An X-Ray FEL Oscillator with ERL-Like E-Beams

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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

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Next Generation X-Ray Sources

• High-gain FELs (SASE) will provide an enormous
  jump in peak brightness from the 3rd generation
  sources
• Intense, low emittance bunches Q 1 nC, IP
  several kA, exn 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
• exn 0.1 mm-mr, Q20 pC, t2ps, frep1.3 GHz, IAV
  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
  l 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)

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ERL Plans Cornell, KEK/JAERI , APS II
Cornell ERL
APS II concept
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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 1984.
• 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)

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Current and Future X-Ray Sources
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Electron Beam Qualities Enabling X-FELO

• Laser-driven DC gun being developed at Cornell
  for frep1.3 GHz
• Thermionic cathod and bunch manipulation for
  frep1-100 MHz
• sDE1.4 MeV, tel2ps

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Principles of an FEL Oscillator

• Small signal gain G DPintra/Pintra
• Start-up (1G0) R1 R2 gt1 (R1 R2 mirror
  reflectivity)
• Saturation (1Gsat) R1 R2 1
• Synchronism
• Spacing between electron bunches2L/n ( L
  length of the cavity)

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Bragg Mirrors

• Requiring total loss per pass to be lt 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 T40K

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Backscattering Reflectivity's for Sapphire and
Diamond ( Perfect Crystals)
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Diamond C(220) ReflectionE04.92 keV
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Sapphire Reflectivity _at_ 14.3 keV
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Sapphire Crystal Quality
Back-reflection topographs of HEMEX sapphire
wafers cut from different boules show different
dislocation densities (a) 103 cm-2, (b) much
lower dislocation density. Sample area
illuminated by x-rays is 2.1 x 1.7 mm2
Chen, McNally et al., Phys. Stat. Solidi. (a) 186
(2001) 365
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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)

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Options for XFEL-O Cavities (Y. Shvydko)
Al2O3xAl2O3 _at_14.3 keV RT0.87, Gsat15,
T3 CxCxmirror _at_12.4 keV RT0.91, Gsat10,
T4 Al2O3xAl2O3xSiO2_at_ 14.4125 keV RT0.82,
Gsat22 , T4
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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 ZRayleigh b
• Steady state GENISIS simulation for general
  intra-cavity power to determine saturation power
  (Sven Reiche)

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Saturation As circulating power increases, the
gain drops and reaches steady state when gainloss
E7 GeV, ?1Å Q19 pC (Ip3.8A), Nu3000 Mirror
reflectivity90 Saturation power19 MW
E7 GeV, ?1Å Q40 pC (Ip8 A), Nu3000 Mirror
reflectivity80 Saturation power21 MW
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Examples XFEL-O
Electrons are not focused but matched to the
optical mode determined by cavity configuration
st2 ps, sDE1.4 MeV, ZRb1012 m
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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

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Start-up Simulation (Reiche)
Pessimistic case
Ip4 A, mirror loss10 Effective net gain6
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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 Gmono(w)
• Eigenmode Gauss-Hermite function
• topt(2teltM)1/2/g1/4 tM1/(2swM) swMmirror
  bandwidth
• Amplitude growth rate of the fundamental mode
• L00.5(g-a)-(0.5u/tM)2-0.5g1/2(tM/tel) upulse
  displacement
• hswM2.8 meV, tel2 ps
• Bandwidth of the fundamental mode
• hswopt2.3 meV ?De/e2 10-7!!

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Tolerances

• Reduction in gainlt1
• Pulse to pulse overlap ult20 fs
• Cavity detuning (tolerance on cavity length)lt3mm
• Change in optical axislt0.1mode angle
• angular tolerance of crystals lt8 nrad
• LIGO technology?

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X-FELO Repetition Rate

• frep 1.5 MHz when one x-ray pulse stored in 100
  m optical cavity
• I60 mA (Q40 pC), P0.4 MW ?May not need ERL
• frep100 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 2 10-5
• These problems may be solved by increasing the
  minimum recovery energy to 30 MeV (higher than
  usual 10 MeV)

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Tunability with two crystals

• Tuning range is very limited (lt2 10-6) due to the
  need to keep 2f lt 4 mr for high reflectivity of
  grazing incidence miror

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Tunable Cavity Scheme (KJK)

• For tuning increase H and decrease S keeping the
  round trip path length the same
• L100m, H01m, S00.1m?De/e5 10-4 (Hmax3.3 m)
• L100m, H01m, S02m ?De/e1 (Hmax14.3 m)
• With this scheme, diamond may be used for most
  cases
• With 2fmax60 degree (444) for 12ltelt15 keV
• (220) for 5ltelt6 keV

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Gun technologies
SCSS CeB6, thermionic, pulsed gun
Cornell laser-driven 750 kV, DC
LBL 50 MHz, laser driven
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Ultra-Low Emittance lt50 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 6th 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-06-093)

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Performance of X-FELO

• Spectral range 5 keVlteglt20 keV
• Full transverse and temporal coherence in 1 ps
  (rms)
• (Dn/n)FWHM2.5 10-7 hDn2 meV (rms)
• Tunable
• 109 photons ( 1 mJ) /pulse
• Peak spectral brightnessLCLS
• Rep rate 1-100 MHz ? average spectral brightness
  (1026 -1029) /(mm-mr)2(0.1BW)
• The average spectral brightness is higher by a
  factor of
• 105-107 than other future light sources
  considered so far, ERL-based or high-gain
  FEL-based
• Current APS about 100-1000 less than ERL

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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.
• Presently _at_ APS 5 109 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 1015 photons/s/meV (14.4
  keV) with 107 Hz repetition rate.

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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)