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LawrenceBerkeleyNationalLaboratoryLawrenceBerkeleyNationalLaboratoryTitle:UpdateonElectron-CloudSimulationsUsingthePackageWARP-POSINSTAuthor:Penn,G.
PublicationDate:10-09-2009PublicationInfo:LawrenceBerkeleyNationalLaboratoryPermalink:http://escholarship.
org/uc/item/0vp975ckUpdateonElectron-CloudSimulationsUsingthePackageWARP-POSINSTJ.
-L.
Vay,C.
M.
Celata,M.
A.
Furman,G.
Penn,M.
Venturini,LBNL,Berkeley,USAD.
P.
Grote,LLNL,Livermore,USA;K.
G.
Sonnad,U.
ofKarlsruhe,GermanyINTRODUCTIONAtPAC05[1]andPAC07[2],wepresentedthepackageWARP-POSINSTforthemodelingoftheeffectofelec-troncloudsonhigh-energybeams.
Wepresentherethelatestdevelopmentsinthepackage.
Threenewmodesofoperationswereimplemented:1)abuild-upmodewhere,similarlytoPOSINST(LBNL)orECLOUD(CERN),thebuild-upofelectroncloudsdrivenbyalegislatedbunchtrainismodeledinoneregionofanaccelerator;2)aquasi-staticmodewhere,similarlytoHEADTAIL(CERN)orQuickPIC(USC/UCLA),thefrozenbeamapproximationisusedtosplitthemodelingofthebeamandtheelec-tronsintotwocomponentsevolvingontheirrespectivetimescales;and3)aLorentzboostedmodewherethesim-ulationisperformedinamovingframewherethespaceandtimescalesrelatedtothebeamandelectrondynamicsfallinthesamerange.
Theimplementationofmodes(1)and(2)wasprimarymotivatedbytheneedforbenchmark-ingwithothercodes,whiletheimplementationofmode(3)fulllsthedrivetowardfullyself-consistentsimulationsofe-cloudeffectsonthebeamincludingthebuild-upphase.
BUILD-UPMODEFigure1:Sketchofthebuild-upmode.
Thedynamicsofelectronsisfollowedforathin(2-D)orthick(3-D)slicelocatedatagivenlocationinthelattice,undertheinuenceofalegislatedparticlebeampassingthroughtheslice.
Inordertofacilitatedirectcomparisonwithbuild-upcodeslikePOSINST[4,5,6,7],ECLOUD(CERN)orCloudland(SLAC),abuild-upmodeclasswasimple-mentedinWarp.
Inthismode,thedynamicsofelectronsisfollowedforathin(2-D)orthick(3-D)slicelocatedatagivenlocationinthelattice,undertheinuenceofalegis-latedparticlebeampassingthroughtheslice(Fig.
1).
RunsWorksupportedbytheUS-DOEunderContractDE-AC02-05CH11231,theUS-LHCLARP,andtheUS-DOESciDACprogramComPASS.
ThisworkusedresourcesofNERSC,supportedbytheUS-DOEunderContractDE-AC02-05CH11231.
jlvay@lbl.
govwereperformedwithWarpandPOSINSTfortheevolu-tionofanelectroncloudsliceinthemiddleofadipole.
TheaverageelectrondensityhistoryisgiveninFig.
2foraPOSINSTrunandthreeWarprunsin:(a)2-D,(b)3-Dwith4cellslongitudinallyandalengthof0.
2σz,and(c)3-Dwith16cellslongitudinallyandalengthof0.
8σz,whereσzisthebeamRMSlength.
Forthe3-Druns,pe-riodicboundaryconditionswereappliedlongitudinallyforeldsandparticles.
SnapshotsofcoloredelectrondensityplotsandverticalphasespacearegiveninFig.
3,takenatt=130ns.
TheseresultsdemonstrateaverygooddegreeofagreementforelectroncloudbuildsimulationsbetweenPOSINST,Warpin2-D,andWarpin3-D.
Figure2:AverageelectrondensityversustimefromPOSINSTandWarpinbuild-upmodesimulations.
QUASISTATICMODEWehaveimplementedaquasistatic[8]modeinWarp.
Inthismode,a2-Dslabofelectronmacroparticlesissteppedbackward(withsmalltimesteps)throughthebeameld(seeFig.
4).
The2-Delectronelds(solvedateachstep)arestackedina3-Darray,thatisusedtogiveakicktothebeam.
Finally,thebeamparticlesarepushedforward(withlargertimesteps)tothenextstationofelectrons,us-ingeithermapsoraLeap-Frogpusher.
