Introduction to Free Electron Lasers and

Fourth-Generation Light Sources

黄志戎 (Zhirong Huang, SLAC)

FEL ReferencesFEL ReferencesFEL ReferencesK.-J. Kim and Z. Huang, FEL lecture note, available electronically

upon request

Charles Brau, Free Electron Lasers (Academic Press, 1990), slightly outdated but good basics

Saldin, Schneidmiller, Yurkov, The Physics of Free Electron Lasers (Springer, 1999), more SASE but much more technical

Web ResourcesWeb ResourcesWeb ResourcesLCLS CDR, http://www-ssrl.slac.stanford.edu/lcls/cdr/LCLS science, http://www.slac.stanford.edu/pubs/slacreports/slac-

r-611.html

European XFEL TDR, http://xfel.desy.de/tdr/index_eng.html

Spring-8 Compact SASE Source CDR, http://www-xfel.spring8.or.jp/SCSSCDR.pdf

Introduction

FEL mechanism

SASE principle

Temporal and transverse characteristics

SASE experiments and projects

Seeding options

ultra-short pulses (if time available)

Lecture OutlineLecture OutlineLecture Outline

Free Electron Lasers• Produced by the resonant interaction of a relativistic

electron beam with a photon beam in an undulator

• Tunable, Powerful, Coherent radiation sources

• 1977- First operation of a free-electron laser at Stanford University

• Today– 22 free-electron lasers operating worldwide– 19 FELs proposed or in construction– More info at http://sbfel3.ucsb.edu/www/vl_fel.html

FEL oscillators Single pass FELs(SASE or seeded)

Atomic, molecular and optical science

High energy density science

Coherent-scattering studies of nanoscale fluctuations

Nano-particle and single molecule (non-periodic) imaging

Diffraction studies of stimulated dynamics (pump-probe)

Abs

orpt

ion

Res

onan

ce R

aman

t0

t1

t2t3

t4 t5

Program developed by international team of scientists working with accelerator and laser physics communities

Aluminum plasma

10-4 10-2 1 10 2 10 4

classical plasma

dense plasma

high density matter

G =1

Density (g/cm-3)

G =10

G =100

t=0

t=τ

“the beginning.... not the end”

SLAC Report 611

Vision of ScienceVision of ScienceVision of Science

Structural Studies on Single Particles andBiomolecules

Requirements: High peak brightness

High photon density

230 fs or shorter pulses

Fast array detectors

Single Molecule: >1012photons

Clusters of ~100 moleculeswith known orientation canbe attempted first

Measurement of static propertiesIs the goal- understandingdynamics is prerequisite

Undulator RadiationUndulatorUndulator RadiationRadiation

λu

forward direction radiation(and harmonics)

undulator parameter K = 0.94 B[Tesla] λu[cm]

Can energy be exchanged between electrons and co-propagating radiation pulse?

λ1

LCLS undulator K = 3.5, λu = 3 cm, e-beam energy from 4.3 GeV to 14 GeV to cover λ1 = 1.5 nm to 1.5 Å

Resonant conditionResonant conditionResonant condition

UVSOR FEL, Okazaki, Japan

Resonant interactionFEL interactionFEL interactionFEL interaction

⎟⎠

⎞⎜⎝

⎛+=2

12

2

2

K0K0 /γ0

λu z

x

λuλ1 γ0

energy energy ηη=(=(γγ--γγ00)/)/γγ00

phase phase θθ=(=(kkrr+k+kuu)z)z--ωωrrttradiation radiation

wavenumberwavenumberundulator undulator

wavenumberwavenumber

Use variables

arrival time at undulator distance

Longitudinal electron motion in combined undulator and Longitudinal electron motion in combined undulator and radiation fields described by pendulum equationsradiation fields described by pendulum equations

Π 0 Π 2 Π 3 Π

λλrr

ηη

θθ

Pendulum equationsPendulum equationsPendulum equations

θθ

for planar undulator

=1 for helical undulator

Three FEL modesThree FEL modes

Self-amplified spontaneous emission (SASE)SelfSelf--amplified spontaneous emission (SASE)amplified spontaneous emission (SASE)

X-ray FEL requires extremely bright beamsXX--ray FEL requires extremely bright beamsray FEL requires extremely bright beamsPower grows exponentially with undulator distance z. For a

