Transla’on among SAD, MAD-X and Bmadresearch.kek.jp/people/dmzhou/BeamPhysics/Lattice...2019/09/19 · Benchmark done in 2015 Great agreement in closed orbit, even in the complicated

Transla'onamongSAD,MAD-XandBmad

DeminZhou

Acknowledgements:

M.Biagini,L.Deniau,R.DeMaria,E.Forest,E.Gianfelice-Wendt,M.Giovannozzi,H.Koiso,M.Lückhof,S.M.Liuzzo,A.Morita,K.Ohmi,Y.Ohnishi,K.Oide,L.vanRiesen-Haupt,D.Sagan,P.Skowronski,P.

Thrane,I.Tecker,Y.Wang,A.Wegscheider,Y.Zhang,F.Zimmermann

WorkshopSAD2019,KEK,Sep.19,2019

Outline

2

➤Introduc'on➤Currentstatus●Actuallynotthelatest➤CasesofBenchmarkstudies➤Someapplica'ons➤Symplec'ctrackinginSAD➤Summaryandfutureplan

1. Introduction

3

➤Mo'va'on:Toimprovecommunica'ons●SAD:TRISTAN,KEKB,J-PARC,SuperKEKB,FCC-ee,…●Bmad/PTC:CESR,ERL,…●MAD/MAD-X/PTC:PS,LEP,LHC,FCCs,…

Asia:SAD|PTC

Europe:MAD/MAD-X/PTC

America:Bmad/PTC

1. Introduction

4

➤Mo'va'on:Toimprovecollabora'onsonprojectslikeSuperKEKBandFCCs

Ref.F.Zimmermannetal.,IPAC’14,MOXAA01.

5

➤Referencesforthistopic●D.Zhouetal.,“La#cetransla,onbetweenacceleratorsimula,oncodesforSuperKEKB”,inProceedingsofIPAC'16,Busan,Korea,May.08-13,2016.●D.Zhou,“SuperKEKBla#cetransla,on”,MAD-Xmee'ng,CERN,Sep.22,2016,h`ps://indico.cern.ch/event/565330/.●D.Zhou,“Recentprogressonla#cetransla,onfromSADtoMAD-XforFCC-ee”,47thFCC-eedesignmee'ng,Feb.24,2017.●D.Zhou,“SAD-MADconvertersurveyandneeds”,FCC-eedesignmee'ng,Mar.03,2017.●D.Sagan,“TheBmadReferenceManual”,h`ps://www.classe.cornell.edu/~dcs/bmad/manual.html.●SADHomePage,h`p://acc-physics.kek.jp/SAD/.●MAD-Xuser’sguide,h`p://mad.web.cern.ch/mad/●SADmanualunderedi'on,h`p://research.kek.jp/people/dmzhou/SAD/Manual/

1. Introduction

http://mad.web.cern.ch/mad/

2. Current status

6

➤Effortsforlagcetransla'ons:SAD<->MAD/MAD-X●MAD->SAD:H.Koiso(KEK),Y.Wang(IHEP),etal.●MAD-X->SAD:A.Morita(KEK,2008)●SAD->MAD:Y.Wang(IHEP),etal.●SAD->MAD-X:A.Morita(KEK),K.Oide(KEK),Y.Wang(IHEP),etal.●……➤Effortsforlagcetransla'ons:Others●SAD<->Bmad:D.Sagan(Cornell),E.Forest(KEK),etal.●Bmad<->UAP<->MAD-X:D.Sagan(Cornell),etal.●Bmad<->MAD/MAD-X,Bmad<->PTC,MAD-X<->PTC:D.Sagan(Cornell),E.Forest(KEK),P.Skowronski,etal.●SAD->AT:N.Carmignani,S.M.Liuzzo(ESRF),etal.●……

Asia America

Europe

2. Current status

7

➤Effortsforlagcetransla'ons●SADandPTC:developedatKEK,manysharedfeatures(transfermaps,symplec'cintegrator,…)●PTCintegratedintoMAD-XandBmad

MAD-X

BmadPTC

AML/UAP

SAD

MAD

NOTE:Thewidthsofthearrowsindicate“translatability”.

