x ray analysis and free electron lasers studies

x ray technique

1. X-RAY FREE-ELECTRON LASERS:
ATTOSECOND & ANGSTROMS
LINDA YOUNG
Argonne National Laboratory
The University of Chicago
Support from US DOE, Office of Basic Energy Sciences,
Chemical Sciences, Biosciences and Geosciences Division
Les Houches 2025
Quantum Dynamics & Spectroscopy of Functional
Molecular Materials and Biological Photosystems
23-28 February 2025

2. From Nobel Lectures in Physics
8 December 2023
Pierre Agostini: just a quick look toward
the future … so far attosecond pulses are
created by visible or infrared lasers…but
maybe the future of attoseconds is not in
the our lab but with this x-ray free-electron
laser…

3. Attosecond x-ray pulses: XFELS v HHG
J. Duris et al, Nature Photonics (2020)
Electron dynamics
+
Atomic spatial resolution

4. 4
Linac Coherent Light Source at SLAC
Injector (35º)
at 2-km point
Existing 1/3 Linac (1 km)
Near Experiment Hall
Far Experiment
Hall
Undulator (130 m)
X-FEL based on last 1-km of existing 3-km linac
New e
-
Transfer Line (340 m)
1.5-15 Å
(14-4.3 GeV)
X-ray Transport
Line (200 m)
LLNL
UCLA
Proposed by C. Pellegrini in 1992

5. 5
Single molecule imaging

6. 6
SCIENCE DRIVERS FOR LCLS
AMO: Atomic Molecular and Optical
SXR: Soft X-ray Materials Science
XPP: X-ray Pump-Probe
XCS: X-ray Correlation Spectroscopy

CXI: Coherent X-ray Imaging
MEC: Materials in Extreme Conditions
AMO
• Understand and control x-ray atom/molecule interactions at ultrahigh x-ray intensity as a
foundation for other applications.
• Provide diagnostics of the LCLS radiation

7. REVOLUTIONARY PROPERTIES OF XFELS - 1
10
10
increase in peak brightness!
7
Stohr, PRL (2017)
Nonlinear & multiphoton phenomena
• Non-resonant response up to 10
20
W/cm
2
• Resonant phenomena – Rabi cycling, SRS
• Stimulated emission – atomic X-ray laser
• Second harmonic generation
• Optical/x-ray wave mixing

8. REVOLUTIONARY PROPERTIES OF XFELS - 2
Extremely versatile !
8
From: Roadmap of ultrafast x-ray atomic
and molecular physics, Young …JPB 2018
• Tunable: 10 eV to >20,000 eV
• Huge pulse energy: ~10
6
pulse
energy compared to HHG
sources for x-rays
• Multicolor, multipulse, sub-
femtosecond pulses
10
12
10
11
Soft x-rays @ LCLS: Franz, Nat Pho. (2024)
Hard x-rays @ EuXFEL: Yan, Nat Pho. (2024)

9. OUTLINE

Producing light to probe the Attosecond-Angstrom frontier
•SASE XFEL
•Seeded XFEL
– Externally seeded soft x-rays @ FERMI
– Self-seeded hard x-rays @ LCLS/EuXFEL/PALFEL
•Two-color XFEL
•Attosecond XFELs
– production and characterization

10. HOW DOES A SASE XFEL WORK?
Single-pass self-amplified spontaneous emission
10
Power gain length
Radiation wavelength
Bostedt… RMP (2016), Huang & Kim PrSTAB (2007)

11. Temporal and spectral properties – SASE XFELs
Simulation for EuXFEL – single pulse @ 1Å wavelength
11
Temporal properties
100s of spikes in e- bunch
spike duration
Spectral rms bandwidth
Geloni… NJP (2010)

12. Why are emitted wavelengths in the X-ray range?
Relativistic electron approaches
periodic B-field of undulator
In electron frame, undulator period
is Lorentz contracted, L/ and B-
field accompanied by E-field
EM wave stimulates electron to
oscillate and emit waves of equal
wavelength.
G. Margaritondo, J Synch Rad (2011)

13. How does microbunching originate?
Interaction between wave & electron plus speed difference (c-u)
G. Margaritondo J Synch Rad (2011)
Slippage =  per L
und

