wakefield calculations and impedance database challenges for the european xfel project at desy igor...

Wakefield Calculations and Impedance Database

Challenges for the European XFEL Project at DESY

Igor Zagorodnov

ICFA mini-Workshop on “Electromagnetic wake fields and

impedances in particle accelerators“

Erice, Sicily23-28. April 2014

32%

22%4%1%11%

23% 2% 4%

COL CAV TDS

BPMA KICK PIP20

PUMCL FLANG

Igor Zagorodnov| Collaboration Meeting at PAL| 2-6. August 2013 | Seite 2

Overview

The European XFEL Project Wakefield Calculations for the XFEL

Cavity and Coupler Wakes Collimators High-Frequency Impedances Resistive, Roughness, Oxide Layer Wakes Wakefields in Undulator Section

Impedance Database Start-to-End Simulations with Wakes Impact of Wakes on FEL Performance Challenges


The European XFEL Project



Linac Coherent Light Source

(LCLS)

Spring-8 Angstrom Compact Laser

(SACLA)

European XFEL

Location USA Japan DeutschlandStart of

commissioning 2009 2011 2016

Accelerator technology normal conducting normal conducting superconducting

Number of light flashes per

second120 60 27 000

Minimum wavelength

0.15 nm 0.1 nm 0.05 nm

Length of the facility

3000 m 750 m 3400 m



Gun

4 accelerator modules

12 accelerator modules

mainlinac

3rd harmonicRF

SASE1laserheater

dogleg collimator

BC2BC1BC0

= 60-120 mm = 60-120 mm = 30-100 mm

bunch compressors

σs = 2 mmIpeak= 50 AQ = 1 nC

σs = 1 mmIpeak= 100 AE = 130 MeV

σs = 0.1 mmIpeak= 1 kAE = 600 MeV

σs = 0.01-0.02 mmIpeak= 5-10 kAE = 2400 MeV

Layout


Cavity and Coupler Wakes

1 8 1 8 1 8

8 cavities + 9 belows =12m 12m 12m

Cryomodule 1 Cryomodule 2 Cryomodule 3

Wakes for short bunches up to 50um have been studied To reach the steady state solution 3 cryomodules are considered For longitudinal case the wakes were studied earlier by A. Novokhatski

et al*. The transverse results are calculated with ECHO**.

**Weiland T., Zagorodnov I, The Short-Range Transverse Wake Function for TESLA Accelerating Structure, DESY, TESLA-2003-19, 2003

*Novokhatski A, Timm M, Weiland T. Single Bunch Energy Spread in the TESLA Cryomodule, DESY, TESLA-1999-16, 1999

Wakefunctions of TESLA Cryomodule



a – iris rtadius, g – cavity gap

0.50|| 2( ) ~ ( )

2

Z c gw s O s

sa

0.502 2

22( ) ~ ( )

Z cw s gs O s

a a

0|| 02( ) exp( ) ~ (1)

Z cw s A s s O

a

101 12 2

2( ) 2 1 1 ~ ( )s sZ c

w s A s s s e O sa a

0 1, ,A s s

One-cell structure Periodic structure

- fit parameters

K.L.F.Bane, SLAC-PUB-9663, LCC-0116, 2003




10-2

10-1

50

100

150

10-2

10-110

1

102

/V pC / /V pCm

1

2 20||W

1

2 21W

/cm /cm

1W

0||W

10-2

10-1

50

100

150

10-2

10-110

1

102

/V pC / /V pCm

1

2 20||W

1

2 21W

/cm /cm

1W

0||W

Comparison of numerical (points) and analytical (lines) integral parameters for the third cryomodule

