Wakefields in XFEL undulator intersections

Igor Zagorodnov

Beam Dynamics Group Meeting

26.02.07

Aluminium

7 -1 -13.66 10 [Ω m ]

-157.1 10 sec

600 nmrough

5 nmoxid

Elliptical chamber length = 5122 mm

Absorber :length 3mmTapers 2*9.5 mm width 9mmheigh 8mm

Copper

7 -1 -15.8 10 [Ω m ]

-142.46 10 sec

0 nmrough

0 nmoxid

Absorber length = 22 mm

Cavity BPM design, Dirk Lipka

elliptical pipe

round pipe

absorber

Round pipe length = 690mm

Copper

7 1 15.8 10 m

-142.46 10 sec

0 nmrough

0 nmoxid

Cavity BPM = 2 Pillbox cavities with gap 10mm and distance 45 mm between them

Elements

Elliptical chamber = 5122 mm

Absorber = 22 mm

Round pipe = 690 mm

Cavity BPM = 2 Pillbox cavities with gap 10mm and distance 45 mm between them

Not considered (see TESLA FEL 2005-10)

216 mm

(5000+1100)-5884=266

Pumping slots = 2*25=50 mm

Flange gaps?Belows?

???

5122+22+690+50==5884 mm

Absorber

4 mm

5 mm4 mm

9.5 mm 3 mm

0.4 mm

15mm

3mm

8.8mm

5 mm

Absorber. Effect of Tapering

4 mm

5 mm4 mm

9.5 mm

3 mm

5 mmg = 4 mm

3 mm

-5 -4 -3 -2 -1 0 1 2 3 4 5-150

-100

-50

0

50

4.5 mm

9.5 mm

5 mm4 mm

6o

~ 0.4og

3o

90o

6o 3o

Loss,

V/pC

Spread,

V/pC

step 89 35

taper 48 39

taper +step 52 26

Absorber. Effect of Tapering

7.5 mm4.5 mm

9.5 mm 3 mm

0.4 mm

15mm

3mm

8.8mm

~ 3o

17.5o

5 mm

9.5 mm

7.5 mm4.5 mm

This taper has no effect.

The taper angle should be about 3 grad.

17.5o

2.4o

Absorber. Long Elliptical Step Collimator

0.4 mm

2 15w mm

3mm

2 8.8g mm

0

0 0 0 0

0 2 20 0 0 0

0 01

Re Re Im Im( , , , ) 4 ln ( ) ( )

cosh( ) sinh( )

nu n n n n

n

x iy x iyx iy x iyT T T T

e d d d dG x y x y x x y y

n nu nu

0 00 0 0 0 0 0( , , , ) ( , , , ) (0, , , )G x y x y G x y x y G g x y

G.Stupakov, K.L.F.Bane, I.Zagorodnov „Optical approximation in the theory of geometric impedance“, in preparation

The semi-analytical approach developed in the paper allows to calculate high-frequency impedance of any short transition.

Loss=86 V/pC

Elliptical 15mm*8.8mm

Absorber 9mm*8mm

Round R=?

Absorber+Round Pipe

0.4 0.5 0.6 0.7

0

50

100

150

200Loss [V/pC]

R [cm]

Elliptical 15mm*8.8mm

Round R=?

Elliptical 15mm*8.8mmER

RE

ER RE

Total

Let us forget about absorber and suggest that we want to have a round pipe. Why do not take a round absorber with R=5mm?

Elliptical+Round Pipe

0.4 0.5 0.6 0.7

0

50

100

150

200

250Loss [V/pC]

R [cm]

Elliptical 15mm*8.8mm

Round R=?

Elliptical 15mm*8.8mmAR

RE

AR RE

Total

EA

Absorber 9mm*8mm

Absorber+Round Pipe+Elliptical Pipe

0.35 0.4 0.45 0.5 0.55 0.60

50

100

150

200Loss [V/pC]

R [cm]

OldType I

Geometric Wakes

0.4 0.45 0.5 0.55 0.6 0.650

20

40

60

80

100

120

140

160

180

200Loss [V/pC]

R [cm]

Old

Type I

Type II

40%

Geometric Wakes

0.4 0.5 0.6 0.70

50

100

150

200

250

4 5 6 70

20

40

60

80

100

120

Loss [kV/nC] Spread [kV/nC]

R [cm] R [cm]

resistive

geom.

L=690mm

Geometric+Resistive Wakes

-5 0 5-200

-150

-100

-50

0

50

resistive

geom.

/s

|| /W V pC

total

R=4.5mm

Loss,

V/pC

Spread,

V/pC

res. 22 27

geom. 87 34

total 109 55

L=690mm

Geometric+Resistive Wakes

-5 0 5-600

-400

-200

0

200

400

Aluminium

7 -1 -13.66 10 [Ω m ]

5122mmL

1 4.4 mmb

resistive total

Loss 225 241

Spread 238 310

kV/nC

|| kV/nCW

ms

Main Pipe (resistive+oxid layer+roughness)

resistive

-157.1 10 sec 600 nmrough

5 nmoxid

(T.Wohlenberg)

-5 -2.5 0 2.5 5

-80

-60

-40

-20

0

|| kV/nCW

ms

only first

pillbox

total

Loss 25 48

Spread 10 19

kV/nC

BPM

2*pillbox

4.5 mm 38.58 mm26.29 mm

45 mm

10 mm

10 mm

BPM

7.5mm

7.5mm

3.8mm7.5mm

7.5mm

7.5mm

Old geometry!

Loss 9*2=18

Spread 4*2=8

kV/nC

Pumping Slots

2 items?

Impedance BudgetUndulator pipe

Pump

(2 items)

BPM

(2 pillboxes)

Round pipe in intersection with absorber

15mm*

8.8mm (5122 mm)

Old geometry

2*10mm pipe R=4.5

absorber 8mm*9mm

(690+22=712mm)

pipe R=5mm

absorber R=5mm

(712mm)

Loss, kV/nC 241 18 48 109 74

Spread, kV/nC 310 8 25 55 41

Loss,

V/pC

Spread,

V/pC

Total geom.

pro section 70 25

resistive (Al)

6.1m 303 325

Old budget from TESLA-FEL 2005-10 (elliptical pipe 15*7.6 mm)

0

50

100

150

200

250

300

350

400

pipe intersection total

new

old

Energy SpreadV/pC

Conclusion In new budget the energy spread is larger by 14 %.

Intersection causes about 25 % of the energy spread.

Round pipe with R=4.5 mm does not increase longitudinal wake.

To suppress the geometric wake the tapers should be less than 3 grad.

Why do not take a round absorber with R=5mm?

A description of 216 mm? (bellows, flange gaps, etc)

0

50

100

150

200

250

300

350

400

pipe intersection total

new

old

pipe93%

intersection7%

pipe77%

intersection23%

Energy SpreadV/pC