Expected Radiation in FLASH with 3rd Harmonic Module

Igor Zagorodnov11.05.2009

BD meeting, DESY

ACC39

Present layout + ACC39 is considered in the talk.Energy 1 GeV.Radiation wavelength ~ 6.5 nm.Bunch charges 1nC, 0.5 nC, 0.25 nC.

Layout and main parameters

1

56

566

5666

127MeV

r = -0.1808[m]

t 0.295198

u -0.437737

E =

==

2

56

566

5666

470MeV

r = -0.048669[m]

t 0.0733141

u -0.0982712

E =

==

3

56

566

5666

1 eV

r = 5.585e-4[m]

t 0.0588

u -0.6417

E G=

==

ACC39

3D simulation setup

ASTRA (m=0 solver, on axis bunch)

CSRtrack (1D model)

W3 2W13W1W1

TM

Linear Transformation (slice centers)

W1-TESLA cryomodule wake

W3- ACC39 wake

TM- transverse matching to thedesign optics

M. Krasilnikov - Input Desk for ASTRA gun simulations for 1nC, 0.5 nC, 0.25nCN. Golubeva – MAD optics (V2, V2+) for 1 GeV

1D (longitudinal phase space) simulation setup

accelerator

compressor

W1 -TESLA cryomodule wakeW3 - ACC39 wakeLS - space charge wakeWin, Wout - wakes to simulate CS and edge radiation in BCs

ACC39

2W1LSWin

W1 W3LSWin

Wout Wout 3W1LSWin

Wout LS

1 1 0 0 0( ) ( ) cos( )E s E s V ks ϕ= + +

1 1 0 0 1( ) ( ( ))E s E s s=

1 0s s=

( )1 2 31 0 0 56 0 566 0 5666 0( )s s s r t uδ δ δ= − + +

3D and 1D simulations with self fields.

space charge +cavity wakes + self fields in BCs

1D model was checked through 3D.Working points are found by optimization in 1D and then checked by 3D.Finally, 1D model is used to estimate the RF tolerances.

3D model 1D model

3D results to fit the 1D model

1D scan to find the working point

1D results to use in the 3D model

Accuracy check of the results for 1nC presented in January

-1 -0.5 0 0.5 1 1.5

x 10-4

0

500

1000

1500

2000

2500

Parallel ASTRA vs. serial one

serial

parallel

Have I started exactly with the same distribution from the cathode?

[m]s [m]s

[MeV]E[A]I

-1 -0.5 0 0.5 1 1.5

x 10-4

0

500

1000

1500

2000

2500

-1 -0.5 0 0.5 1 1.5

x 10-4

0

500

1000

1500

2000

25001000k particles

Mesh 25*50

Mesh 50*100

Mesh 24*64

1000k200k

Accuracy check of the results for 1nC presented in January

Different number of particles and mesh lines in ASTRA

[m]s

[A]I

[m]s

[A]I

-2 -1 0 1 2-200

-150

-100

-50

0

50

100

150

200

Numerical (ECHO)

Analytical

-4 -2 0 2 4-200

-150

-100

-50

0

50

100

150

200

bunch

Accuracy check of the results for 1nC presented in January

Check of the wakefield model from the gun up to BC2

/s σ

||

kV

nCW

||

kV

nCW

Numerical(ECHO)

Analytical

bunch

/s σ

0 100 200 3001

2

3

4

5

6

7

8x 10

-6

Phase shift between BCs (Q=1nC, optics V2).

prxε

[ ]m×rad

0 50 100 150 200 250 300 3500

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

-6

[ ]degψ∆

[ ]m×rad

[ ]degψ∆

Maximal slice emittance in [−σ,σ]Projected emittance

pryε

xσε

yσε

[ , ]max ( )sl

ssσ

σ σε ε

∈ −=[ ]60 deg ?ψ∆ = − −

10 20 30 40 50 60 700

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

10 15 20 25

5

10

15

20

V2

V2+

V2m

V2+

V2

V2m

-60o

-50 0 500

1

2

3

4

5

-50 0 500

1

2

3

4

5

V2+V2

Phase shift between BCs (Q=0.5nC).