1.46A 30 1.74 10s 3

1 0.92 10s 35.57mma a

|| 0( ) 344exp( )[V/pC/module]w s s s

3

1 1

V( ) 10 1 1 exp

pC×m×module

s sw s

s s

( ), 0O s s

(1), 0O s




0 0 . 1 0 . 2 0 . 30

2 0 0

4 0 0

6 0 0

- 5 0 5

- 6 0 0

- 4 0 0

- 2 0 0

0/s

1 / // V mW p C

/s c m

1 / // V mW p C

7 0 0 m

w a k e f u n c t i o n

0 0 . 1 0 . 2 0 . 30

2 0 0

4 0 0

6 0 0

- 5 0 5

- 6 0 0

- 4 0 0

- 2 0 0

0/s

1 / // V mW p C

/s c m

1 / // V mW p C

7 0 0 m

w a k e f u n c t i o n

Comparison of numerical (grays) and analytical (dashes) transverse wakes

Transverse wake of TESLA Cryomodule



Coupler Kick



TESLA Report 2004-01, DESY, 2004

Transverse Deflecting Structure



Third-Harmonic Section


Collimator Wakes

The bunch moves very close to the aperture wall!

r

z

b

d

1b2b

d

1b2b

Figure 1: Top half of a symmetric collimator.

Round collimator. Regimes

Inductive

11 2 1b

Diffractive

1 1

2/ bd

1b2b

d

1b2b

Figure 1: Top half of a symmetric collimator.

Round collimator. Regimes

Inductive

11 2 1b

Diffractive

1 1

2/ b

2

~b

Tapered Collimators


Collimator Wakes

I .Zagorodnov et al, DESY, TESLA-2003-19, 2003M.Dohlus et al., DESY, FEL Report 2010-04, 2010

200mm

d 100mm

3mma

20.25mmb

200mm

d 100mm

3mma

20.25mmb

0 5 10 15 20200

300

400

500

600

700

800

V/pC

d/mm

0

||L

1

220||W

0 5 10 15 20200

300

400

500

600

700

800

V/pC

d/mm

0

||L

1

220||W

0 5 10 15 2020

0.5

1

1.5

2

2.5

V/pC/mm

d/mm

1

L

1

221W

0 5 10 15 2020

0.5

1

1.5

2

2.5

V/pC/mm

d/mm

1

L

1

221W

V/pC/mm

d/mm

1

L

1

221W

25μm


Collimator Wakes

Zagorodnov I., Bane K., Wakefield Calculations for 3D Collimators, in Proceedings of EPAC 2006 Conference, Edinburgh, Scotland, 2006 (SLAC-PUB-11938)

Short/Long 3D Step Collimators

0.01 0.1 1 10

2

3

4

5[V/pC/mm]k

[cm]d

short

long

0.01 0.1 1 10

2.5

3

3.5

4

4.5

5

σ=0.1mm

=0.5mm=0.3mm

long

in+out

[V/pC/mm]k

[cm]d

short

0.01 0.1 1 10

2

3

4

5[V/pC/mm]k

[cm]d

short

long

0.01 0.1 1 10

2

3

4

5[V/pC/mm]k

[cm]d

short

long

0.01 0.1 1 10

2.5

3

3.5

4

4.5

5

σ=0.1mm

=0.5mm=0.3mm

long

in+out

[V/pC/mm]k

[cm]d

short

0.01 0.1 1 10

2.5

3

3.5

4

4.5

5

σ=0.1mm

=0.5mm=0.3mm

long

in+out

[V/pC/mm]k

[cm]d

short

Kick factor vs. collimator length. A round collimator(left), a square or rectangular collimator ( s = 0.3 mm, right).


Collimator Wakes

Zagorodnov I., Bane K., Wakefield Calculations for 3D Collimators, in Proceedings of EPAC 2006 Conference, Edinburgh, Scotland, 2006 (SLAC-PUB-11938)

Short/Long 3D Step Collimators 0.5 longshortk k

|| 2 eZ Z

1 2

2 21 22

0

1(*)eZ ds ds

Q Z

1 2

212

0

1(**)eZ ds

Q Z

0 0( ) ( )i x Z Q x x

i ix

( ) 0i x

i ix 1,2i

long short

1

2


Collimator WakesShort/Long Round Collimators

shortlong

|| (0)eck Z

2 ( ) (0)e ek c Z Z

1.5 1 1|| 0 1 20.5 log( )k cZ b b

02 2

2 1

1 1

2

Z ck

b b

20 2

2 42 1

1

4

Z c bk

b b

1 2

2 21 22

0

1(*)eZ ds ds

Q Z

1 2

212

0

1(**)eZ ds

Q Z

long short


High-Frequency Impedances

AS

BS

apS

z

x

y

L

AS

BS

apS

z

x

y

L

AS

BS

apS

z

x

y

L

2 /L a

0|| 1 2 1 2 1 2

2( , ) ( , ) ( , ) ( , ) ( , )

