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

Schematics of Self-Seeded FEL 2 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

Transform Limited Pulses 3 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

Single Spike vs Self-Seeding 4 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

Two-Stage FEL with Monochromator 5 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 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

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 1.2 - 17 mJ Peak Power Pinput 10 - 400 MW E-beam size (rms) s 50 -15 mm Resolving power R > 20000 Throughput htotal 0.2 – 0.005 % Output peak Power Poutput 10 - 20 kW Time delay DT 10.8 – 9.6 ps

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

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 13.761030 4.204372 0.036709 5.981053 0.351780 1.993796 1.656204 27.984945 2000 eV 3.901582 0.339127 6.021674 0.311159 3.400840 0.249160 27.984572

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 – 0.005 %) Still looking for design to have higher efficiency Use blazed profile -- efficiency increases by x10 Use coating to improve reflectivity

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

6-nm Case: Electron Bunch 12 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

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

6-nm SASE FEL Parameters 14 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

6-nm Case - Requirement on Seed Power 15 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

6-nm Seeded FEL Parameters 16 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

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

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

6-nm Case - Transform Limit 19 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

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

6-nm Seeded FEL: Polarization 21 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

6-nm Seeded FEL : Polarization 22 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

6-Å Case: Electron Bunch 23 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

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

saturation around 32 m with power ~10 GW 25 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 6 Å SASE FEL Properties 6 Å FEL temporal profile at 30 m in the first undulator: challenge

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

6-Å Case - Requirement on Seed Power 28 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

6-Å Seeded FEL Parameters 29 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

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

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

6-Å case — transform limited 32 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

Self-Seeding Summary at 6 nm and 6 Å 33 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 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

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

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

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 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!