2. Current status

8

➤Archiveforexamplesoflagcetransla'on●MAD-Xsvnrepository:h`p://svnweb.cern.ch/world/wsvn/madx/branches/madX-SAD/tools/translators/[ThankstoL.DeniauandI.Tecker]●Alterna've:h`p://research.kek.jp/people/dmzhou/SAD/Translator/●Classifiedbyroutesoftransla'ons●Usedprograms:MAD-X/PTC,SAD,Bmad/PTC,UAP●Samplejobspreparedfordemonstra'onandbenchmarks

NOTE:PleaseinformmeIFtherearepossiblecopyrightviola'ons!

http://svnweb.cern.ch/world/wsvn/madx/branches/madX-SAD/tools/translators/



http://research.kek.jp/people/dmzhou/SAD/Translator/

2. Current status

9

➤Archiveforexamplesoflagcetransla'on●Sub-directoriesforSADtoMAD-Xtransla'on:

10

➤AbenchmarkofMAD-XandSAD:CLICFFS●Condi'ons:*Track“orbit”foratestpar'cle*Nosouedgefringe,nosolenoid●Hardedgefringe:SAD=PTC≈MAD-X●Forlongitudinaltransforma'on:SAD=PTC≈MAD-X(SegngsforPTC:ICASE=6,TIME=true)

CourtesyofPaulThrane

3. Cases of benchmark studies

➤AbenchmarkofMAD-XandSAD:CLICFFS●Condi'ons:*Twisswithmomentumoffset*Nosouedgefringe,nosolenoid●Hardedgefringe:Negligible●SAD:High-orderchroma'cityduetoDRIFT●MAD-X/PTC:ICASE=5(Needpropersegngs?)

ForaDRIFT:

11

�(�, s) = �0 +s2

�0(1+�)2

CourtesyofPaulThrane


➤AbenchmarkofBmad,PTCandSAD:SuperKEKBsler_1689●Benchmarkdonein2015●Greatagreementinclosedorbit,eveninthecomplicatedIR●“Timepatching”wastreateddifferently●Closedorbit(or“fixedpoint”)isthefirstthingtocompare

12


-8

-6

-4

-2

0

2

4

6

8

0 500 1000 1500 2000 2500 3000

X [m

m]

s [m]

SADBmad

PTCX

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 500 1000 1500 2000 2500 3000

Y [m

m]

s [m]

SADBmad

PTCY

-8

-6.4

-4.8

-3.2

-1.6

0

1.6

3.2

4.8

6.4

8

0 500 1000 1500 2000 2500 3000

Z [m

m]

s [m]

SADBmad

PTCZ

-4

-3.2

-2.4

-1.6

-0.8

0

0.8

1.6

2.4

3.2

4

0 1 2 3 4 5

X [m

m]

s [m]

SADBmad

PTCXaroundIP

-2

-1.6

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

2

0 1 2 3 4 5

Y [m

m]

s [m]

SADBmad

PTCYaroundIP

Bmad SAD

➤AbenchmarkofBmadandSAD:SuperKEKBsler_1684●Benchmarkdonein2014●Similarsizeofdynamicaperture●Detailsaredifferent,showingminordifferencesfornonlinearmaps

13


➤AbenchmarkofBmadandSAD:SuperKEKBsler_1684●Benchmarkdonein2014●Similarfootprintoftunespread●Detailsaredifferent,showingminordifferencesfornonlinearmaps

14


Bmad SAD

➤AbenchmarkofBmadandSAD:FCC-ee●RecentstudybyL.vanRiesen-Haupt●GreatagreementbetweenMAD-XandSAD

15


➤AbenchmarkofBmadandSAD:FCC-ee●RecentstudybyL.vanRiesen-Haupt●DiscrepancyagainstPTCmightbeduetoslicing(and/orintegra'onscheme)?

