Transla’on among SAD, MAD-X and Bmadresearch.kek.jp/people/dmzhou/BeamPhysics/Lattice...2019/09/19...
Transcript of Transla’on among SAD, MAD-X and Bmadresearch.kek.jp/people/dmzhou/BeamPhysics/Lattice...2019/09/19...
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
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➤Introduc'on➤Currentstatus●Actuallynotthelatest➤CasesofBenchmarkstudies➤Someapplica'ons➤Symplec'ctrackinginSAD➤Summaryandfutureplan
1. Introduction
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➤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
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➤Mo'va'on:Toimprovecollabora'onsonprojectslikeSuperKEKBandFCCs
Ref.F.Zimmermannetal.,IPAC’14,MOXAA01.
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➤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
2. Current status
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➤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
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➤Effortsforlagcetransla'ons●SADandPTC:developedatKEK,manysharedfeatures(transfermaps,symplec'cintegrator,…)●PTCintegratedintoMAD-XandBmad
MAD-X
BmadPTC
AML/UAP
SAD
MAD
NOTE:Thewidthsofthearrowsindicate“translatability”.
2. Current status
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➤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!
2. Current status
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➤Archiveforexamplesoflagcetransla'on●Sub-directoriesforSADtoMAD-Xtransla'on:
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➤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:
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�(�, s) = �0 +s2
�0(1+�)2
CourtesyofPaulThrane
3. Cases of benchmark studies
➤AbenchmarkofBmad,PTCandSAD:SuperKEKBsler_1689●Benchmarkdonein2015●Greatagreementinclosedorbit,eveninthecomplicatedIR●“Timepatching”wastreateddifferently●Closedorbit(or“fixedpoint”)isthefirstthingtocompare
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3. Cases of benchmark studies
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-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
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3. Cases of benchmark studies
➤AbenchmarkofBmadandSAD:SuperKEKBsler_1684●Benchmarkdonein2014●Similarfootprintoftunespread●Detailsaredifferent,showingminordifferencesfornonlinearmaps
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3. Cases of benchmark studies
Bmad SAD
➤AbenchmarkofBmadandSAD:FCC-ee●RecentstudybyL.vanRiesen-Haupt●GreatagreementbetweenMAD-XandSAD
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3. Cases of benchmark studies
➤AbenchmarkofBmadandSAD:FCC-ee●RecentstudybyL.vanRiesen-Haupt●DiscrepancyagainstPTCmightbeduetoslicing(and/orintegra'onscheme)?
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3. Cases of benchmark studies
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➤Oldfindings●Mytalkto20thKEKBAcceleratorReviewCommi`ee,Feb.23,2015.
4. Some applications
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4. Some applications➤Oldfindings●Mytalkto20thKEKBAcceleratorReviewCommi`ee,Feb.23,2015.
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➤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
4. Some applications
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➤Resonancedrivingterms(RDTs)indicatelagcenonlinearity
4. Some applications
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➤RDTsindicatelagcenonlinearity
4. Some applications
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➤RDTsindicatelagcenonlinearity
4. Some applications
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➤RDTsindicatelagcenonlinearity
4. Some applications
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➤RDTsindicatelagcenonlinearity:Analy'ctheoriesaccordingtoJ.Bengtsson,SLSNote9/97●Linearchroma'city:
●Chroma'cbetafunc'ons:
●Chroma'cdispersion:
4. Some applications
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➤RDTsindicatelagcenonlinearity:Analy'ctheoriesaccordingtoJ.Bengtsson,SLSNote9/97●Firstordergeometricterms(amplitude-dependent):
4. Some applications
➤Integra'onofRDTsalongthewholering●Almostperfectcancella'onof3rdorderRDTsinthearcsec'ons
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νx-2νy[(Jx)1/2(Jy)] νx[(Jx)1/2(Jy)]
νx[(Jx)3/2]3νx[(Jx)3/2]
4. Some applications
➤Integra'onofRDTsalongthewholering●FFScontributesmostofresidualRDTs
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3νx[(Jx)3/2] νx[(Jx)3/2]
νx-2νy[(Jx)1/2(Jy)] νx[(Jx)1/2(Jy)]
4. Some applications
➤Integra'onofRDTsalongthewholering●Almostperfectcancella'onof3rdorderRDTsinthearcsec'ons
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3νy[(Jy)3/2]
2νx-νy[(Jx)(Jy)1/2] νy[(Jy)3/2]
νy[(Jy)1/2(Jx)]
4. Some applications
➤Integra'onofRDTsalongthewholering●FFScontributesmostofresidualRDTs
3νy[(Jy)3/2]
2νx-νy[(Jx)(Jy)1/2] νy[(Jy)3/2]
νy[(Jy)1/2(Jx)]
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4. Some applications
➤Detuningalongthewholering●w/constraints:chroma'ccorrec'on
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dβy/dδ
dνx/dδ dνy/dδ
dβx/dδ
4. Some applications
➤Detuningalongthewholering●w/constraints:chroma'ccorrec'on
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dβy/dδ
dνx/dδ dνy/dδ
dβx/dδ
4. Some applications
➤Detuningalongthewholering-secondorder●w/constraints:chroma'ccorrec'on
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d2βy/dδ2
d2νx/dδ2 d2νy/dδ2
d2βx/dδ2
4. Some applications
➤Detuningalongthewholering-secondorder●w/constraints:chroma'ccorrec'on
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d2βx/dδ2 d2βy/dδ2
d2νx/dδ2 d2νy/dδ2
4. Some applications
➤Dispersionalongthewholering●w/constraints:Nospecialcontrolonchroma'cdispersions?
