Simulation Studies on ILC Bunch Compressors with SLEPT
description
Transcript of Simulation Studies on ILC Bunch Compressors with SLEPT
Simulation Studies on ILC Bunch Compressors with SLEPT
Dou WANG and Kiyoshi KUBO
2009.06.23
ILC-CLIC LET Beam Dynamics Workshop
outline
• Coupler’s kicks• DFS• Simulations including longitudinal motion• Summary
Coupler’s Kicks
In the ILC cavities, the power and HOM couplers break the structure symmetry =>two effects ◇ coupler’s wakefields ◇ RF kick
• These have been newly introduced in the code SLEPT• Emittance growth in Bunch Compressor was simulated
without errors.
Coupler’s Kicks - Wake modeling-1
Fig. 1,2, Wake potential for 9 mm, 1 mm and 0.3 mm bunch. Data from cavity field calculation (rectangular: horizontal, circle: vertical) and from the simplified model
(lines).
( ) ( ') ( ') ' ( ') 's
tW s s W s s ds s ds
( )W s as b s
Simplified wake function is used in the simulations.
Wake potential:
Coupler’s Kicks - Wake modeling-2
From the numerical results of the coupler wakepotentials[1] (see
Fig. 1 and Fig. 2), we get the approximate wake function in SLEPT.
Long bunch (9 mm) :
Short bunch (0.3 mm and 1 mm) :
• Within 3-sigma of the bunch lengths, the calculated
wakepotentials from this simplified model have a good
agreement with the data from cavity field calculation.
( )[ / ] 2.862 [ ] 0.6786 [ ]
( )[ / ] 3.731 [ ] 0.8545 [ ]
x
y
W s V pC s m s m
W s V pC s m s m
( )[ / ] 5.928 [ ] 0.1500 [ ]
( )[ / ] 6.770 [ ] 0.0894 [ ]
x
y
W s V pC s m s m
W s V pC s m s m
Coupler’s Kicks - RF kick modelingRF-kick voltage is expressed as[2] :
: vector of transverse RF kick for on-crest particle,
Va :accelerating voltage, k: wave number of RF, G: accelerating gradient,
L: cavity length, rf : accelerating RF phase, c :RF kick phase.)
Numerical result for an on-crest-accelerated particle in ILC cavity is[3]:
2 2 60 69.8105.3 69.8 126.3 10 , 2.5562
105.3x
ca
Varctg
V
0 2 2 6 11.17.3 11.1 13.3 10 , 2.1525
7.3y
ca
Varctg
V
(vertical) 1.113.7
l)(horizonta 8.693.10510/ 6
0i
iVV a
)](exp[/)( 0 ksiGLVVsV crfa
0V
Then, amplitudes and phases are:
Coupler’s Kicks - Simulations
Simulations are done only in the RF sections, not in the wiggler sections.• Lattice of RDR base design was used.• Only single bunch emittance growth is considered• No error is included
• BC1 RF section (1-to-1 correction, no misalignment)• Final dispersion corrected emittance growth is 0.21 nm
1. 95E- 08
2. 00E- 08
2. 05E- 08
2. 10E- 08
2. 15E- 08
2. 20E- 08
2. 25E- 08
2. 30E- 08
2. 35E- 08
0 10 20 30 40 50 60
s (m)
proj
ecte
d ve
rtic
al e
mitt
ance
(m) RFk onl y
wake onl y
w+RF ki ck
linear dispersion corrected vertical emittance vs. distance from the entrance
projected vertical emittance vs. distance from the entrance
1. 99E- 08
2. 00E- 08
2. 01E- 08
2. 02E- 08
2. 03E- 08
2. 04E- 08
0 10 20 30 40 50 60
s (m)
line
ar d
ispe
rtio
n co
rrec
ted
vert
ical
emi
ttan
ce (
m)
RF ki ck onl y
wake onl y
w+RFk
Coupler’s Kicks - BC1 result
• BC2 RF section (1-to-1 correction, no misalignment)• Final dispersion corrected emittance growth is 4.41 nm
linear dispersion corrected vertical emittance vs. distance from the entrance
projected vertical emittance vs. distance from the entrance
1. 5E- 08
2. 0E- 08
2. 5E- 08
3. 0E- 08
3. 5E- 08
4. 0E- 08
4. 5E- 08
5. 0E- 08
0 100 200 300 400 500 600 700
s (m)
proj
ecte
d ve
rtic
al e
mitt
ance
(m)
RFk onl ywake onl yw+RFk
1. 5E- 08
2. 0E- 08
2. 5E- 08
3. 0E- 08
3. 5E- 08
4. 0E- 08
4. 5E- 08
5. 0E- 08
0 100 200 300 400 500 600 700
s ( s)
line
ar d
ispe
rsio
n co
rrec
ted
vert
ical
emi
ttan
ce(m
)
RF ki ck onl ywake onl yw+RFk
Coupler’s Kicks - BC2 result
•Comparison with A. Latina’s result (using PLACET) for BC2 [2]
Two results about RF kick effect agree well, but the wakefield effect from our result is larger than A. Latina’s .