1-D, mono-energetic beam

peak current

emittance

FEL Pierce parameter ρ ∼radiation power

SASE power reaches saturation at ~ 20 LGFEL performance depends exponentially on e-beam

qualities

beam power

beta function17 kA

Beam focusingBeam focusingBeam focusingFocusing of electron beam in the undulator

π

π

⎟⎠

⎞⎜⎝

⎛+=2

12

2

2

K0K0 /γ0

λu z

x

λuλ1 γ0

electron with an angle ψ

Emittance effectEmittanceEmittance effecteffect

ψ

Resonant condition

Require average change in λ1 over gain length << λ1

Emittance requirement

Smaller βx increase beam density, ideally

Slippage and FEL slicesSlippage and FEL slicesSlippage and FEL slicesDue to resonant condition, light overtakes e-beam by

one radiation wavelength λ1 per undulator period

electron bunchoptical pulse

electron bunchoptical pulse

z

Interaction length = undulator length

Slippage length = λ1 × undulator period(100 m LCLS undulator has slippage length 1.5 fs,

much less than 200-fs e-bunch length)Each part of optical pulse is amplified by those

electrons within a slippage length (an FEL slice)

Only slices with good beam qualities (emittance, current, energy spread) can lase

SASE temporal spikesSASE temporal spikesSASE temporal spikes

1 % of X-Ray Pulse Length1 % of X-Ray Pulse Length

• Due to noisy start-up, SASE has many intensity spikes

• LCLS spike ~ 1000 λ1 ~ 0.15 μm ~ 0.5 fs!

• From one spike to another, no phase correlation

Each spike lases indepedently, depends only on the local (slice) beam parameters

LCLS pulse length ~ 200 fswith ~ 400 SASE spikes~ x-ray energy fluctuates 5%

• Spontaneous undulator radiation phase space is the incoherent sum of the electron phase space, consists of many spatial modes

• SASE: higher-order modes have stronger diffraction +FEL gain is localized within the electrons

selection of the fundamental mode (gain guiding)

fully transversely coherent even εx > λ1/4 π

x

X’ 2πεx

λ1/2 (diffraction limit)

Transverse coherenceTransverse coherenceTransverse coherence

from S. Reiche

Z=25 m Z=37.5 m Z=50 m

Z=62.5 m Z=75 m Z=87.5 m m

LCLS transverse mode simulationLCLS transverse mode simulationLCLS transverse mode simulation

εn = 1.2 μm, γ=28000, λ1=1.5 Ǻ, εn/γ = εx,y = 3.6 λ1/(4π)

Peak Brightness Enhancement From Storage Ring Light Sources To SASE

#of photonsΩx Ωy Ωz

B = (Ωi- phase space area)

Enhancement Factor

# of photons Nlc

~ 106

Undulator in SR SASE

αΝe αΝeNlc

ΩxΩy (2πεx) (2πεy)

ΩZ

compressed

Δωω

⋅σ Z

c⎛ ⎝ ⎜

⎞ ⎠ ⎟ = 10 −3 ×10 ps Δω

ω⋅

σ Z

c⎛ ⎝ ⎜

⎞ ⎠ ⎟ = 10 −3 ×100 fs 210

210λ 2( )2

B 1023 1033 1010

Nlc: number of electrons within a coherence length lc

• FEL instability creates energy and density modulation at λ,

λ

small signal, linear regime

t

E λ

near saturation, nonlinear regime

• Near saturation, strong bunching at fundamental λ producesrich harmonic components

• Coherent harmonics drive by fundamental λ (En ∝ E1n)

gain length = LG/n (n is harmonic order)similar transverse coherencespikier temporal structure

Nonlinear harmonic generationNonlinear harmonic generationNonlinear harmonic generation

• Theory and simulations predicts third harmonic reaches up to 1% of fundamental at saturation

• IR wavelengths:

UCLA/LANL (λ = 12μ, G = 105)LANL (λ = 16μ, G = 103)BNL ATF/APS (λ = 5.3μ, G = 10, HGHG = 107 times S.E.)

