1. Self-seeding for the soft x-ray line in LCLS upgrade
J. Wu (SLAC)
48th ICFA Advanced Beam Dynamics Workshop on Future Light Sources
March 1-5, 2010 SLAC National Accelerator Laboratory Menlo Park, California

2. Schematics of Self-Seeded FEL2
Schematics of Self-Seeded FEL
Originally proposed at DESY [J. Feldhaus, E.L. Saldin, J.R. Schneider, E.A. Schneidmiller, M.V. Yurkov, Optics Communications, V.140, p.341 (1997) .]
Chicane and gratings in two orthogonal planes x and y
chicane
1st undulator
2nd undulator
grazing mirrors
FEL
slit
SASE FEL
Seeded FEL
grating
electron
electron dump

3. Transform Limited Pulses3
Transform Limited Pulses
For a Gaussian photon beam
Gaussian pulse, at 1.5 Å, if Ipk= 3 kA, Q = 250 pC, sz  10 mm, then transform limit is: sw/w0  10-6
LCLS normal operation bandwidth on order of 10-3
LCLS electron bunch, double-horn but central part effectively flat top,
for flat top distribution
Improve longitudinal coherence, and reduce the bandwidth improve the spectral brightness

4. Single Spike vs Self-Seeding4
Single Spike vs Self-Seeding
Reaching a single coherent spike?
LG = 1 m, 20LG= 20 m, for lu= 2 cm, there is ~1000 periods
Take 1 nm as example, single spike  1 micron
Low charge might reach this, but bandwidth will be broad
Narrow band, “relatively long” pulse  Self-Seeding.
In the following, we focus on 250-pC case with a “relatively” long bunch, and look for “narrower” bandwidth and “good” temporal coherence
For shorter wavelength (< 1 nm), single spike is not easy to reach, but self-seeding still possible

5. Two-Stage FEL with Monochromator5
Two-Stage FEL with Monochromator
Seeding the second undulator (vs. single undulator followed by x-ray optics)
Power loss in monochromator is recovered in the second undulator (FEL amplifier)
Shot-to-shot FEL intensity fluctuation is reduced due to nonlinear regime of FEL amplifier
Peak power after first undulator is less than saturation power  damage to optics is reduced
With the same saturated peak power, but with two-orders of magnitude bandwidth reduction, the peak brightness is increased by two-orders of magnitude

6. 6
Monochromator
J. Hastings suggested varied line spacing gratings (to provide focusing) as the monochromator for the soft x-ray self-seeding scheme
Y. Feng, M. Rowen, Ph. Heimann (LBL), and J. Krzywinski et al. are designing
J. Arthur, U. Bergmann, P. Emma, W. Fawley (LBL), J. Galayda, B. Kuske (HZB), C. Pellegrini (UCLA), and J. Schneider (DESY) et al. are giving general advices

7. Feng-Rowen-Heimann-Krzywinski-Hastings-Wu-et al.
Optics Specs
Feng-Rowen-Heimann-Krzywinski-Hastings-Wu-et al.
Performances
Parameter
symbol
value
unit
Energy range e
200 – 2000 eV
Pulse length (rms) t
34 – 12 fs
Pulse energy E mJ
Peak Power
Pinput MW
E-beam size (rms) s
50 -15 mm
Resolving power R
> 20000
Throughput
htotal
0.2 – 0.005 %
Output peak Power
Poutput kW
Time delay DT
10.8 – 9.6 ps

8. Feng-Rowen-Heimann-Krzywinski-Hastings-Wu-et al.
Optics Components
Feng-Rowen-Heimann-Krzywinski-Hastings-Wu-et al.
Cylindrical horizontal focusing M1
Focus at reentrant point
Planar pre-mirror M2
Vary incident angle to grating G
Planar variable-line-spacing grating G
Focus at exit slit
Exit slit S
Spherical vertical focusing mirror M3
Re-focus at reentrant point
electron-beam M1 M3 g M2
source
point
re-entrant
point h G

9. Geometry (Dispersion Plane)
Feng-Rowen-Heimann-Krzywinski-Hastings-Wu-et al.
Optical components
Deflecting mirror; Pre-mirror; VLS Grating; Collimation mirror M1 M2 Gv M3 ZR
w0’’ w0
w0’ L1
LM1M2
rM2G
r’G
rM3
r’M3
DLRe-entrant
rtotal L1
LM1M2
rM2G
r’G
rM3
r’M3
DLRe-entrant
rtotal
200 eV
2000 eV

