An X-Ray FEL Oscillator with ERL-Like E-Beams Kwang-Je Kim ANL & Univ. of Chicago May 23, 2008 Seminar at Wilson Lab Cornell University

KJK, Cornell, May 23, Next Generation X-Ray Sources High-gain FELs (SASE) will provide an enormous jump in peak brightness from the 3 rd generation sources –Intense, low emittance bunches; Q= 1 nC, I P ~ several kA,  x n ~ 1 mm-mr –LCLS, European X-FEL, SCSS, Fermi,.. Multi-GeV Energy Recovery Linacs (ERLs) will provide high average brightness with low intensity, ultra-low emittance bunches at high rep rate –  x n ~ 0.1 mm-mr, Q=20 pC,  ~2ps, f rep ~1.3 GHz, I AV up to 100 mA –Cornell, MARS, KEK-JAERI, APS,.. ERLs have so far been regarded only as a spontaneous emission source We show that an X-ray FEL Oscillator (X-FELO) for ~1-Å based on high energy ERL beams is feasible with peak spectral brightness comparable to and average spectral brightness much higher than SASEs (to be published in PRL)

KJK, Cornell, May 23, ERL Plans: Cornell, KEK/JAERI, APS II APS II concept Cornell ERL

KJK, Cornell, May 23, X-Ray Cvities for Oscillators: History X-ray FEL Oscillator (XFEL-O) using Bragg reflector was first proposed by R. Colella and A. Luccio at a BNL workshop in This was also the workshop where a high-gain FEL(SASE) was proposed by R. Bonifacio, C. Pellegrini, and L. M. Narducci X-Ray optical cavities to improve the performance of high- gain FELs have been studied recently: –Electron out-coupling scheme by B. Adams and G. Materlik (1996) –Regenerative amplifier using LCLS beam ( Z. Huang and R. Ruth, 2006)

KJK, Cornell, May 23, Current and Future X-Ray Sources

KJK, Cornell, May 23, Electron Beam Qualities Enabling X-FELO Laser-driven DC gun being developed at Cornell for f rep =1.3 GHz Thermionic cathod and bunch manipulation for f rep =1-100 MHz   E =1.4 MeV,  el =2ps Q (nC)I p (A)  nx (10 -7 m) Pessimistic Cornell High-Coherence Mode Optimistic

KJK, Cornell, May 23, Principles of an FEL Oscillator Small signal gain G=  P intra /P intra –Start-up: (1+G 0 ) R 1 R 2 >1 (R 1 & R 2 : mirror reflectivity) –Saturation: (1+G sat ) R 1 R 2 =1 Synchronism –Spacing between electron bunches=2L/n ( L: length of the cavity)

KJK, Cornell, May 23, Bragg Mirrors Requiring total loss per pass to be < 20%, the reflectivity of each Bragg mirror should be well over 90% Possible crystal candidates are –Diamond Highest reflectivity & hard ( small Debye-Waller reduction) Multiple beam diffraction in exact backscattering needs to be avoided ( can use as a coupling mechanism?) –Sapphire High reflectivity without multiple beam diffraction Small thermal expansion coefficient and large heat conductivity at T=40K

KJK, Cornell, May 23, Backscattering Reflectivity's for Sapphire and Diamond ( Perfect Crystals)

KJK, Cornell, May 23, Diamond C(220) Reflection:E 0 =4.92 keV

KJK, Cornell, May 23, Sapphire 14.3 keV

KJK, Cornell, May 23, Sapphire Crystal Quality Back-reflection topographs of HEMEX sapphire wafers cut from different boules show different dislocation densities: (a) 10 3 cm -2, (b) much lower dislocation density. Sample area illuminated by x-rays is 2.1 x 1.7 mm 2 Chen, McNally et al., Phys. Stat. Solidi. (a) 186 (2001) 365

KJK, Cornell, May 23, X-Ray Focusing Focusing is required to adjust the mode profile Bending the Bragg mirrors for a desired curvature (~50m) may destroy high-reflectivity Possible options: –Grazing-incidence, curved-mirrors for non backscattering configuration –Compound refractive lenses of high transmissivity can be constructed ( B.Lengeler, C. Schroer, et. Al., JSR 6 (1999) 1153)

KJK, Cornell, May 23, Options for XFEL-O Cavities (Y. Shvyd’ko) Al 2 O 3 xAl 2 O keV R T =0.87, G sat =15%, T=3% 12.4 keV RT=0.91, G sat =10%, T=4% Al 2 O 3 xAl 2 O 3 xSiO keV RT=0.82, G sat =22 %, T=4%

KJK, Cornell, May 23, Gain Calculation Analytic formula for low signal including diffraction and electron beam profile –Sufficiently simple for Mathematica evaluation if electron beam is not focused, distributions are Gaussian, and Z Rayleigh =  * Steady state GENISIS simulation for general intra- cavity power to determine saturation power (Sven Reiche)

KJK, Cornell, May 23, Saturation: As circulating power increases, the gain drops and reaches steady state when gain=loss E=7 GeV, λ=1Å Q=19 pC (Ip=3.8A), N u =3000 Mirror reflectivity=90% Saturation power=19 MW E=7 GeV, λ=1Å Q=40 pC (Ip=8 A), N u =3000 Mirror reflectivity=80% Saturation power=21 MW