[m]z[m]z

[m]xβ[rad]µ

[µm]s[µm]s

[mm×mrad] [mm×mrad]

xε

yε

xε

yε

Work points(Track1D)

6.932

18.771

25.198

ϕ2,

[deg]

530.937

531.261

531.845

V3,

[MV]

0379.867194.96315.99614.848142.3721

16.9413

16.993

V39,

[MV]

183.034

193.356

ϕ39,

[deg]

0345.8111.098141.6110.25

0362.72214.521143.1930.5

ϕ3,

[deg]

V2,

[MV]

ϕ1,

[deg]

V1,

[MV]

Charge,

nC

0 0.5 1141

142

143

144

145

0 0.5 115.8

16

16.2

16.4

16.6

16.8

17

17.2

0 0.5 1340

350

360

370

380

390

0 0.5 111

12

13

14

15

0 0.5 1182

184

186

188

190

192

194

196

0 0.5 15

10

15

20

25

30

0 00

0 0

2 ( ) ( ) 3 (0) max ( )min 0.25 , 1809s

s

I I I I I s II A

I

σ σεε

− − + − + − + =

1V39V 2V

1ϕ 39ϕ2ϕ

[MV]

[deg]

[nC]Q

[nC]Q

Tolerances (Track1D)

-0.2 -0.1 0 0.1 0.20

0.5

1

1.5

2

2.5

3

-0.2 -0.1 0 0.1 0.20

0.5

1

1.5

2

2.5

3

-0.2 -0.1 0 0.1 0.20

0.5

1

1.5

2

2.5

3

-1 -0.5 0 0.5 10

0.5

1

1.5

2

2.5

-1 -0.5 0 0.5 10

0.5

1

1.5

2

2.5

-1 -0.5 0 0.5 10

0.5

1

1.5

2

2.5

[MV]

1V 39V2V

1ϕ39ϕ 2ϕ

[deg]

0

C

C

0

C

C

1 nC

0.25 nC

0.5 nC

1 nC

0.25 nC0.5 nC

0.25 nC

0.5 nC

1 nC

Tolerances

0.25

0.5

1

0.25

0.5

1

0.25

0.5

1

Charge, nC

1.560.02

0.110.010.140.14ACC39

0.620.05ACC1

0.100.06

0.140.03

0.58

0.44

0.56

Phase, degree

2.2

2.6

4.6

ACC2

V, MV

Tolerances (10 % change of compression)

Q=1nC (S2E)

-100 -50 0 50 1000

500

1000

1500

2000

2500

-100 -50 0 50 1000

0.5

1

1.5

2

2.5

-100 -50 0 50 100-1

-0.5

0

0.5

1

1.5

2

[µm]s

[mm×mrad]xε

yε

[m]s [m]s

[MeV]E[A]I

[m]s

x

x

σ

y

y

σ

1D

3D

1D3D

-100 -50 0 50 100997

998

999

1000

1001

1002

1003

1004

Q=0.5nC (S2E)

-50 0 500

500

1000

1500

2000

2500

3000

-50 0 500

0.5

1

1.5

2

2.5

-50 0 50-1.5

-1

-0.5

0

0.5

1

1.5

[µm]s

[mm×mrad]xε

yε

[m]s [m]s

[MeV]E[A]I

[m]s

x

x

σy

y

σ

1D

3D1D

3D

-50 0 50997

998

999

1000

1001

1002

1003

1004

Q=0.25nC (S2E)