• Visible and UV:

LEUTL (APS): Ee ≤ 400 MeV, Lu = 25 m, 120 nm ≤ λ ≤ 530nmVISA (ATF): Ee = 70 MeV, Lu = 4m, λ = 800 nmTTF (DESY): Ee < 300 MeV, Lu = 15 m, λ = 80–120 nmSDL (NSLS): Ee < 200 MeV, Lu = 10 m, λ = 800–260 nmTTF2 (DESY): Ee ~ 450 MeV, Lu = 27 m, λ = 30 nm

All Successful, TTF2 (FLASH) is in user operation mode

SASE Demonstration Experimentsat Longer Wavelengths

10-1100101102103104105106

Opt

ical

ene

rgy

[a.u

.]

10-1100101102103104105106

Distance [m]0 5 10 15 20 25

10-1100101102103104105106

A

B

C

(S. Milton et al., Science, 2001)

A B C

σt (ps) 0.19 0.77 0.65

I (A) 630 171 184

εn (μm) 8.5 8.5 7.1

σδ (%) 0.4 0.2 0.1

λ (nm) 530 530 385

Observations agree with theory/ computer models

LEUTL FELLEUTL FEL

10-2

10-1

100

101

102

103

104

105

2 2.5 3 3.5 4

Ener

gy (n

J)

z(m)

Nonlinear Harmonic Radiation at VISA*

Associated gain lengths

L2 = 9.8cmL3 = 6.0cm

Ln = Lg / nLf = 19cm

Fundamental

2nd harmonic

3rd harmonic

⇒

Mode (n)

Wavelength (nm)

Energy (μJ)

% of E1

1 845 52

2 421 .93 1.8

3 280 .40 .77

Using the relation of 2nd and 3rd harmonic energies as given by Z. Huang and K.J.Kim

E2 =K

γkuσ x

Energy Comparison

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2K2K3

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2b2b3

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2E3

b -bunching parametersKn -Coupling coefficients

April 20, 2001

Nonlinear Harmonic Energy vs. Distance

* A. Tremaine et al., PRL (2002)

Statistical fluctuation Transverse coherence

after double slit after cross

Observations at TTF FEL*

0

1

X [mm]

Y [

mm

]In

ten

sity

[ar

b.u

nit

s]

0

2

4

6

X [mm]−2 −2

−1

2

0

−2

0 0 22

* V. Ayvazyan et al., PRL (2002); Eur. Phys. J. D (2002)

LCLSLCLS must extend FEL wavelength by another two must extend FEL wavelength by another two orders of magnitude from 13 nm orders of magnitude from 13 nm 1 nm 1 nm 1 1 ÅÅ

SLAC linac tunnelSLAC linac tunnel research yardresearch yard

LinacLinac--00L L =6 m=6 m

LinacLinac--11L L ≈≈9 m9 m

ϕϕrf rf ≈≈ −−2525°°

LinacLinac--22L L ≈≈330 m330 mϕϕrf rf ≈≈ −−4141°°

LinacLinac--33L L ≈≈550 m550 mϕϕrf rf ≈≈ 00°°

BC1BC1L L ≈≈6 m6 m

RR5656≈≈ −−39 mm39 mm

BC2BC2L L ≈≈22 m22 m

RR5656≈≈ −−25 mm25 mm DL2 DL2 L L =275 m=275 mRR56 56 ≈≈ 0 0

DL1DL1L L ≈≈12 m12 mRR56 56 ≈≈0 0

undulatorundulatorL L =130 m=130 m

6 MeV6 MeVσσz z ≈≈ 0.83 mm0.83 mmσσδδ ≈≈ 0.05 %0.05 %

135 MeV135 MeVσσz z ≈≈ 0.83 mm0.83 mmσσδδ ≈≈ 0.10 %0.10 %

250 MeV250 MeVσσz z ≈≈ 0.19 mm0.19 mm

σσδδ ≈≈ 1.6 %1.6 %

4.30 GeV4.30 GeVσσz z ≈≈ 0.022 mm0.022 mm

σσδδ ≈≈ 0.71 %0.71 %

13.6 GeV13.6 GeVσσz z ≈≈ 0.022 mm0.022 mm

σσδδ ≈≈ 0.01 %0.01 %

LinacLinac--XXL L =0.6 m=0.6 m

ϕϕrfrf= = −−160160°°

21-1b,c,d

...existinglinac

L0-a,b

rfrfgungun

21-3b24-6dX 25-1a

30-8c

Commission in Jan. 2007Commission in Jan. 2007 Commission in Jan. 2008Commission in Jan. 2008

