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+ SwissFEL Operation Modes and Longitudinal Dynamics of the SwissFEL Hard X-Ray Facility Bolko Beutner - PSI Microbunching Workshop 11.4.2012

Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

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Page 1: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL

Operation Modes and Longitudinal Dynamics of the

SwissFEL Hard X-Ray Facility

Bolko Beutner - PSI

Microbunching Workshop 11.4.2012

Page 2: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

• Introduction

• SwissFEL

• SwissFEL Injector Test Facility

• Operation Modes

• Stability Studies

• Summary

Contents

11.04.2012 2 Bolko Beutner - Paul Scherrer Institute

Page 3: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL SwissFEL

11.04.2012 3

SwissFEL at PSI between Basel and Zuerich in northern Switzerland

• Phase I:Hard X-ray SASE line (Aramis) down to 0.1 nm at 5.8 GeV

• Phase II: Soft X-ray seeded FEL line (Athos) about 10-1 nm at 2.1-3.4 GeV

Different seeding options like Self-seeding, HHG,

EEHG and combinations of them

are presently under study

Bolko Beutner - Paul Scherrer Institute

Page 4: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL SwissFEL

11.04.2012 4

WLHA 250 MeV Injector

SwissFEL

assembly hall

OBLA C-band

test stand

PSI-West

PSI-East

Bolko Beutner - Paul Scherrer Institute

Page 5: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL SwissFEL

11.04.2012 5

Injector

BC 1

Linac 1

BC 2

Linac 2 Linac 3 Collimator

Athos

Aramis

S-Band C-Band

• S-Band 2.5 cell RF gun (100 MV/m)

• S-Band Booster 1/2 (20 / 16 MV/m)

• X-Band Linearizer (20 MV/m)

• C-Band Main Linac (26-28.5 MV/m)

• Bunch Compressor with movable

girder system 0 – 5 deg

with R56 of -55mm at 3.8deg in BC1

and -20mm at 2.1 deg in BC2

Bolko Beutner - Paul Scherrer Institute

Aramis

Collimator

Linac 3

Linac 2 Linac 1

BC 1

BC 2

Booster 1/2

Page 6: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL SwissFEL Overview

11.04.2012 Bolko Beutner - Paul Scherrer Institute 6

0.7- 7 nm, 100 Hz

> 1 nm: transform limited

Athos Undulators 12 x 4 m; gap 24 - 6.5 mm

λu = 40 mm; K= 1 - 3.2; LU= 58 m

BC 2

Linac 1 Linac 2 Linac 3

Aramis Undulators

Switch

Yard

C band (36 x 2 m)

27 MV/m, - 20.9 ºC band (16 x 2 m)

27.5 MV/m, 0 º

210 m

2.0 GeV; 2.7 kA

σz= 6 μm (21 fs)

255 m

3.0 GeV

σδ = 0.34 %

εN,proj. = 0.47 μm

498 m

2.1- 5.8 GeV, 2.7 kA

σz= 6.2 μm (21 fs)

σδ = 0.006 %

εN,slice = 0.29 μm

εN,proj. = 0.51 μm

Energy tuning

C band (52 x 2 m)

max 28.5 MV/m, 0 º

12 x 4 m; gap 3.2 – 5.5 mm

λu = 15 mm; K= 1.2; LU= 58 m

THz Pump: FLUTE

S band (54 MeV; 3 nC)

0.1 – 5 THz; > 0.1 mJ

1 (0.8) - 7 Å

5 – 20 fs; 100 Hz

S band

(2 x4 m)

14/16 MV/m

0 / 0 º

Gun

Laser

Heate

r

Booster 1 Booster 2

BC 1

S band

(4x4 m)

16 MV/m

- 17 º

X band

(2 x 0.75 m)

13.3 MV/m

+ 180 º

z = 16 m

E = 130.4 MeV, I = 20 A

σz= 871 μm (2.9 ps)

σδ = 0.15 %

εN,slice = 0.23 μm

εN,proj. = 0.27 μm

63 m

355 MeV, 150 A

σz= 124 μm (413 fs)