16


17

➤Oldfindings●Mytalkto20thKEKBAcceleratorReviewCommièe,Feb.23,2015.

4. Some applications

18

4. Some applications➤Oldfindings●Mytalkto20thKEKBAcceleratorReviewCommièe,Feb.23,2015.

19

➤Nonlinearop'miza'onwithchroma'cconstraints[byH.Sugimoto,SuperKEKBmini-op'csmee'ng,Sep.8,2016]●Chroma'cβx,yandνx,ycorrespondtoRDTsofh2000e/h0200e(X),h0020e/h0002e(Y),andh1100e(X),h0011e(Y),respec'vely


20

➤Resonancedrivingterms(RDTs)indicatelagcenonlinearity


21

➤RDTsindicatelagcenonlinearity


22



23



24

➤RDTsindicatelagcenonlinearity:Analy'ctheoriesaccordingtoJ.Bengtsson,SLSNote9/97●Linearchroma'city:

●Chroma'cbetafunc'ons:

●Chroma'cdispersion:


25

➤RDTsindicatelagcenonlinearity:Analy'ctheoriesaccordingtoJ.Bengtsson,SLSNote9/97●Firstordergeometricterms(amplitude-dependent):


➤Integra'onofRDTsalongthewholering●Almostperfectcancella'onof3rdorderRDTsinthearcsec'ons

26

νx-2νy[(Jx)1/2(Jy)] νx[(Jx)1/2(Jy)]

νx[(Jx)3/2]3νx[(Jx)3/2]


➤Integra'onofRDTsalongthewholering●FFScontributesmostofresidualRDTs

27

3νx[(Jx)3/2] νx[(Jx)3/2]

νx-2νy[(Jx)1/2(Jy)] νx[(Jx)1/2(Jy)]


➤Integra'onofRDTsalongthewholering●Almostperfectcancella'onof3rdorderRDTsinthearcsec'ons

28

3νy[(Jy)3/2]

2νx-νy[(Jx)(Jy)1/2] νy[(Jy)3/2]

νy[(Jy)1/2(Jx)]


➤Integra'onofRDTsalongthewholering●FFScontributesmostofresidualRDTs

3νy[(Jy)3/2]

2νx-νy[(Jx)(Jy)1/2] νy[(Jy)3/2]

νy[(Jy)1/2(Jx)]

29


➤Detuningalongthewholering●w/constraints:chroma'ccorrec'on

30

dβy/dδ

dνx/dδ dνy/dδ

dβx/dδ


➤Detuningalongthewholering●w/constraints:chroma'ccorrec'on

31

dβy/dδ

dνx/dδ dνy/dδ

dβx/dδ


➤Detuningalongthewholering-secondorder●w/constraints:chroma'ccorrec'on

32

d2βy/dδ2

d2νx/dδ2 d2νy/dδ2

d2βx/dδ2


➤Detuningalongthewholering-secondorder●w/constraints:chroma'ccorrec'on

33

d2βx/dδ2 d2βy/dδ2

d2νx/dδ2 d2νy/dδ2


➤Dispersionalongthewholering●w/constraints:Nospecialcontrolonchroma'cdispersions?

34

dηy/dδ

d2ηx/dδ2 d2ηy/dδ2

dηx/dδ


➤Dispersionalongthewholering●w/constraints:Nospecialcontrolonchroma'cdispersions?

35

dηx/dδ dηy/dδ

d2ηx/dδ2 d2ηy/dδ2


➤Chroma'ccouplingalongthewholering●w/constraints:Chroma'ccouplingcontrolled

36

d2R/dδ2

d3R/dδ3

dR/dδ


➤Chroma'ccouplingalongthewholering●w/constraints:Chroma'ccouplingcontrolled

37

dR/dδ d2R/dδ2

d3R/dδ3


➤px2pyterm:CompareSAD●Hard-edgefringefieldsoffinalfocusquadsareimportantsources

38


➤px2pyterm●Howquad.hard-edgefringescontribute?