Accelerator issues• RF photocathode gun

– 1 μm normalized emittance, reasonable peak current

• Emittance preservation in linacs (SLC experiences)

• Bunch compression– coherent synchrotron radiation – microbunching instability (mitigated by a laser heater)

• Machine stability– energy jitter (wavelength jitter)– bunch length and charge jitters (FEL power jitter)– transverse jitters (power and pointing jitters)

• Undulator– straight trajectory to μm level (beam-based alignment)– undulator parameter tolerance (e.g., ΔK/K ~ 10-4)

SASE x-ray FELs such as the LCLS will lay the foundation for next-generation x-ray facilities

Due to its noisy startup, SASE is transversely coherent but temporally chaotic (LCLS 1.5 Å simulation by S. Reiche)

Monochromator can be used to select a single mode, but flux is reduced (by ~600) and intensity fluctuates 100%

Various schemes to improve temporal coherence proposed

Beyond SASEBeyond SASE

temporal spectral

High-gain harmonic generation (HGHG), starting from a seed laser at longer wavelengths (200-300 nm)

Two-stage self seeding: derive the x-ray seed from monochromized SASE for the next-stage amplification

Regenerative amplifier FEL: feedback monochromizedSASE for regenerative amplification

…

Methods to improve temporal coherenceMethods to improve temporal coherence

HGHG PrincipleHGHG Principle

DModulator Radiator

λ1 λh=λ1/h

seed laser

to next stage

……...electrons

L.-H. Yu, PRA44, 5178 (1991)

•Stable central wavelength

•Fourier transform limited

•Larger ratio of output/spontaneous radiation

•Short pulse (20fs)

•Stable Intensity from shot to shot

•Can be cascaded to short wavelength

•Narrow bandwidthAdvantages of HGHG

Wavelength, nm

Inte

nsity

, a.u

. HGHG

SASE 104

E-beam

laser

BNL SDL FEL results

L. H. Yu et al., PRL91, 074801 (2003)

Fresh bunch technique: Shift laser pulse from one part of an electron bunch (used part, with large energy spread) to a fresh part of the electron bunch

Before Shifter After Shifter

Electron bunch

Laser pulse

This makes it possible to use large energy modulation: Bunching parameter ~ order of 1

Cascading to shorter wavelengthsCascading to shorter wavelengthsWhole bunch harmonic cascade: each stage energy

modulation must be smaller than the next stage FEL parameter ρ

Time jitter between laser and e-beam must be less than 100 fs

Bunch compressor

Linear accelerator

Bunch compressor

Vertical transport

line

FEL

Linearizer X-band cavityBeam switchyard

Injector

FEL-1

FEL-2

•Spectral range covered by two undulator linesFEL 1: 100 – ~40 nm (12–30eV) single stageFEL 2: ~40 – 10 nm (30–124eV) two stages

Fermi FEL at Sincrotrone Trieste (Italy)

Also BESSY HGHG FEL with wavelength range 40 nm - 1 n(http://www.bessy.de/publicRelations/publications/files/TDR_WEB.pdf)

Two-stage self-seeding option*

* J. Feldhaus et al. / Optics Communications 140(1997) 341-352

Basic requirements:1) The 1st section operates in linear high-gain regime, <PSASE>~10MW2) The micro bunching is smeared out after the magnetic chicane3) The monochromator resolution Δω/ω≈5·10-5

4) The seeding power PSEED~10kW >> shot noise power PSHOT~10W5) The seed pulse is amplified to saturation in the 2nd undulator section

Schematic view of the seeding option for FLASH

V. Miltchev (DESY)

Electron beam optics 1, 2)

1) B. Faatz et. al., NIM A475, 603 (2001)

2) R. Treusch et. al. "The Seeding Project for the FEL in TTF Phase II", HASYLAB annual report 2001

