Self-seeding Free Electron Lasers

1. Self-seeding Free Electron Lasers J. Wu FEL Physics Group Beam Physics Department Oct. 26, 2010 Accelerator Research Division Status Meeting

2. Brief description of a Self-Amplified Spontaneous Emission (SASE) Free Electron Laser (FEL) as LCLS Schemes to improve the longitudinal coherence Self-seeding as one of the possibilities Monochromator Crystals for hard x-ray Variable Line Spacing Gratings for soft x-ray Issues Electron bunch centroid energy jitter Electron bunch energy profile imperfectness Outline jhwu@slac.stanford.edu J. Wu, FEL Physics Group

3. A laser (standing for Light Amplification by Stimulated Emission of Radiation) is a device which produces electromagnetic radiation, often visible light, using the process of optical amplification based on the stimulated emission of photons within a so-called gain medium. The emitted laser light is notable for its high degree of spatial and temporal coherence, unattainable using other technologies. Spatial coherence typically is expressed through the output being a narrow beam which is diffraction-limited, often a so-called "pencil beam." Temporal (or longitudinal) coherence implies a polarized wave at a single frequency whose phase is correlated over a relatively large distance (the coherence length) along the beam. What is a laser Conceptual physics, Paul Hewitt, 2002 jhwu@slac.stanford.edu J. Wu, FEL Physics Group

4. SASE FEL Starts from undulator Spontaneous Emission random startup from shot noise  intrinsically a chaotic polarized light, e.g., in the linear exponential growth regime, the FEL energy fluctuation distribution falls on a g-distribution function Collective effects Self-Amplified Spontaneous Emission (SASE) Guided mode  mode selection  transverse coherence Slippage  temporal coherent within slippage distance  coherent spike SASE FEL SASE FEL

5. SASE FEL—Transverse Coherence • Gain guiding—mode selection for LCLS courtesy S. Reiche

6. SASE FEL—Temporal Coherence • Photon slips (advances) over electron bunch, the electrons being swept by the same photon wavepacket (which is also growing due to bunching) will radiate coherently  coherent length  coherent spike • Spike duration on order of . For LCLS, less than 1 fs (0.3 mm) at saturation Speed of light = c Speed of electron < c

7. FEL power along the undulator LCLS 1.5 Å SASE FEL Performance Instability: saturation Instability: exponential growth Saturation early with power on order of GW

8. FEL bandwidth along the undulator LCLS 1.5 Å SASE FEL Performance Bandwidth on order of 1E-3 Bandwidth decreases as 1/z1/2

9. FEL temporal profile at 60 m LCLS 1.5 Å SASE FEL Performance

10. FEL spectrum at 60 m LCLS 1.5 Å SASE FEL Performance

11. Temporal Coherence • Reason for wide bandwidth: coherent length shorter than the entire pulse length • Decrease the entire pulse length  low charge, single spike • Increase the coherent length  seeding with coherent length to be about the entire pulse length LCLS low charge operation mode [Y. Ding et al., PRL, 2009]

12. SASE and seeded FEL FEL Types: Amplifiers & Oscillators Harmonic Generation EEHG, HGHG, etc. (external seeding) in/n Modulator Buncher Radiator SASE Amplifier Laser or HHGSeeded Amplifier (external seeding) Oscillator (self-seeding) Mirror Mirror J.B. Murphy and J. Wu, The Physics of FELs, US Particle Accelerator School, Winter, 2009

13. 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 & monochromator for electron and photon 13 Schematics of Self-Seeded FEL chicane 1st undulator 2nd undulator FEL SASE FEL Seeded FEL monochromator electron electron dump

14. For a transform limited Gaussian photon beam For flat top 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 Improve longitudinal coherence, and reduce the bandwidth improve the spectral brightness The coherent seed after the monochromator should be longer than the electron bunch; otherwise SASE will mix with Seeded FEL 14 Transform Limited Pulses

15. Reaching a single coherent spike? 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 is still possible 15 Single Spike vs Self-Seeding

16. Seeding the second undulator (vs. single undulator followed by x-ray optics) Power loss in monochromator is recovered in the second undulator (FEL amplifier) Peak power after first undulator is less than saturation power  damage to optics is reduced 16 Two-Stage FEL with Monochromator With thesamesaturated peak power, but with two-orders of magnitudebandwidthreduction, thepeak brightness is increased by two-orders of magnitude

17. For hard x-ray, crystals working in the Bragg geometry can serve as the monochromator Original proposal invokes 4 crystals to form the photon monochromator, which introduces a large optical delay  a large chicane has to introduce for the electron to have the same amount of delay  is not favored. Two electron bunch scheme More recent proposal uses single diamond crystal  the monochromatized wake as a coherent seed Hard x-ray self-seeding Monochromator 17 Y. Ding et al., 2010; G. Geloni et al., 2010 G. Geloni et al., 2010

18. LCLS: Two-bunch HXR Self-seeding ~ 4 m SASE Seeded U1 U2 Si (113) Si (113) Before U2 Spectrum After U2 Y. Ding, Z. Huang, R. Ruth, PRSTAB 13, 060703 (2010) G.Geloniet al., DESY 10-033 (2010),

19. Single diamond crystal proposal G. Geloni et al., 2010

20. Single diamond crystal proposal G. Geloni et al., 2010

21. Power distribution after the SASE undulator (11 cells). Spectrum after the diamond crystal 6 GW 10-5 Power distribution after diamond crystal FWHM 6.7  10-5 G. Geloni et al., 2010