39

Vert.offsetsinFFquads

N.Ohuchietal.,IPAC’13


➤px2pyterm●Howquad.hard-edgefringescontribute?

40

COD


➤px2pyterm●Howquad.hard-edgefringescontribute?+Magnetoffsets+COD=>3rdgeometricterms

41


➤Luminositycalcula'ons●~1/3causedbypx2pyterm(fromFFS,strengthcalculatedbyPTC)●~1/2causedbychroma'ceffects(includinginterplaywithgeometricnonlineari'es?)●~1/6minorcontribu'onfromothernonlineari'es

42


➤Luminositycalcula'ons●Importantchroma'cnonlinearterms(specifictosler_1689.sad):py2δ,ypyδ,pxyδ,xpyδ●BasicallySuperKEKBissensi'vetoY-mo'oncoupledtoX-andZ-direc'ons

43


Quadrupole:

Referencesynchronouspar'cle:

5. Symplectic tracking in SAD

44

➤Hamiltonian●Hamiltonianforarela'vis'cpar'cleinanelectromagne'cfieldinCartesiancoordinatesystem:

●HamiltonianusedinSAD:

H =q(~p� q ~A)2c2 +m

20c

4 + q�

H(x, px, y, py, z, �) =E

P0v0� (1 +

x

⇢x+

y

⇢y)q

(1 + �)2 � (px � Ax)2 � (py � Ay)2 � (1 +x

⇢x+

y

⇢y)As

P0 = �0m0v0

p = P/P0 = 1 + � px = Px/P0, py = Py/P0

Ax =qAx

P0=

Ax

B⇢, Ay =

qAy

P0=

Ay

B⇢, As =

qAs

P0=

As

B⇢

~A ⌘ (Ax, Ay, As) = (0, 0,1

2B1(y

2 � x2))B1 = @By/@x

K1 =B1

B0⇢=

eB1

P0Solenoid: ~B = (0, 0, Bs)

~A ⌘ (Ax, Ay, As) = (�1

2Bsy,

1

2Bsx, 0)


45

➤ADRIFT(L)isnonlinear…●HamiltonianforaDRIFT:

●Symplec'ctransforma'on(exactsolu'on):

H(x, px, y, py, z, �) =1

v0

s

p2c2 + (m0c

2

P0)2 �

qp2 � p2x � p2y

x2 = x1 +px1p

p2�p2x1�p2

y1

L,

px2 = px1,y2 = y1 +

py1pp2�p2

x1�p2y1

L,

py2 = py1,z2 = z1 � ( pp

p2�p2x1�p2

y1

� vv0)L = z1 + (1� pp

p2�p2x1�p2

y1

)L� v0�vv0

L


46

➤ADRIFTwithsolenoidfield(L,BZ)●HamiltonianforaDRIFT+solenoidfield:

●Symplec'ctransforma'on(exactsolu'on):

●TheSOLelementinSADisspecial:NOa`ributeofL●Thenextcase:L≠0,BZ≠0,K0≠0,SK0≠0[Solvable]

H(x, px, y, py, z, �) =E

P0v0�q

p2 � (px + 12bzy)

2 � (py � 12bzx)

2 bz =eBz

P0

x2 = x1 +(1+�) sin�

bzpxi +

(1+�)(1�cos�)bz

pyi,

y2 = y1 � (1+�)(1�cos�)bz

pxi +(1+�) sin�

bzpyi,

px2 = pxi cos�+ pyi sin�� bz2(1+�)y2,

py2 = �pxi sin�+ pyi cos�+ bz2(1+�)x2,

z2 = z1 +

p1�p2

xi�p2yi�1p

1�p2xi�p2

yi

��v

�L

� = bzL(1+�)

p1�p2

xi�p2yi

,

pxi = px1 +bzy1

2(1+�) ,

pyi = py1 � bzx12(1+�) ,

�v = v0�vv0


47

➤Fringefields:Bendsouedgefringe(FromBmadmanual)


48

➤Fringefields:Quad.souedgefringe(FromBmadmanual)


49

➤Fringefields:Hardedgefringe(FromBmadmanual)

Note:Thisequa'onisgeneral,applyingforBEND,QUAD,SEXT,…toarbitraryorder.ButBENDisspecial!


