PhD Thesis Avoiding vacuum arcs in high gradient normal conducting RF structures Kyrre Ness Sjøbæk Department of Physics University of Oslo September 2016 9 2 1 6- 1 0 2 S- SI E H16 T0 N-/2 0 R1 E/ C14 Abstract InordertobuildtheCompactLInearCollider(CLIC),acceleratingstructuresreachingex- tremelyhighacceleratinggradientsareneeded. Suchstructureshavebeenbuiltandtested usingnormal-conductingcopper, poweredbyX-bandRFpowerandreachinggradientsof 100 MV/m and above. One phenomenon that must be avoided in order to reliably reach such gradients, is vacuum arcs or “breakdowns”. This can be accomplished by carefully designingthestructuregeometrysuchthathighsurfacefieldsandlargelocalpowerflows areavoided. The research presented in this thesis presents a method for optimizing the geometry of acceleratingstructuressothatthesebreakdownsaremadelesslikely,allowingthestructure tooperatereliablyathighgradients. Thiswasdoneprimarillybasedonaphenomenological scalingmodel,whichpredictedthemaximumgradientasafunctionofthebreakdownrate, pulselength,andfielddistributioninthestructure. Themodeliswritteninsuchawaythatit allowsdirectcomparisonofdifferentcriteria,i.e.thepeakelectricfield,thepeaklocalpower flow or “modified Poynting vector” S , and the global power flow per iris circumference. c Usingthismethod,asetofhighlyoptimizedacceleratingcellswerecreated,aswasaC++ librarycapableofestimatingtheperformanceofanRFstructurebasedontheseaccelerating cells. ThislibrarywasusedintherebaselingingoftheCLICmachine. Inadditiontothis,thethesisalsopresentsaparticleincellsimulationoftheinitialstages ofavacuumarc. Thismodelfollowsthedevelopmentofthearcfromasmallfieldemitter intoamulti-amperedischarge,trackingtheevolutionoftheplasmaandthecircuit,aswellas theinteractionbetweentheplasmaandthesurface. Fromthismodel,ourunderstandingof theimportanceoftheionbombardmentundertheplasmasheathwasimproved,especially the ion energy distribution and its effect on sputtering vs. the effective sputtering yields requiredforthearctosustainitselfandgrow. 3 Acknowledgments In the work leading up to this thesis I’ve had the good fortune of being a part of both the CERNCLICRFgroupandtheOsloexperimentalparticlephysicsgroup. Thisenvironment hasenabledmetolearnalotaboutacceleratorphysics,vacuumarcs,RFoptimization,elec- tromagnetics, high-performance computing and programming, how to present my results, andmanyotherthings. First,IwouldliketoexpressmygratitudetomythreesupervisorsSteinarStapnes,Erik Adli,andAlexejGrudiev: Steinar,youbroughtmeintohighenergyphysics,firstwithde- tectorsandlateraccelerators,whicharebothfieldsthatIenjoyworkingwith. Thankyoufor openingalotofdoors,makingsurethatIcouldfocusontheresearch,andallowingmeto workfromwhereIneededto. Erik,eventhoughyouattimeswerelocatedfaraway,youstill managedtofollowtheproject. Thankyouforgivingmelotsofvaluableadvice,guidance, discussions,intellectualchallengesandexplanations. Alexej,youintroducedmetoacceler- atorstructuresandRFdesign,andcameupwithmanyoftheunderlyingideasformythesis. Thank you for teaching me how optimize the structures for a given machine, and helping meunderstandhowtheycanarcandbreakdown. Inaddition,IwouldliketothankWalter Wuenschforvaluableadviceandaskingmanyveryusefulquestions,andforhelpingmefeel athomeintheCERNgroup. Youallgavemetheopportunitytogotoseveralconferences (IPAC’12,MevArc’12/’13,andHG’13),twolongvisitstotheACDdepartmentatSLAC, and several schools and courses (CAS’11, LCS’11, CW’10), something that gave me the oportunitymetolearnalot,andforwhichIamverygrateful. IwouldalsoliketothankHelgaTimkoforteachingmealotaboutPICandforbringingme intotheArcPICproject,aswellasLottaMether,FlyuraDjurabekovaandKaiNordlundfor manyenlighteningdiscussionsonvacuumarcsandnanoscalesurfacephysics,andthecom- plexinteractionsbetweenthem. ManythankstotheACDgroupatSLACwithArnoCandel, KiHwanLee,OleksiyKononenko,ChoNg,andKwokKoforallowingmetouseandhelp- ingmeunderstandtheACE3Pcode. AlsothankstoDanielSchultefordiscussionsrelatedto theworkIdidwiththeoptimizationandperformancepredictionofRFstructures,aswellas makingitusefulwiththere-baseliningstudies. Furthermore,thankstomyfellowcolleagues andfriendsNickholasShipmanandAndersKorsbäckforhelpingmeunderstandtheCERN DCsparkexperiments,aswellasReidarLillestøl,RobinRajamäki,AndriyNosych,Vasim Khan, Hugo Day, Miriam