B ap

B B A BS S

Z ds dsc

r r r r r r r r r r

10( , ) ( )A i i r r r r

ASr( , ) 0A i r r

ASr

10( , ) ( )B i i r r r r

BSr( , ) 0B i r r

ASr

1,2i

,Optical Approximation


High-Frequency ImpedancesTransverse Impedance of Laser Mirror of RF Gun

R

a

2d

Y

X apS

R

a

2d

Y

X

R

a

2d

Y

X apSapS

2

( ) 2 22 2 2 2

0

1( ) 2 1 ln

2m

yR

Z R a adaR a d

( ) 1 4 3 3 4 2 2 3 4 2( ) 4 2 4 ( )dyZ A aR d a d R d a d Q R R d Q d

( ) 4 2 2 2 2 2 2 2 4 4 4 4 21( ) ( ) 6 8 8q

yZ ad R d a a d R d aQ B a R d R a dAB

-1tand

a

-1 -1cot tand a

Q d

2 2Q dR

2 2B a d 2 2 4 2

04A a R d

ky(0,0),

V/pC

ky(d),

V/pC/m

ky(q),

V/pC/m

Analytical 0.124 13.1 12.1Numerical 0.120 13.1 11.6

ky(0,0),

V/pC

ky(d),

V/pC/m

ky(q),

V/pC/m

Analytical 0.12 13 12Numerical 0.08 24 7.5

0.5 mm 2 mm


High-Frequency ImpedancesTransverse Impedance of OTR Screens

R

ha

d

apS

R

ha

d

apS

( )2 2

0

1( ) ( , ) ( , )

4m

yZ F a h F h aaR h

2 2 1 1 2 2 2 2

2 2( , ) 2 cot tan ln

x dF x y R x y ay R x d d y

xR x

2 4 6 8 100

1

2

3

4

5

6

[mm]a

kV

nCyk

d = 4 mm

2 4 6 8 10

0.5

1

1.5

2

d = 6 mm

d = 12.5 mm

0

0[%]x x

x

[mm]a2 4 6 8 10

0

1

2

3

4

5

6

[mm]a

kV

nCyk

d = 4 mm

2 4 6 8 10

0.5

1

1.5

2

d = 6 mm

d = 12.5 mm

[mm]a

kV

nCyk

d = 4 mm

2 4 6 8 10

0.5

1

1.5

2

d = 6 mm

d = 12.5 mm

0

0[%]x x

x

[mm]a

0 2 2

0 0 0

1 13 6

y y

y y y

S S

2y

z

eQkS

E


High-Frequency ImpedancesLongitudinal Impedance of Round-to-Rectangular Transitions in Bunch Compressors