S band

100 MV/m

51 º from

0 crossing

R56 = 66.6 mm

Θ = 4.2 º

σδ = 1.07 %

R56 = 20.7 mm

Θ = 2.15 º

σδ = 0.57 %

Energy tuning

C band (8 x 2 m)

max 28.5 MV/m, 0 º

Deflector

Deflector

2.5- 3.4 GeV, 2.7 kA

426 m

Collimation

• Aramis Hard X-Ray Undulator – SASE

• Athos Soft X-Ray Undulator – Self-seeding and SASE

• Two bunch operation is foreseen with 28ns spacing

• Photon energy of Athos and Aramis are decoupled

by a c-band module (1 klystron for 4 cavities) after

the switchyard

• Laser based THz pump source in Athos line

Page 7: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

• Energy gain in s-band Booster 2 shifted from initial 250MeV to

330MeV (limited by RF)

• Laser heater

• No diagnostic section after BC1 – Emittance measured with

“advanced” quad scan.

• BC1 shifted downstream – closer to c-band Linac 1

Considerations about Microbunching

11.04.2012 Bolko Beutner - Paul Scherrer Institute 7

Energy gain of Booster 2 (4 structures

4m each / 2 klystrons) is increased to

about 200MeV.

Page 8: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

Phase I : Electron Source and Diagnostics

Injector Test Facility

11.04.2012 Bolko Beutner - Paul Scherrer Institute 8

Phase II : Two S-band accelerating structures, no BC

Phase III : The full machine

Slit phase space measurements

Phase I: 0.69+- 0.04 mm mrad

(28.5.2010 22h36 240pC 4mm)

Beutner

Page 9: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Bunch Compressor

11.04.2012 Bolko Beutner - Paul Scherrer Institute 9

BC1 during assembly BC1 completed

Movable support with dipole 2 & 3

Dipole 1

Dipole 4

Movable support for dipole 2 & 3

• Bunch Compressor with Movable Girder for the inner Dipoles

• alpha[deg] = 0.0123 * x[mm]

• Dipole Projected Length: LB = 250mm

• Projected length of Drift Arm: L12 = 4375mm

alpha [deg] B[T]

200MeV

R56[mm]

0 0 0

1 0.0466 -2.767

2 0.0931 -11.07

3 0.1397 -24.90

4 0.1861 -44.27

5 0.2326 -69.17

Page 10: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL BC Movable Girder

11.04.2012 Bolko Beutner - Paul Scherrer Institute 10

Alignment precision of components after adjustment: 20 m

Vertical deflection of girder reference surface

Courtesy of P. Wiegand & K. Dreyer

Vertical deflection of girder reference surface

Manufacturing and alignment precision of reference surfaces: e vertical < 200 m

Page 11: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Photoinjector Laser System

11.04.2012 Bolko Beutner - Paul Scherrer Institute 11

A. Trisorio et al. Appl. Phys B, 105, 255 (2011).

Output energy

Typical SwissFEL working points for the 266nm TiSa:

Target profile for 200 pC: duration=10 ps, sub-ps rise/fall time

Target profile for 10 pC: duration=3.7 ps, sub-ps rise/all time

Using a Dazzler the target flat top and other shape

can be easily programmed Flat top pulse duration 4.6 ps,

rise time (10-90%) = 0.5 ps

modulation on the plateau <5% rms

Two photon absorption and diffraction efficiency limits the output energy (<35 μJ) Energy not sufficient to generate 200 pC in Cu cathode. The UV Dazzler could be applied to the 10 pC working point for the SwissFEL

Carlo Vicario

Page 12: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Pulse Stacking

11.04.2012 Bolko Beutner - Paul Scherrer Institute 12

• At the SwissFEL injector 5 α-cut BBOs and 10 cm dispersive glass are used to overlap

32 pulses, each 0.6 ps long.

• Total efficiency >70%.

• AR coated α-cut BBO for λ>190 nm with relative low

losses.

