A. Zholents, PQE, January, 2006 X-ray free electron lasers Alexander Zholents LBNL An introduction to the afternoon session John Arthur, SLAC Applications

A. Zholents, PQE, January, 2006

X-ray free electron lasersAlexander Zholents

LBNL

An introduction to the afternoon session

John Arthur, SLAC

Applications of the intense coherent x-ray pulses from LCLS

John Corlett, LBNL

Proposals and concepts for future FELs

Andrew Sessler, LBNL

Transverse-longitudinal correlations: FEL performance and emittance exchange


X-ray FEL essentials

Layout of XFEL at DESY (Germany)

Electron beam production system: Q=1nC, n=1 mm-mrad

Electron beam delivery system: E=20 GeV, Ipeak=5kA

Electron beam utilization for emission of x-rays: l=1Å, =100fs, E=1mJ

More info about future x-ray FEL facilities in the talk of John Corlett and use of these facilities in the talk of John Arthur in the following session

mcourtesy T. Limberg


u

S N S N S N S N S N S N S N S N

N S N S N S N S N S N S N S N S

1. Undulator

By – peak magnetic field

Emission of x-rays

2. Electron beam

3. Laser (not always needed)

2

2

2

2

11 ⎟⎟

⎠

⎞⎜⎜⎝

⎛−−=⎟⎟

⎠

⎞⎜⎜⎝

⎛⊥

cv

cvz

γ

mc

eBK

K

c

v uy

π

γ 2;

2==⊥

undulator parameter

vz


N S N S N S N S N S N S N S N S

S N S N S N S N S N S N S N S N

FELs “power” is in bunching *

( ) ( ) ( )tieEE 00electronsingle

ωωωω −=

( ) ( ) ( )⎥⎦

⎤⎢⎣

⎡−+==

−

=

−∑2

0 2

1

electron single

2

1electron singleelectrons 1

zkN

j

tiN eNNNWeWW jωω

Radiation power

Electrons should stay bunched within π 2//1 xkz =≈Δ

( ) ( ) ( )∑=

−=N

j

tiN

jeEE1

0electrons0ωωωω

*) Motz 1953; Phillips 1960, Madey 1971


E/EE/E

zz

V = V0sin()V = V0sin()

RF AcceleratingRF AcceleratingVoltageVoltage

RF AcceleratingRF AcceleratingVoltageVoltage

z = R56E/Ez = R56E/E

Path Length-EnergyPath Length-EnergyDependent BeamlineDependent Beamline

Path Length-EnergyPath Length-EnergyDependent BeamlineDependent Beamline

E/EE/E

zz

E/EE/E

zz

‘chirp’‘chirp’

RF “buncher”

courtesy P.Emma


Energy modulation of electrons in the undulator by the laser light

Electron trajectory through undulator

)2/21/(22 KLu += γ

Undulator period

N

S

S

N

S

S

N

N

e-

u

Light

Magnetic field in the undulator

B B0sin(kuz)

E

k

B

E

k

B

V

V

0≠⋅VE

Laser wavelength

Laser “buncher”

FEL resonance conditionWhile propagating one undulator period, the electron is delayed with respect to the light on one optical wavelength

=


Laser pulse energy Spontaneous emission energy

A~ EL∫∫ (,r)+ER(,r)

2dSd

)cos(/2 ϕ RLRALARALAA ++=LR

≥

Field energy in the far field region of undulator radiation in the presence of the laser field:

Laser field Electron spontaneous emission

Energy modulation

E E =2 A

LA

RΔω

L/Δω

Rcos(ϕ )(ϕ)

LNuN LR1;1 ≅≅

Number of undulator periodsNumber of optical cycles

ϕ is the electron phase relative to the laser wave at the undulator entrance

Laser “buncher” (2)

Laser pulse widtho

z


Laser “buncher” (3)

,4LR

A αh≅

E LLAαh8≅2

=1/137 photon energy

(in 50 fs FWHM pulse)

Numerical example:

h L

L R

A L 5 nJ

E ≈ 150 keVto be compared with uncorrelated electron beam energy spread of ~ 100 keV

K = 3

( for K >> 1 )Spontaneous emission energy

(30-th harmonic of Ti:Sapphire laser produced using High-order Harmonic Generation)

