PhD Thesis Avoiding vacuum arcs in high gradient normal conducting RF structures

171 Pages·2016·22.8 MB·English

PhD Thesis
Avoiding vacuum arcs in high gradient
normal conducting RF structures
Kyrre Ness Sjøbæk
Department of Physics
University of Oslo
September 2016
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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.
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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
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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
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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
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CONTENTS
F.6. 2DArcPICCodeDescriptionandUser/DeveloperManual(secondedition) 170
F.7. UpdatedbaselineforastagedCompactLinearCollider . . . . . . . . . . . 171
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