Selfseeding Free Electron Lasers J Wu FEL Physics

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

Outline 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 October 26, 2010 ARD Status meeting jhwu@slac. stanford. edu J. Wu, FEL Physics Group 2

What is a laser 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. October 26, 2010 ARD Status meeting jhwu@slac. stanford. edu J. Wu, FEL Physics Group Conceptual physics, Paul Hewitt, 2002 3

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 selection transverse coherence – Slippage temporal coherent within slippage distance coherent spike

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

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 Speed of light = c Speed of electron < c – Spike duration on order of. For LCLS, less than 1 fs (0. 3 mm) at saturation 6

LCLS 1. 5 Å SASE FEL Performance FEL power along the undulator Instability: saturation Instability: exponential growth Saturation early with power on order of GW 7

LCLS 1. 5 Å SASE FEL Performance FEL bandwidth along the undulator Bandwidth on order of 1 E-3 Bandwidth decreases as 1/z 1/2 8

LCLS 1. 5 Å SASE FEL Performance FEL temporal profile at 60 m 9

LCLS 1. 5 Å SASE FEL Performance FEL spectrum at 60 m 10

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

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

13 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 & monochromator for electron and photon chicane 1 st undulator 2 nd undulator FEL SASE FEL electron monochromator Seeded FEL electron dump

Transform Limited Pulses 14 For a transform limited Gaussian photon beam – For flat top – Gaussian pulse, at 1. 5 Å, if Ipk= 3 k. A, Q = 250 p. C, sz 10 mm, then transform limit is: sw/w 0 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

15 Single Spike vs Self-Seeding 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 -p. C 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

16 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) – 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

Hard x-ray self-seeding Monochromator 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 Y. Ding et al. , 2010; G. Geloni et al. , 2010 – More recent proposal uses single diamond crystal the monochromatized wake as a coherent seed G. Geloni et al. , 2010

LCLS: Two-bunch HXR Self-seeding ~4 m SASE U 1 U 2 Si (113) Before U 2 18 After U 2 Si (113) Seeded Spectrum Y. Ding, Z. Huang, R. Ruth, Ruth PRSTAB 13, 060703 (2010) G. Geloni et al. , DESY 10 -033 (2010),

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

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

Power distribution after the SASE undulator (11 cells). 6 GW Spectrum after the diamond crystal 10 -5 Power distribution after diamond crystal FWHM 6. 7 10 -5 G. Geloni et al. , 2010

Soft x-ray self-seeding monochromator Optical components (assuming dispersion in vertical plane) – (horizontal) Cylindrical focusing M 1: Focusing at re-entrant point – (rotational) Planar pre-mirror M 2: 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 M 3: Re-collimate at reentrant point e-beam 1 st undulator source point M 3 M 1 g 2 nd undulator M 2 re-entrant point h G Y. Feng, J. Hastings, P. Heimann, M. Rowen, J. Krzywinski, J. Wu, FEL 2010 Proceedings. 22

23 6 -Å Case: Electron Bunch Peak current ~3 k. A Undulator period 5 cm, Betatron function 4 m For 250 p. C case, assuming a step function current profile, sz 7 mm. Gain length ~ 2. 1 m SASE spikes ~ 160

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

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

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

27 6 -Å Case - Requirement on Seed Power Effective SASE start up power is 1. 3 k. W. Use small start up seed power 100 k. W. – 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 2 nd und. 2 GW 0. 1 MW

6 -Å Self-Seeded FEL Performance Temporal profile at ~25 m in the 2 nd undulator for seed of 100 k. W ~12 mm 28

6 -Å Self-Seeded FEL Performance 29 FEL spectrum at ~25 m in the 2 nd undulator for seed of 100 k. W FWHM 5. 2 10 -5

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 30

Self-Seeding Summary at 6 nm and 6 Å Parameter Emittance Peak Current Pulse length rms Bandwidth FWHM Limited Bandwidth Seed Power on Mono Efficiency Over all Efficiency Sat. Power Sat. Length Brightness Increment 6 nm 0. 6 1 35 6Å 0. 6 3 12 unit mm k. A fs 24 15 100 50 10 20 5 30 50 5. 2 4. 4 100 2000 0. 2 0. 5 10 35 150 10 -5 k. W MW % 10 -4 GW m J. Wu, P. Emma, Y. Feng, J. Hastings, C. Pellegrini, FEL 2010 Proceedings. (2010) 31

Issues 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 R 56 ~ 3 mm Timing jitter 12 fs – FEL detuning theory; positive detune longer gain length, higher saturation power; negative detune longer gain length, lower saturation power October 26, 2010 ARD Status meeting X. J. Wang et al. , Appl. Phys. Lett. 91, 181115 (2007). jhwu@slac. stanford. edu J. Wu, FEL Physics Group 32

Issues The previous slide shows the power fluctuation due to centroid energy jitter, the spectrum bandwidth seems to be less affected. October 26, 2010 ARD Status meeting jhwu@slac. stanford. edu J. Wu, FEL Physics Group 33

Issues 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 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). October 26, 2010 ARD Status meeting jhwu@slac. stanford. edu J. Wu, FEL Physics Group 34

Issues 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) October 26, 2010 ARD Status meeting jhwu@slac. stanford. edu J. Wu, FEL Physics Group 35

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

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

LCLS Self-Seeded FEL Performance FEL spectrum at 40 m FWHM 10 -5 The nonuniform energy profile affects the bandwidth October 26, 2010 ARD Status meeting jhwu@slac. stanford. edu J. Wu, FEL Physics Group 38

Issues Electron bunch energy profile imperfectness – Study a linear energy chirp together with a second order curvature on the electron bunch, where 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 October 26, 2010 jhwu@slac. stanford. edu (2009); ARD Status meeting J. Wu, FEL Physics Group 39

Issues Electron bunch energy profile imperfectness – Electron bunch can have an energy modulation, J. Wu, A. W. Chao, J. J. Bisognano, LINAC 2008 Proceedings, p. 509 (2008); B. Jia, Y. K. Wu, J. J. Bisognano, A. W. Chao, J. Wu, Phys. Rev. ST Accel. Beams 13, 060701 (2010); October 26, J. J. 2010 Welch, R. A. Bosch, B. Jia, A. A. jhwu@slac. stanford. edu J. Wu, Lutman, FEL 2010 proceedings. (2010). ARD Status meeting J. Wu, FEL Physics Group 40

Summary LCLS excellent electron beam quality leads to short gain length, early saturation. This makes possible to add more functions Two-stage FEL with monochromator reduces 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 41

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. …… 42