-20 0 20 400

500

1000

1500

2000

2500

-20 0 20 400

0.5

1

1.5

2

2.5

-20 0 20 40-2

-1

0

1

2

y

y

σ

[µm]s

[mm×mrad]xε

yε

[m]s [m]s

[MeV]E[A]I

[m]s

x

x

σ

1D

3D

1D3D

-20 -10 0 10 20 30 40997

998

999

1000

1001

1002

1003

1004

-100 -50 0 50 100997

998

999

1000

1001

1002

1003

1004

-50 0 50997

998

999

1000

1001

1002

1003

1004

-20 -10 0 10 20 30 40997

998

999

1000

1001

1002

1003

10041 nC 0.5 nC 0.25 nC

Density function ( , )s Eρ

[µm]s

[MeV]E

-1 -0.5 0 0.5 10

0.5

1

1.5

2

2.5

-100 -50 0 50 100 1500

500

1000

1500

2000

2500

192649σz, mkm

1078574σx, mkm

4979154FWHM, mkm

617565σy, mkm

0.250.51Q,nC

' 'x y x y x yx y x y Iγ γ ε ε β β α α∆Slice parameters extracted from S2E simulations

-1 -0.5 0 0.5 1-3

-2

-1

0

1

z

z z

σ−

z

z z

σ−

[mm×mrad]xε

0x

x

σ0 74µmxσ =

Slice parameters[A]I

[mm]s

1 nC

0.5 nC

0.25 nC

1 nC

0.25 nC

1 nC

0.5 nC

0.25 nC

FEL code ALICE• 1D/2D/3D • 3D azimuthal field solver (Neumann)• Leap-Frog integrator• Perfectly Matched Layer• transverse motion• simplified model• parallel (MPI)• tested on examples from the book of E.L. Saldin at al “The Physics …“, and by comparison with code Genesis 2.0 of S. Reiche

Radiation energy statistics (700 runs)

0 5 10 15 20 2510

-3

10-2

10-1

100

101

102

103

10 15 20 25

100

200

300

400

500

600

700

800

900

1000

0 5 10 15 20 250

5

10

15

20

25

10-2

100

102

0

5

10

15

20

25

[µJ]E

[m]z [m]z

[m]z

[µJ]E

[%]Eσ [%]Eσ

[µJ]E

1 nC

0.5 nC

0.25 nC

1 nC

0.5 nC

0.25 nC

1 nC

0.5 nC

0.25 nC

Radiation energy statistics

0.5 1 1.50

2

4

6

8

0.5 1 1.50

0.5

1

1.5

2

0.5 1 1.50

1

2

3

4

5

z=10mσ=23%

z=18mσ=8.7%

z=26mσ=4.2%

0.5 1 1.50

1

2

3

4

0.5 1 1.50

1

2

3

4

5

6

7

p(E

)

0.5 1 1.50

2

4

6

8

10

12

14

z=10mσ=11%

z=18mσ=5.1%

z=26mσ=2.8%

0.5 1 1.50

0.5

1

1.5

2

2.5

0.5 1 1.50

1

2

3

4

5

6

0.5 1 1.50

2

4

6

8

10

z=10mσ=17%

z=18mσ=6.8%

z=26mσ=3.7%

E

E

( )p E 1 nC 0.5 nC 0.25 nC

Gamma distr.

Temporal structure

-50 0 50 1000

0.005

0.01

0.015

0.02

0.025

0.03

-50 0 50 1000

0.5

1

1.5

2

2.5

-50 0 50 1000

0.5

1

1.5

2

2.5

3

3.5

4

-100 0 1000

0.005

0.01

0.015

0.02

0.025

0.03

-100 0 1000

0.5

1

1.5

2

2.5

3

-100 0 1000

1

2

3

4

5

-200 -100 0 100 2000

1

2

3

4

5

-200 -100 0 100 2000

0.5

1

1.5

2

2.5

3

-200 -100 0 100 2000

0.002

0.004

0.006

0.008

0.01z=10m

z=18m

z=26m

z=10m

z=18m

z=26m

z=10m

z=18mσ=6.8%

z=26m

( )[GW]P s

[µm]s

1 nC 0.5 nC 0.25 nC

Temporal structure

5 10 15 20 250

50

100

150

200

250fs

FWHM

5 10 15 20 250

10

20

30

40

50µm

zσ

[m]z [m]z

1 nC

0.5 nC

0.25 nC

1 nC

0.5 nC

0.25 nC

0 100 200 300 400 5000

0.2

0.4

0.6

0.8

1

0 50 100 150 2000

0.2

0.4

0.6

0.8

1

0 100 200 3000

0.2

0.4

0.6

0.8

1

Temporal structure. Degree of contrast.