22. Optical components (assuming dispersion in vertical plane) (horizontal) Cylindrical focusing M1: Focusing at re-entrant point (rotational) Planar pre-mirror M2: Varying incident angle to grating G (rotational) Planar variable-line-spacing grating G: Focusing at exit slit Adjustable/translatable exit slit S (vertical) Spherical collimation mirror M3: Re-collimate at re-entrant point Soft x-ray self-seeding monochromator 22 e-beam M3 M1 2nd undulator 1st undulator g M2 source point re-entrant point h G Y. Feng, J. Hastings, P. Heimann, M. Rowen, J. Krzywinski, J. Wu, FEL2010 Proceedings. (2010)

23. 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 23 6-Å Case: Electron Bunch

24. 6-Å FEL power along the first undulator 24 6-Å SASE FEL Parameters saturation around 32 m with power ~10 GW LCLS-II uses about 40 meter long undulators

25. 6 Å FEL temporal profile at 30 m in the first undulator: challenge 25 6 Å SASE FEL Properties

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

27. Effective SASE start up power is 1.3 kW. Use small start up seed power 100 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. 27 6-ÅCase - Requirement on Seed Power 0.1 MW 2 GW

28. Temporal profile at ~25 m in the 2ndundulator for seed of 100 kW 6-ÅSelf-Seeded FEL Performance 28 ~12 mm

29. FEL spectrum at ~25 m in the 2ndundulator for seed of 100 kW 6-ÅSelf-Seeded FEL Performance 29 FWHM 5.210-5

30. 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 6-Åcase — transform limited 30

31. Self-Seeding Summary at 6 nm and 6 Å 31 J. Wu, P. Emma, Y. Feng, J. Hastings, C. Pellegrini, FEL2010 Proceedings. (2010)

32. Electron centroid energy jitter can lead to both timing jitter and also a detuning effect Take 6 nm as example, FEL parameter r ~ 1.2 ×10-3 R56 ~ 3 mm Timing jitter 12 fs Issues • FEL detuning theory; positive detune  longer gain length, higher saturation power; negative detune  longer gain length, lower saturation power X.J. Wang et al., Appl. Phys. Lett. 91, 181115 (2007). jhwu@slac.stanford.edu J. Wu, FEL Physics Group

33. The previous slide shows the power fluctuation due to centroid energy jitter, the spectrum bandwidth seems to be less affected. Issues jhwu@slac.stanford.edu J. Wu, FEL Physics Group

34. Electron bunch energy profile imperfectness In the second undulator, with the injection of monochromatized coherent seed, the FEL process is essentially a seeded FEL Study a linear energy chirp on the electron bunch first, The FEL bandwidth where and Issues J. Wu, P.R. Bolton, J.B. Murphy, K. Wang, Optics Express 15, 12749 (2007); J. Wu, J.B. Murphy, P.J. Emma et al., J. Opt. Soc. Am. A 24, 484 (2007). jhwu@slac.stanford.edu J. Wu, FEL Physics Group

35. Take 1.5 Å as example Initial coherent seed bandwidth 10-5; The electron energy chirp is taken for four cases: over the rms bunch length, the rms correlated relative energy spread is 0.5 r (green), r (purple), 2.5 r (blue), and 5 r (red) Issues jhwu@slac.stanford.edu J. Wu, FEL Physics Group

36. Start with 10-6 bandwidth, 10 MW seed, well cover the entire electron bunch the FEL power along the undulator LCLS Self-Seeded FEL Performance Saturation early with power on order of GW

37. FEL temporal profile at 40 m LCLS Self-Seeded FEL Performance

38. FEL spectrum at 40 m The nonuniform energy profile affects the bandwidth LCLS Self-Seeded FEL Performance FWHM 10-5 jhwu@slac.stanford.edu J. Wu, FEL Physics Group

39. Electron bunch energy profile imperfectness Study a linear energy chirp together with a second order curvature on the electron bunch, where Issues A.A. Lutman, G. Penco, P. Craievich, J. Wu, J. Phys. A: Math. Theor.42, 045202 (2009); A.A. Lutman, G. Penco, P. Craievich, J. Wu, J. Phys. A: Math. Theor.42, 085405 (2009); jhwu@slac.stanford.edu J. Wu, FEL Physics Group

40. Electron bunch energy profile imperfectness Electron bunch can have an energy modulation, Issues J. Wu, A.W. Chao, J.J. Bisognano, LINAC2008 Proceedings, p. 509 (2008); B. Jia, Y.K. Wu, J.J. Bisognano, A.W. Chao, J. Wu, Phys. Rev. ST Accel. Beams13, 060701 (2010); J. Wu, J.J. Welch, R.A. Bosch, B. Jia, A.A. Lutman, FEL2010 proceedings. (2010). jhwu@slac.stanford.edu J. Wu, FEL Physics Group

41. LCLS excellent electron beam quality leads to short gain length, early saturation. This makes possible to add more functions Two-stage FEL with monochromatorreduces the bandwidth by 2 order of magnitude with similar peak power  increases the brightness by 2 order of magnitude Some details about electron energy centroid jitter and energy profile imperfectness has been looked into Summary

42. Thanks for your attention! Thanks to Y. Cai for providing this chance! Special thanks to: P. Emma, Z. Huang, J. Arthur, U. Bergmann, Y. Ding, Y. Feng, J. Galayda, J. Hastings, C.-C. Kao, J. Krzywinski, A.A. Lutman, H.-D. Nuhn, T.O. Raubenheimer, M. Rowen, P. Stefan, J.J. Welch of SLAC, W. Fawley, Ph. Heimann of LBL, B. Kuske of HZB, J.B. Murphy, X.J. Wang of BNL, C. Pellegrini of UCLA, and J. Schneider of DESY for fruitful discussions. ……