45eV

Laser pulse energy

=

=

=


modulator

bunching chicane XUV light

Nu=100

radiator

Nu=100

30 nm, 5 nJ, 50 fs = 100 kW 30 nm, 30 MW

Laser “buncher” (4)Optical klystron*

*) Skrinsky, Vinokurov,1977

e- e-

XUV light

fragment of e-beam: modulation fragment of e-beam: bunching

A. Zholents, PQE, January, 2006A. Zholents, San-Diego, April, 2004

bunching chicane Laser light

time delay chicane

240 nm 48 nme-

modulator radiatore-

lightmodulator radiator

48 nm e-

light

12 nm

Harmonic cascade FEL*

Position of FEL pulse in full electron beam pulse

Unperturbed electrons

~100-fs seed laser pulse

tail head

radiator radiatormodulator

Fresh bunch techniqueππ

phase

energ

y

π π

evolution of e-beam phase space New undulator

resonant at L/n, and bunched beam radiates atn-th harmonic

bunching chicane

*) Csonka 1980; Kincaid 1980; Bonifacio 1990; L.-H. Yu 1990

z


Power vs. z andγ- scatterplots

At each modulator, radiation interacts with “fresh” e-

At each harmonic upshift (modulator to radiator), macro-particle phase multiplied by n

Bunching effects of dispersive section visible in change from Z=6 m in 48-nm modulator to Z=0.4 m scatterplot in 12-nm radiator

Z=0 m Z=1.8 m Z=3.6 m

Z=0 m

Z=0 m

Z=0.4 m

Z=3 m Z=6 m

240-nmmodulato

r

1.0 GW

4.0 GW 48-nm

radiator

48-nmmodulat

or

2504

1.2 GW 12-nm

radiator

2504

4.0 GW

48-nmmodulato

r

2510

2508

En

erg

y

(MeV

)

(radians)

(radians)

- +

-5 +5

- +(radians)

+4-4 (radians)2496

2496

2490

2492

Z=5.4 m

Z=3.4 m

Z=4.4 m

Z=2.4 m

GINGER simulationsW. Fawley, LBNL


GINGER simulation of 4-stage cascade configuration (240 nm 1 nm); W. Fawley

Input laser seed initialized with broadband (a) phase noise (b) amplitude noise

Fields resolved in simulation on 240 nm/c temporal resolution or better

Results:•Noise reaches minimum at 48-nm stage (slippage aveg.)•In later stages noise increases due to harmonic multiplication of low frequency components

RMS phase noise d(t)/dt after removal of average component

d

(t)/

dt

(A

.U.)

(a)(b)

12 nm 4 nm 1 nm48 nm240 nm

EXIT

Noise evolution from imperfect seed*

*) Saldin et al., 2002

innoise

signal2

outnoise

signal

⎟⎟⎠

⎞⎜⎜⎝

⎛≈⎟⎟

⎠

⎞⎜⎜⎝

⎛ −

PP

nPP

Noise can be aproblem at 1 Å


Self-Amplified Spontaneous Emission FEL*

*) Kondratenko, Saldin 1980; Bonifacio, Pellegrini, Narducci 1984

Similar to optical lasers, SASE x-ray FEL starts from spontaneous emission butavoids use of mirrors

courtesy S. Reiche

courtesy Z. Huang

Density modulation (shot noise at start or microbunching latter) drivesenergy modulation and vice-versa

Instability reaches saturation after all electrons are microbunched (or rate of de-bunching equals rate of bunching)

gain lengthπ

4u≈

Prad≈Pbeam


The FEL parameter Small diffraction, radiation field interacts locally with the

electron beam, i.e. optical guiding* (some similarity with fiber optics)

No guiding, strong diffraction

2

1

~

AI

I

γ

3

1

24

π

π

γ u

b

x

AI

IIA = 17 kA

e-beam emittance

beta-function

for K>>1

peak current

light emittance; x – x-ray wavelength

Key parameters: Eb

x

AI

I π

;

4; beam energy spread causes

de-bunching *) Moore 1984; Scharlemann, Sessler, Wurtele 1985


Transverse coherence

π4

xb When

spontaneous undulator radiation consists of many spatial modes, i.e. incoherent sum of individual electron emissions

But FEL gain is localized within the electrons and higher-order modes have stronger diffraction :gain guided selection of fundamental mode results in fully transverse coherence even at

π4

xb

x

X’ b e-beam

π4

x light beam (diffraction limited)

courtesy S. Reiche

Radiation field at different locations along the undulator


Temporal coherence

-15

15

-60. -40. -20. 00. 20. 40. 60.

tc/

E(t), a.u.

