Pulse-Splitting in Seeded Free Electron Lasers · 2010. 9. 9. · Observation of a pulse splitting • Study of the double pulse behavior: – Related to local overbunching / follows

Pulse-Splitting inSeeded Free Electron Lasers

M. Labat, N. Joly, S. Bielawski, C. Szwaj, C. Bruni, M.E. Couprie

1008-FEL’10

• Amplifier medium:– Relativistic e- @ E ≈ MeV-GeV

from accelerator (storage ring or LINAC)

– Periodic magnetic fieldgenerated in an undulator

Electron beamtrajectory

Magnetic fieldB

Introduction to seeded FELsPrinciple of an FEL

• Optical radiation:– Spontaneous emission:

Synchrotron radiation

– External source or seed :Conventionnal laser, etc.. λλλλ

Introduction to seeded FELsPrinciple of an FEL

Seeded FEL

Resonant wavelength:

• Injection of a coherent seed enables:– Reduction of the saturation length – Higher temporal coherence – Higher shot to shot stability– Shorter and controlled pulse duration– Stronger nonlinear harmonic generation– More efficient cascading configurations

• Seed sources:– Conventional lasers: λ > 250 nm– High order Harmonics Generated in gas (HHG): 270 > λ > 1 nm

L.H. Yu, Phys. Rev. A 44 (1991).

D. Garzella et al., NIMA 528, 502 (2004).

M.E. Couprie et al., NIMA 528, 507 (2004).

HHG + HGHG : Coherent compact FELs at very short wavelengths

Introduction to seeded FELsAdvantages of seeded FELs

0.1

2

4

6

1

2

4

6

10

2

4

E (G

eV)

0.1 1 10 100 Wavelength (nm)

SASE X-FELs:SLS, LCLS, EXFEL, SCSS-XFEL,

BEJING-XFEL, PAL-XFEL, PSI-XFEL

FLASH

Seeded FELs:AEC, BATES,

BESSY FEL, DUVFEL, FERMI, LBNL,

LCLS-II, MAX-IV, NLS, SCSS-proto,

SDUV-FEL, SPARC,SPARX, WIFEL

Electron beam energy vs FEL wavelength of the current and expected FELs

Introduction to seeded FELsSeeded FELs around the world

0.1

2

4

6

1

2

4

6

10

2

4

E (G

eV)

0.1 1 10 100 Wavelength (nm)

AEC (P1)

SASE X-FELs:SLS, LCLS, EXFEL, SCSS-XFEL,

BEJING-XFEL, PAL-XFEL, PSI-XFEL

FLASH

AEC (P2)

Seeded FELs:AEC, BATES,

BESSY FEL, DUVFEL, FERMI, LBNL,

LCLS-II, MAX-IV, NLS, SCSS-proto,

SDUV-FEL, SPARC,SPARX, WIFEL

BATES

SPARC

SCSS-proto

Seeded FELswith HHG

Electron beam energy vs FEL wavelength of the current and expected FELs

WIFEL

AEC (P3)

Introduction to seeded FELsSeeded FELs around the world

FERMI

SPARXNLS

SFLASH

FLASH-II

PSI-XFEL

The ARC-EN-CIEL projectIntroduction

• 4th generation light source:– Synchrotron radiation from undulators (IR to X-rays):

U20 and U30 (planar + helical)– 4 Free Electron Lasers:

3 seeded HGHG(λ � 0.3 nm) + 1 oscillator (VUV)

High current1 MHz

Low current10 kHz

Injectors

The ARC-EN-CIEL projectLight sources

High current1 MHz

Low current10 kHz

Injectors

The ARC-EN-CIEL projectWritting of the CDR

Simulations with SRW

Simulations with PERSEO

…!!

http://www.perseo.enea.ithttp://www.esrf.eu/Accelerators/Groups/InsertionDevices/Software/SRW

Synchrotron radiation

FELradiation

• Electron beam:– E=220 MeV, I=300A, σz=450 fs-rms, ε=1.2.π.mm.mrad

• Seed: – 114 nm – 200 kW in 150 fs-fwhm

• Undulators:– Modulator: 100 periods of 26 mm– Dispersive section: R56=1.5 µm– Radiator: 260 periods of 30 mm

