Argonne National Laboratory is managed by The University of Chicago for the U.S. Department of Energy

Quasi 3D ellipsoidal laser pulse by pulse tailoring and chromatic effect

Yuelin LiAdvanced Photon Source, Argonne National Laboratory

ylli@aps.anl.gov

2

Some accelerator related laser work at APS

FROG diagnostics of SASE FEL (Y. Li et al., PRL 89, 234801 (2002); 91, 243602 (2003))

EO sampling– Off line EO testing experiment: nonlinear EO crystal response (Li et al.,

Appl. Phys. Lett. 88, 251108 (2006)) – FNAL, NIU and ANL collaboration on EO sampling

Laser beam interaction– Ultrafast X-ray source generation (Li et al, PRST-AB 5, 044701 (2002))– Ultrafast Gamma-ray generation (Li et. al., APL 88, 021113 (2006))– Ultrashort positron source (Li et. al., APL 88, 021113 (2006))

Laser pulse shaping– Transverse pulse shaper for LCLS– 3-D laser pulse shaping (This talk, FEL06, LINAC06, and Li, OL in press)

Laser plasma accelerator– PIC simulation on beam parameter control (Shen, submitted to PRL)

3

Content APS Context: APS ERL upgrade An ellipsoidal beam and its properties How to generate an ellipsoidal beam

– Self evolving– 3D laser pulse shaping

Comparison and Challenges– Accelerating, image/space charge field

Shaping transplant Zoned lens References

– O.J. Luiten, S.B. van der Geer, M.J. de Loos, F.B. Kiewiet, and M.J. van der Wiel, Phys. Rev. Lett 93, 094802 (2004).

– B.J. Claessens, S.B. van der Geer, G.Taban, E.J.D. Vredenbregt, and O.J. Luiten, Phys. Rev. Lett 95, 164801 (2005).

– C. Limborg-Deprey and P. Bolton, Nucl. Instrum. Methods A557, 106 (2006).

– Y. Li and X. Chang, Proc FEL 2006, Berlin, Aug 26-Sept 1, 2006, paper THPPH053. – J. Rosenzweig, Nucl. Instrum. Methods A557, 87 (2006).– H. Tomizawa et al, Nucl. Instrum. Methods A557, 117 (2006).

4

The Advanced Photon Source, and its ERL upgrade plan

Pulse duration: 100 ps FWHM

Challenges (laser related …)High current and low emittance beam must be generated at the injector

Drive laser power and pulse shapingNon interceptive, single short measurement of the beam profile

Laser technique provides the highest resolution so far Timing must adequate

Laser remains an option

5

What is an ellipsoidal beam

An ellipsoidal beam is an ellipsoid with flat charge density distribution through out

Linear space charge force

– Linear to position– Decoupled in trans and longi

C. Limborg-Deprey and P. Bolton, Nucl. Instrum. Methods A557, 106 (2006).

Advantages– Compensate for all emittance growth due to space charge effect LR

QEr 2

1

6

Points to ponder

Physics/Engineering– How to generate such beam– To what extant distortion is acceptable

• No perfect Ellipsoidal beam can be generated • Any perfect ellipsoidal beam will be distorted

– Space charge effect at electron emission– RF and Schottky effect– No optics are perfect– …..

Economics– Cost versus benefit

• 40% to 50% reduction of emittance for LCLS, 15% shorter saturation length will result (Limborg),

• from total 33 undulators to 29, save on undulators alone: 4*$474 k (P. Hartog, ANL).

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Content APS Context: APS ERL upgrade An ellipsoidal beam and its properties How to generate an ellipsoidal beam

– Self evolving– 3D laser pulse shaping

Comparison and Challenges – Accelerating, image/space charge field

Shaping trans plant? References

8

Realization of an Ellipsoid I: Luiten Scheme(A ground breaking work)

Luiten, “How to realize uniform 3-dimensional ellipsoidal electron bunches”, Phys. Rev. Letters 93, 094802 (2004)

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Physical limitations: more details

Cornell DC gun with 500 kV, peak 5MV/m

Bazarov, PRST-AB 8, 034202 (2005)

Laser: 100 fs with parabolic transverse distribution with 1 mm radius

Pro– Easy: Need a short pulse (100 fs)

with initial parabolic transverse distribution, no longi shaping needed

Con– Cannot put too many charges– May lack of control on final beam

sizes

RF gun

DC gun

Luiten

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Realization of an ellipsoidal beam 2: Laser pulse shaping: Advantages: take a full control Difficulties