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dηy/dδ
d2ηx/dδ2 d2ηy/dδ2
dηx/dδ
4. Some applications
➤Dispersionalongthewholering●w/constraints:Nospecialcontrolonchroma'cdispersions?
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dηx/dδ dηy/dδ
d2ηx/dδ2 d2ηy/dδ2
4. Some applications
➤Chroma'ccouplingalongthewholering●w/constraints:Chroma'ccouplingcontrolled
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d2R/dδ2
d3R/dδ3
dR/dδ
4. Some applications
➤Chroma'ccouplingalongthewholering●w/constraints:Chroma'ccouplingcontrolled
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dR/dδ d2R/dδ2
d3R/dδ3
4. Some applications
➤px2pyterm:CompareSAD●Hard-edgefringefieldsoffinalfocusquadsareimportantsources
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4. Some applications
➤px2pyterm●Howquad.hard-edgefringescontribute?
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Vert.offsetsinFFquads
N.Ohuchietal.,IPAC’13
4. Some applications
➤px2pyterm●Howquad.hard-edgefringescontribute?
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COD
4. Some applications
➤px2pyterm●Howquad.hard-edgefringescontribute?+Magnetoffsets+COD=>3rdgeometricterms
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4. Some applications
➤Luminositycalcula'ons●~1/3causedbypx2pyterm(fromFFS,strengthcalculatedbyPTC)●~1/2causedbychroma'ceffects(includinginterplaywithgeometricnonlineari'es?)●~1/6minorcontribu'onfromothernonlineari'es
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4. Some applications
➤Luminositycalcula'ons●Importantchroma'cnonlinearterms(specifictosler_1689.sad):py2δ,ypyδ,pxyδ,xpyδ●BasicallySuperKEKBissensi'vetoY-mo'oncoupledtoX-andZ-direc'ons
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4. Some applications
Quadrupole:
Referencesynchronouspar'cle:
5. Symplectic tracking in SAD
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➤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)
5. Symplectic tracking in SAD
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➤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
5. Symplectic tracking in SAD
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➤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
5. Symplectic tracking in SAD
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➤Fringefields:Bendsouedgefringe(FromBmadmanual)
5. Symplectic tracking in SAD
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➤Fringefields:Quad.souedgefringe(FromBmadmanual)
5. Symplectic tracking in SAD
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➤Fringefields:Hardedgefringe(FromBmadmanual)
Note:Thisequa'onisgeneral,applyingforBEND,QUAD,SEXT,…toarbitraryorder.ButBENDisspecial!
5. Symplectic tracking in SAD
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➤Fringefields:HardedgefringeforBEND●Twomodelsfoundforhard-edgefringe*E.Forest:“Parallel-plate”shape(populartheory)*Y.Cai:Roundshape(SLAC-PUB-11181,applyforSCmagnets?)
SCmagnet(FromS.Russenschuck’stextbook,2010)
Usualcase(FromSuperKEKBTDR)
5. Symplectic tracking in SAD
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➤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<∞
5. Symplectic tracking in SAD
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➤Fringefields:HardedgefringeforBEND●Maxwelliansolu'onforhard-edgedipolefield*G.Lee-Whi'ngetal.=>E.Forestetal.*S.Caspietal.=>M.Bassegetal.=>Y.Caietal.
Ay 6= 0Ay = 0
5. Symplectic tracking in SAD
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➤Fringefields:HardedgefringeforBEND●Maxwelliansolu'onforhard-edgedipolefield*G.Lee-Whi'ngetal.=>E.Forestetal.*S.Caspietal.=>M.Bassegetal.=>Y.Caietal.
Fielddistribu'onwithhard-edge:Fielddistribu'onwithhard-edge:
5. Symplectic tracking in SAD
54
➤Fringefields:HardedgefringeforBEND●Maxwelliansolu'onforhard-edgedipolefield*G.Lee-Whi'ngetal.=>E.Forestetal.*S.Caspietal.=>M.Bassegetal.=>Y.Caietal.
ImplementedinSAD:
ApplyforLHCandFCCs?:
5. Symplectic tracking in SAD
55
➤Solenoidregion●ThemostcomplicatedpartinSAD●SADusesGEOandBOUNDtodefineasolenoidregion●Acceptableelementsinsidesolenoidregion:DRIFT,BEND(ANGLE=0),QUADandMULT●Tosimplifythetransforma'on:InaSOLregion,thecoordinateisshiuedontheaxisofthesolenoid,noma`erhowthedesignorbitbendsthere.
5. Symplectic tracking in SAD
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➤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
5. Symplectic tracking in SAD
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➤Tiltedsolenoid:FCC-eeasanexample●SAD:Orbitpatching
●Beamline:(-ES3L-LX2-ES2L-LX1-ES1L-IPIPES1RLX1ES2RLX2ES3R)
6. Summary
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➤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