KJK, Cornell, May 23, Examples XFEL-O Å)Å) E (GeV) Q (pC)  nx (10 -7 m) K U (cm) NUNU G 0 (%) R T (%) P sat (MW)   =2 ps,   =1.4 MeV, Z R =  *=10~12 m Electrons are not focused but matched to the optical mode determined by cavity configuration

KJK, Cornell, May 23, Simulation of Oscillator Start-up Time-dependent oscillator simulation using GENO (GENESIS for Oscillator) written by Sven –Taking into account FEL interaction (GENESIS), optical cavity layout, and mirror bandwidth (Reiche) To reduce CPU –Follow a short time-window (25 fs) –Track a single frequency component for all radiation wavefronts since other components are outside the crystal bandpass –Even with these simplifications, one pass takes about 2 hr

KJK, Cornell, May 23, Start-up Simulation (Reiche) Pessimistic case I p =4 A, mirror loss=10% Effective net gain~6%

KJK, Cornell, May 23, Super-mode Analysis (adapted from G. Dattoli, P. Elleaume) Describes gain and spectrum narrowing in the exponential gain regime taking into account the profiles of I(z-ct) and G mono (  ) Eigenmode: Gauss-Hermite function –  opt =(2  el *  M ) 1/2 /g 1/4 :  M =1/(2   M ) :   M =mirror bandwidth Amplitude growth rate of the fundamental mode  0 =0.5(g-a)-(0.5u/  M ) g 1/2 (  M /  el ): u=pulse displacement h   M =2.8 meV,  el =2 ps Bandwidth of the fundamental mode –h   opt =2.3 meV   = !!

KJK, Cornell, May 23, Tolerances Reduction in gain<1% –Pulse to pulse overlap u<20 fs –Cavity detuning (tolerance on cavity length)<3  m Change in optical axis<0.1*mode angle –angular tolerance of crystals <8 nrad LIGO technology?

KJK, Cornell, May 23, X-FELO Repetition Rate f rep = 1.5 MHz when one x-ray pulse stored in 100 m optical cavity –I=60  A (Q=40 pC), P=0.4 MW  May not need ERL f rep =100 MHz with ERL? –Thermal loading on crystals is tolerable (probably) –Electron rms energy spread increases from 0.02 % to 0.05% –With increased energy spread, the loss in the ERL return pass becomes –These problems may be solved by increasing the minimum recovery energy to 30 MeV (higher than usual 10 MeV)

KJK, Cornell, May 23, Tunability with two crystals Tuning range is very limited (< ) due to the need to keep 2  < 4 mr for high reflectivity of grazing incidence miror L 22 Grazing Incidence Mirror Crystal H

KJK, Cornell, May 23, Tunable Cavity Scheme (KJK) For tuning; increase H and decrease S keeping the round trip path length the same –L=100m, H 0 =1m, S 0 =0.1m   = (H max =3.3 m) –L=100m, H 0 =1m, S 0 =2m   =1% (H max =14.3 m) With this scheme, diamond may be used for most cases: –With 2  max ~60 degree: (444) for 12<  <15 keV –(220) for 5<  <6 keV S A B CD H 22 L

KJK, Cornell, May 23, Gun technologies SCSS: CeB6, thermionic, pulsed gun LBL 50 MHz, laser driven Cornell laser-driven 750 kV, DC

KJK, Cornell, May 23, Ultra-Low Emittance <50 MHz Injector (P. Ostroumov, Ph. Piot, KJK) Use a small diameter thermionic cathode to extract low emittance beam Provide 500 kV extracting voltage using low frequency ~50 MHz room temperature RF cavity Using chicane and slits form a short ~ 1 nsec bunch Remove energy modulation by a 6 th harmonic cavity Use a pre-buncher an booster buncher to form low longitudinal emittance of the bunched beam Accelerate to ~50 MeV using higher harmonic SC cavities Use an RF cosine-wave chopper to form any required bunch repetition rate between 1 MHz and 50 MHz. (ANL Invention Application, IN )

KJK, Cornell, May 23, Performance of X-FELO Spectral range: 5 keV<   <20 keV Full transverse and temporal coherence in ~1 ps (rms) –  /  FWHM = ; h  =2 meV (rms) Tunable 10 9 photons (~ 1  J) /pulse –Peak spectral brightness~LCLS Rep rate MHz  average spectral brightness ( ) #/(mm-mr) 2 (0.1%BW) The average spectral brightness is higher by a factor of – than other future light sources considered so far, ERL- based or high-gain FEL-based –Current APS about less than ERL

KJK, Cornell, May 23, Science Drivers for XFEL-O Inelastic x-ray scattering (IXS) and nuclear resonant scattering (NRS) are flux limited experiments! Need more spectral flux in a meV bandwidth! Undulators at storage rings generate radiation with ≈ 100−200 eV bandwidth. Only ≈ 10 −5 is used, the rest is filtered out by meV monochromators. APS: ≈ 5 × 10 9 photons/s/meV (14.4 keV) XFEL-O is a perfect x-ray source for: –high-energy-resolution spectroscopy (meV IXS, neV NRS, etc.), and –imaging requiring large coherent volumes. –Expected with XFEL-O ≈ photons/s/meV (14.4 keV) with 10 7 Hz repetition rate.

KJK, Cornell, May 23, Concluding Remarks A X-FELO around 1-Å is feasible with high-quality e- beams contemplated from future ERLs However, the rep rate of an X-FELO can be 100 MHz or lower to 1 MHz  Injector may be less challenging An X-FELO is new type of future light sources ( in addition to high-gain FELs and ERLs)