• The orthogonal output polarizations makes the

optical temporal diagnostic (which are polarization

sensitive) and attenuation of the beam and the two

pulses operation more complicated

• Poor flexibility, only symmetric shapes

Dispersive glass

L L/2 L/4 L/8

α-BBO α-BBO α-BBO α-BBO

c

LnLnttt

eo

eod

45 deg o e

L

Birefringent

Medium

td

Optical axis

Carlo Vicario

Page 13: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Injector Recent Results

11.04.2012 Bolko Beutner - Paul Scherrer Institute 13

Page 14: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Injector Recent Results

11.04.2012 Bolko Beutner - Paul Scherrer Institute 14

Beam parameters 4/5 April:

• 100 pC beam charge

• Ti:Sapph laser (pulse stacked

mode)

• 100% transmission

• 223.5 MeV

– First S-band cavity only at half

power (requires more

conditioning)

Page 15: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Operation Modes

11.04.2012 15

• Standard operation

• 200 pC

• Maximum FEL pulse energy

• Longest FEL pulse length

• Lowest charge operation

• 10 pC

• Short FEL pulse length

• Single-spike in soft X-ray

• Strong residual energy chirp

• 200 pC

• Large FEL Bandwidth (>1%) for

single short Absorption

spectroscopy.

• Attosecond FEL pulse

• 10 pC

• Strongest compression

• Single-spike in hard X-ray

Charge Wakefield Limited

Diagnostic Limit

Special Cases

Similar FEL Gain length for all standard

modes

=> ~ “constant”

Bolko Beutner - Paul Scherrer Institute

Page 16: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Compression Schemes

11.04.2012 16

Linac 1 BC 2 Linac 2+3 Collimator

compression wakes remove chirp double dogleg

(slight decompression)

over-compression wakes add to chirp double dogleg

(slight compression)

compression wakes partially remove chirp chicane

(compression)

Bolko Beutner - Paul Scherrer Institute

Standard modes (200pC – 10pC):

Large Bandwidth mode (200pC):

Attosecond mode(10pC):

Page 17: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Operation Modes Summary

11.04.2012 17

mode V_s

[MV/m]

P_s

[deg]

V_x

[MV/m]

P_x

[deg]

V_c

[MV/m]

P_c

[deg]

200pC 14.13 13.73 17.36 161.94 26.82 21.49

200pC 14.88 23.66 15.50 -176.05 26.45 19.31

lbw 15.22 27.05 15.07 -165.98 26.92 22.01

10pC 14.61 25.57 20.37 -167.74 26.38 19.41

50pC 14.75 27.50 17.71 -166.40 26.05 17.08

100pC 14.40 26.02 16.71 -172.60 26.00 16.61

S X C

Soft limit 14.8 MV/m 25 MV/m 27 MV/m

hard limit 16 MV/m 30 MV/m 27.5 MV/m

E1=330MeV

E2=2.1GeV

Energies of the Chicanes:

after BC2 at Aramis

Bolko Beutner - Paul Scherrer Institute

Profile optimization are obtained by

an iterative semi-analytical

procedure developed by Zagorodnov

and Dohlus: “Semianalytical modelling of multistage bunch

compression with collective effects”

PRSTAB 14,014403 (2011)

Page 18: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Operation Modes Summary

11.04.2012 18

q C1 C2 Z’2 Z’’2 I peak εx0 εy0 I/(ex0 ey0)1/2

200 7 170 0.5 0 3.72 0.320 0.304 1.193e4

200 10 140 0.5 0 2.98 0.307 0.300 0.987e4

200 10 -180 -0.5 0 3.44 0.349 0.289 1.084e4

10 5 300 0 0 1.10 0.136 0.102 0.930e4

50 8 250 0 0 2.29 0.217 0.190 1.124e4

100 10 200 0.2 0 2.76 0.236 0.230 1.181e4

directly after BC2

q C1 C2 Z’2 Z’’2 I peak εx0 εy0 I/(ex0 ey0)1/2

200 7 170 0.5 0 3.60 0.295 0.308 1.195e4

200 10 140 0.5 0 3.00 0.302 0.300 1.012e4

200 10 -180 -0.5 0 3.97 0.344 0.289 1.259e4

10 5 300 0 0 0.83 0.132 0.097 0.733e4

50 8 250 0 0 2.08 0.243 0.190 0.966e4

100 10 200 0.2 0 2.64 0.246 0.238 1.090e4

at Aramis entrance

Current and emittance of central slice are compared

=> similar “gain” parameter of about 1e4

Bolko Beutner - Paul Scherrer Institute

Page 19: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Operation Modes – after BC2

