Linac Based Photon Sources: XFELS Coherence Properties J. B. Hastings Stanford Linear Accelerator Center
Coherent Synchrotron Radiation Coherent Synchrotron Radiation coherent power N 6 10 9 incoherent power λ 1/3 Wavelength σ z vacuum chamber cutoff Power
Microbunching through SASE Process At entrance to the undulator Exponential gain regime Saturation(maximum bunching) Excerpted from the TESLA Technical Design Report, released March 2001
LCLS at SLAC 1.5-15 Å LCLS 2 compressors one undulator X-FEL based on last 1-km of existing SLAC linac X-FEL based on last 1-km of existing SLAC linac
Peak Brightness Enhancement From Undulator Radiation To SASE #of photons B = (Ω i - phase space area) Ω x Ω y Ω z Undulator SASE Enhancement Factor # of αν photons N lc ~ 10 6 e αν e N lc Ω x Ω y (2πε x ) (2πε y ) ( λ 2 ) 2 10 2 Ω Z ω ω σ Z c =10 3 10 ps ω ω σ Z c =10 3 100 fs compressed 10 2 B 10 23 10 33 10 10 N lc : number of electrons within a coherence length l c
Peak Brilliance of FEL s Peak Brilliance of FEL s photons per phasespace volume per bandwidth X-Ray 1 Å 1 Å 10 6 by FEL gain ~10 9 10 3 by e quality, 10 3 by e quality, long undulators courtesy T. Shintake
Transverse Coherence Spontaneous undulator radiation phase space is the incoherent sum of the electron phase space, consists of many spatial modes X 2πε x x λ/2 (diffraction limit) SASE: higher-order modes have stronger diffraction + FEL gain is localized within the electrons selection of the fundamental mode (gain guiding) Fully transversely coherent even ε x > λ/4 π
Gain Guiding (LCLS) Z=25 m Z=37.5 m Z=50 m Z=62.5 m Z=75 m Z=87.5 m m Courtesy of S. Reiche (UCLA)
Observations at TTF FEL* Statistical fluctuation Transverse coherence after double slit after cross 1 0 Intensity [arb.units] Y [mm] 1 6 4 2 0 2 0 2 2 0 2 X [mm] X [mm] * V. Ayvazyan et al., PRL (2001); Eur. Phys. J. D (2002) 2 0 2
Temporal Characteristics E(t)= j E 0 (t-t j ), t j is the random arrival time of j th e - N u λ E 0 : wave packet of a single e - l c ~ 100-1000 λ < bunch length c l 2 c π λ N σ ω u ρ Sum of all packets E(t) bunch length
Longitudinal Modes Due to noise start-up, SASE is a chaotic light temporally with M L coherent modes (M L spikes in intensity profile) M L bunch length coherence length Its longitudinal phase space is M L larger than FT limit (room for improvement) Integrated intensity fluctuation M L M L is NOT a constant, decreases due to increasing coherence in the exponential growth, increases due to decreasing coherence after saturation) I I 1 =
Manipulating the Longitudinal Phase Space Produce shorter pulses Fix the central wavelength Alter the longitudinal coherence
Manipulating the Longitudinal Phase Space Cut the electron beam: shorter bunches Self-Seed Self seed with chirped electron beam Produce a chirped photon beam: use a monochromator to slice a small time portion of the the beam in energy => a short pulse in time Seed with an external source
σ E /E Magnetic Bunch Compression Magnetic Bunch Compression Ε/Ε Ε/Ε Ε/Ε or over- σ compression z0 σ z0 z chirp z V = V 0 sin(ωτ) z = R 56 Ε/Ε RF RF Accelerating Voltage Path Path Length-Energy Dependent Beamline undercompression σ z z
0.55 fs
Self Seeding, N = 1
Self-seeding option at the TESLA VUV FEL No Seed Seed
Short pulses: Chirped pulse slicing chirp Ε/Ε z SASE FEL Electron bypass Monochromator FEL Amplifier Energychirped electron beam 1 st Undulator 2 nd Undulator Frequency -chirped Input radiation radiation Ε/Ε 10 3 Pulse Slicing Output radiation
Monochromator: short pulse limit 20 10 Monochromator with smaller bandwidth slices out shorter pulse δt out = δt in x δω mono /δω chirp But uncertainty principle gives a limit δω mono x δt out 1/2 Output pulse fwhm (fs) 0 Effect of uncertainty principle (E=8 kev) Effect of slicing (1% chirp on 120fs rms pulse) 0 5 10 15 20 25 Monochromator resolution δω/ω (rmsx10-5 ) Note that if the uncertainty principle dominates, then the output pulse has complete longitudinal coherence For LCLS at 8 kev with 1% chirp, the minimum pulse length is about 3.5 fs fwhm, using a monochromator resolution of 3.3x10-5 rms. Some practical monochromator options: Crystal reflection rms resolution Output pulse fwhm Ge(111) 14x10-5 9 fs Si(111) 5.7x10-5 4.1 fs Si(220) 2.5x10-5 4.1 fs
But, the FEL is a challenge: For LCLS, slice emittance >1.8 µm will not saturate For LCLS, slice emittance >1.8 µm will not saturate ε N = 1.2 µm ε N = 2.0 µm P = P 0 P = P 0 /100 courtesy S. Reiche SASE FEL is not forgiving instead of mild brightness loss, power nearly switches OFF electron beam must meet brightness requirements
End of presentation
SASE FEL Electron Beam Requirements SASE FEL Electron Beam Requirements radiation wavelength transverse emittance: ε Ν < 1 µm at 1 A, 15 GeV peak current undulator period (~1.5 µm realistic goal) energy spread: <0.08% at I pk = 4 ka, K 4, λ u 3 cm, beta function undulator field FEL gain length: 20L g > 100 m for ε Ν 1.5 µm Need to increase peak current, preserve emittance, and maintain small energy spread, all simultaneously AND provide stable operation