Colling, Tomoko Muranaka, Nikolay Schwerg, Yngve Levin- sen, Tobias Persson, Alexander Gerbershagen, Veronica Berglyd Olsen, and many others formanygooddiscussionsandlotsoffun. Finally,manythankstomynewcolleaguesatthe CERNABPgroupwithHelmutBurkhardt,AndreaSantamaríaGarcía,RiccardodeMaria, Miriam Fitterer, Roderik Bruce, Regina Kwee-Hinzmann, Benoit Salvant, Massimo Gio- vanozzi,andmanyotherswhoI’vebeenworkingwithforthelast11/2years–I’velearned alotfromallofyouaswell. Atlast,averyspecialthankstomybestfriend,fellowstudent,andwifeHelgaHolmestad; Yousupportedme, engagedindiscussions, readmypapers, andkeptmemotivatedinthe timeittooktopiecethematerialstogethertothisthesis. 5 Contents Abstract 3 Acknowledgments 5 Contents 7 1. Introduction 11 1.1. Particlecolliders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2. TheCompactLInearCollider(CLIC) . . . . . . . . . . . . . . . . . . . . 14 1.3. Acceleratingstructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.4. Vacuumarcs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.5. Simulationtools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5.1. ACE3P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5.2. 2DArcPIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.6. Applicationsofhighgradientaccelerationoutsidehigh-energyphysics . . . 21 1.7. Lookingahead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2. RF structures for particle acceleration 25 2.1. RFacceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2. Eigenmodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.1. Theeigenmodesofpillboxcavities. . . . . . . . . . . . . . . . . . 26 2.3. Travelingwavestructures . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4. FiniteelementcalculationofRFmodes . . . . . . . . . . . . . . . . . . . 31 2.4.1. PhasedifferencebetweenE(cid:126) andB(cid:126) . . . . . . . . . . . . . . . . . . 32 2.4.2. CalculationoffieldpatternsusingOmega3P. . . . . . . . . . . . . 33 2.4.3. ExtractionofRFparametersfromthefieldpattern . . . . . . . . . 35 3. High gradient acceleration challenges 39 3.1. RFbreakdownsinacceleratingstructures . . . . . . . . . . . . . . . . . . 39 3.2. ModelsofRFbreakdowns . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.2.1. SurfaceelectricfieldandtheKilpatriccriterion . . . . . . . . . . . 40 3.2.2. Powerflowthroughthestructureandiriscircumference. . . . . . . 42 3.2.3. ThemodifiedPoyntingvectorS . . . . . . . . . . . . . . . . . . . 42 c 3.3. ScalingphenomenologyforRFbreakdowns . . . . . . . . . . . . . . . . . 46 3.3.1. Highgradientlimits . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.4. Pulsedsurfaceheatingfrommagneticfields . . . . . . . . . . . . . . . . . 51 3.5. Summaryandconclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 52 7 CONTENTS 4. Simulation of vacuum arcs 53 4.1. Vacuumarcs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.1.1. Theoriginoftheemissionsite . . . . . . . . . . . . . . . . . . . . 55 4.1.2. Coldfieldemissionofelectrons . . . . . . . . . . . . . . . . . . . 55 4.1.3. Evaporationofneutralatoms . . . . . . . . . . . . . . . . . . . . . 57 4.1.4. Sputtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2. Simulationmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.2.1. 2DArcPicandTheParticleinCell(PIC)method . . . . . . . . . . 59 4.2.2. Monte-Carlocollisions . . . . . . . . . . . . . . . . . . . . . . . . 60 4.2.3. Parallelizationofcollisions . . . . . . . . . . . . . . . . . . . . . . 61 4.2.4. Accuracyofthefieldsolverneartheemitteratr =z =0 . . . . . . 63 4.2.5. Shockley-Ramo . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.2.6. Circuitmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.2.7. Surfacephysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.3. Simulationresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.3.1. Effectsofvaryingthemodelparameters . . . . . . . . . . . . . . . 75 4.4. Discussion,conclusions,andoutlook . . . . . . . . . . . . . . . . . . . . . 75 5. Cell geometry optimization 77 5.1. Cellgeometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.2. Optimizationalgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.2.1. 1Dfitfrequencytuning . . . . . . . . . . . . . . . . . . . . . . . . 82 5.2.2. 2Dsurfacefitfrequencytuning. . . . . . . . . . . . . . . . . . . . 