Therstimple-mentationwasforacceleratorlatticestreatedinthesmoothapproximation.
Amoredetailedlatticedescriptionwasimplementedlater(seebelow).
Thismodeallowsfordi-rectcomparisonwiththequasistaticcodesHEADTAIL[9],QuickPIC[10],PEHTS[11]orCMAD[12].
Theparal-lelizationismono-dimensional(alongs)usingpipelining,similarlytoQuickPIC(seeFig.
5).
Wehavesimulatedane-clouddriveninstabilityinanLHC-likeringwithWarpinaquasistaticmode,andHEADTAIL.
Weusedthepa-rametersfromtable1inadrift(Fig.
6)andinadipole(Fig.
7).
SomeoftheparameterswerepurposelychosentoFigure3:Snapshotsofelectrondensityandverticalphasespacefrombuild-upsimulationsusing(left)POSINST,(middle)Warpin2-D,(right)Warpin3-D.
beunphysicallylarge,soastomagnifytheireffects.
Thetwocodespredictsimilaremittancegrowthunderthevar-iousconditions,withexcellentqualitativeagreementandgoodtoverygoodquantitativeagreement.
Wetentativelyattributethequantitativediscrepanciestodifferencesinim-plementationsincluding:adaptiveversusxedgridsizes,differenteldsolversandparticlepushers,differenteldinterpolationproceduresnearinternalconductors,slightlydifferentvaluesofphysicalconstants,etc.
Table1:Parametersusedforsimulationsofe-clouddriveninstabilitystudiesintheLHC.
circumferenceC26.
659kmbeamenergyEb450GeVbunchpopulationNb1.
1*1011rmsbunchlengthσz0.
13mrmsbeamsizesσx,y0.
884,0.
884mmbetafunctionsβx,y66.
,71.
54mbetatrontunesQx,y64.
28,59.
31chromaticitiesQx,y1000.
,1000.
synchrotrontuneν0.
59momentumcompactionfactorα0.
347*103rmsmomentumspreadδrms4.
68*102BOOSTEDFRAMEAPPROACHItwasshownin[13]thatitwaspossibletoperformsim-ulationsofelectron-driveninstabilitiesfromrstprinciples(e.
g.
usingstandardParticle-In-Cellmethods),atmuchre-ducedcomputingcostbyperformingthecalculationinaFigure4:Sketchofthequasistaticmode.
A2-Dslabofelectronmacroparticlesissteppedbackward(withsmalltimesteps)throughthebeameld.
The2-Delectronelds(solvedateachstep)arestackedina3-Darray,thatisusedtogiveakicktothebeam.
Finally,thebeamparticlesarepushedforward(withlargertimesteps)tothenextstationofelectrons.
Figure5:Sketchoftheparalleldecompositionforthequa-sistaticmode.
Thebeamisdistributedamongnslices,thatareuniformlyspreadamongNprocessors.
Usingapipeliningalgorithm,slicesonagivenprocessorarepushedfromonestationtothenext,withoutwaitingfortheslicesofthepreviousprocessorstoreachthesamestation.
suitableLorentzboostedframe.
Numericaldevelopmentsthatwereneededhavebeenimplemented,includinganewparticlepusherandeldsolver,andaredescribedin[14].
Specialhandlingofinputsandoutputsbetweentheboostedframeandthelaboratoryframearedescribedin[15].
TwoWarpcalculationsofanelectronclouddriveninstabilityFigure6:FractionalemittancegrowthfromWarp(red)andHEADTAIL(black)simulationsofane-clouddriveninsta-bilityindriftsofanLHC-likeringforanelectronback-grounddensityof1014m3for(top)ν=α=δrms=Qx=Qy=0,(middle)Qx=Qy=0,(bottom)parame-tersfromtable1.
showedverygoodagreement[14]betweenafullPICcal-culationinaboostedframeandacalculationusingthequa-sistaticmode,forsimilarcomputationalcost.
FURTHERDEVELOPMENTSWehaverecentlyaddedthecapabilitytouselinearmapstopushparticlesinacceleratorlattices,withinthequa-sistaticmodeandthefullPICmodeinaLorentzboostedframe.
GoodquantitativeagreementwasobtainedbetweenWarpusingthequasistaticmodeandCMAD[12].
SimilarcalculationswiththefullPICmethodinaboostedframeareinprogress.
Figure7:FractionalverticalemittancegrowthfromWarpandHEADTAILsimulationsindipolesofanLHC-likeringforthreeassumedinitialelectrondensities.
ACKNOWLEDGMENTSWethankG.
Rumoloforprovidingthesourceandin-valuablesupportforusingthecodeHEADTAIL.
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