11.04.2012 19

10pC

50pC

100pC

200pC 4kA

200pC large bandwidth

200pC 3kA

Bolko Beutner - Paul Scherrer Institute

Page 20: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Operation Modes – at Aramis

11.04.2012 20

200pC 4kA

200pC 3kA

200pC large bandwidth

50pC

100pC

10pC

Bolko Beutner - Paul Scherrer Institute

Page 21: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL FEL Performance 200pC

11.04.2012 21

Sven Reiche

Bolko Beutner - Paul Scherrer Institute

Page 22: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Large Bandwidth Mode

11.04.2012 22

head

tail

Long. Phasespace at Aramis

Spectrum of Aramis output pulse

Bolko Beutner - Paul Scherrer Institute

Page 23: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

• Full compression

=> - single FEL Spike

- instable operation

- longitudinal coherence

Attosecond Mode

11.04.2012 23 Bolko Beutner - Paul Scherrer Institute

Page 24: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

Expected Performance

S-Band Phase [deg] 0.018

S-Band Voltage [rel] 1.8 * 1e-004

X-Band Phase [deg] 0.072

X-Band Voltage [rel] 1.8 * 1e-004

Linac 1 Phase [deg] 0.036

Linac 1 Voltage [rel] 1.8 * 1e-004

Linac 2 Phase [deg] 0.0360

Linac 2 Voltage [rel] 1.8 * 1e-004

Linac 3 Phase [deg] 0.0360

Linac 3 Voltage [rel] 1.8 * 1e-004

Charge 1%

initial arrival time [fs] 30

Initial Energy [rel] 1e-004

BC1 angle [rel] 5 * 1e-005

BC2 angle [rel] 5 * 1e-005

• Jitter sensitivities Sj are used to estimate total stability performance σA,

taking into account the expected subsystem stability σj (last slide) and

the number of independent sources N (i.e. Klystrons)

Stability Performance

11.04.2012 24

100pC mode

Bolko Beutner - Paul Scherrer Institute

10pC mode

Page 25: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

• Tolerable Stability goals for the User Community are:

– Arrival time 100fs (20fs)

– Peak Current/Bunch length 50 % (5 %)

– Central Wavelength 0.1 % (0.05 %) (ultimate) stability goals are given in brackets

200pC Modes

11.04.2012 25

200pC 3kA 200pC 4kA large bandwidth

Bolko Beutner - Paul Scherrer Institute

Page 26: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Microbunching Studies for SwissFEL

11.04.2012 Bolko Beutner - Paul Scherrer Institute 26

0.7- 7 (30) nm, 100 Hz

> 1 nm: transform limited

Athos Undulators

BC 2Linac 1 Linac 2 Linac 3

Aramis Undulators

Switch

Yard

C band (32 x 2 m)

26.5 MV/m, - 20.9 º

C band (28 x 2 m)

26.5 MV/m, 0 º

C band (44 x 2 m)

26.5 MV/m, 0 º

D’Artagnan

THz Pump

1 (0.8) - 7 Å5 – 20 fs; 100 Hz

S band

(2 x4 m)

14/16 MV/m

0 / 0 º

Gun

Booster 1 Booster 2 BC 1

S band

(4x4 m)

16 MV/m

- 17 º

X band

(2 x 0.75 m)

17 MV/m

+ 180 º

S band

100 MV/m

51 º

Laser

Heate

r

z=16m

I=20A=871 m (2.9 ps)

E=130.4 MeV

σz μ

z=63m

I=150A=124 m (413 fs)

E=355 MeV

z μσ

z=203m

I=2.7kA=6.2 m (21 fs)

