Transcript Slides
X-Ray Free-Electron Laser Amplifiers and
Oscillators for Materials and Fundamental
Research
Kwang-Je Kim
ANL and U. of Chicago
ICABU Meeting
November 12, 2013
DaeJeon, Korea
Relativity and Synchrotron Radiation
Electron velocity v c; 𝜸 = 𝟏/ 𝟏 −
𝒗 𝟐
𝒄
g ~ 2000× electron energy [GeV]
– APS; Ee=7 GeV, g~ 14,000!!
Emission within an angle ~1/ g from the electron
motion
– about 70 mrad for APS
About a ≅1/137 photons per 1/g trajectory bending
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More efficient x-ray production with an “undulator”
Compact undulator with permanent magnets
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Radiation by one electron in Nu period undulator
The e- emits EM wave in the forward direction due to its x-acceleration.
Consider the wave fronts from successive undulator periods:
lu
K/g
e
E-field direction
l1
Nul1
The e- is slower since (1) c > v c(1-1/2g2), and (2) its trajectory is curved.
Thus, the EM wave slips ahead of the e- in one undulator period by a
distance l1=wavelength:
l1=lu(1+K2/2)/2g2 , e1[keV]=12.4/l1[Å]
After travelling Nu periods of the undulator, an Nu-cycle wave-train is
formed:
Dzrad = Nul1 , Dw/w =1/Nu
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An Nu-cycle wave-train
c
Length of the train Dz=lNU
𝟐
Spectral intensity 𝒅𝑾(𝝎)/𝒅𝝎~ 𝑬(𝝎) ~ (sin x/x)2
x=pNU(w- w1)/w, peaked around w1 with relative
bandwidth Dw/w ~ 1/NU
Dz ×Dw/w ~ l1 ( equivalent to pure state in QM)
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Undulator radiation from electrons
randomly distributed in a “bunch”
Normally Dzel >> Nul1 “Chaotic light”
Each wavetrain has random phase intensity ∝ 𝑵𝒆
Spectral property is the same as that of a single
electron Dw/w=1/Nu
Temporal phase space area Wz ~(Dw/w) Dzel
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Transverse coherence
The phase space area Wx= (DxDf) of incoherent e-beam
can be divided into smaller and smaller area
With coherent beam the phase space area Wx cannot be
divided to area smaller than DxDf =l/2
Undulators are placed in the straight sections of low
emittance, high current electron storage rings “the
third generation light source”
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Amplification in the presence of e-beam
When the EM wavelength satisfies the undulator condition, an electron
sees the same EM field in the successive period sustained energy
exchange
A0
A1
A2
A3
l1
An e- arriving at A0 loses energy to the field (ev E <0). Similarly the eat distance nl1, n=1,2,… also loses energy. However, those at l1(1/2 +n)
away gain energy.
The electron beam develops energy modulation (period length l1).
