Longitudinal Impedance Budget from LINAC to SASE2

Igor Zagorodnov

Beam Dynamics Group Meeting

13.11.06

SASE2

SASE1

(W.Decking)

Wakefield sources

- Resistance of the pipe (r=25mm, L=456m, Aluminium)

- Collimators (r=2mm, L=50cm, 4 items, TIMETAL 6-4 )

- Kickers (r=10mm, L=10m, 3 items, R/Lm )

500d mm

2 2b mm1 25b mm

Collimator (geometrical wake)

||( ) ( )QW s Z I s

|| 2 (0)eZ Z

0 1

2

(0) ln2

e Z bZ

b

|| 303Z

Diffractive regime: the geometrical wake repeats the bunch shape

TIMETAL 6-4 alloy (Titanium)(E.Schutz MVA)

6 1 10.6 10 m

500d mm

2 2b mm1 25b mm

http://www.timet.com/timetal6-4frame.html

Collimator (resistive wake)

1

0

( ) ( )( ) 1

2 2s sZ ZR

Z iR c Z

0 sec

0 mrough

0 nmoxid

( ) ( ) ( )Ls s sZ Z Z

( )( )si

Z

( )LsZ i L

0( )1 i

0.5 ( 0.02 )oxid roughL

M.Dohlus. TESLA 2001-26, 2001K.L.F.Bane, G.V.Stupakov, SLAC-PUB-10707, 2004

0 1 2

x 10-4

-3000

-2000

-1000

0

1000

TIMETAL 6-4 alloy (Titanium)

6 1 10.6 10 m

500d mm

2 2b mm1 25b mm

Geom. Res. Total

Loss 827 329 1156

Spread 501 359 829

Peak -1665 -823 -2411

/kV nC

|| /W kV nC

s m

Collimator

total

resistive

bunch

0 1 2

x 10-4

-20

-10

0

10

20

Aluminium

7 1 13.66 10 m

456d m

1 25b mm

resistive total

Loss 6.6 7.4

Spread 5.9 6.5

Peak -14.5 -15.9

/ /kV nC m

|| / /W kV nC m

s m

Pipe (resistive+oxid layer+roughness)

resistive

bunch

-157.1 10 sec

600 mrough 5 nmoxid

(T.Wohlenberg)

10d m

2 10b mm1 25b mm

Kicker (geometrical wake)

||( ) ( )QW s Z I s

|| 110Z

|| 2 (0)eZ Z

0 1

2

(0) ln2

e Z bZ

b

(T.Wohlenberg)

6 1 10.76 10 m

Kicker (resistive wake)

1

7 2 612 1.1 10 1.3 10m mm

10d m

2 10b mm1 25b mm

0 sec 0 mrough

0 nmoxid

(T.Wohlenberg)

0 1 2

x 10-4

-2000

-1000

0

1000

2000

Geom. Res. Total

Loss 300 894 1195

Spread 182 469 592

Peak -604 -1526 -1905

/kV nC

|| /W kV nC

s m

Kicker

totalresistive

bunch

10d m

2 10b mm1 25b mm6 1 10.76 10 m

0 1 2

x 10-4

-1

-0.5

0

0.5

1x 10

4

Pipe (456m)

Collimators (4 items)

Kickers (3*10m)

Total

Loss 3359 4623 3584 11565

Spread 2963 3315 1777 7617

Peak -7248 -9645 -5714 -21636

|| /W kV nC

s m

TOTAL (LINAC to SASE2)

collimators

pipe bunch

kickers

/kV nC

0

51015

202530

354045

pipe collimators kickers

Loss

Spread

Peak

%

Energy spread due to wakefields between LINAC and SASE 2

0 1 2

x 10-4

-0.1

-0.05

0

0.05

0.1

0.15

s m

0

%E

E

0 17.5 GeVE

bunch

0 0.5 1 1.5

x 10-4

3.416

3.418

3.42

3.422

3.424

3.426

x 104

s m

bunch

before SASE2

after LINAC

Energy losses between LINAC and SASE2 vs. pipe radius R

5 10 15 20 25 300

0.05

0.1

0.15

0.2

5 10 15 20 25 300.06

0.08

0.1

0.12

0.14

0.16

5 10 15 20 25 300.1

0.2

0.3

0.4

0.5

0

%rmsE

E

0

%E

E

0

max%

E

E

Spread

[mm]R

Loss Peak

[mm]R [mm]R

With oxid layer and roughness

Geometrical+resistive

0 1 2

x 10-4

-4

-2

0

2

4x 10

4

undulator pipe (42*5.1m)

intersection pipe (41*0.7m)

absorbers(41*0.3m items)

Total Total

(old geometry)*

Loss 9395 869 1689 1.19e4 1.11e4

Spread 16560 1723 1470 1.95e4 1.89e4

Peak -33789 -3435 -4200 -4.1e4 -4.0e4

|| /W kV nC

s m

TOTAL (SASE2)

undulator pipe

bunch

absorbers

/kV nC

pipe in intersection

(T.Wohlenberg)

* M. Dohlus et al, TESLA-FEL 2005-10

Energy spread between LINAC and SASE2 vs. pipe radius R(normalized to the spread in SASE2)

10 20 30 40 500

50

100

150

2 2

2%

Linac SASErms

SASErms

E

E

Spread

[mm]R

total

collimators

Conclusion

0

51015

202530

354045

pipe collimators kickers

Loss

Spread

Peak

Impact on FEL performance?(spectrum from SASE simulations?)

10 20 30 40 500

50

100

150

2 2

2%

Linac SASErms

SASErms

E

E

Spread

[mm]R

total

collimators

Appendix A. Kick factors of flat and round collimators are equal

2b2b x

yround flat

Appendix A. Kick factors of flat and round collimators are equal

0 0 0 0( , , , ) cos( )d dk r r k r

0 0 0( , , , )x dk x y x y k x

0 0 0( , , , )y dk x y x y k y

0 0 0( , , , )x xd xqk x y x y k x k x

0 0 0( , , , )y yd yqk x y x y k y k y

2b2b x

yround flat

xd xqk k xq yqk k

z

y

0yy=

0 0 0( , , , )y yd xdk x y x y k y k y

Appendix A. Kick factors of flat and round collimators are equal

0 0 0( , , , )y dk x y x y k y0 0 0( , , , )y yd yqk x y x y k y k y

2b2b x

yround flat

0.5yd dk k 0.5xq xd dk k k

y yd yq dk k k k

Kick of the flat collimator is equal to the kick of the round one

z

y

0yy

=

=

=0.5

Appendix B. XFEL collimator vs. cryomodule

1 25mmb

50d cm

2b

02 2

2 1

1 1

2long Z c

kb b

Appendix B. XFEL collimator vs. cryomodule

b2,

mm

Kick,

V/pC/m

1 18*103

2 4.5*103

3 2.0*103

4 1.1*103

5 0.7*103

[V/pC/m/module]Kick

25 ~6.5

For the bunch with sigma=25mkm the kick from the collimator with apperture b2=2mm is equal to the kick of ~700 cryomoduoles

Emmitance growth?