apSR w

g0

apSR w

g0

( 2 )|| 9R SZ

( 2 )|| 0S RZ

2 2.5 3 3.5 4 4.5 50

10

20

30

40

50

60

70

80

rct2R

R2rct

Total

[cm]R

||Z

10cmw 2cmg

1 2 3 4 50

20

40

60

80

100

120

140

160

rct2R

R2rct Total

[cm]g

||Z

10cmw 5cmR

2 2.5 3 3.5 4 4.5 50

10

20

30

40

50

60

70

80

rct2R

R2rct

Total

[cm]R

||Z

10cmw 2cmg

1 2 3 4 50

20

40

60

80

100

120

140

160

rct2R

R2rct Total

[cm]g

||Z

10cmw 5cmR

1 2 3 4 50

20

40

60

80

100

120

140

160

rct2R

R2rct Total

[cm]g

||Z

10cmw 5cmR


High-Frequency ImpedancesImpedances of Round Misaligned Pipe

z

y

x2g

2R Rs 2Rs R

z

y

x2g

2R Rs 2Rs R

M. Dohlus et al, High Frequency Impedances in European XFEL, DESY 10-063, 2010

0 0.1 0.2 0.3 0.4 0.50

50

100

150

Rs2R

R2Rs

Total

/g R

|| (0)Z

Rs2R=R2Rs

Total

/g R

||( )Z g

0 0.1 0.2 0.3 0.4 0.50

50

100

150

Rs2R

R2Rs

Total

/g R

|| (0)Z

Rs2R=R2Rs

Total

/g R

||( )Z g


High-Frequency Impedances

R

R2g apS

0

Rg

x

y

R

R2g apS

0

Rg

x

y


Resistive, Roughness, Oxide Layer Wakes

1

0

( ) ( )( ) 1

2 2s sZ ZR

Z iR c Z

0( ) ( )( )s s

jZ Z

0( )

1 j

The effect of the oxide layer and the roughness can be taken into account through the inductive surface impedance

( ) ( )s sZ Z j L 0

10.01oxid ro

r

rughd dL

||2

2 cZ Z

a

~ 2r

M.Dohlus. TESLA 2001-26, 2001A.Tsakanian et al, TESLA-FEL 2009-05

Round Resistive Pipe with Roughness and Oxide Layer


Resistive, Roughness, Oxide Layer Wakes

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

-0.5

0

0.5

1

1.5x 10

14

Round vs. Elliptical pipe

||

kV

mW

/s Loss, V/pC

Spread, V/pC

round 237 285

elliptical 239 274

Mathcad script for arbitrary shape with roughness and oxide layer (author M. Dohlus)http://www.desy.de/fel-beam/s2e/codes.html

25μm 1nCq

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

-1

0

1

2x 10

14||

kV

mW

/s

12.5μm 0.56nCq


Wakefields in Undulator



N Element from to

Effective

Length Material Conduct.Relax. Time

Oxid layer

Roughness

mm mm mm 1/Omm/m sec nm nm

1 Eliptical pipe 0 5288 5161 Aluminium 3,66E+07 7,10E-15 5 300

2 Pump 5161 5266 105 Aluminium 3,66E+08 7,10E-15 5 300

3Absorber/Round

transition 5266 5288 22 Copper 5,80E+07 2,46E-14 5 300

4 Round pipe 5288 6100 652 Copper 5,80E+07 2,46E-14 5 300

5 Below 5288 5318 30 BeCu 174 2,78E+07 2,46E-14 5 300

6 BPM 5373 5473 100Stainless Steel 304 1,40E+06 2,40E-15 5 300

7 Below 5513 5543 30 BeCu 174 2,78E+07 2,46E-14 5 300

8Round/Eliptical

transition 6100 6100 0

1

2 3 45 6 7 8



-0.01 -0.005 0 0.005 0.01

-150

-100

-50

0

50 Loss (Spread), V/pC

step 110 (43)

taper 10mm 74 (48)

taper 20mm 50 (43)

|| [ / ]W V pC

[ ]s cm

step

taper 10mm

Absorber in 3D (2005)

25μm


Wakefields in UndulatorImpedance of Eliptical-to-Round Transition with Absorber

absorberround pipe

elliptical pipe

absorberround pipe

elliptical pipe

ASBS

apS0

Rw

gAS

BSapS

0R

wg

0.4 0.5 0.6 0.70

50

100

150

E2R R2E

Total

[cm]R

||kV

nCk

0.4 0.5 0.6 0.70

50

100

150

200

250

A2R R2E

Total

[cm]R

||kV

nCk

0.4 0.5 0.6 0.70

50

100

150

E2R R2E

Total

[cm]R

||kV

nCk

0.4 0.5 0.6 0.70

50

100

150

200

250

A2R R2E

Total

[cm]R

||kV

nCk

Dependence of the loss factor from the radius of the round pipe. The left graph presents the results without the absorber, the right graph presents the results with the absorber included. The black dots show the numerical results from CST Particle Studio.