10. Monochromator Might need more than one monochromators Efficiency:10
Monochromator
Might need more than one monochromators
Efficiency:
Monochromator efficiency
Phase space conservation: bandwidth reduced by one to two-order of magnitudes
Overall efficiency will be on order of a percent to a few 10-5 (about 0.2 – %)
Still looking for design to have higher efficiency
Use blazed profile -- efficiency increases by x10
Use coating to improve reflectivity

11. LCLS SASE FEL Parameters11
LCLS SASE FEL Parameters
S-2-E electron distribution: slice emittance entering the undulator
Slice Emittance small  Gain Length Short

12. 6-nm Case: Electron Bunch12
6-nm Case: Electron Bunch
Peak current ~1 kA
Undulator period 5 cm, Betatron function 4 m
For 250 pC case, assuming a step function current profile, sz ~ 22 mm
Gain length ~ 1.4 m
SASE spikes ~ 70

13. LCLS high-brightness electron beam13
LCLS high-brightness electron beam
S-2-E electron distribution: electron current profile entering the undulator
tail
head

14. 6-nm SASE FEL Parameters14
6-nm SASE FEL Parameters
6-nm FEL power along first undulator
saturation around 28 m with ~5 GW
Present LCLS-II plan uses 40 meter long undulators

15. 6-nm Case - Requirement on Seed Power15
6-nm Case - Requirement on Seed Power
Effective SASE start up power is 200 W.
In a bandwidth of 2.210-5, there is only 0.5 W
Use small start up seed power 10 kW…
Monochromator efficiency  10% (at 6 nm)
Phase space conservation: bandwidth decreases 1 to 2-orders of magnitude (about 70 spikes)
Take total efficiency 2.010-3 Need 10 MW on monochromator to seed with 10 kW in 2nd und.
50 MW
100 kW

16. 6-nm Seeded FEL Parameters16
6-nm Seeded FEL Parameters
FEL power along 2nd undulator for seed power of: 10 MW (black), 100 kW (red), 10 kW (cyan)
Saturation around 18, 25 and 29 m with power ~5 GW

17. 6-nm Seeded FEL Parameters17
Temporal profile at ~26 m in 2nd undulator for seed of 100 kW (black) and 10 kW (red)
~35 mm

18. 6-nm Seeded FEL Parameters18
6-nm Seeded FEL Parameters
FEL spectrum at ~23 m in 2nd undulator for seed of 100 kW
FWHM 2.410-4

19. 6-nm Case - Transform Limit19
6-nm Case - Transform Limit
Effective pulse duration 35 mm (sz  10 mm)
Transform limited Gaussian pulse  bandwidth is 1.110-4 FWHM
(For uniform pulse  1.510-4 FWHM)
Here the seeded FEL bandwidth is close to the transform limited bandwidth

20. Polarization The second undulator can be APPLE type20
Polarization
The second undulator can be APPLE type
Linear (black), circular (red), or elliptical polarization
Pol. ~ 100%

21. 6-nm Seeded FEL: Polarization21
Temporal profile in 2nd undulator with seed of 100 kW for planar (black) and circular (red)
~35 mm
Planar at 26 m; Circular at 18 m

22. 6-nm Seeded FEL : Polarization22
6-nm Seeded FEL : Polarization
FEL spectrum in 2nd undulator with seed of 100 kW circular polarization
FWHM 2.410-4
Circular at 15 m

23. 6-Å Case: Electron Bunch23
6-Å Case: Electron Bunch
Peak current ~3 kA
Undulator period 5 cm, Betatron function 4 m
For 250 pC case, assuming a step function current profile, sz  7 mm.
Gain length ~ 2.1 m
SASE spikes ~ 160

24. LCLS high-brightness electron beam24
LCLS high-brightness electron beam
S-2-E electron distribution: electron current profile entering the undulator: compress more
tail
head

25. saturation around 32 m with power ~10 GW25
6-Å SASE FEL Parameters
6-Å FEL power along the first undulator
saturation around 32 m with power ~10 GW
Present LCLS-II plan uses 40 meter long undulators

