Promises and Challenges for X-Ray FEL Oscillators

1. Promises and Challenges for X-Ray FEL Oscillators Kwang-Je Kim ANL and U of C X-Ray FEL WS October, 23-25, 2008 LBNL

2. An X-Ray FEL Oscillator (XFELO) • A Concept for XFELO was first proposed by R. Colella and A. Luccio , Opt. Comm. 50, 41 (1984) • Use of x-ray cavity for improving high-gain FEL coherence was considered by B. Adams and G. Materlik (1997) and Z. Huang and R. Ruth (PRL, 96, 144801, 2006) • With the ultralow emittance beams, such as studied for ERLs, an XFELO was shown to be feasible ( KJK, Y. Shvyd’ko, and S. Reiche, PRL, 100, 244802 (2008)

3. XFELO versus SASE for Hard X-Rays • In SASE, initial noise is amplified in a single passby a million-fold Intense e-bunches, marginal temporal coherence (10-3) , & pulsed operation • In XFELO, an optical pulse is trapped in an x-ray cavity consisting of narrow-bandwidth, high-reflectivity crystals, interacting with electron bunches over several hundred passes, spectrum being filtered in each pass Low intensity e-bunches, transform-limited temporal coherence (10-7) & CW operation

4. Example Cases of SASE (LCLS) and XFELO

5. Brightness of Current and Future X-ray Sources 101 102 103 104 105 Energy (eV) Scientific Needs for Future X-Ray Sources in the US: A White Paper October 2008(SLAC-R-910/LBNL-1090E)

6. High spectral brightness, 1 meV bandwidth, and 1 MHz rep rate will “Revolutionize” known techniques and find new applications • High resolution spectroscopy • Inelastic x-ray scattering • Moessbauer spectroscopy • Nuclear diffraction and imaging • Hard x-ray photoemission spectroscopy • Bulk-sensitive Fermi surface study • Coherent imaging with near atomic resolution (~1 nm) • Smaller focal spot with the absence of chromatic aberration

7. Diamond Reflectivity & Bandwidth(Y. Shvyd,ko) • High reflectivity ~ 99% for 5-30 keV • Needs perfect crystals Small volumes from large samples • High thermal conductivity and low expansion coeff at 100K • Effect of heat loading may be small • Multiple reflection for C can be avoided by slightly off from exact backscattering and glancing angle mirrors

8. Electron Beam Requirements • The requirements for XFELO beams • Normalized rms emittance < 0.1 mm-mr • Bunch charge < 40 pC • Bunch length (rms)= 0.2-2 ps (transform-limited spectral width << mirrror bandwidth)  Peak current >10 A • Energy spread < 1.4 M eV • Bunch rep rate > 1 MHz • The ERL injector in high coherence mode (Cornell) satisfies the requirements • The LCLS injector @ low charge mode demonstrated the bunch quality performance • A novel type of injector is being developed

9. Gain and saturation • Without electron beam focusing, gain can be analytically computed taking into account energy spread, emittance, and diffraction (KJK, 1992) • Gain is optimum when bz~ZR~Lu/(2p) • Gain decreases as intra cavity power increases • Saturation when gain=loss G Psat Intra-cavity power

11. Simulation • GENESIS (S. Reiche) took 1 month to simulate evolution to saturation • “One-dimensional” FEL code with z-dependent radiation-beam coupling (R. Lindberg) • Eliminates transverse dimension by integrating over the unperturbed electron orbits and by using the Gaussian laser mode of largest FEL gain • Bench-marked against GINGER and GENSIS for single pass gain • Used for initial characterization of the gain and the longitudinal radiation profile from initial start-up to nonlinear saturation • GINGER (W. Fawley, R. Lindberg, Y. Shvyd’ko) • Implemented the Bragg crystal frequency response for each pass • Begun systematic analysis of transverse radiation characteristics and the initial start-up from noise

12. The Complex Amplitude Reflectivity of a Crystal • The w -dependent phase shift is due to the fact that the effective reflecting surface is inside the crystal (extinction depth) • The angular dependence of the reflectivity can be neglected in most cases • One thin (50 m) for 4% out-coupling and one thick (200 m) for full reflection

