Self-seeding Free Electron Lasers

Self-seeding Free Electron Lasers

J. WuFEL Physics Group

Beam Physics DepartmentOct. 26, 2010

Accelerator Research Division Status Meeting

October 26, 2010ARD Status meeting

jhwu@slac.stanford.eduJ. Wu, FEL Physics Group 2

Brief description of a Self-Amplified Spontaneous Emission (SASE) Free Electron Laser (FEL) as LCLSSchemes to improve the longitudinal coherence– Self-seeding as one of the possibilitiesMonochromator– Crystals for hard x-ray– Variable Line Spacing Gratings for soft x-rayIssues– Electron bunch centroid energy jitter– Electron bunch energy profile imperfectness

Outline

jhwu@slac.stanford.eduJ. 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, 2002October 26, 2010ARD Status meeting

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

Gain guiding—mode selection for LCLS

courtesy S. Reiche

SASE FEL—Transverse Coherence

6

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

SASE FEL—Temporal Coherence

cN FELw /

7

FEL power along the undulatorLCLS 1.5 Å SASE FEL Performance

Saturation early with power on order of GW

Instability:exponential growth

Instability:saturation

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FEL bandwidth along the undulatorLCLS 1.5 Å SASE FEL Performance

Bandwidth on order of 1E-3

Bandwidth decreases as 1/z1/2

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FEL temporal profile at 60 mLCLS 1.5 Å SASE FEL Performance

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FEL spectrum at 60 mLCLS 1.5 Å SASE FEL Performance

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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

Temporal Coherence

LCLS low charge operation mode [Y. Ding et al., PRL, 2009]

SASE and seeded FELFEL Types: Amplifiers & Oscillators

SASE Amplifier

Laser or HHGSeeded Amplifier (external seeding)

Modulator Buncher Radiatorin/n

Harmonic GenerationEEHG, HGHG, etc. (external seeding)

Oscillator (self-seeding)

Mirror MirrorJ.B. Murphy and J. Wu, The Physics of FELs, US Particle Accelerator School, Winter, 2009

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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

Schematics of Self-Seeded FEL

chicane

electron

1st undulator 2nd undulator

SASE FEL Seeded FELmonochromator

electron dump

FEL

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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 brightnessThe coherent seed after the monochromator should be longer than the electron bunch; otherwise SASE will mix with Seeded FEL

Transform Limited Pulses

18.12ln22/1 FWHM tt swssw

61.1FWHM tsw

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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 coherenceFor shorter wavelength (< 1 nm), single spike is not easy to reach, but self-seeding is still possible

Single Spike vs Self-Seeding

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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

Two-Stage FEL with Monochromator

With the same saturated peak power, but with two-orders of magnitude bandwidth reduction, the peak brightness is increased by two-orders of magnitude

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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

G. Geloni et al., 2010

Y. Ding et al., 2010; G. Geloni et al., 2010

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LCLS: Two-bunch HXR Self-seeding

~ 4 m

Si (113) Si (113)

SASE

SeededU1 U2

Y. Ding, Z. Huang, R. Ruth, PRSTAB 13, 060703 (2010)G.Geloni et al., DESY 10-033 (2010),

Before U2 After U2 Spectrum

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).

Spectrum after the diamond crystal

Power distribution after diamond crystal

6 GW

10-5

FWHM 6.7 10-5

G. Geloni et al., 2010

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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

2nd undulatorM1 M3

G

h

g

M2

e-beam

source point

re-entrant point

1st undulator

Y. Feng, J. Hastings, P. Heimann, M. Rowen, J. Krzywinski, J. Wu, FEL2010 Proceedings. (2010)

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Peak current ~3 kAUndulator period 5 cm, Betatron function 4 mFor 250 pC case, assuming a step function current profile, sz 7 mm.Gain length ~ 2.1 mSASE spikes ~ 160

6-Å Case: Electron Bunch

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6-Å FEL power along the first undulator6-Å SASE FEL Parameters

saturation around 32 m with power ~10 GW

LCLS-II uses about 40 meter long undulators

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

6 Å SASE FEL Properties

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

6 Å SASE FEL Properties

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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 5.010-5 Need 2 GW on

monochromator to seed with 0.1 MW in 2nd und.

6-Å Case - Requirement on Seed Power

2 GW 0.1 MW

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Temporal profile at ~25 m in the 2nd undulator for seed of 100 kW

~12 mm

6-Å Self-Seeded FEL Performance

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FEL spectrum at ~25 m in the 2nd undulator for seed of 100 kW

FWHM 5.210-5

6-Å Self-Seeded FEL Performance

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Effective pulse duration 12 mm, sz ~ 3.5 mm Transform limited Gaussian pulse bandwidth is 3.210-5 FWHM.(For uniform pulse 4.410-5 FWHM)The seeded FEL bandwidth (5.210-5 FWHM) is close to the transform limited bandwidth

6-Å case — transform limited

Parameter 6 nm 6 Å unitEmittance 0.6 0.6 mmPeak Current 1 3 kAPulse length rms 35 12 fsBandwidth FWHM 24 5.2 10-5

Limited Bandwidth 15 4.4 10-5

Seed Power 100 100 kWPower on Mono 50 2000 MWMono Efficiency 10 0.2 %Over all Efficiency 20 0.5 10-4

Sat. Power 5 10 GWSat. Length 30 35 mBrightness Increment 50 150

Self-Seeding Summary at 6 nm and 6 Å 31

J. Wu, P. Emma, Y. Feng, J. Hastings, C. Pellegrini, FEL2010 Proceedings. (2010)

October 26, 2010ARD Status meeting

jhwu@slac.stanford.eduJ. Wu, FEL Physics Group 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 powerX.J. Wang et al., Appl. Phys.

Lett. 91, 181115 (2007).

October 26, 2010ARD Status meeting

jhwu@slac.stanford.eduJ. 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

October 26, 2010ARD Status meeting

jhwu@slac.stanford.eduJ. 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

dtd

s

gwg

m0

2

2

,

2,

2

,,, 216)(

181)(

s

GFsfs

zz

w

www s

sss

rm zkw zk

zw

sGF

2

,33)( rwsw

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, 2010ARD Status meeting

jhwu@slac.stanford.eduJ. 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

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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

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FEL temporal profile at 40 mLCLS Self-Seeded FEL Performance

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FEL spectrum at 40 m

The nonuniform energy profile affects the bandwidth

LCLS Self-Seeded FEL Performance

FWHM 10-5

October 26, 2010ARD Status meeting

jhwu@slac.stanford.eduJ. Wu, FEL Physics Group

October 26, 2010ARD Status meeting

jhwu@slac.stanford.eduJ. 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

00

2

ts dt

dgwg

m

22,

2ˆ,ˆ,

1)()( ss ww zz GF

22ˆ

rm -

32ˆ

r

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);

02

2

20

2

-ts dt

d gwg

October 26, 2010ARD Status meeting

jhwu@slac.stanford.eduJ. 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. Beams 13, 060701 (2010);J. Wu, J.J. Welch, R.A. Bosch, B. Jia, A.A. Lutman, FEL2010 proceedings. (2010).

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

Summary

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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. ……