14. Exponential growth of microbunching and saturation
14
@ saturation: electron no longer gives energy to wave
 ∝ ( I
peak / 

x)
1/3
=  P
ebeam power
bandwidth
coherence length
rho
Bostedt… RMP (2016)

15. Electron beam conditions for FEL amplification
15
APS e-beam

x = 300 µm

y = 10
µm

t = 100 ps

x’ = 12 µrad

y’ = 4 µrad
dE/E ≈ 1e-3
LCLS e-beam

x = 30 µm

y = 30 µm

t = 10 fs

x’
= .5 µrad

y’
= .5 µrad
dE/E ≈ 0.4e-3
• e beam emittance on the order of
undulator emittance
 FEL gain length shorter than Rayleigh
range of radiation

 e beam relative energy spread less
than FEL parameter, 

x = 
x 
x’ = 
r
L

16. APRIL 10, 2009: LCLS LASES AT 1.5 Å
16
LCLS
2009
In my life before SLAC, I had the privilege to participate (in various capacities) in the design, construction and
commissioning of two linacs, two synchrotrons, four storage rings and three FELs (free-electron lasers). Now I have
had the privilege to be in SLAC's Main Control Center on April 10, when the Linac Coherent Light Source became a 1.5
Ångstrom laser. I don't expect I will ever, as long as I live, see such a beautiful, smooth turn-on of any light source.
With each undulator placed on the beam path, the FEL power increased by a factor of about 2.3; two hours into the
first attempt at lasing, the pinpoint of FEL light from twelve undulators was nearly 2,000-fold more intense than plain
old undulator radiation. The team called it quits at 11:30 p.m. that night. When they returned at 8:00 a.m. the next
morning, the FEL light came back as soon as the shutter was opened. - John Galayda
21:03:03
21:33:52
10 mm
From John Galayda

17. 10

18. Opt Comm 1984

19. Undulator radiation – incoherent v coherent
Stringent wrt synchrotron parameters
Incoherent - synchrotron Coherent - XFEL
I
x-ray ∝,(N
bunch)
2
I
x-ray ∝,N
bunch
Typical FEL: 10 pC : N
bunch ~ 10
8Typical synch: 1 nC : N
bunch ~ 10
10

20. Temporal and spectral properties – SASE XFELs
Simulation for EuXFEL – single pulse @ 1Å wavelength
20
Geloni… NJP (2010), Krinsky & Gluskstern PRSTAB (2003)
Temporal properties
100s of spikes in e- bunch
spike duration:
Spectral properties
spectral spike width ~ 1/T
bunch
rms bandwidth

21. OUTLINE

Producing light to probe the Attosecond-Angstrom frontier
•SASE XFEL
•Seeded XFEL
– Externally seeded soft x-rays @ FERMI
– Self-seeded hard x-rays @ LCLS/EuXFEL/PALFEL
•Two-color XFEL
•Attosecond XFELs
– production and characterization

22. SEEDING
Most straightforward way to increase longitudinal coherence
G. Lampert …M. Couprie, Nat Phys (2008)
Seed HHG: 0.53 – 4.3 nJ,
160 nm, 50 fs
FEL ebeam: 150 MeV, 1 ps
~1000X intensity gain @ 160 nm
Pulse profile given by seed
Harmonic yields
3
rd
0.3 nJ @ 53 nm
5
th
12 pJ @ 32 nm
Shot-to-shot stability
Need external laser synchronization

23. Problem is to have a seed for x-rays
External seed power >> SASE noise
But noise power grows with frequency:
New method needed: electron beam manipulation
Energy modulation (seed laser + und)
—› Density modulation (via mag chicane)
—› Radiation at n
th
harmonic
Proposed L. H. Yu, PRA (1991), demo for IR L. H. Yu … Science (2000)
HGHG: High gain harmonic generation
10
7
gain for:  = m, 2 =  m

24. HGHG works at EUV wavelengths!
Seed: 266 nm, 150 fs
FEL: 4
th
– 13
th
harmonics (65 -20 nm).
~40 µJ, ~85 fs @ 32.5 nm

25. HGHG works at EUV wavelengths!
transverse coherence
YAG screen, 72 m downstream. Two slit interference; 20µm slits, sep 0.8 mm