E=2.04 GeV

z μσ

z=500m

I=2.7kA=6.2 m (21 fs)

E=2.1 - 5.8 GeV

z μσ

z=271m

E=2.1 or 3.4 GeV

LOW ENERGY HIGH ENERGY

t-tMEAN

(s)

Re

sid

ua

l p

(m

ass u

nits)

= 100 m

-8 -6 -4 -2 0 2 4 6 8

x 10-13

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0

20

40

60

80

100

120

140

160

180

t-tMEAN

(s)

Re

sid

ua

l p

(m

ass u

nits)

= 20 m

-8 -6 -4 -2 0 2 4 6 8

x 10-13

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.50

50

100

150

200

-8 -6 -4 -2 0 2 4 6 8

x 10-3

0

500

1000

1500

2000

2500

3000

Time (ns)

Inte

nsity (

a.u

.)

Q = 200 pC - x =

y = 0.27 mm

Astra

Starting pulse

-3 -2 -1 0 1 2 3 4

x 10-14

0

2

4

6x 10

-6

Time (s)

No

rma

lize

d

x (m

ra

d) Q = 200 pC

Design

Modified profile

-3 -2 -1 0 1 2 3 4

x 10-14

0

0.5

1x 10

-6

Time (s)

No

rma

lize

d

y (m

ra

d)

Design

Modified profile

START 2 END “REALISTIC PULSE”

Simona Bettoni

Page 27: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

• Different operation modes and compression setups

– Standard mode (200pC – 10pC) with similar peak current allows for a

continuous trade-off between photon pulse length and photon number

– Minimized energy spread for 200pC 3kA mode

• SwissFEL Injector Test Facility is ready to study Beam Dynamics

and Microbunching effects experimentally

• Expected RF stability is sufficient to satisfy user requests

– Main jitter sources are S-band amplitude, X-band phase, and beam

charge

• Microbunching Issues in the Lattice design:

– Laser Heater is mandatory in this design (see Simonas Talk)

– Energy of BC1 was increased from 250MeV to 330-350MeV

– FODO diagnostics section downstream of BC1 was removed

Summary

11.04.2012 27 Bolko Beutner - Paul Scherrer Institute

Page 28: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

11.04.2012 28

Thank You

for Your Attention!

Bolko Beutner - Paul Scherrer Institute

Page 29: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Expected Performance from Monte-Carlo

Calculations

11.04.2012 29

• In the simulation runs discussed on the previous slides only single

error sources were changed to determine the sensitivities. And

eventually the expected performance.

• In order to confirm the reliability of the method a set of 100

randomized machine parameter sets were simulated.

MC results

Sensitivity results

goals

arrival time [fs]

7.5 7.8 20

peak current [%]

8.9 9.4 5

beam energy [%]

0.014 0.012 0.05

Bolko Beutner - Paul Scherrer Institute

Page 30: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

11.04.2012 30 Bolko Beutner - Paul Scherrer Institute

Page 31: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

• Operation modes

11.04.2012 31

q Z1 Z2 Z2p Z2pp Ipeak ex ey I/sqrt(ex ey)

200 7 170 0.5 0 3.60 0.295 0.308 1.195e4

200 10 -180 -0.5 0 3.97 0.344 0.289 1.259e4

10 6 400 0 0 1.12 0.213 0.100 0.769e4

10 10 500 0.5 0 1.42 0.212 0.100 0.977e4

10 10 500 0 0 1.43 0.214 0.101 0.970e4

50 10 200 0.5 0 1.65 0.199 0.190 0.852e4

50 10 250 0 0 2.09 0.233 0.183 1.012e4

100 10 200 0.5 0 2.65 0.245 0.228 1.121e4

100 10 200 0.2 0 2.64 0.246 0.238 1.090e4

Bolko Beutner - Paul Scherrer Institute

Page 32: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Stability Studies

11.04.2012 32

elegant Evaluation Point

for Jitter Astra

Example of jitter analysis done with elegant:

Second order fits are done and if necessary the range

of the fit is adapted manually

First term of this fit is used as

sensitivity Si

Arrival time is numerical resolution

limited to 0.1 fs

Bolko Beutner - Paul Scherrer Institute

Page 33: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

• A recent design change of SwissFEL (modifications of Athos line,

decoupling of Aramis and Athos via a c-band module in Athos) the

beam energy at BC2 is fixed to 2.1 GeV compared to 2.04GeV

before.

