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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.
REFERENCES[1]JLVayetal,ParticleAcceleratorConference,Knoxville,TN(2005),papersROPB006andFPAP016[2]M.
A.
Furmanetal,ParticleAcceleratorConference,Albu-querque,NM(2007),paperTUXAB03[3]D.
P.
Grote,A.
Friedman,J.
-L.
Vay.
I.
Haber,AIPConf.
Proc.
749(2005)55.
[4]M.
A.
FurmanandG.
R.
Lambertson,LBNL-41123/CBPNote-246,PEP-IIAPNoteAP97.
27(Nov.
25,1997).
Proc.
Intl.
WorkshoponMultibunchInstabilitiesinFutureElectronandPositronAccelerators"MBI-97"(KEK,15-18July1997;Y.
H.
Chin,ed.
),KEKProceedings97-17,Dec.
1997,p.
170.
[5]M.
A.
FurmanandM.
T.
F.
Pivi,LBNL-49771/CBPNote-415(Nov.
6,2002).
PRST-AB5,124404(2003),http://prst-ab.
aps.
org/pdf/PRSTAB/v5/i12/e124404.
[6]M.
A.
FurmanandM.
T.
F.
Pivi,LBNL-52807/SLAC-PUB-9912(June2,2003).
[7]M.
A.
Furman,LBNL-41482/CBPNote247/LHCProjectReport180(May20,1998).
[8]P.
Sprangle,E.
Esarey,andA.
Ting,Phys.
Rev.
Letters64,2011-2014(1990).
[9]G.
RumoloandF.
Zimmermann,PRST-AB5121002(2002).
[10]C.
Huang,V.
K.
Decyk,C.
Ren,M.
Zhou,W.
Lu,W.
B.
Mori,J.
H.
Cooley,T.
M.
Antonsen,Jr.
andT.
Katsouleas,J.
ofCom-put.
Phys.
217,658-679(2006).
[11]K.
Ohmi,SingleBunchElectronCloudInstabilityforaRoundBeam(Memo),19.
Nov.
2002.
[12]M.
Pivi,TheseproceedingsWE1PBI01.
[13]J.
-L.
Vay,Phys.
Rev.
Lett.
,98(2007)130405.
[14]J.
-L.
Vay,Phys.
Plas.
,15(2008)056701.
[15]J.
-L.
Vayetal,TheseproceedingsTU1PBI04.
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.
REFERENCES[1]JLVayetal,ParticleAcceleratorConference,Knoxville,TN(2005),papersROPB006andFPAP016[2]M.
A.
Furmanetal,ParticleAcceleratorConference,Albu-querque,NM(2007),paperTUXAB03[3]D.
P.
Grote,A.
Friedman,J.
-L.
Vay.
I.
Haber,AIPConf.
Proc.
749(2005)55.
[4]M.
A.
FurmanandG.
R.
Lambertson,LBNL-41123/CBPNote-246,PEP-IIAPNoteAP97.
27(Nov.
25,1997).
Proc.
Intl.
WorkshoponMultibunchInstabilitiesinFutureElectronandPositronAccelerators"MBI-97"(KEK,15-18July1997;Y.
H.
Chin,ed.
),KEKProceedings97-17,Dec.
1997,p.
170.
[5]M.
A.
FurmanandM.
T.
F.
Pivi,LBNL-49771/CBPNote-415(Nov.
6,2002).
PRST-AB5,124404(2003),http://prst-ab.
aps.
org/pdf/PRSTAB/v5/i12/e124404.
[6]M.
A.
FurmanandM.
T.
F.
Pivi,LBNL-52807/SLAC-PUB-9912(June2,2003).
[7]M.
A.
Furman,LBNL-41482/CBPNote247/LHCProjectReport180(May20,1998).
[8]P.
Sprangle,E.
Esarey,andA.
Ting,Phys.
Rev.
Letters64,2011-2014(1990).
[9]G.
RumoloandF.
Zimmermann,PRST-AB5121002(2002).
[10]C.
Huang,V.
K.
Decyk,C.
Ren,M.
Zhou,W.
Lu,W.
B.
Mori,J.
H.
Cooley,T.
M.
Antonsen,Jr.
andT.
Katsouleas,J.
ofCom-put.
Phys.
217,658-679(2006).
[11]K.
Ohmi,SingleBunchElectronCloudInstabilityforaRoundBeam(Memo),19.
Nov.
2002.
[12]M.
Pivi,TheseproceedingsWE1PBI01.
[13]J.
-L.
Vay,Phys.
Rev.
Lett.
,98(2007)130405.
[14]J.
-L.
Vay,Phys.
Plas.
,15(2008)056701.
[15]J.
-L.
Vayetal,TheseproceedingsTU1PBI04.
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