14. Some Examples ( R. Lindberg) For all cases: ex=0.2 mm-mr, sE=1.4 MeV, st(electron)=1 ps, undulator gap=5mm

15. Tunable X-ray Cavity • Two crystal scheme is not tunable since q should be kept small for high reflectivity of the grazing incidence mirror • A four crystal scheme is tunable by changing h and d2, keeping the pass length constant, and by appropriately rotating the crystals so that the incidence and reflection angles are the same. R. M.J.Cotterill, APL, 403,133 (1968), KJK(2008)

16. Optics Design of the Cavity Rayleigh lengths Z1 and Z2: Change of w1 due to crystal angular error Dq:

17. An example: • Z1=10 m to maximize gain for Lu=60 m • Z2=250 m to reduce the angular divergence at crystals by a factor of 5 • X1X2=0.1 so that the cavity is stable • f=51.3 m, l1=1.02 m, l2=75.4 m • Choose h=d2=1 m d1=12.06 m • Require the optical axis displacements Dx and Dx’ at W1 are 1/10 of mode rms size and angle • Dq < 20 nr ( tight but better than two crystal case considered before) May be satisfied via null detection feedback (import LIGO technology)

18. X-ray lenses • Compound Refractive Lenses (CRLs) is ideal if it can be made from single crystal Be. However, loss is large with currently available polycrystalline Be due to small angle scattering from grain boundaries. • Grazing incidence mirrors ( common in x-ray beam line of an SR facility) can provide focusing with small loss < 4%. • The tolerance in slope error from geometrical optical consideration is 0.25 mr, appears to be feasible. • Wave optics calculation is planned

19. Repetition Rate • frep= 1 MHz when a single x-ray pulse stored in 150 m optical cavity (<< 3rd generation SR & ERL, >> high-gain FEL) • X-ray power incident on crystal, ~100 W on 70 m rms radius, appears to be manageable for diamond crystals • May need to cool to 100 K to increase thermal conductivity (x10) and decrease the thermal expansion coefficient (x10) • Electron beam power is low: • I=40 mA (Q=40 pC), Pbeam=0.3 MW Energy recovery useful but not mandatory • frep=100 MHz with ERL? • Heating of crystals is an issue • Electron rms energy spread increases from 0.02 % to 0.05%

20. A Novel Injector Design Using Old Concept(P. Ostroumov, Ph. Piot, KJK) • Use thermionic cathode rather than photocathode • Low emittance demonstrated for pulsed DC gun with CeB6 cathode[1] • Avoid difficulties with photocathode drive laser in stability & uniformity • Avoid space charge degradation at low energy • Use a VHF cavity considered for photocathode application[2], cut out a short portion (0.5 ns) of each period, and condition the pulse [1] K. Togawa, et al., PRSTAB 10, 020703(2007) [2] J. Staples, et al.,PAC 2007

21. An Ultra-Low Emittance CW Injector 1 2 3 4 5 6 7 8 9 10 11 12 13

22. Options for Accelerator Configuration • Due to ultra-low emittance matched to hard x-rays, the electron energy for an XFELO can be significantly lower than SASE of the same wavelength • 12 keV: 7 GeV for XFELO and 15 GeV for SASE • The magnetic field in undulator is also lower • An XFELO can be inserted in a high energy ERL • With small bunch charge (< 50 pC) and 1MHz rep rate, energy recovery is not necessary; A straight SCRF linac will be a simpler option • To reduce the length/cost, e-beams may be recirculated a few times

23. An XFELO Facility Using a CW Recirculating SCRF Linac.

24. Ultimate Next-Generation CW X-ray Facility Providing Both High-Coherence XFELO & Ultra-Short Pulse (10 fs) Low Intensity SASE (10-3 of LCLS)

25. Conclusions • An XFELO provides fully coherent x-ray beams with meV energy resolution in the spectral range 5-30 keV (could be beyond, also harmonics) with average brightness several orders of magnitudes higher than SASE • XFELO uses low intensity electron bunches at low rep rate (1 MHz) ultra-low emittance matched to x-ray emittance electron energy can be small (~7 GeV for 1 Å) low current, low power beam CW, recirculating SCRF accelerator • The cost for a dedicated XFELO facility based on CW recirculating SCRF linac is modest • Several R&D items: perfect crystals, heat loading, focusing elements, stability & stability,..