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EuCARD-PRE-2012-004
European Coordination for Accelerator Research and Development
PUBLICATION
Beam-beam simulations: dynamicaleffects and beam-beam limit for LEP3
Ohmi, K (KEK, Tsukuba, Japan)
07 December 2012
The research leading to these results has received funding from the European Commissionunder the FP7 Research Infrastructures project EuCARD, grant agreement no. 227579.
This work is part of EuCARD Work Package 4: AccNet: Accelerator Science Networks.
The electronic version of this EuCARD Publication is available via the EuCARD web site
or on the CERN Document Server at the following URL :
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Beam-
beam
simulations:
dynamicaleffects
and
beam-b
eamlimitfo
rLEP3
K.O
hmi
KEK-A
CCEL
4Dec,2012
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Paramete
rsofLEP3
givenbyF.Zimmerm
ann
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ParametersofTLEP-H
givenby
F.Z
immer
mann
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3Db
eam-beam
inter
action
!y=1mm,"z=
2.3(LEP3)-1.7
(TLEP-h)mm.For"z>!y,the
beam-beamf
orcevariessig
nificantlyalon
gthebunchlength.
Abunchisd
ividedintoseveralslices
whichcontain
manymacro
-particles.
Collisioniscalculatedslicebyslice.
Strong-strong
V0(s)
V0(s,0
)=
Sexp
:
s
0
H0ds:
=
i=
exp
:
p2 x
,i
+
p2 y
,i
2
s:,
Nsl,
i=1
exp
:V1
0,+
(s,i
),i
(+,
s,i
)V0,+
(s,i
)s:
Nsl,
+
j=1
exp
:V1
0,
(s+,j
)+,j
(,
s+,j
)V0,
(s+,j
)s:
driftbetweenslices
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3D
symple
cticintegratorforslice-
by
-sliceco
llision
!P
otentialisc
alculatedatsfandsb.
!P
otentialisinterpolated
tosibetweensfandsb.
sf
sb
s
i
!Sincetheintera
ctiondependsonz,energykickshouldbe
takenintoaccountd!/dz.
!Werepeatthes
ameprocedu
reexchangingparticleand
slice.
sf
sb
s
i
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Potentia
landlin
earkick
ofhe
slice
-by-slicecollision
potentialisinterp
olated.
potentialatcente
rof
slice,BAD
metho
d
KEKBcase
K.Ohmietal.,PRST7,104401
(2004)
ky
=
2
(s)/y
2
=
py
/x
j
(s)=
j(sb)+
j(sf)
j(sb)
sf
sb
(s
sb)
j
(s)=
j
(sc
)
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C
onvergen
ceforthe
slicenum
ber
Allparticlesini-thsliceare
kickedb
ycp
Interpo
lation
ByM.Tawada
KEKBcase
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S
imulatio
n
!R
adiationdampingrate
!
LEP3!xy/T0
=0.036,!s/T
0=0.043
!
TLEP-H
!xy/T0=0.013,!s/T0=0.00875
!T
rackpartic
les1000tu
rns(2000turnsforha
lf
ring),>10xT0/!xy.
!T
argetlumin
ositypercollision
!
LEP3
L=2.675x1033cm
-2s-1
!
TLEP-H
L=
6.125x1032cm-2s-1
!N
macrop=1,00
0,000nzslice=16
8
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Sim
ulation
I(firsttrial)
#x=0.52
,#y=0.5
8
Comparisonbetwe
enIP=1and
2.
ExpectLgeo~2.6
75x1033
Shortterm
behavior
Linit=Lgeo
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Beam
size
#x=0.5
2,#
y=0.5
8
IP=1
IP=
2
Dynam
icbeta
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Firstimpre
ssionofthe
simulationresults
Dynamicbetaworkswellf
orIP=1inthis
operating
point,(
0.52
,0.5
8),b
utd
oesnotfor
IP=2.
Thisisreasonab
leresult.
Luminosit
yforIP=1isnotverygood.
Usually
this
operating
pointshowedhigherlu
minositytha
n
targetoneinKEKB.
Verticalbeams
izeinc
reasesinshorttime.
Largesynchrotrontuneaffects.
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Syste
maticst
udy:Tun
escan
IP=2,#x=0.5
2,scan#y
Head-tailtypeofcoh
erentmotionappear
#y
>0.8.
Incohere
nt#y~0.7
5?
Lgeo~2.6
75x1033
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Tune
scanII
IP=2,#y=0.5
8(0.29
x2),s
can#x
Co
herentmotio
nappearsat#
y>0.8
Lgeo~2.67
5x1033
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Slightuppe
rofinteger
BestL
uminosity,
butlo
werthan
deisgn
.
Lgeo~2.67
5x1033
#x
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Bunch
populat
ionand
specific
luminosity
L=2.6x1033c
m-2s-1
isachievedatNe=1.1x1
012.
Lgeo~
2.6
75x1033
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T
LEP-H
#y=0.58
(0.2
9x2),sc
an#x
16
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TLEP-H
!D
esignluminosity
6
.1x1032isreachable.
!B
etterresultthanLEP3.
!"
sislowerthanLEP3. 17
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S
ynchrot
rontune(LEP3)
!L
uminositydegradationatlarges
ynchrotron
tuneisseen.
#x=0.0
2,#
y=0.1
9
IP=2
18
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S
ummary
!B
eam-beam
simulationshasbee
nperforme
d
forLEP3an
dTLEP-H.
!R
oughtune
scanwas
done.
!Toachieve
thedesign
luminosity
inLEP3,
1
0%morebunchpopu
lationisne
cessaryat
least.TLEP
-Hcanach
ievethedesign.
!T
helargesynchrotron
tunedegra
desthe
luminosityp
erformance.
!
Thetreatme
ntofsynchrotronmotion
andz
dependenceofthebeam
-beamforce
shouldbe
checked.
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C
hoiceofoperatingpoin
t
!
("x,"y)=(0.5
1,0.55-0.5
9)isthebe
stfordyna
mic
betainhorizontaland
integrabilityinvertica
lin
everye+e-
collidersw
ithsingleIP.
!
("x,"y)=(0.0
2,0.10-0.1
8)for2IP.Thehorizontal
tunemayn
otbeacceptable.
!
Luminosity
dependenceintunespaceis
showninth
ispresentation.(Nos
trategyfor
optimizationnow.)
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