26. HGHG works at EUV wavelengths!
spectral stability
8
th
harmonic BW shot-by-shot spectrum

27. Soft x-ray FEL: HGHG using two stages
Cascade & fresh bunch used to achieve radiation @ higher harmonics
λ
2=λ
seed/(h
1×h
2)
λ
1=λ
seed/h
1
Shortest wavelength:
4.3 nm, ∼200 nJ,
h
1=6,h
2=10
λ
seed = 266 nm
t
seed = 180 fs
t
FEL ∝ 1/h
1/2
Allaria et al, Nat Photon (2013)
??????
FEL∼7??????
seed/(6h
1/3
)Finetti … PRX (2017)
h
13 ~ 90 fs

28. SELF-SEEDING FOR HARD X -RAYS
Power after diamond xtal
Monochromatic
seed power
5 MW
6 µm
XFEL spectrum
after diamond xtal
Diamond C(004): 100µm
 = 0.15 nm, 
 = 57
o
Geloni et al., J. Mod. Opt. (2011)

29. HARD X-RAY SELF SEEDING REALIZED AT LCLS
Bandwidth <10
-4
at 8-9 keV and tunable
But … did not achieve saturation and power jitter still present
~50% power fluctuation shot-to-shot
Spectral intensity HXRSS ~ 1.7x SASE
J. Amann et al., Nature Photonics 6, 693 (2012)

30. FIRST SELF-SEEDING CREW (partial) - 2012

31. MORE HXRSS DEVELOPMENTS
2012
2019
LCLS
SACLA
PALFEL
2021
BW ~ 1/40 SASE:
Spectral density 1.7X SASE
BW ~ 1/10 SASE
Spectral density: 6X SASE
BW ~ 1/70 SASE
Spectral density: 40X SASE

32. MODERN HXRSS - @ MHz repetition rate
EuXFEL - mJ level @ MHz rep rates w/ heat loading effects
Tunable: 6-14 keV
@9 keV:
SASE: 2.2 mJ, 20 eV BW
100µJ/eV
HXRSS: 1.2 mJ, 0.8 BW
1000µJ/eV
Pk intensity: 10X SASE
Shan Liu et al. Nat Photon (2023)

33. OUTLINE

Producing light to probe the Attosecond-Angstrom frontier
•SASE XFEL
•Seeded XFEL
– Externally seeded soft x-rays @ FERMI
– Self-seeded hard x-rays @ LCLS/EuXFEL/PALFEL
•Two-color XFEL
•Attosecond XFELs
– production and characterization

34. Two-color x-ray pulse pairs
Sections of long undulator array tuned to different wavelengths
Twin bunches at photo-cathode accelerated to different energies
Lutman… PRL (2013)
Marinelli… Nat Comm (2015)
•Higher intensity than split und

35. OUTLINE

Producing light to probe the Attosecond-Angstrom frontier
•SASE XFEL
•Seeded XFEL
– Externally seeded soft x-rays @ FERMI
– Self-seeded hard x-rays @ LCLS/EuXFEL/PALFEL
•Two-color XFEL
•Attosecond XFELs
– production and characterization

36. Single-spike attosecond soft x-ray pulses!
XLEAP: With measurement of pulse duration w/ c-VMI streaking
J. Duris…J. Cryan, A. Marinelli, Nature Photonics (2020)
905 eV
Δτ
FWHM ~ 280 as
570 eV
Δτ
FWHM ~ 480 as
Pulse energy
~ 50 µJ

37. Characterization of attosecond pulses
Photoelectron angular streaking x-ray w/ overlapped circ polzd IR
pulse
Rotating electric field of circ polz laser deflects
photoionized electrons in radial direction. Instant of
ionization mapped to angle of momentum vector.
Attoclock
Eckle …U Keller, Nature Physics (2008)
Implementation @ LCLS
Co-axial VMI

38. Characterization of attosecond pulses
Photoelectron angular streaking with overlapped circ polzd IR pulse
No streaking laserw/streaking laser Difference

39. =
3
Z. Guo … J. Cryan, A. Marinelli,
Nature Photonics (2024) May
Synchronized attosecond
x-ray pulse-pair generation
Terawatt-scale attosecond X-ray
pulses from a cascaded
superradiant free-electron laser
P. Franz … J. Cryan, A. Marinelli,
Nature Photonics (2024) May