E t( )= ei t k z j( )

j

Bunch length

Cooperation length (slice):π

2

xc

SASE output exhibits “chaotic light” properties

Number of longitudinal modes: M ≈ (bunch length)/slice

Fluctuation in the x-ray pulse energy ~ 1/√M

Slice properties, i.e. slice peak current, emittance and energy spread define performance


Temporal coherence (2)

M decreases as coherence builds up during the exponential gain reaching minimum at saturation (~200 at LCLS)

courtesy W. Fawley


Production of bright electron beams: generation

e-beam peak brightness

Eb

I

2~ unites in a single expression key

parameters for x-ray FELs

Peak brightness of different photocathode e-guns (2002)

courtesy P. Piot

~100 A, n=1 mm-mrad

rapid acceleration near to the cathode to avoid space charge dilution

DESY-Zeuthennew generation of e-guns


Production of bright electron beams: preservation

q Non-linear effects in bunch compression: rf waveform, T566

q Longitudinal and transverse wakefields in acceleratorq Space charge effects (mainly longitudinal)q Coherent synchrotron radiation (CSR) and emittance excitationq Resistive wall wakefields in undulators

Physics phenomena affecting the e-beam while acceleration and compression

q Jitter in the rf phase and amplitude in accelerating structuresq Intensity and timing jitters in photocathode gun laserq Misalignment of rf structures and magnetic elementsq Power supply ripples

Technical issues


E/E = 0E/E = 0

x = Rx = R1616((ss))E/EE/E

bend-plane emittance growthbend-plane emittance growth

ee––RR

zz

coherent radiation coherent radiation forforzz

overtaking length:overtaking length: L L00 ~(24 ~(24zzRR22))1/31/3

E/E < 0E/E < 0

ssxx

Powerful radiation generates energy spread in bends Powerful radiation generates energy spread in bends

Causes bend-plane emittance growth (short bunch worse) Causes bend-plane emittance growth (short bunch worse)

Energy spread breaks achromatic system Energy spread breaks achromatic system

LL00

ll

CSR wake is strong at very small scales (~1 m)CSR wake is strong at very small scales (~1 m)

Coherent Synchrotron Radiation (CSR)

courtesy P. Emma


• Initial density modulation induces energy modulation through longitudinal space charge forces, converted to more density modulation by a compressor

t

Current

1%10%

growth of slice energy spread (and emittance)

t

EnergySpace charge

Gain=10

compression

Longitudinal space charge, CSR and microbunching instability

courtesy Z. Huang

saturation due to overmodulation stops the growth


Spectral dependence of the gain of the microbunching instability

Microbunching instability (2)

Entire machine with its accelerating sections, drifts and chicanes acts as an amplifier for initial density perturbation and can be characterized by a spectral gain function (in an analogy to the FELs) *

*) Z. Huang et. al, Phys. Rev. ST –Acc. and Beams, v.5, 074401(2002)

1400

(m)50 150 200

Instability increases rms energy spread by a factor of 5-10

FERMI FEL project


Laser heater as an instrument for a suppression of microbunching instability1,2

1) E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, DESY Report No. TESLA-FEL-2003-03, 2003.

2) Z. Huang, et. al, Phys. Rev. ST –Acc. and Beams, V.7, 074401, (2004).

800Laser heater 2.5 keV Laser heater 5 keV

Laser heater 7.5 keV Laser heater 10 keV

1200

150 300

Laser “heater” (laser-e-beam interaction induce energy spread) provides “Landau damping” effect through controlled increase of the energy spread at the beginning of acceleration


Alignment errors and orbit distortions are responsible for transverse wakefields produced by e-beam, and transverse wakefields twist e-beam into a banana shape

courtesy P. Emma

zz

•Slice emittance is not affected•Centroid shift and variation can be important

Wakefields

Other wakefields:• Longitudinal wakes, • Resistive wall wakes, • Surface roughness wakesalso do not affect slices and produce similar global variations that nevertheless can be dangerous for FEL performance


Pushing over the limits …

further improvements can be obtained by using:1) electron beam conditioning*2) enhanced SASE

* Talk of J. Wurtele, Wednesday evening

A. Zholents, PQE, January, 2006*) Sessler, Whittum, Yu in 1992

• allows relaxed emittance requirement in FEL

z

y undulator

E/E

y

without conditioning

z

y

E/E

y

with conditioning

z

y

Electron beam conditioning*provides correlation of electron transverse amplitudes with electron energies to prevent de-bunching of electrons (more in Sessler’s talk in the following session)


e-beam

( )11 sin~ zkLγ( )dsyxzz ∫ ++= 22

12 2

1( )22 sin~ zkLγ

( ) ( )121 cos~ zkJJk LyxL += γγγyx JJ +~

Caution: approximately one half of electrons have wrong sign of correlation

510~/ RFL kk !!!

