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
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