Higher energy electrons are faster density modulation develops
Coherent EM of wavelength l1 is generated “Free electron laser”
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SASE: Initial undulator radiation is amplified
to intense, quasi-coherent radiation
Saturation
Exponential
Gain Regime
Transverse mode
z = 25 m
z = 37.5 m
Undulator Regime
z = 50 m
z = 90 m
Electron Bunch
Micro-Bunching
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SASE: Microbunching in each coherent
region
# of coherent regions= nlc
# of electrons in one coherent region = Nlc =Ne/nlc
Radiation intensity = (Nlc)2nlc= (Ne)2/nlc =Ne Nlc
X-ray FELs are driven by linear accelerators
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An FEL for x-rays requires high e-beam
qualities not achievable from storage
rings photo-cathode gun & a linear acc
BNL type LCLS S-band RF
Photocathode
KEK/JAERI DC gun
LBNL 180 MHz RF Photocathode
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Hard X-Ray FELs in Operation & Under
Construction
LCLS-I, II 2009, 2018
14.5 GeV, 120 Hz NC
XFEL 2015
17.5 GeV, 3000 x 10 Hz SC
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SACLA 2011
8.5 GeV, 60 Hz NC
PAL XFEL 2015
10 GeV, 100 Hz NC
SWISS FEL 2017
5.8 GeV, 100 Hz
NC
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Various R&D programs are in progress to
enhance the performance of high-gain XFEL
SASE is temporally incoherent fluctuation in spectrum and
intensity
Coherent soft x-rays (l< 1 nm) via seeding
– Laser HHG, Cascaded HGHG, EEHG, self-seeding
Self-seeding for hard x-rays
Other spectrum enhancing schemes
– iSASE, pSASE, two color generation
LCLS-II will incorporate CW capability
by a super-conducting linac
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Free Electron Laser Oscillator
A low-gain device with high Q optical cavity
Optical pulse formed over many electron passes
Difficult for x-rays
– Electron beam qualities
– High-reflectivity normal incidence mirror
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X-Ray FEL Oscillator (XFEL-O)
An FEL oscillator is feasible in hard x-ray region by using
Bragg mirrors
– R. Collela and A. Luccio, 1983; KJK, Y. Shvyd’ko, and S. Reiche, 2008
Tuning is possible with a four mirror configuration
– R. M.J.Cotterill, (1968) KJK & Y. Shvyd’ko (2009)
Ultra-high spectral resolution ( meV) with storage ring like
stability
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Example Parameters
Electron beam:
– Energy 6 GeV, Bunch charge ~ 25-50 pC low intensity, Bunch length
(rms) 1 (0.1 ps) Peak current 20 (100) A, Normalized rms emittance
0.2 (0.3) mm-mr, rms energy spread ~ 210-4 , Constant bunch rep rate @ ~1
MHz
Undulator:
– Lu= 60 (30) m, lu ~2.0 cm, K=1.0 – 1.5
Optical cavity:
– 2- or 4- diamond crystals and focusing mirrors
– Total round trip reflectivity > 85 (50) %
XFELO output:
– 5 keV w 25 keV
– Bandwidth: Dw/w ~ 1 (5) 10-7 ; rms pulse length = 500 (80) fs
– # photons/pulse ~ 1109
– Rep rate ~ a few MHz(limited by crystal heat load and damage)
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Diamond is the best material. The tolerance on optical
element placement (10 nr), and R. & fig. errors for
focusing mirrors appear feasible.
Null feedback on HRM to 50 nr
High heat diffusivity at < 100K
Yamauch, JTEC, R~ 99%, fig error< 1 mr
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Damage issue of diamond crystals for
XFELO cavity
Power density on XFELO
crystal
– 1 kW/mm2
Power density for APS
HHL crystal
Power density of
focused beam for ESRF
experiment in 1994
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XFELO applications
High resolution spectroscopy
– Inelastic x-ray scattering
Mössbauer spectroscopy
– 103/pulse, 109/sec Moessbauer gs (14.4 keV, 5 neV BW)
X-ray photoemission spectroscopy
– Bulk-sensitive Fermi surface study with HX-TR-AR PES
X-ray imaging with nm resolution
– Smaller focal spot with the absence of chromatic aberration
picosecond time resolution
A second user WS was held at POSTECH in Feb 2013
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Nuclear-resonance-stabilized XFELO(B.W.
Adams and K.-J. Kim, to be published)
The XFEL-O output pulses are copies of the same circulating
intra-cavity pulse By stabilizing cavity RT time to less than
0.01l/c, the spectrum of XFELO output becomes a comb
The extreme-stabilized XFEL-O will establish an x-ray-based
length standard and have applications in fundamental physics
such as x-ray Ramsey interferometer to probe quantum gravity,
etc.
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PossibleAccelerator
system
Injector for XFELO is available from ERL research
The 17GeV pulsed Euro XFEL can be operated 7GeV CW
A 2-loop, 3 pass system using 25 CEBAF C-100
cryomodule for 2.3 GeV acceleration can fit CEBAF
tunnel for multi-XFELO operation
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Legend of evolving bright & coherent xray sources
Brightness=
invariant measure=
# of Photons/phase
space volume
Phase space volume
= Wx Wy Wz
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