– Simultaneous evolving longitudinal and transverse profile Existing Methods

– Pulse stacking (Tomizawa, NIMA 557, 117 (2006), and this workshop) and other manipulation (Limbrorg-Deprey, ibid, 106 )

– Cold electron harvesting (Classen, PRL 95, 164801 (2005) ) Pulse tailoring with chromatic aberration (this talk)

– Eliminated method: Pulse stacking by zoned lens, dynamic focusing using Kerr lensing

)(n0.20 0.22 0.24 0.26 0.28 0.30

1.49

1.50

1.51

1.52

1.53

1.54

1.55

Fused silica

n

(m)

t

tBeam

size

11

111)()(

1RR

nf

11

Dynamic focusing effect through Kerr lensing

-2 -1 0 1 2-0.6

-0.3

0.0

0.3

0.6

(a)

t (ps)

z (m

m)

0

0.2

0.4

0.6

0.9

1.1

0

2

4

(b)

r (

m)

-2 -1 0 1 2

0

2

4

(c)

t (ps)

(a) On-axis laser pulse envelope as a function of the defocusing distance; the intensity as a function of time and radius for a pulse without (b) and with the SPM effect (c). The calculation assumes an f=150 mm lens with R=12 mm and d=5 mm. The pulse wavelength is 0.249 nm with m=15 at laser intensity of 5×1011 W/cm2.

(a)

(c)

(b)

Li, Opt Lett, accepted for publication

n(t)=n+n2*I(t), n2=2.3810-16 W/cm2

df ~ dn ~ 1%

d /L/c * dn/dt, for dn=1% and dt=1 ps, L=1 cm, d / =1/3

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3D Laser pulse shaping:phase tailoring and chromatic aberration

)(1

)(0

0 tddn

nftf

Ntf

tw)(

)(

2/12

1)(

TtWtw

2/12

1)(

Ttt

T

tTTtttdttt 1

2

00 sin12

)()(

2/12

0 1)(

TtAtA

Focal length and beam size as a function of frequency

Required beam size as a function of time for ellipsoidal beam

The phase and the amplitude of the pulse are therefore

0.0

0.5

1.0

-2 0 2-100

-50

0

50

100

-0.06 -0.05 -0.04 -0.03 -0.020.0

0.5

1.0

(r

ad)

t (ps)

I (A

rb. u

nits

)

11

111)()(

1RR

nf

Lens formula

13

3D Laser Pulse shaping: Numerical model

Full wave optics (Fresnel diffraction) adapted from Kempe et. al (JOSA B 9, 1158 (1992))

Group velocity dispersion and group velocity delay effect considered up to the second order

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The resulting 3D laser pulse:

An ellipsoidal laser pulse generated vis laser pulse tailoring and the chromatic aberration at the focal plane of a 20 mm diameter zoneplate with focal length of 150 mm. The isosurface plots shows the structure at 0.05, 0.1, 0.15 and 0.2 relative intensity. A zone plate has chromatic aberration similar to a lens.

-8 -6 -4 -2 0 2 4 6 80.0

0.2

0.4

0.6

0.8

1.0

t (ps)

r (m

m)

0

36

72

108

144

180

Li and Chang, FEL 2006

Li and Chang, LINAC 2006

Structure due to group delay in optics

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Performance simulationLongitudinal and transverse emittances

Z (cm)

R (cm)

Ez(MV/m)

Z (cm)

R (cm)

Ez(MV/m) 0 20 40 60 80 100 120

0.5

1.0

1.5

0 20 40 60 80 100 120

0.0

2.0

4.0

6.0

8.0

(a)

Trna

sver

se e

mitt

ance

(mm

mra

d)

Distance (cm)

a b c d e

(b)

Long

itudi

nal e

mitt

ance

(deg

keV

)

Distance (cm)

16

Practical arrangement and challenges

Stretcher

Shaper (Phase and amplitude, can be static)

Compressor

A CPA laser

Image relay to Cathode

0.0

0.5

1.0

-2 0 2-100

-50

0

50

100

-0.06 -0.05 -0.04 -0.03 -0.020.0

0.5

1.0

(ra

d)

t (ps)

I (A

rb. u

nits

)