1 nC 0.5 nC 0.25 nC

10.5

0.5

( ) ( ) ( )C P t dt P t dtτ

τ

τ−∞

− −∞

=

∫ ∫

[fs]τ [fs]τ [fs]τ

( )C τ ( )C τ( )C τ

10m

26m18m

10m

26m

18m

-1.5 -1 -0.5 0 0.50

0.5

1

1.5

-1.5 -1 -0.5 0 0.50

0.5

1

1.5

-1.5 -1 -0.5 0 0.50

0.5

1

1.5

-1.5 -1 -0.5 0 0.50

0.5

1

1.5

-1.5 -1 -0.5 0 0.50

0.5

1

1.5

-1.5 -1 -0.5 0 0.50

0.5

1

1.5

-1.5 -1 -0.5 0 0.50

0.5

1

1.5

-1.5 -1 -0.5 0 0.50

0.5

1

1.5

-1.5 -1 -0.5 0 0.50

0.5

1

1.5

z=10mFWHM=0.49%

z=18mFWHM=0.38%

z=26mFWHM=0.41%

z=10mFWHM=0.54%

z=18mFWHM=0.43%

z=26mFWHM=0.46%

z=10mFWHM=0.52%

z=18mFWHM=0.38%

z=26mFWHM=0.41%

ωω

∆

( )[a.u.]P ωSpectrum

1 nC 0.5 nC 0.25 nC

First order correlation

2 1

fs

t t−

1[fs]t

1 1 2 1( , )g t t t−1 nCQ = 0.5 nCQ = 0.25 nCQ =

10 mz =

18 mz =

26 mz =

*1 2

1 1 21 2

( ) ( )( , )

( ) ( )E E

E t E tg t t

t tσ σ=ɶ ɶ

Coherence time

-200 -100 0 100 2002

3

4

5

6

7

8

-50 0 50 1002

4

6

8

-100 -50 0 50 100 1502

3

4

5

6

7

8

1[fs]t

1 nCQ =

0.5 nCQ =

0.25 nCQ =

10 mz =

18 mz =26 mz =

2

1( ) ( , ') 'c t g t t dtτ = ∫

1[fs]t1[fs]t

[fs]cτ

[fs]cτ

[fs]cτ

Summary

50-140100-200200-300Radiation pulse duration at

80% of contrast, fs

0.4-0.60.4-0.5Spectrum width, %

4-5Coherence time, fs

10001000Beam energy, MeV

without*with harmonic module

0.5-10.250.51Bunch charge, nC

35-150

400

0.7-2

2

25-100

200

0.6-2

1.7

2-43Averaged peak power, GW

22-3220Saturation length, m

50-150700Energy in the rad. pulse, mkJ

15-50100-250Radiation pulse duration

FWHM, fs

1.3-2.22Peak current, kA

1.5-3.51.2-2Slice emmitance,mm-mrad

66.5Wavelength, nm

*) E.L.Saldin at al, Expected properties of the radiation from VUV-FEL at DESY,TESLA FEL 2004-06, 2004.

Summary

ASTRA – tracking in stright sections with SCCSRtrack – tracking through dipolesMAD 8 – optics matchingGlueTrackM – master script for 3D S2ETrack1D – semi-analytical tracking of long. phase spaceECHO – wake fieldsALICE – FEL process

Acknowledgements to

M. Dohlus, M. Krasilnikov, T. Limberg, W. Decking,N. Golubeva, E. Schneidmiller