1. 5E- 08
2. 0E- 08
2. 5E- 08
3. 0E- 08
3. 5E- 08
4. 0E- 08
4. 5E- 08
5. 0E- 08
0 100 200 300 400 500 600 700
s ( s)
line
ar d
ispe
rsio
n co
rrec
ted
vert
ical
emi
ttan
ce(m
)
RF ki ck onl ywake onl yw+RFk
Coupler’s Kicks - Comparison with past result
DFS - method
• It’s impossible to change the initial energy of test beam for ILC bunch compressor.
• SLEPT DFS has been newly improved in order to change the RF phase of accelerating cavities besides of changing the initial energy of test beam.
• DFS:
minimize
• DFS was tested on the RF section of ILC BC2.
2 2{ 0 }i i i
i
w y y y
DFS result - sensitivity to each error -1
△=5°, weight=5000, random seeds=20
20
20. 5
21
21. 5
22
0 100 200 300 400 500 600
cavi ty vert i cal off set (um)
proj
ecte
d em
itta
nce
(nm)
0
50
100
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200
250
0 100 200 300 400 500 600
cavi ty t i l t (urad)
proj
ecte
d em
itta
nce
(nm)
20. 062
20. 064
20. 066
20. 068
20. 07
20. 072
0 100 200 300 400 500
quadrupol e vert i cal off set (um)
proj
ecte
d em
itta
nce
(nm)
20
20. 1
20. 2
20. 3
20. 4
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quadrupol e rotat i on (urad)
proj
ecte
d em
itta
nce
(nm)
DFS - sensitivity to each error -2
• Almost no dependence on Quad offset and Quad rotation
• Some dependence on cavity offset, BPM offset and BPM resolution
• Strong dependence on cavity tilt
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BPM vert i cal off set (um)
proj
ecte
d em
itta
nce
(nm)
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45
0 2 4 6 8 10
BPM resol ut i on (um)
proj
ecte
d em
itta
nce
(nm)
DFS - effect of cavity tilt -1
20
40
60
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140
1 10 100 1000 10000
wei ght
proj
ecte
d em
itta
nce
(nm)
dPH=5dPH=10dPH=15dPH=20dPH=25dPH=30
20
30
40
50
60
1 10 100 1000 10000
wei ght
disp
ersi
on c
orre
cted
emi
ttan
ce (
nm)
dPH=5dPH=10dPH=15dPH=20dPH=25dPH=30
Cavity tilt only TiltC=300urad, random seeds=40
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30
0 5 10 15 20 25 30 35
dPH (deg)
mini
mum
vert
ical
emi
ttan
ce (
nm) proj ected emi ttance
di spersi on corrected emi ttance
DFS - effect of cavity tilt -2
All errors except for cavity tilt. Quadrupole vertical offset: 300 um, Quadrupole rotation: 300 urad
Cavity vertical offset: 300 um
BPM vertical offset: 300 um (aligned independently)
BPM resolution: 1 um
random seeds=40
20
22
24
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28
30
1 10 100 1000 10000 100000 1000000 1E+07
wei ght
disp
ersi
on c
orre
cted
emit
tanc
e (n
m)
dPH=5dPH=10dPH=15dPH=20dPH=25dPH=30
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0 5 10 15 20 25 30 35
dPH (deg)
mini
mum
vert
ical
emi
ttan
ce (
nm)
proj ected emi t tance
di spersi on corrected emi t tance
DFS - effect of cavity tilt -3
Our modified DFS is not very effective to cavity tilt.
Large emittance for large weight.
With all other errors except for cavity tilt, the final emittance growth can be controlled to 0.5 nm.