82 5.3. Optimizationgoals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.3.1. Minimizingthebreakdownrate . . . . . . . . . . . . . . . . . . . 83 5.3.2. Minimizingpulsedsurfaceheating . . . . . . . . . . . . . . . . . . 84 5.4. Peakfieldextraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.4.1. Outerwall. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.4.2. Iris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.5. TheAcdOptiGUIoptimizationtool . . . . . . . . . . . . . . . . . . . . . . 85 5.6. Atypicaloptimizedcell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.7. Thecelldatabase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.8. Summaryandconclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6. Wake fields 97 6.1. Wakefieldmodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.2. Wakefunctions,bunchpotentials,andimpedance . . . . . . . . . . . . . . 98 6.2.1. Theimpedancespectrumofadampedresonance . . . . . . . . . . 100 6.3. Thefundamentaltheoremofbeamloading . . . . . . . . . . . . . . . . . . 100 6.4. Transversekicks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.5. ThePanofsky-Wenzeltheorem . . . . . . . . . . . . . . . . . . . . . . . . 102 6.6. Dipolewake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.7. CalculatingwakefieldsusingACE3P . . . . . . . . . . . . . . . . . . . . 106 6.7.1. Treatmentoftheimpedancespectra . . . . . . . . . . . . . . . . . 109 6.7.2. Wakefielddampingwaveguides . . . . . . . . . . . . . . . . . . . 111 6.7.3. Wakefieldsfromtypicalcelldesignandthecelldatabase . . . . . . 114 6.8. Summaryandconclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 116 8 CONTENTS 7. Structure parameter calculation 117 7.1. ConvertingcellgeometryparameterstocellRFparameters: thecelldatabase117 7.2. Frequencyscaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 7.2.1. Acceleratingmodeparameters . . . . . . . . . . . . . . . . . . . . 118 7.2.2. Transversewakefieldmodeparameterswithwaveguidedamping . . 119 7.3. ParameterinterpolationalongtheRFstructure . . . . . . . . . . . . . . . . 120 7.4. Fieldprofile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7.5. Powerandvoltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7.6. Pulseshape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7.7. RF-to-beamefficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 7.8. Peakfieldsandpulselengthlimits . . . . . . . . . . . . . . . . . . . . . . 129 7.8.1. Pulselengthlimitsfromscalinglaws . . . . . . . . . . . . . . . . 131 7.8.2. Pulselengthlimitsfrompulsedsurfaceheating . . . . . . . . . . . 131 7.9. Transversewakefields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 7.10.ValidationofthemodelandtheCLICoptilibrary . . . . . . . . . . . . . . 136 7.10.1. GradientprofileG(z)calculation . . . . . . . . . . . . . . . . . . 136 7.10.2. Accuracyofpowerrequirementpredictions . . . . . . . . . . . . . 137 7.10.3. Pulselengthandbreakdownrate . . . . . . . . . . . . . . . . . . . 138 7.10.4. Wakefield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 7.11.Summaryandconclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 138 8. Summary, conclusions, and outlook 139 Bibliography 141 A. Finite element calculation of electromagnetic eigenmodes 155 Publications: Papers and reports 159 B. Design of an accelerating structure for a 500 GeV CLIC using ACE3P 159 C. Surface field optimization of accelerating structures for CLIC using ACE3P on remote computing facility 161 D. New Criterion for Shape Optimization of Normal-Conducting Accelerator Cells for High-Gradient Applications 163 E. FromFieldEmissiontoVacuumArcIgnition: aNewToolforSimulatingCopper Vacuum Arcs 165 F. CLIC notes and other materials 167 F.1. BenchmarkingofOmega3Pfiniteelementelectromagneticeigenmodesolver167 F.2. LongitudinalspacechargeeffectsintheCLICdrivebeam . . . . . . . . . . 167 F.3. Design of waveguide damped cells for 12 GHz high gradient accelerating structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 F.4. TheCLICoptiRFstructureparameterestimator . . . . . . . . . . . . . . . 169 F.5. BreakdownlocalizationintheFixedGapSystem . . . . . . . . . . . . . . 169 9 CONTENTS F.6. 2DArcPICCodeDescriptionandUser/DeveloperManual(secondedition) 170 F.7. UpdatedbaselineforastagedCompactLinearCollider . . . . . . . . . . . 171 10