1. 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 Li Advanced Photon Source, Argonne National Laboratory ylli@aps.anl.gov

2. 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. 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. 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 shaping Non interceptive, single short measurement of the beam profile Laser technique provides the highest resolution so far Timing must adequate Laser remains an option

5. 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

6. 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).

7. 7 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. 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)

9. 9 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

10. 10 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 t t Beam size

11. 11 Dynamic focusing effect through Kerr lensing (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 5×10 11 W/cm 2. (a) (c) (b) Li, Opt Lett, accepted for publication n(t)=n+n 2 *I(t), n 2 =2.38  10 -16 W/cm 2 df ~ dn ~ 1% d  /  L/c * dn/dt, for dn=1% and dt=1 ps, L=1 cm, d  /  =1/3

12. 12 3D Laser pulse shaping: phase tailoring and chromatic aberration 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 Lens formula

13. 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

14. 14 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. Li and Chang, FEL 2006 Li and Chang, LINAC 2006 Structure due to group delay in optics

15. 15 Performance simulation Longitudinal and transverse emittances

16. 16 Practical arrangement and challenges Stretcher Shaper (Phase and amplitude, can be static) Compressor A CPA laser Image relay to Cathode Spatial shaper

17. 17 A planned bench test for 800 nm To demonstrate the feasibility –Need zone plate for 800 nm –Do not need amplifier DAZZLER Or SLIM Oscillator Delay Zone plate Crystal

18. 18 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. 19 Comparison with self evolving scheme ShapingSelf-Evolving Longitudinal sizeTunableFluctuate with charge and accelerating field Transverse sizeTunable Longitudinal symmetryTunable (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 distortionTo be investigated (Optimization) To be investigated (Optimization) Tolerance to cathode response timePicosecond for 20 ps pulse: more flexible for cathode choices None: only metal, low QE Efficiency (frequency conversion etc) LowHigh ImplementationComplicated and can be expensive Large bandwidth Relatively easy Possible optical and cathode damage

20. 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

21. 21 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. 22 Shaping transplant? Sum frequency modulation Frequency mixing crystal Long, narrow bandwidth laser pulse,  2 (Spatially shaped to flat top) Shaped Ellipsoidal pulse,  1 Shaped 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. 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. 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. 25 Timing control f snsn rnrn t n : zone effective thickness r n : zone radius f: focal length p n : optical path of each zone t tntn

26. 26 Intensity profile control f snsn rnrn Fn: Total flux d n : Zone size, controllable I n : input laser distribution, controllable T n : segment optical transmission, controllable t dndn

27. 27 Spatial profile: ideally f snsn rnrn dndn 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. 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 micron Original Add delay for each zone Shuffling

29. 29 When off focus by 1.5 mm R, 0-0.16 mm R, 0-0.08 mm Just off focus Tuning the focii Polarization separation Spatial shaping is still difficult