• Final wavelength = 114 nm

Simulation of a VUV seeded FELParameters for AEC – FEL1

Peak power evolution in the:

modulator radiator

0 2 4 6 81.10

30.01

0.1

1

10

100

1.103

1.104

1.105

1.106

1.107

1.108

1.109

z (m)

Pea

k P

ower

zf

0 1 2 31 .10

7

1 .106

1 .105

1 .104

1 .103

0.01

0.1

1

z (m)

Pea

k P

ow

er (

MW

)

Simulation of a VUV seeded FELPerformances of AEC – FEL1

H1

H3

H5

H1

H3

10-4

10-2

100

102

P (

MW

)

121086420

z (m)

12.6

z (m

)

0154t (µm)

0

1.0

0.8

0.6

0.4

0.2

0.0

P (

uni

t. ar

b.)

400350300250200150100

ζ (µm)

Longitudinal profile

Peak power

Simulation of a VUV seeded FEL« Performances » of AEC – FEL1

Looking at spatio-temporal diagrams

t (µm)

12.6

0

Exponential growth

Saturation

Modulation(lethargy)

1.0

0.8

0.6

0.4

0.2

0.0

P (

uni

t. ar

b.)

400350300250200150100

ζ (µm)

Longitudinal profile


Looking at spatio-temporal diagrams

t (µm)

10-4

10-2

100

102

P (

MW

)

121086420

z (m)

Peak power

z (m

)

154t (µm)0


71.98 20.57 30.85 82.27 133.68

1st harmonic

z (um)

Po

wer

(a.

u.)

71.98 20.57 30.85 82.27 133.680

0.5

13rd harmonic

z (um)

71.98 20.57 30.85 82.27 133.680

0.5

15th harmonic

z (um)

1st Harmonic


3rd Harmonic 5th Harmonic

z (a

rb.u

n.)

z (a

rb.u

n.)

z (a

rb. u

n.)

t (arb.un.)t (arb.un.)t (arb.un.)

• Electron beam:– E=1 GeV, I=1500A, σz=200 fs-rms, ε=1.2.π.mm.mrad

• Seed: – 8.9 nm– 30 kW in 50 fs-fwhm

• Undulators:– Modulator: 200 periods of 26 mm– Dispersive section: R56=1.5 µm– Radiator: 500 periods of 15 mm

• Final wavelength = 8.9 nm

Simulation of a XUV seeded FELParameters of AEC – FEL2

33.05 9.44 14.16 37.77 61.37

1st harmonic

z (um)

Po

wer

(a.

u.)

33.05 9.44 14.16 37.77 61.370

0.5

13rd harmonic

z (um)

33.05 9.44 14.16 37.77 61.370

0.5

15th harmonic

z (um)

Simulation of a XUV seeded FEL« Performances » of AEC – FEL2

1st harmonic 3rd harmonic 5th harmonic

z (a

rb.u

n.)

z (a

rb.u

n.)

z (a

rb. u

n.)

t (arb.un.)t (arb.un.)t (arb.un.)

40− 20− 0 20 400

0.2

0.4

0.6

0.8

ζcr

µm

ζcr Length+

µm

0.8 1.6 2.4

Power

Bn_1

Bn_31 GeV e- beam.

Seed: 300 kW @ 8.9 nm. 200xU26 – R56 – 500xU26.

z (a

rb.u

n.)

t (arb.un.)

Pulse splitting and overbunching

40− 20− 0 20 400

0.2

0.4

0.6

0.8

ζcr

µm

ζcr Length+

µm

0.8 1.6 2.4

40− 20− 0 20 400

0.2

0.4

0.6

0.8

ζcr

µm

ζcr Length+

µm

2.4 3.6

Power

Bn_1

Bn_31 GeV e- beam.

Seed: 300 kW @ 8.9 nm. 200xU26 – R56 – 500xU26.

z (a

rb.u

n.)

t (arb.un.)