• Proposed scheme gains factor of 105 in efficiency by utilizing laser and wiggler for electron energy modulation instead of RF cavities:

Laser-assisted electron beam conditioning*

*) Zholents 2005


Example: LCLS-like FEL with 2 times of LCLS emittance

1 - no conditioning, 2 - ideal conditioning (all electrons), 3 - proposed conditioner.

GENESIS simulationsBeam parameters:energy = 14 GeV peak current = 3.4 kA, energy spread = 1.2 MeV, emittance = 2.4 mm-mrad, beta-function = 20 m.

Laser-assisted electron beam conditioning (2)


E ~ 4.5 GeV

• Laser peak power ~ 10 GW (“easy”)• Short wiggler, ~ 10 periods

BunchingAccelerationModulation30-100 fs pulseL~0.8 to 2.2m

Electron beam after bunching

Pe

ak c

urr

ent

, I/I 0

z /L

20-25 kA

E ~ 14 GeV

One optical cycle

ESASE-Enhanced Self-Amplified Spontaneous Emission*

*) Zholents 2004

Laser pulse width


“Start-to-End” simulations• 3-m FODO lattice period

–drifts+quads occupy ~ 0.5m–not compatible with current LCLS lattice design

ESASE (2)Example for LCLS with =12 m

ESASE cases saturate by 50 m with 50-100 times power contrast over unmodulated part of the electron bunch - the opportunity for an absolute synchronization of a probe x-ray pulse to a pump laser pulse

courtesy W. Fawley

“standard” LCLS

ESASE


Combined field of two lasersEnergy modulation of electrons

produced in interaction with two lasers

Attosecond x-rays using ESASE*

*) Zholents, Penn 2005


Peak current after chicane

one laser

two lasers

Attosecond x-rays using ESASE (2)


background from 100 fs e-bunch

side peaks

main peak

attosecond pulse

x-ray pulse energy growth over the length of the undulator

35 GW

Attosecond x-rays using ESASE (3)main peak

side peaks

entire bunch

~350as


Summary X-ray FELs are as good as the electron beam is, i.e.:

• peak current• slice emittance• slice energy spread Production of a high-brightness electron beams and

preservation of the electron beam quality is affected by:• space charge• coherent synchrotron radiation• microbunching instability• various wake fields

Laser-assisted manipulation of electrons in the phase space is a promising concept for future FELs :

• electron beam conditioning• enhanced self-amplified spontaneous emission


Outlook: future FEL-based multi-user x-ray facility

• Future facility will be as much laser beam based as electron beam based and will have a multi -FEL x-ray production “farm”. This “farm” will be fed by a high-repetition rate linac (up to MHz) equipped with a high brightness source of electrons.

• Optical lasers will be used for a production and shaping the electron bunches and for seeding the x-ray radiation. An advent of high-average power lasers will boost high-repetition rate FELs.

High repetition rate linac FEL “farm”

Laser(s)


Use of FELs will expand beyond FELs based on the SASE method (in a construction phase at present) towards FELs producing laser-like nearly Fourier transform limited x-ray beams at various wavelengths with controlled pulse duration, bandwidth, and polarization.

Outlook: future FEL-based multi-user x-ray facility


Gratefully acknowledged:

K. Bane, J. Corlett, M. Cornaccia, P. Craevich, S. DiMitri, D. Dowel, P. Emma, W. Fawley, W. Graves, J. Hasting, Z. Huang, K.-J. Kim, S. Leone, S. Lidia, G. Penn, R. Schoenlien, A. Sessler, J. Staples, G. Stupakov, J. Wu, J. Wurtele, M. Zolotorev

Thank you !


courtesy B. Faatz


Documents

A. Zholents, PQE, January, 2006 X-ray free electron lasers Alexander Zholents LBNL An introduction to the afternoon session John Arthur, SLAC Applications