How wigglers and undulators have contributed to synchrotron radiation research

Sebastian Doniach, Derek Mendez, Daniel Ratner and Jongmin Sung

How the wiggler beamlines were introduced at SSRL

SSRL Users Newsletter October 1993 Wiggler beam lines 4 and 7 were eventually built starting in 1978

Atomic structure of nanoparticles and biomolecules: the magic of crystallography

Experiments on crystalline samples at the LCLS by Chapman and collaborators

but how to deal with non-crystalline samples?

for large enough objects, singe particle diffraction is feasible Single mimivirus particles intercepted and imaged with an X-ray laser (resolution 32 nm) Hajdu and collaborators 7 8 | N AT U R E | VO L 4 7 0 | 3 F E B R U A RY 2 0 1 1

but for nano particles and protein molecules, the samples tend to look like this:

The natural nanomineral ferrihydrite is an important component of many environmental and soil systems and has been implicated as the inorganic core of ferritin in biological systems.

from: “Ordered ferrimagnetic form of ferrihydrite reveals links among structure, composition, and magnetism” F. Marc Michel et al PNAS ∣ February 16, 2010 ∣ 2787–2792 vol. 107 ∣ no. 7 ∣

X-ray scattering from ferrihydrite nano particles screenshot Argonne APS 60keV xrays

SSRL undulator beamline 12-2 screenshot Ferrihydrite sample 16 keV x-rays

LCLS Si powder commissioning shot

a possible solution?

post-detector interferometry

Hanbury-Brown and Twiss (1950’s): by correlating signals from 2 telescopes the effective aperture is increased to the distance between the telescopes

(The Very Large Array consists of 27 radio antennas in a Y-shaped configuration on the Plains of San Agustin fifty miles west of Socorro, New Mexico.)

2-photon correlated scattering

q 1 ☐ q q 2 ☐ Extract 2 photon events by calculating the autocorrelation: multiply I(q 1 ) x I(q 2 ) and subtract x Wochner et al PNAS 2009 Measurments on a hard sphere polymethylmethacrylate (PMMA) system with radius of 117 nm.

The basis for Correlated X-ray Scattering (CXS)

The basis for Correlated X-ray Scattering (CXS) – contn’d

The result of averaging over all molecular orientations is: So the correlator measures the distribution of photons resulting from two scattering events from the same molecule This is an example of “post-detector interferometry” (Hanbury-Brown and Twiss) and requires a high x-ray fluence (flux x exposure time) since the proportion of double scattering to single scattering goes as (fluence) 2 .

Kam’s theorem (1978) Kam showed that the correlator is a function only of the magnitudes q1, q2 and the angle between them and is independent of molecular orientation hence for scattering from many molecules, we can define the 4-point correlation function

correlated x-ray scattering

Scattering events where two photons scatter off the same molecule Scattering rate C4(q 1 ,q 2 ,cos( q )) measures density of pairs r ij molecule oriented at angle q within the relative to pairs r km C4 is independent of the overall molecular orientation r j note: this is a bulk measurement r i r k q r m

Double scattering event -> true correlation Scattered x-ray Q 1 Scattered x-ray Q 2 Incoming x-rays K 0

Psuedo correlations:

Independent scattering events from particles with close to the same orientation.

problem: Kirian et al showed that these contribute to the correlator at the same order of magnitude as the paired scattering events.

solution: Measure inter-shot correlations which

can not

include the paired scattering events since scattering off the same molecule can not occur in 2 different shots.

2 single scattering events -> psuedo correlation Scattered x-ray Q1 Incoming x-rays K 0 Scattered x-ray Q 2

the correlators are well represented as series of harmonics around a circle of given Q:

0  2 

d



e i

 0  2 

S

( q )

S

( q   )

d

q   

S

* (  )

S

(  )  For a given shot, principal components can be derived which best fit the statistics of the |

S

(  ) | 2 values for the ensemble of orientations in the shot.



is wide angle Correlated x-ray scattering able to resolve structural details at Å resolution?

simulation test: simulate multiple shots each with 1000 different orientations with a regular lattice model, and compare with simulations for a distorted lattice model in which one of 4 atoms in the fcc unit cell is moved by 10% of the cell size.

Note that “Statisticians, like artists, have the bad habit of falling in love with their models.” George E. P. Box

With sufficient statistics (numbers of shots) we believe the data can provide Å level constraints on model parameters over a large range of {Q1, Q2}’s

next steps: high fluence data at wiggler/undulator beamlines

Acknowledgments: Gordon Brown and Jim Spudich labs: Clement Levard, Marc Michel, Shirley Sutton caveat - “Prediction is very difficult, especially about the future.” -- Niels Bohr