40. Synchronization of  pulses
Correlation plots to determine  delay
XLEAP generation of 
 configuration reuses
microbunching to achieve sub-fs delay
Measurement of  &  delay & jitter
with cVMI and circular polzd streaking
CF
4 w/ T
laser = 4.3 fs
 = 370 eV. 2  = 740 eV
Duration ~ 700 as () and 530 as (2)
Relative jitter ~ 270 as
Z. Guo … J. Cryan, A. Marinelli,
Nature Photonics (2024) May

41. Generation of attosecond pulse trains (APT)
Combining 3 or 4 harmonics from externally seeded FEL - FERMI
Beating of multiple phase-locked harmonics produces attosecond pulse trains
Attosecond pulses 10’s of microjoules, 10s to 100s attoseconds
Seed laser
??????
UV=3??????
NIR
~264 nm
Maroju…Sansone, Nature (2020), Appl Sci (2021)

42. Reconstruction of APT – CoBRA:
correlation-based reconstruction of attosecond pulses
Analogous to RABBIT scheme from HHG – but with two sidebands
CoBRA
Maroju…Sansone, Nature (2020)

43. RABBIT
reconstruction of attosecond beating by interference of two-photon transition
See Pierre Agostini – 2023 Nobel Lecture. “Genesis of an attosecond pulse train”

44. RABBIT
reconstruction of attosecond beating by interference of two-photon transition
See Pierre Agostini – 2023 Nobel Lecture. “Genesis of an attosecond pulse train”

45. RABBIT
reconstruction of attosecond beating by interference of two-photon transition
See Pierre Agostini – 2023 Nobel Lecture. “Genesis of an attosecond pulse train”
attosecond pulse train

46. RABBIT and CoBRA SPECTRA
Cirelli… Nat Comm (2018) Maroju … Sansone Nature (2020)

47. Phase measurements of FEL harmonics
3 fs delay jitter —› correlation plots of oscillating components of
sidebands to extract phase
Maroju…Sansone, Nature (2020)

48. Attosecond pulse trains @ FERMI FEL
Phase & intensity control between harmonics - unlike HHG
Photoelectron spectra
Correlation plots
Reconstructed APT waveforms
Maroju…Sansone, Nature (2020)Demonstrated control over APT waveform

49. TEMPORAL STRUCTURE OF SASE FELS
Single spike pulse duration limit – depends on e- bunch duration & 
r
49
Spike duration ~ cooperation length = slippage in one gain length
Single spike duration: <1 fs @ 1Å
>1 fs @ 10Å

50. SINGLE SPIKE DEMONSTRATIONS IN HXR
50
5.6 & 9 keV: S. Huang … PRL 119, 154801 (2017)
7 eV bandwidth
dt = 250-as estimated
pulse energy 10 µJ
5.6 keV: A. Marinelli… APL 111, 151101 (2017)
4.5 eV bandwidth
dt ~ 400-as estimated
pulse energy 10 µJ

51. OUTLINE

Producing light to probe the Attosecond-Angstrom frontier
•SASE XFEL
•Seeded XFEL
– Externally seeded soft x-rays @ FERMI
– Self-seeded hard x-rays @ LCLS/EuXFEL/PALFEL
•Two-color XFEL
•Attosecond XFELs
– production and characterization

52. OPPORTUNITIES w/XFELs
▪ Extreme focusing —› nonlinear phenomena
Extreme focusing of hard X-ray free-electron laser pulses enables 7 nm focus width and
10
22
W cm
−2
intensity
J. Yamada et al., Nature Photonics 18,685–690 (2024)

▪High repetition rate —› big data —› rare events
ExaFEL: extreme-scale real-time data processing for X-ray free electron laser science
J. P. Blaschke et al., Frontiers in High Performance Computing Oct 2024
▪ More accessibility: biology, chemistry, materials, condensed
matter physics, warm dense matter
Tunable, synchronized attosecond pulse pairs +

53. SHINE
8 GeV, SC accel, 1 MHz
3 undulators, 0.4-25 keV
10 endstations
User expts 2027
The Innovation 2(2), 100097 (2021).