1 0.45cmw 1 0.4cmg

0 0.75cmw

0 0.44cmg



Loss,V/pC

Spread,V/pC

Peak,V/pC

pump 15 10 -24

pillbox 40 16 -57

25mkm

-0.01 -0.005 0 0.005 0.01-60

-40

-20

0

Pillbox 2D/3D

Pump

|| [ / ]W V pC

[ ]s cm

Pump



2%

7%

8%

5%

3% 8%

67%

El. Pipe

Pump

Absorber

Round Pipe

Bellow

R/E transition

BPM

19%

geom

res.+oxd.+rough

Energy Spread for Gaussian Bunch (25 μm)


Transitive Resistive and Geometrical Wakes in Undulator


A.Tsakanian, PhD Thesis, 2010


There are hundreds of wakefield sources in XFEL beam line.

The bunch shape changes along the beam line. Hence, a database with wake functions for all element is

required. The wake functions are not functions but distributions

(generalized functions). How to keep information about such functions? We need a model.

Impedance Database


(0) ( 1)1( ( ) ( )) ( ) ( )w s c s cw s R L w

Cc

sss

( 1) 1( ) ( ), 0,w s o s ss

singular part (cannot be tabulated directly)

(0) ( 1)1( ) ( ) ( )Z Z R i L Z

i C

Wake function model

regular part

resistive inductivecapacitive

it describes singularities s-a, <1a

~ ( )W s ds ~ ( )W s ~ ( )W s

Impedance Database


02

( )2

Z c gw s

sa 0(

21) (

2)

Zsgw s

a

Pillbox Cavity

0( ) ln ( )Z b

w s c sa

Step-out transition

0 lnZ b

aR

Tapered collimator

2 0( ) ( )4

Zw s c r dr s

c s

0

4

Zr dr

cL

(0) ( 1)1( ( ) ( )) ( ) ( )w s c s cw s R L w

Cc

sss

Impedance Database


(0)

( 1)2

1( ) (

( ) (

) ( ) ( )( )

)( )

s s

s

w s s RC

L s

sW s ds ds c

c c ds

s

s

s

w s s

Wake potential for arbitrary bunch shape

derivative of the bunch shape

Impedance Database


The main form of database contains a list of elements with parameters R, L, C and links to tables of and .

Impedance Database


-60 -40 -20 0 20 40 60-200

-150

-100

-50

0

50

100

150

200

Undulator wake for Q=1nC

[μm]sTotal wake

resistive wake

bunch

Impedance Database

||[kV/m]W


Impedance DatabaseAccelerator wakes. Q=1nC

19%

42%

4%2%

1%

1%

1%

10%

14% 2% 4%

COL CAV TDS BPMAOTRA BPMR TORAO KICKPIP20 PUMCL FLANG

collimators

cavities

“warm” pipe


Impedance Database

Longitudinal+Transverse Wakes 3D


1 130MeVE

Beam dynamics simulation (2010)

1,1M

Gun

1,3M

2M 3M 4M

LH

DL 1BC 2BC 3BC2 700MeVE 3 2400MeVE 4 14GeVE

ASTRA ( tracking with 3D space charge, DESY, K. Flötmann)

W1 -TESLA cryomodule wake (TESLA Report 2003-19, DESY, 2003)

W3 - ACC39 wake (TESLA Report 2004-01, DESY, 2004)TM - transverse matching to the design optics

W3W1

TM4W1

TM64W1

12W1

TM

Full 3D simulation method (200 CPU, ~10 hours)

CSRtrack (tracking through dipoles, DESY, M. Dohlus, T. Limberg)

1.6 kmz

Start-to-End Simulations with Wakes


Start-to-End Simulations with Wakes

CSRtrack+ASTRA(Guangyao Feng)

Elegant(Hyunchang Jin)

