Impedance Budget from LINAC to SASE2

Igor Zagorodnov

Beam Dynamics Group Meeting

3.12.07

overview

wake sources = geometric & resistive (=surface effects)

definitions (average & rms)

collimator: geometric, surface effects, all ~40%

pipe: surface effects ~40%

kicker: geometric, surface effects, all ~20%

total

total vs. pipe radius

comparison with effects in LINAC

comparison with SASE2 ~SASE2 / 2

total vs. pipe radius normalized to SASE2

SASE2

SASE1

(W.Decking)

-50 0 50 1000

1000

2000

3000

4000

5000

6000

Wakefield sources

- Resistance of the pipe (r ~ 20 mm, L=456 m, Aluminium)

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

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

0.56 nСq 12.5 μm

[μm]s

[A]I

1 nСq 25 μm Bunch shape

from S2E simulationsby Martin Dohlus

( ) bunch shapes

2 2 ( ) ( ) energy lossQ W Q W s s ds

0.50.5 22 2 2( ) ( ) ( ) energy spreadQ W W Q W s W s ds

Collimator (geometrical wake)

||( ) ( )QW s Z I s

|| 2 (0)eZ Z0 1

2

(0) ln2

e Z bZ

b

|| 276Z

Optical approximation: the geometrical wake repeats the bunch shape.

500 mmd

2 2 mmb 1 20 mmb

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

6 1 10.6 10 m

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

Collimator (resistive wake)

1

0

( ) ( )( ) 1

2 2s sZ ZR

Z iR c Z

0 sec

300 nmrough

5 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

500 mmd

2 2 mmb 1 20 mmb

0 1 2

x 10-4

-2500

-2000

-1500

-1000

-500

0

500

1000

Geom. Res. Total

Loss 754 332 1086

Spread 457 365 791

Peak -1518 -833 -2272

/kV nC

|| /W kV nC

s m

Collimator

total

resistive

bunch

500 mmd

2 2 mmb 1 20 mmb

0 1 2

x 10-4

-30

-20

-10

0

10

20

30

Aluminium

7 1 13.66 10 m

456md

1 20 mmb

resistive total

Loss 8.4 9.0

Spread 8.5 9.3

Peak -19.8 -21

/ /kV nC m

|| kV/nC/mW

ms

Pipe (resistive+oxid layer+roughness)

wake

bunch

-157.1 10 sec

300 nmrough 5 nmoxid

(T.Wohlenberg)

Kicker (geometrical wake)

||( ) ( )QW s Z I s

|| 110Z

|| 2 (0)eZ Z

0 1

2

(0) ln2

e Z bZ

b

(T.Wohlenberg)

10 md

2 10 mmb 1 20 mmb

Kicker (resistive wake)

2.4 15 sece

300 nmrough

5 nmoxid

(T.Wohlenberg)

8 2 612 4.4 10 0.53 10m mm

6 1 11.9 10 m

10 md

2 10 mmb 1 20 mmb

0 1 2

x 10-4

-2000

-1500

-1000

-500

0

500

1000

1500

Geom. Res. Total

Loss 227 659 886

Spread 137 412 519

Peak -457 -1222 -1544

/kV nC

|| /W kV nC

s m

Kicker

total

resistive

bunch

10 md

2 10 mmb 1 20 mmb

M. Ivanyan, A. Tsakanian, Phys. Rev. ST-AB, 2006

• Analytical solution for the fields inside tube for finite Lorenz factor

• Perform the ultrarelativistic limit

A.W. Chao, SLAC-PUB- 2946, 1982A. Piwinski, DESY-94-068, 1994• Usual Approach

• Tube with finite thickness

Method: matching technique

Problem: fields are diverges in outer space for γ

Tube with infinite thickness

skin-depth < tube thickness

• Solution in General Case

B. Zotter, S. Kheifets, 1997.

A. Tsakanian

Ceramic Kicker Vacuum chamber: Ceramic with Titanium-Stabilized High Gradient Steel (TSHGS) coats

1-m 12-10 R/L - Resistance

m 0.7 - Thickness

-1-16 mΩ100.18946)(2.0841σ

TSHGS Parameters

m 0.9 -Lenght

m 0.01 - Radius

Vacuum Chamber Parameters

Impedance of XFEL Ceramic Kicker Vacuum Chamber with Metallic Coats.

410~tan

1.9

r

Ceramic Parameters

A. Tsakanian

Longitudinal monopole impedance as function of dimensionless wave number for several cases of vacuum chamber material: 1. Ceramic with TSHGS coats. 2. TSHGS single layer tube with finite and infinite thickness. 3. Copper single layer tube.

0sk

s0 characteristic distance: mcas 4.63/231

02

0

Monopole Term Longitudinal Impedance Per Unit LengthA. Tsakanian

transverse A.T.

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 4103 4343 2659 11105

Spread 4222 3164 1557 8682

Peak -9680 -9088 -4633 -22595

|| /W kV nC

s m

TOTAL (LINAC to SASE2)

collimators

pipebunch

kickers

/kV nC

0

10

20

30

40

50

pipe collimators kickers

Loss

Spread

%

5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

5 10 15 20 25 300

0.05

0.1

0.15

0.2

Energy losses between LINAC and SASE2 vs. pipe radius R

0

%rmsE

E

0

%E

E

Spread

[mm]R

Loss

[mm]R

1( )O R1( )O R

0 0.5 1 1.5

x 10-4

3.414

3.416

3.418

3.42

3.422

3.424x 10

4

0 1 2

x 10-4

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Energy spread due to wakefields between LINAC and SASE 2

s m

0

%E

E

0 17.5 GeVE

bunch

Energy from S2E simulationsby Martin Dohlus

after LINAC

Before SASE2

bunch

1

2 3

4

5 6 7 8Katrin Schuett, ZM1Dirk Lipka, MDI

0 1 2

x 10-4

-5

0

5x 10

7

Geometric Total

Loss 0.69e4 1.77e4

Spread 0.33e4 1.89e4

Peak -1.2e3 -4.67e4

|| /W V nC

s m

TOTAL (SASE2)

Total wake

bunch

Geometric

/kV nC

(for comparison)

5 10 15 20 25 300

50

100

150

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

2 2

2%

Linac SASErms

SASErms

E

E

[mm]R

total

collimatorskickers

pipe

0

10

20

30

40

50

pipe collimators kickers

Loss

Spread

R=20mm