=> New c-band structures with now 113 cell are required

to increase energy gain per structure

=> Recalculations of wake fields

Design Change

11.04.2012 33 Bolko Beutner - Paul Scherrer Institute

Short-range dipole wakefields in accelerating structures for the NLC

Karl L.F. Bane - SLAC

Formulas from:

Page 34: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Update on RF Stability

11.04.2012 34

S band phase stability 0.018 deg

Voltage stability 1.8 10 -4

0.015 deg

1.2 10 -4

4 kly sband 4 kly sband 2 kly sband

Presented at FLAC 11/2010 Summer 2011 version

Bolko Beutner - Paul Scherrer Institute

System stability expectations are updated by measured data compared to the

initial assumptions and the number of klystrons is reduced from 4 to 2.

Page 35: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Stability Studies

11.04.2012 35

• A little theory of machine jitter

– Sensitivity Sj is the linear correlation between an error source j (with

occurs N times) and the performance goal .

– The jitter of j sj contribute to the total jitter which has to fulfil:

– If j is allowed to use the whole budget for the tolerance is:

– If more sources jitter the tolerances are effectively tighter:

– Since has to be fulfilled on gets for aj:

In this study the sensitivities Sj and tolerances are determined by elegant

simulations. The total jitter using some expected performance values are

compared with the goals. A determination of aj is not done here.

Bolko Beutner - Paul Scherrer Institute

Page 36: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL X-band vs. C-band Linearization

11.04.2012 36

n – basic harmonic

m – higher harmonic

Voltage of “Linearizer Cavity”:

Simple Considerations:

• Quadratic term in correlated energy spread can

be compensated by an rf field on a higher

harmonic operated at 180 deg (anti-on-crest)

• Voltage of “Lineariser Cavity” depends on the

square of harmonic number ratio

• Between the x-band (4th harmonic) and the c-

band (2nd harmonic) the voltage ration is ¼.

Vlin,X ~ 20MV/m * 2 * 0.75m = 30MV

=> Vlin,C ~ 30MV * (4/2)2 = 120MV

=> 120MV / (4*1.92m) = 15.63MV/m

moderate gradient requirements for one

standard c-band module

120-30MeV = 90MeV are missing – compensation in

S-band booster required!!

Bolko Beutner - Paul Scherrer Institute

Page 37: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL X-band vs. C-band Linearization

11.04.2012 37

Design for complete SwissFEL compression setup (LiTrack):

BC1: E1 = 330MeV R56 = -55mm

BC2: E2 = 2.1GeV R56 = -22mm

Booster [MV] Linearizer [MV] Linac 1 [MV]

X-band 243.2 24.5 1841.6

C-band 337.2 121.7 1841.5

Current profile and longitudinal phase space after BC2:

Required energy gain per section:

C-band linearization is possible but requires more Voltage !!

Bolko Beutner - Paul Scherrer Institute

Page 38: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

• The FEL Process requires a high peak (few kA) while the

slice emittance is sufficiently low (<1 mm mrad)

Why Bunch Compression?

11.04.2012 38

current

slice emittance

Slice emittance is fine in the

central part …

But peak current is too low

=> no SASE

Slice emittance is slightly increased by self-

field effects but still ok in the centre…

Peak current is sufficiently high

=> SASE in the central part of the bunch

compression

If the compression is not uniform only a

small fraction of the particles might

contribute to the FEL!

Bolko Beutner - Paul Scherrer Institute

Page 39: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL What we would like to have?

11.04.2012 39

current

slice emittance

For good FEL performance we would like to have a large fraction of the

bunch to fulfill the condition of high peak current and low slice emittance.

=> large fraction of particle contribute to lasing

The longitudinal profile should be flat to achieve homogeneous photon

properties along the pulse.