2013

G.Feng et al. FEL Report 2010-04, 2013


New Results and Comparison with Elegant

Comparison with Elegant, Q = 1nC


New Results and Comparison with Elegant

Comparison with Elegant, Q = 250 pC


-60 -40 -20 0 20 40 60-200

-150

-100

-50

0

50

100

150

200

||[kV/m]W

[μm]s

-40 -20 0 20 40 600

0.5

1

1.5

2

2.5

xM

yM

[a.u]I

[μm]s

total wake

resistive wake

bunch

SASE for Nominal Bunch Parameters

Mismatch and wake Q=1nC


-40 -20 0 20 40 600

5

10

15

20

Radiation Q=1 nC

5 -14.8 10 mopt

dK

dz

Averaged through 8000 slices

85mz

0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5

4

4.5

+Wake+Taper

+Wake

mJE

mz

GWP

μms



-20 -10 0 10 20-200

-100

0

100

200

-2 -1 0 1 2 3

x 10-5

0

0.5

1

1.5

2

2.5

3 ||[kV/m]W

[μm]s

xM

yM

[a.u]I

[μm]s

Mismatch and wake Q=250 pC

Total wake

resistive wake

bunch



Radiation Q=250 pC

5 -14.8 10 mopt

dK

dz

0 50 100 1500

0.5

1

1.5

2

-15 -10 -5 0 5 10 150

5

10

15

20

25

30

35

40

Averaged through 2400 slices

60mz

+Wake+Taper

+Wake

mJE

mz

GWP

μms



Accelerator wakes. Q=1nC

19%

42%

4%2%

1%

1%

1%

10%

14% 2% 4%

COL CAV TDS BPMAOTRA BPMR TORAO KICKPIP20 PUMCL FLANG

collimators

cavities

“warm” pipe

Impact of Accelerator Wakes on SASE


-50 0 50-50

0

50|| [MV]W

[μm]s [μm]s

5.3 4e 0

0

E E

E

Full wake

Cavities wake

Full wake

Cavities wake

current


Accelerator wakes. Q=1nC


-50 0 500

5

10

15

20

25

0 50 100 1500

1

2

3

4

5

[μm]s

mJE

mz

full wake

(full wake) x 4

(full wake) x 8

GWP at z=85 m

Beam matched in the peak current. Q=1nC

current



-50 0 50

-5

0

5

10

15

20

25

-0.6 -0.4 -0.2 0 0.2 0.40

0.2

0.4

0.6

0.8

1

full wake

(full wake) x 4(full wake) x 8

Beam matched in the peak current. Q=1nC

0

0

% FWHM=0.14%

FWHM=0.23%

FWHM=0.6%

0

0

E E

E

[μm]s

Normalized spectrum at z=85 m



Accelerator wakes. Q=250 pC.

32%

22%4%1%11%

23% 2% 4%

COL CAV TDS

BPMA KICK PIP20

PUMCL FLANG

collimators

cavities

“warm” pipe



-20 -10 0 10 20-30

-20

-10

0

10

20

30

|| [MV]W

[μm]s [μm]s

5.3 4e 0

0

E E

E

Full wake

Cavities wake

Full wake

Cavities wake


Accelerator wakes. Q=250 pC.


-20 -10 0 10 20-5

0

5

10

15

full wake

(full wake) x 4

(full wake) x 8

-0.6 -0.4 -0.2 0 0.2 0.40

0.2

0.4

0.6

0.8

1Normalized spectrum at z=85 m

0

0

%

FWHM=0.29%

FWHM=0.30%

FWHM=0.38%

0

0

E E

E

[μm]s


Beam matched in the peak current. Q=250 pC


Summary

Accelerator wake

Bunch charge, nC

1 0.25 0.02

Energy in the radiation pulse at z=175 m, mJ

x1 9 2.3 0.46

x4 8 2.3 0.44

x8 6 2.3 0.43

Spectrum width at z=85m, %

x1 0.14 0.29 0.55

x4 0.23 0.30 0.58

x8 0.6 0.38 1.0

We have considered only the longitudinal wake in a quite coarse model (adding the missed part of the accelerator wake at the undulator entrance). The transverse wakes are neglected.



Challenges

Chamber Wakefields in Bunch Compressors Impact of All (Longitudinal+Transverse) Wakes on

the Results of Start-to-End SimulationsTransverse Impedance Database Impact of Transverse Wakes on FEL Performance

wakefield calculations and impedance database challenges for the european xfel project at desy igor...

Documents

wakes impact of wakes

xfel cavity

european xfel project

12m12m cryomodule

mev layout slide

european xfel project

oxide layer wakes wakefields

g cavity gap