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

150

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

0 100 200 300 400 500 600

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

16

18

20

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24

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30

0 100 200 300 400 500

BPM vert i cal off set (um)

proj

ecte

d em

itta

nce

(nm)

15

20

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30

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40

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

80

100

120

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

20

22

24

26

28

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

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

20

21

22

23

24

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

22

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

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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

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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.