Spatial shaper

17

A planned bench test for 800 nm

To demonstrate the feasibility– Need zone plate for 800 nm– Do not need amplifier

DAZZLER

Or SLIMOscillator

Delay

Zone plate

Crystal

0.0

0.5

1.0

-2 0 2-100

-50

0

50

100

-0.06 -0.05 -0.04 -0.03 -0.020.0

0.5

1.0

(ra

d)

t (ps)

I (A

rb. u

nits

)

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Content APS Context: APS ERL upgrade An ellipsoidal beam and its properties How to generate an ellipsoidal beam

– Self evolving– 3D laser pulse shaping

Comparison and Challenges – Accelerating, image/space charge field

Shaping transplant? References

19

Comparison with self evolving scheme

Shaping Self-Evolving

Longitudinal size Tunable Fluctuate with charge and accelerating field

Transverse size Tunable Tunable

Longitudinal symmetry Tunable (ideally) Proportional to charge

Charge:Remained to be investigated

Largely tunable due to tunable bunch length, space charge effect can be reduced somewhat

Limited by space charge effect

Tolerance to distortion To be investigated(Optimization)

To be investigated(Optimization)

Tolerance to cathode response time Picosecond for 20 ps pulse: more flexible for cathode choices

None: only metal, low QE

Efficiency (frequency conversion etc)

Low High

Implementation Complicated and can be expensiveLarge bandwidth

Relatively easyPossible optical and cathode damage

20

Challenges and further work

Laser challenge: experiments needed – Bandwidth requirement and flat top input beam– Does phase information survive amplification frequency conversion?

Beam limitation: simulation needed– Integrated optimization with emittance compensation is necessary for

determining the usefulness (BAZAROVAND SINCLAIR Phys. Rev. ST Accel. Beams 8, 034202 (2005))• Charge limitation• Tolerance on beam distortion due to high charge and other effect• Effect of sub structures

Comparison with self evolving scheme is necessary Adaptive set up

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Content APS Context: APS ERL upgrade An ellipsoidal beam and its properties How to generate an ellipsoidal beam

– Self evolving– 3D laser pulse shaping

Comparison and Challenges – Accelerating, image/space charge field

Shaping transplant?

22

Shaping transplant? Sum frequency modulation

Frequency mixing crystal

Long, narrow bandwidth laser pulse, 2

(Spatially shaped to flat top)

Shaped Ellipsoidal pulse, 1Shaped Ellipsoidal pulse, 2 +1

The problem: – Pulse too long for self evolving except for a tight cigar beam– Band width too small for direct shaping

Solution: mixing with a shaped laser– Seed beam (shaped) doe not have to be very intense: Poling crystal

for high conversion efficiency– Need very detail evaluation to determine if it is practical

23

Content APS Context: APS ERL upgrade An ellipsoidal beam and its properties How to generate an ellipsoidal beam

– Self evolving– 3D laser pulse shaping

Comparison and Challenges – Accelerating, image/space charge field

Shaping transplant? Zone lens for 3D

24

3-D laser pulse shaping by zoned lens

A zoned lens is a lens with circular zones like a Fresnel lens Temporal shaping: by controlling the thickness of each zone and its

transmission Transverse shaping: shape and transmission of each zone

A Fresnel lens

25

Timing control

f

sn

rn

tn: zone effective thicknessrn: zone radiusf: focal lengthpn: optical path of each zone

nnn sfrp 22

t

tn

26

Intensity profile control

f

sn

rn

Fn: Total fluxdn: Zone size, controllableIn: input laser distribution, controllableTn: segment optical transmission, controllable

)()(2 rTrIdrF nnnnn

tdn

27

Spatial profile: ideally

f

sn

rn

dn

By tailoring the shape of each zone, it is possible to control the size and the shape of the beam at the focus, maybe flattop disks with different sizes.

t

28

Preliminary results on zoned lens: Temporal shaping is straight forward A 9-zone lens with an 1.5 ps. 249 nm Gaussian pulse with 150 mm focal

length

Time, 18 ps

r, 8

mic

ron

Original Add delay for each zone Shuffling

29

When off focus by 1.5 mm

R, 0

-0.1

6 m

m

R, 0

-0.0

8 m

m

R, 0

-0.0

8 m

m

Just off focus Tuning the focii Polarization separation

Spatial shaping is still difficult