Bolko Beutner - Paul Scherrer Institute

Page 40: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL SwissFEL

11.04.2012 Bolko Beutner - Paul Scherrer Institute 40

Linac Undulator

Exp.Hall

Injector

Surface areas not accessible by wild game

Page 41: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL First BC Results

11.04.2012 Bolko Beutner - Paul Scherrer Institute 41

head

tail

108deg

“on-crest”

106deg 104deg head

tail lon

gitu

din

al a

xis

energy axis

90deg

First Test of BC:

• only FINSB03 was operational

=> 60MeV => Space Charge “Blow up”

• No X-band

Beutner, Prat, Guetg

“on-crest”

~108deg

Page 42: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

• Objectives long profiles

11.04.2012 Bolko Beutner - Paul Scherrer Institute 42

Page 43: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL CDR Setup (manually tuned)

11.04.2012 43

200pC

10pC

Bolko Beutner - Paul Scherrer Institute

head

head

head

head

Page 44: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Semi-analytic Bunch Compression Setup

11.04.2012 44

Initial longitudinal position s0 [m]

Initial longitudinal position s0 [m]

lon

g. P

os. a

fte

r B

C1

s1 [m

] lo

ng

. P

os. a

fte

r B

C2

s2 [m

]

Bunch compression can be

described by the correlation

between initial position and

final position (after each

chicane).

A one sigma region is used to neglect beam tails

Bolko Beutner - Paul Scherrer Institute

In practice these numbers

are obtained by polynomial

fits.

Page 45: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

• First derivative Zn is the inverse compression factor between the

start to the end of BC n.

• Z’n is the position of the current peak after BC n.

• Z’’n is the overall flatness of the current profile after BC n. It can be

increased to suppress “spikes”

Compression Parameterisation

11.04.2012 45 Bolko Beutner - Paul Scherrer Institute

Page 46: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Optics Measurements and Matching

11.04.2012 Bolko Beutner - Paul Scherrer Institute 46

Multiknob FODO

E. Prat

B. Beutner

Best emittance

measurement with

Nd:YLF laser (Gaussian)

(20 April 2011)

Page 47: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Optics Matching

11.04.2012 Bolko Beutner - Paul Scherrer Institute 47

Page 48: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL How to set up bunch compression?

11.04.2012 48

Initial longitudinal phase-space:

Energy gain in linac section:

Long. phase-space after acceleration:

Path length effects of the chicanes:

Bolko Beutner - Paul Scherrer Institute

Page 49: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Overview of he Problem

11.04.2012 49

“requested” compression profile f0:

RF setup of the machine:

“symbolic” tracking of particles – A0 is an representation

of the formulas on the previous slides:

The desired setup of the RF systems is symbolically

written as:

The problem can be split into two:

Setup of main linac after the linearizer cavity to achieve final bunch shape

Setup of injector to achieve correct setup of long. phase-space after

linearizer

Bolko Beutner - Paul Scherrer Institute

Page 50: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

Linac Setup:

• Problem to be solved: What RF setings and initial phase-space

distribution is required to achive the

requested bunch shape?

• Example solution for a two stage compression setup:

Setup of main Linac

11.04.2012 50

As a result we obtain the required phase-space

after the injector α and the RF setup X, Y.

Bolko Beutner - Paul Scherrer Institute

Page 51: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

Injector Setup:

• Problem to be solved: What RF settings in the injector

generate the required

phase-space distribution before the

first chicane?

• Problem can be formulates as:

with the solution:

Injector Setup

11.04.2012 51

initial phase-phase space

Bolko Beutner - Paul Scherrer Institute

Page 52: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

• Idealized machine model:

• “real” machine model:

• RF settings are obtained in an iterative

procedure.