40− 20− 0 20 400

0.2

0.4

0.6

0.8

ζcr

µm

ζcr Length+

µm

0.8 1.6 2.4

40− 20− 0 20 400

0.2

0.4

0.6

0.8

ζcr

µm

ζcr Length+

µm

2.4 3.6

40− 20− 0 20 400

0.2

0.4

0.6

0.8

ζcr

µm

ζcr Length+

µm

0.8 1.6 2.4

Phase space of selected slices

Power

Bn_1

Bn_31 GeV e- beam.

Seed: 300 kW @ 8.9 nm. 200xU26 – R56 – 500xU26.

z (a

rb.u

n.)

t (arb.un.)


40− 20− 0 20 400

0.2

0.4

0.6

0.8

ζcr

µm

ζcr Length+

µm

0.8 1.6 2.4

40− 20− 0 20 400

0.2

0.4

0.6

0.8

ζcr

µm

ζcr Length+

µm

2.4 3.6

40− 20− 0 20 400

0.2

0.4

0.6

0.8

ζcr

µm

ζcr Length+

µm

0.8 1.6 2.4


1.6 2.4 3.2


Power

Bn_1

Bn_31 GeV e- beam.

Seed: 300 kW @ 8.9 nm. 200xU26 – R56 – 500xU26.

z (a

rb.u

n.)

t (arb.un.)


40− 20− 0 20 400

0.2

0.4

0.6

0.8

ζcr

µm

ζcr Length+

µm

2.4 3.6

z (a

rb.u

n.)

t (arb.un.)

Simulation of a XUV seeded FELPulse splitting and overbunching

Pulse splitting is related to local overbunching

Pulse splitting dependencies

Pulse splitting dependenciesVs synchronization

1 GeV e- beam. Seed: 300 kW @ 8.9 nm. 200xU26 – R 56 – 500xU26.

Pulse splitting follows the gain medium

1 GeV e- beam. Seed: 300 kW @ 8.9 nm. 200xU26 – R 56 – 500xU26.

Pulse splitting dependenciesVs synchronization

Pulse splitting dependenciesVs pulse duration

1 GeV e- beam. Seed: 50 kW @ 14 nm. 700xU26.

Pulse splitting dependenciesVs pulse duration

1 GeV e- beam. Seed: 50 kW @ 14 nm. 700xU26.

Pulse splitting occurrence depends in seed duration

Pulse splitting dependenciesVs power

30 kW 3 kW300 kW

1st harmonic

3rd harmonic

1 GeV e- beam. Seed @ 8.9 nm. 200xU26 – R 56 – 500xU26

Pulse splitting dependenciesVs power

30 kW 3 kW300 kW

1st harmonic

3rd harmonic

Pulse splitting occurrence does not depend in power

• Simulation of VUV and XUV seeded FELS (ARC-EN-CIEL):� Observation of a pulse splitting

• Study of the double pulse behavior:– Related to local overbunching / follows gain medium– Related to seed pulse duration– Not due to excessive seeding power

� Requires a better understanding

Pulse splitting in seeded FELsIntermediate conclusion

Start over fromFEL fundamental equations

Modeling of a seeded FELThe 1-D Colson-Bonifacio model

W.B. Colson, Phys. Lett. A 59 (1976) B. Bonifacio et al., PRA 40 (1989)

• Modeling of the e- beam:– Ne particles in the phase space (Φ,p):

• Φj: relative phase

• pj: relative normalized energy

– Particles distribution:• Φj: uniform distribution within [-π;π]

• pj: normal distribution centred at 0 with standard deviation σγ.


• Modeling of the e- beam:– Ne particles in the phase space (Φ,p)– Particles distribution

• Modeling of the radiation:– Radiation potentiel vector A(z,t)

• Dimensionless coordinates:– z: along the undulator in slippage length units– t: along the electron bunch in cooperation length units


• FEL equations:



Evolution of the particles in the phase space

(Φj,pj)

Propagation of the field A in the electronic medium

• FEL equations:



Evolution of the particles in the phase space

(Φj,pj)

Propagation of the field A in the electronic medium

Source term

• FEL equations:



Source term

Bunching coefficientMacroscopic electronic density

t

• Integration of the FEL equations:– Description of the particles dynamics– Description of the evolution of the radiation pulse– Analysis of the spatio-temporal regimes of the seeded FEL

with dimensionless parameters

Modeling of a seeded FELNumerical tool

N. Joly

• « Slippage parameter »:

