbeenimproved[16]andadoptedbymany labs[17–19].
TheperformanceofanSRFcavitydependsonthemaximumvaluesofthepeak surfacefieldsthatcanbetoleratedwithoutincreasingthemicrowavesurfaceresistancesubstantially,orwithoutcausingabreakdownofsuperconductivity.Ahigh surfaceelectricfieldcancausefieldemissionofelectrons,degradingthe Q0 .Ahigh surfacemagneticfieldmaylimitthegradientofthecavitythroughheatingata defectfollowedbythermalrunaway(Figure2.4),orthroughamagnetictransition tothenormalstateatthelocalcriticalmagneticfield.Theultimateacceleratingfield achievableforanidealNbcavityissetbytherfcriticalmagneticfield,theoretically
housing
GE varnish
Allen-Bradley resistor (100 Ω) 1 cm0.4 cm
Figure2.3 (a)Asinglethermometerboardholding21carbon-resistorthermometers.The shapeoftheboardmatchesthecontourofa1-cellcavity[10]CourtesyofJ.Knobloch, CornellUniversity.(b)Asinglethermometerencasedinepoxy.Thesensingelementisa 100 Ω Allen–Bradleycarbonresistorthesurfaceofwhichisgrounddowntojustexpose thecarbonelementforhighersensitivity.Source:CourtesyofJ.Knobloch,Cornell University.(c)Schematicofthethermometerhousingshowingthespring-loadedpogostick thathelpstokeepcontactwiththecavitywall,andtheleadsofmanganinwiretolimitthe strayheatinput.Thefaceofthethermometerispaintedwithinsulation. Source:[10,16]/withpermissionofAIPPublishingLLC.
equaltothesuperheatingcriticalmagneticfield[21], H sh .Foridealniobium, H sh at2Kisabout0.22T,whichtranslatestoamaximumacceleratingfieldofabout 52MV/mforatypicalshape �� = 1niobiumstructure,androughly30MV/mfora typical ��< 1Nbstructure.
OtherimportantdesignfeaturesforanSRFstructurediscussedfurtherin[22]are cell-to-cellcouplingformulticellstructures,Lorentz-force(LF)detuningcoefficient,
Pogostick
Mangamin wires
Stycast epoxy
G10
2.2FabricationandProcessingonNb-BasedSRFStructures
Figure2.4 (a)Thermometerspositionedonacavitywall.Apiezon-Ngreasepromotes thermalcontactbetweenthethermometerandthecavitywall.Someboardsare removedtoexposethecavity.[10,16].CourtesyofJ.Knobloch,CornellUniversity& withpermissionofAIPthroughCCC.(b)Sampletemperaturemapshowingheatingata sub-mmdefectsitethatleadstoquenchathigherfields.(c)AthigherRFfield,the defectheatinggrowstocauseaquenchofsuperconductivity,andalargeregionofthe cavitysurfacearoundthedefectshowshightemperatures.Source:[20]/H.Padamsee, CornellUniversity.
inputpowerrequiredforbeampower(Pb ),couplingstrengthofinputcoupler(Qext ), higherordermode(HOM)frequencies,HOMshuntimpedancesandHOM Q values. Mechanicalpropertiesalsoplayaroleinensuringstabilityunderatmosphericloadingandtemperaturedifferentials,tominimizeLorentz-forcedetuning,andtokeep microphonicsdetuningundercontrol.
2.2FabricationandProcessingonNb-BasedSRF Structures
ToappreciatethelatestprogressintheperformanceandapplicationsofSRFcavitiesitishelpfultobrieflyreviewthemainfeaturesofcustomaryfabricationand processingmethods.Theshortreviewwillhelpunderstandhowtheevolutionof
fabricationandsurfacetreatmentpracticescoupletothesolutionoftheperformance difficultiesmentionedabove,suchasthehydrogen Q-disease,fieldemissionand quench.Moredetailinformationaboutthefabricationandprocessingisavailable in[4,5,22].
2.2.1CavityFabrication
Severalindustriesprovideniobiumsheetswithwell-definedcavityspecifications [23].Thesheetsareinspectedforflatness,uniformgrainsize(typically50 μm), near-completeanduniformrecrystallization,RRRvalue(>300),andgoodsurface quality(absenceofscratches).HereRRRstandsforResidualResistivityRatio,and isameasureofthepurityofNb.Sincethemanyfabricationstagescanembed “defects,”suchasimpurityinclusions,pits,bumps,orscratches,eachsheetfrom industryisscannedwitheddy-currentscanning[24,25]toweedoutdefective sheets.Defectscanleadtobreakdownofsuperconductivity(quench)eitherbyoverheating,orbyloweringthelocalcriticalfield,resultinginamagneticquench.The highRRRNbhelpstostabilizedefectheatingduetothehighthermalconductivity thataccompaniesthehighRRR.
Fora �� ∼ 1structures,half-cellsarestamped,spun,orhydro-formed,checkedwith thecoordinatemeasuringmachine(CMM)forthecorrectshape,thentrimmedfor weldpreparations.Cavitypartsaregivenalight(20 μm)(BufferedChemicalPolish) BCPetchtoprepareforelectronbeamwelding.Electronbeamweldingisacritical processwithcarefullydevelopedparameters.Asmoothweldunderbeadwithcompleteabsenceofspatterisessentialforhighfieldperformance.Thiscanbeachieved withdefocusedelectron-beamwelding[26],orbyusingarasterwitharhombicor circularpatternasdescribedin[27].ToavoidRRRdegradation,thevacuuminthe electron-beamweldershouldbebetterthan2 × 10 5 Torr.Allweldsareinspected forcomplete,smoothunderbead,flatontheinside,andnoweldspatter.Aftercompletingasingle-cellormulticellstructure,theinsidesurfaceisinspectedoptically. Aspecialopticalinspectionapparatushasbeendevelopedandwidelyadopted[28]. Mechanicalmeasurementsensurestraightnessandcorrectdimensions.Theelectricfieldprofilealongthebeamaxisischeckedandadjusted.Thegoalisusually 98%fieldflatness.A“flat”fieldprofileisachievedbytuningthecellsrelativeto eachotherbysqueezingorstretchingthecellsmechanicallytoadjustandproperly matchthefrequencyofeachcell.
Mostlow-�� resonatorsaremadefrombulkniobiumwithhighRRR(150–300). Fabricationofpartsincludemachining,forming,rolling,andwelding.Recently,wire electricdischargemachining(EDM)hasbeendevelopedtogetherwithindustry[6] whichhaslittlepossibilityforforeignmaterialinclusionsascomparedtotraditional machining.Partsarejoinedtogetherbyelectronbeamweldinginhighvacuum.
2.2.2Preparation
Niobiumcavitiesundergoafirststageetching(100–150 μm)toremovethe“surface damage”layer.Methodsusedformaterialremovalarestandardbufferedchemical