20
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24
26
28
30
1 10 100 1000 10000 100000 1000000 1E+07
wei ght
disp
ersi
on c
orre
cted
emit
tanc
e (n
m)
dPH=5dPH=10dPH=15dPH=20dPH=25dPH=30
Cavity tilt only All errors except cavity tilt
20
30
40
50
60
1 10 100 1000 10000
wei ght
disp
ersi
on c
orre
cted
emi
ttan
ce (
nm)
dPH=5dPH=10dPH=15dPH=20dPH=25dPH=30
DFS - including all the errors -1
Standard Errors: Quadrupole vertical offset: 300um
Quadrupole rotation: 300urad
Cavity vertical offset: 300um
Cavity tilt: 300urad
BPM vertical offset: 300 um
(aligned independently)
BPM resolution: 1 um
• random seeds=40
40
60
80
100
120
140
160
1 10 100 1000 10000
wei ght
proj
ecte
d em
itta
nce
(nm)
dPH=2dPH=5dPH=10dPH=15dPH=20dPH=25dPH=30
20
30
40
50
60
1 10 100 1000 10000
wei ght
disp
ersi
on c
orre
cted
emi
ttan
ce (
nm)
dPH=2dPH=5dPH=10dPH=15dPH=20dPH=25dPH=30
DFS - including all the errors -2
• DFS is not very effective because of cavity tilt.• The minimum final emittance growth can be controlled to 7 nm
including all the errors.
1
10
100
1000
10000
0 5 10 15 20 25 30 35
dPH (deg)
opti
mum
weig
ht
proj ected emi ttance
di spersi on corrected emi ttance
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25
30
35
40
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50
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60
0 5 10 15 20 25 30 35
dPH (deg)
mini
mum
vert
ical
emi
ttan
ce (
nm)
proj ected emi ttance
di spersi on corrected emi ttance
Simulations including longitudinal motion
SLEPT used to fix relative longitudinal position for saving time of wakefield calculations.
It is being improved to include longitudinal motion.
• Two types sections in the beam line:– Normal section: Z does not change. Wakefields exist. We use present prog
ram.– Special section: Z can change. No wakefields. We use new program.
• For special section beginning: slice beam particle beam (add Z to each macro-particle) end: particle beam slice beam; reset wakefields for slice beam.
Simulations including longitudinal motion - check bunch length change
012345
6789
10
0 100 200 300 400 500 600 700 800 900 1000 1100
s (m)
bunc
h le
ngth
(mm
)
W1: bunch length can be compressed from 9 mm to 1.2 mm
W2: bunch length can be compressed from 1.2 mm to 360 um
• Simulation results for the whole ILC bunch compressor from real bend model.
The setting may be for 6 mm initial length?
Simulations including longitudinal motion - check transverse emittance
No misalignment. No correction
• Without any misalignment, the vertical emittance will increase by 0.08 nm naturally.
19. 98
20
20. 02
20. 04
20. 06
20. 08
20. 1
20. 12
0 100 200 300 400 500 600 700 800 900 1000 1100
s (m)
vert
ical
emi
ttan
ce (
nm)
Simulations including longitudinal motion - check the effect of one-to-one
0. 00E+00
5. 00E+04
1. 00E+05
1. 50E+05
2. 00E+05
2. 50E+05
3. 00E+05
3. 50E+05
0 100 200 300 400 500 600 700 800 900 1000 1100
s(m)di
sper
sion
cor
rect
ed e
mitt
ance
(nm
)
no correct i on1- to- 1
Only quadrupole vertical error: 300urad, 20 random seeds
• The final emittance will be 8 um after one-to-one.
• One-to-one alone is not enough, other correction methods are inevitable.
• The code is still under development.
0. 00E+00
1. 00E+03
2. 00E+03
3. 00E+03
4. 00E+03
5. 00E+03
6. 00E+03
7. 00E+03
8. 00E+03
9. 00E+03
0 100 200 300 400 500 600 700 800 900 1000 1100
s(m)
disp
ersi
on c
orre
cted
emi
ttan
ce (
nm)
1- to-1
Should be checked
summary
1. Coupler wake has been newly introduced to SLEPT. Final vertical emittance growth in RDR BC RF section including coupler RF kick and w
akes is : BC1: 0.21 nm BC2: 4.41 nm2. DFS changing RF phase was introduced in SLEPT. 3. This DFS is not very effective to cavity tilt. (Should be checked.)4. With all other standard errors except for cavity tilt, the final emittance g
rowth can be controlled to 0.5 nm. But the final emittance growth will be 7 nm including all the errors.
5. SLEPT is being improved to include Z-position change for BC and the bunch length can be compressed from 9 mm to 360 um according to our simulation. Orbit corrections for the modified code including the special sections are under development.
References
[1] Andrea Latina, private communication, (2008).[2] Andrea Latina, et al, “Emittance Growth in ML and BC w
ith Couplers’ RF-Kick and Wakefields”, LCWS, Chicago, November 2008.
[3] N. Solyak, et al, “RF Kick in the ILC Acceleration Structure”, MOPP042, EPAC08.