50

➤Fringefields:HardedgefringeforBEND●Twomodelsfoundforhard-edgefringe*E.Forest:“Parallel-plate”shape(populartheory)*Y.Cai:Roundshape(SLAC-PUB-11181,applyforSCmagnets?)

SCmagnet(FromS.Russenschuck’stextbook,2010)

Usualcase(FromSuperKEKBTDR)


51

➤Fringefields:HardedgefringeforBEND●Maxwelliansolu'onforhard-edgedipolefield*G.Lee-Whi'ngetal.=>E.Forestetal.*S.Caspietal.=>M.Bassegetal.=>Y.Caietal.

Themodelforharmonicsexpansion.Thefieldisconfinedinsideacircle

withr<r0(FromS.Russenschuck’stextbook,

2010)

Themodelforwidemagnet.Thefiledisconfinedatregionof

-b<y<band-∞<x<∞


52


Ay 6= 0Ay = 0


53


Fielddistribu'onwithhard-edge:Fielddistribu'onwithhard-edge:


54


ImplementedinSAD:

ApplyforLHCandFCCs?:


55

➤Solenoidregion●ThemostcomplicatedpartinSAD●SADusesGEOandBOUNDtodefineasolenoidregion●Acceptableelementsinsidesolenoidregion:DRIFT,BEND(ANGLE=0),QUADandMULT●Tosimplifythetransforma'on:InaSOLregion,thecoordinateisshiuedontheaxisofthesolenoid,nomaèrhowthedesignorbitbendsthere.


56

➤Solenoidregion●DRIFTwithBZ≠0●BENDwithBZ≠0:L≠0,K0≠0,SK0≠0,ANGLE=0[Solvable]●QUADwithBZ≠0:L≠0,K1≠0,SK1≠0[Solvable?]●Thegeneralcase:MULTwithBZ≠0[Needmul'-stepintegra'on]*Step1:Solenoidfringeattheentrance*Step2:Rota'onofcoordinatetocancelSK1*Step3:Calculatethenumberslicesfortracking*Step4:NonlinearMaxwellianfringemapattheentrance*Step5:Linearsouedgefringeattheentrance*Step6:Bodypartusing“driu-kick-driu”integra'on*Step7-11:Mapsatexit

Solenoidaxis


57

➤Tiltedsolenoid:FCC-eeasanexample●SAD:Orbitpatching

●Beamline:(-ES3L-LX2-ES2L-LX1-ES1L-IPIPES1RLX1ES2RLX2ES3R)

6. Summary

58

➤Lagcetransla'on●Translatorscollected●ExamplesuploadedtoMAD-Xsvnrepositoryandmywebpage●BenchmarkofSAD,BmadandMAD-X/PTCforseveralprojects➤Applica'ons●Synchrotronradia'onsimula'onusingBmad(Synrad3D)●RDTcalcula'onsusingPTC●AnalysisoflagcenonlinearityinSuperKEKBandsimula'onsofbeam-beamwithnonlinearity➤Futureplan●Translatorstobeimproved(jointefforts)●Acceleratordesign/simula'ons:Applica'ons

Transla’on among SAD, MAD-X and Bmadresearch.kek.jp/people/dmzhou/BeamPhysics/Lattice...2019/09/19 · Benchmark done in 2015 Great agreement in closed orbit, even in the complicated

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