– Machine setup from the idealized formulas are feed into a start-to-end

simulation

– results are compared with the “requested” beam parameters

– Their difference is feed into the idealized formulas to obtain an

correction to the machine settings

Real Machine

11.04.2012 52 Bolko Beutner - Paul Scherrer Institute

Page 53: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

• Convergence after about 10 iterations (each step takes a few

minutes)

• Oscillations of the peak current are mitigated by application of a

fraction of the correction term

Iterative Procedure

11.04.2012 53

longitudinal [m]

Curr

ent

[A]

Peak c

urr

ent

[A]

Iteration step

i.e. x 0.5

Bolko Beutner - Paul Scherrer Institute

Page 54: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

This semi-analytic procedure is used to obtain desired bunch profiles

much more efficient than manual parameter tuning.

It is possible to obtain “similar” profiles while changing parameters of

the linac => optimization of the machine

Compression Setup

11.04.2012 54

C2 Z’2 Z’’2 = 0

Bolko Beutner - Paul Scherrer Institute

Page 55: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

RF Gradient Requirements

11.04.2012 55

S X C

Soft limit 14.8 MV/m 25 MV/m 27 MV/m

hard limit 16 MV/m 30 MV/m 27.5 MV/m

Bolko Beutner - Paul Scherrer Institute

Page 56: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

• With the presented theory of multi-stage compression we can obtain

“similar” bunch profiles with different machine setups.

• For these varying machine setups, which share the same resulting

bunch, the RF stability performance can be compared.

=> parameter Scans

• Especially the distribution of the compression factors between the

two chicanes is relevant here.

Parameter Optimization Strategy

11.04.2012 56

C2 = 125

Bolko Beutner - Paul Scherrer Institute

C1

Page 57: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Undulator Wakes

11.04.2012 57 Bolko Beutner - Paul Scherrer Institute

Sven Reiche

Page 58: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL Progress C-band Cavity Prototype

11.04.2012 Bolko Beutner - Paul Scherrer Institute 58

RF designs

mech. design & UP

machining

Assembly & brazing

LL RF measurements

T = 21 deg, P = 10-6

mbar, f = 5713.8 MHz

-60.00

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

5.550E+09 5.600E+09 5.650E+09 5.700E+09 5.750E+09 5.800E+09 5.850E+09

Frequency [Hz]

Re

fle

cti

on

[d

B]

S11

HP RF set-up HP RF processing

since 3.11.11! H. Braun

Page 59: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL

C-band Concept

11.04.2012 Bolko Beutner - Paul Scherrer Institute 59

Two bunch energy balance with SLED

48000000

49000000

50000000

51000000

52000000

53000000

54000000

55000000

56000000

57000000

58000000

2300 2350 2400 2450 2500 2550 2600

phase jump

phase mod.

2 Kly.

Longitudinal long range wakes

Transverse long range wakes

Page 60: Operation Modes and Longitudinal Dynamics of the SwissFEL ... · Soft limit 14.8 MV/m 25 MV/m 27 MV/m hard limit 16 MV/m 30 MV/m 27.5 MV/m E1=330MeV E2=2.1GeV Energies of the Chicanes:

+ SwissFEL + SwissFEL FEL Operation Modes

11.04.2012 Bolko Beutner - Paul Scherrer Institute 60

FEL Beam Design Parameters Nominal Operation Mode Special Operation Mode

Long Pulses Short Pulses Large Bandwidth Ultra-Short Pulses

Charge (pC) 200 10 200 10

Energy spread (keV) 350 250 17000 (FW) 1000

Saturation length (m) 47 50 50 50

Saturation pulse energy (µJ) 150 3 100 15

Effective saturation power (GW) 2.8 0.6 2 50

Photon pulse length (fs, rms) 21 2.1 15 0.1

Beam radius (µm) 26.1 17 26 17

Divergence (µrad) 1.9 2 2 2.5

Number of photons (×109) 73 1.7 50 7.5

Spectral Bandwidth, rms (%) 0.05 0.04 3.5 (FW) 0.1

Peak brightness

(# photon/mm2.mrad2.s1.0.1% bandwidth)

7.1032 1.1032 8.1030 1,3.1033

Average brightness

(# photon/mm2.mrad2.s1.0.1% bandwidth)

2,3.1021 5,7.1018 3.1019 7,5.1018

CDR Design Parameters

Optimized Longitudinal Layout is not fully included in these numbers

S. Reiche / R. Ganter