• « Superradiant parameter »:

Analysis of the spatiotemporal regimesA few dimensionless parameters

B. Bonifacio et al., PRA 40 (1989)

• Radiation potentiel vector:

• Additional dimensionless « seed » parameter :

Analysis of the spatiotemporal regimesNew tools for seeded FELs

shot noise seed

Analysis of the spatiotemporal regimes« Initial » regimes



S >> 1Short bunch limit

S >> 1Weak superradiance


S ≤ 1Long bunch limit

1 ~ S >> KStrong superradiance

1 > S > KSteady-state








z

t t

zz

t

Se=0.25, K=0.025 Se=1, K=0.01Se=10







Today designs for S ≤ 1LCLS: S~0.01EXFEL: S~0.02FERMI: S~0.1SPARC: S~0.07

• Condition for occurrence:– S ≤1 and 1>S>K

(small slippage)

• Properties:– (1) Lethargy– (2) Exponential growth– (3) Saturation– (4) Power oscillations

Analysis of the spatiotemporal regimesThe steady-state FEL

z

t

(1)

(2)

(3)(4)

(1)

(2)

(3)

(4)

• Condition for occurrence:– 1 ~ S >> K

(strong slippage)

• Properties:– (1) Lethargy– (2) Exponential growth– (3) No saturation– (4) …

Analysis of the spatiotemporal regimesThe strong superradiance

z

t

(1)

(2)

(3)(4)

(4)

R. Bonifacio et al., PRA 40 (1989).

(1)

(2)

(3)

Analysis of the spatiotemporal regimesThe strong superradiance

T. Watanabe, PRL 98 (2007).

• Demonstration @ NSLS in 2007:

Analysis of the spatiotemporal regimesThe new regime



1 ~ S >> K1 > S > K

Sseed < 1 Sseed ~ 1 Sseed > 1 Sseed < 1 Sseed ~ 1 Sseed > 1



1 ~ S >> K1 > S > K

Sseed < 1Steadystate

Sseed ~ 1Pulse

splitting

Sseed > 1Strong

SR

Sseed < 1Strong

SR

Sseed ~ 1Strong

SR

Sseed > 1Strong

SR

Se=0.25, K=0.025 Se=1, K=0.01

Sseed=2Sseed=0.025 Sseed=10Sseed=10Sseed=2Sseed=0.25

Analysis of the spatiotemporal regimesThe pulse splitting

M. Labat et al., PRL 103 (2009)

z

t

Se=0.25, K=0.025, Sseed=2

0

10

-5 60

The pulse splitting regime

(c) Sseed=10

(b) Sseed=2

(a) Sseed=0.25

(a)

(b)

(c)

Superradiance

Steady-state

t

z

z

z

Output power

The pulse splitting regimeGain


Sseed=2

(a)t=20

(b)t=30

t

z

Gain

(a) (b)

G|A|²


Sseed=2

(a)t=20

(b)t=30

t

z

Gain

(a) (b)

G|A|²

Local gain � Local saturation � Progressive saturation along the pulse

Pulse splitting

The pulse splitting regimeApproximative splitting equation


t

z


• For Se<1 and Sseed~1:

• Solution of FEL equations:

• At saturation:

t

z

B. Bonifacio et al., NIMA239 (1985)


t

z

Local gain � Local saturation � Progressive saturation along the pulse

Pulse splittingCONFIRMS

Can we observe a pulse splittingon an existing seeded FEL ??

The pulse splitting regimeNext step

Pulse splitting in seeded FELsConclusion

• Simulation of VUV and XUV seeded FELS (ARC-EN-CIEL):� Observation of a pulse splitting

• Studies under PERSEO:� Rough understanding

• Integration of FEL equations:� Observation of a pulse splitted regime

• Analysis of dimensionless parameters:� Definition of the regime conditions of occurrence� Better understanding of the phenomenon

Let’s make experiment….

Documents

Pulse-Splitting in Seeded Free Electron Lasers · 2010. 9. 9. · Observation of a pulse splitting • Study of the double pulse behavior: – Related to local overbunching / follows