1st undulator section

2nd undulator section

14.5 m

bypass 22 m

30 m

3°

vertical focusing quadrupole

undulator

vertical defocusing quadrupole

sextupole

bypass dipole

tuning bypass dipole

tuning bypass

for each radiation wavelength λR

• tune the quad strength to achieve linear regime in the 1st section

• use the bypass magnets to match to the optics in the 2nd section

Minimizing CSR and optics effects

V. Miltchev (DESY)

Regenerative Amplifier FEL (RAFEL)

Demonstrated in IR (~16 μm, LANL): NIMA429, 125 (1999)

RAFEL: high-gain, small feedback, multi-bunch scheme

Proposed for VUV FELs DESY: B. Faatz et al., NIMA 429, 424 (1999)Daresbury 4GLS: N. Thompson et al., FEL2005

X-ray RAFEL

e-beam

x-ray

undulator

Bragg mirror

Bragg mirror

Bragg mirror

x-ray

e-beam

chicane

We propose and analyze an x-ray RAFEL using narrow-bandwidth Bragg crystals*

Alternative backscattering geometry may also be used

* Z. Huang & R. Ruth, PRL96, 144801 (2006)

6 5 4 3 2 1 0 1 2 3 4 5 6

x 10 -6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Δω/ωr

refle

ctiv

ity

Bragg’s lawDiamond crystals as Bragg Mirrors

8 6 4 2 0 2 4 6 8

x 10 -6

0

0.2

0.4

0.6

0.8

1

Δω/ωr

refle

ctiv

ity

Diamond (high heat load, low absorption) at 60 degreeC (400), 1.55 Ǻ π-polarized C (511), 1.2 Ǻ σ-polarized

XOP simulations

200 150 100 50 0 50 100 150 2000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

time (fs)

pow

er (

GW

)

1 2 3 4 5 6 7 8 9 10

10-4

10 -3

10 -2

10 -1

100

101

number of x -ray passes

radi

atio

n en

ergy

at u

ndul

ator

end

(m

J)

1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

rela

tive

rms

ener

gy fl

uctu

atio

n

A possible RAFEL configuration for LCLS

output power

X-ray manipulation of a frequency-chirped SASE

E-beam manipulation: selective emittance spoiling

…

Methods to generate ultra-short x-ray pulsesMethods to generate ultra-short x-ray pulses

X-ray Pulse SlicingInstead of compression, use a monochromator to select a slice of the chirped SASE

t

ω

compression

SASE FELMonochromator

Single-stage approach

monochromator

short x-ray slice

Two-stage Pulse Slicing• Slicing before saturation reduces power load on

monochromator• Second stage seeded with sliced pulse (microbunching

removed by bypass)• Allows small bandwidth for unchirped bunches

• Larger FEL bandwidth than at saturation when slicing, potentially longer x-ray pulse length than 1-stage

• Synchronization between sliced pulse and the part of electrons having the “right” energy

SASE FELMonochromator

FEL Amplifier

Chicane

C. Schroeder et al., NIMA483, 89 (2002)

Minimum Pulse DurationMinimum Pulse DurationThe rms pulse duration σt after the monochromator

t

ω

u

ωσu/ωσ

Minimum pulse duration is limited to for either compression or slicing

SASE bandwidth reaches minimum (~ρ=5×10−4) at saturation, minimum rms pulse duration = 6 fs for 1% E-chirp

u/ωσS. Krinsky & Z. Huang, PRST-AB6, 050702, (2003)

Large Large xx--zz correlation inside a bunch compressor chicanecorrelation inside a bunch compressor chicane

E-beam manipulation for fs and as x-rays

2.6

mm

rms

2.6

mm

rms

0.1 mm rms0.1 mm rms

Easy access to Easy access to timetime coordinate coordinate along bunchalong bunch

LCLS BC2

Slotted-spoiler Scheme

1 μm emittance

P. Emma et al. PRL92, 074801 (2004)

6 μm emittance

1 μm emittance

15-μm Be foil1515--μμm Be foilm Be foil

2 fsec fwhm2 fsec fwhm

fs and as x-ray pulsesfs and as x-ray pulses• A full slit of 250 μm unspoiled electrons of 8 fs (fwhm)

2~3 fs x-rays at saturation (gain narrowing of a Gaussian electron pulse)

• stronger compression + narrower slit (50 μm) 1 fs e-

500 as x-rays (close to a single coherence spike!)

“the beginning.... not the end”