26. 26
6 Å SASE FEL Properties
6 Å FEL temporal profile at 30 m in the first undulator: challenge

27. 27
6 Å SASE FEL Properties
6 Å FEL spectrum at 30 m in the first undulator
Spiky spectrum: challenge

28. 6-Å Case - Requirement on Seed Power28
6-Å Case - Requirement on Seed Power
Effective SASE start up power is 1.3 kW.
In a bandwidth of 6.610-6, there is only 1.6 W
Use small start up seed power 20 kW…
Monochromator efficiency ~ 0.2 % (at 6 Å)
Phase space conservation: bandwidth decreases 1 to 2-orders of magnitude (~ 160 spikes)
Take total efficiency 5.010-5 Need 2 GW on monochromator to seed with 0.1 MW in 2nd und.
2 GW
0.1 MW

29. 6-Å Seeded FEL Parameters29
6-Å Seeded FEL Parameters
Power along 2nd undulator for seed power of 10 MW (black), 1 MW (red), and 100 kW (cyan)
Saturation around 22, 30, and 32 m with power on order of 10 GW

30. 6-Å Seeded FEL Parameters30
Temporal profile at ~25 m in the 2nd undulator for seed of 100 kW
~12 mm

31. 6-Å Seeded FEL Parameters31
6-Å Seeded FEL Parameters
FEL spectrum at ~25 m in the 2nd undulator for seed of 100 kW
FWHM 5.210-5

32. 6-Å case — transform limited32
6-Å case — transform limited
Effective pulse duration 12 mm, sz ~ 3.5 mm
Transform limited Gaussian pulse  bandwidth is 3.210-5 FWHM.
(For uniform pulse  4.410-5 FWHM)
The seeded FEL bandwidth (5.210-5 FWHM) is close to the transform limited bandwidth

33. Self-Seeding Summary at 6 nm and 6 Å33
Self-Seeding Summary at 6 nm and 6 Å
Parameter
6 nm
6 Å
unit
Emittance
0.5 mm
Peak Current 1 3 kA
Pulse length rms 35 12 fs
Bandwidth FWHM 31
5.2
10-5
Limited Bandwidth 15
4.4
Seed Power
100 kW
Power on Mono 50
2000 MW
Mono Efficiency 10
0.2 %
Over all Efficiency 20
10-4
Sat. Power 5 GW
Sat. Length 30 m
Brightness Increment
150

34. 34
Harmonic Generation
With a self-seeding scheme cleaning up 6 Å (2 keV) FEL, one can try Harmonic Generation
Open gap for harmonic generation (4 ~ 6 keV)
Electron energy in the following: 7 GeV
Two Chicanes
GW level 4 ~ 6 keV FEL
2 GW 2 keV FEL
0.1 MW 2 keV FEL
lw = 5 cm
6 Å Undulator
6 Å Undulator
3 ~ 2 Å Undulator
~30 m
15 ~20 m
25 ~ 45 m
Variable Line Spacing Gratings

35. Nominal Value (planar undulator )35
Nominal Value (planar undulator )
Taking lw = 4 cm, Ipk = 3.0 kA, en = 0.6 mm-mrad, and b = 4 m  6Å FEL: LG < 2 m
Take 2 GW as the incident power to the gratings
Take 5.0 ×10-5 as the over all efficiency to get coherent seed
Incident power into the second undulator is 0.1 MW
1/LG

36. Nominal Value (planar undulator )36
Nominal Value (planar undulator )
Constraint
Neither the first nor second undulator can induce slice energy spread larger than r for the harmonic FEL in the third undulator, which is about 9.6×10-4

37. Nominal Value (planar undulator )37
Nominal Value (planar undulator )
Set second undulator to be 20 m
4 keV FEL saturates around 25 m to a few GW
6 keV FEL saturates around 45 m to GW level
We can invoke helical undulator for 6 keV FEL, LG = 2.4 m, r = 1.2 ×10-3 (planar undualtor LG = 3.4 m, r = 9.6 ×10-4)
4 keV FEL
6 keV FEL

38. 38
Discussion
We study the performance of a self-seeding FEL for wavelength between 6 nm to 6 Å with LCLS achieved electron bunch parameters
It might be possible to get 4 keV or even 6 keV photon via harmonic generation within the given space in the soft x-ray line after self-seeding.
Further optimization of the system is underway
Your input is very welcome!