Science with FELs:Inelastic scattering as a probe of elementary

excitations in matter

Jerome Hastings

Signal

Scattering angle

Energy/Momentum Conservation

Instrument function

Energy – Momentum Relationship Photons, Electrons, Neutrons

High Energy Density matter is interesting

• Hot Dense Matter (HDM) occurs in:• Supernova, stellar interiors,

accretion disks• Plasma devices: laser

produced plasmas, Z-pinches• Directly and indirectly driven

inertial fusion experiments

• Warm Dense Matter (WDM) occurs in:• Cores of large planets• Systems that start solid and

end as a plasma• X-ray driven inertial fusion

experiments

HED

WDM

Hydrogen phase diagram

The High Energy Density Science space

Density (g/cc)10-4 10-2 0

Tem

pera

ture

(K)

102

106

1010 Relativistic Plasma

Radiative Plasma

Non-ideal Plasma

102 104

Degenerate and strongly coupled

Plasma

HED spacePressure > 1 Mbar

G = 0.1

G = 1

T e = E Fermi

Long Pulse Laser 10 J

Warm Dense Matter

Elastic scattering

the structure factor: a critically important quantity

10

• Pressure • Collisions

Excess ion pressure

Ion pressure

Total

Ideal gas pressure

Equation of State, Line broadening, Stopping Powers, Transport, Opacity,…

X-rays visualize Matter in Extreme Conditions

11

Density,Temperature,Pressure

X-rays visualize Matter in Extreme Conditions

12

Density,Temperature,Pressure

Let us first have a look at low temperature/pressure conditions

X-rays visualize Matter in Extreme Conditions

13

Simulations of solid Aluminum

Bragg equation: nl = 2d sinq

• Orange: isosurface of the electronic density (delocalized electrons)

• Grey: 2nd isosurface (n=1,2 localized electrons)• Blue sphere: Al nuclei

Solid

Compressed Solid

Melting

X-rays visualize Matter in Extreme Conditions

14

When Bragg peaks disappear a broad fluid peak

takes over – this feature contains information about the

structure of Warm Dense Matter

Melting

Warm Dense Matter

Warm Dense Matter

Plasma theory does not agree with data

15

• Theory includes screening by free electron, but no short-range repulsion

Ideal Plasma Theory

Warm Dense Matter State: new properties

16

DFT-MD simulations show warm dense matter

• Quantum simulations of Warm Dense Matter

• (delocalized conduction) are disturbed from the very regular structure in the lattice

• Properties of both• Hot dense gas or plasma• Solid

Data indicate coexistence

17

DFT-MD simulations show co-existence regime

• Simulations show Bragg peak and broad fluid peak

• Plasma and compressed solid co-exist)Co-

existence

Phonons

Elementary excitations in solids

David A. Reis

Stanford PULSE Institute,

Applied Physics and Photon Science

Stanford University and SLAC National Accelerator Laboratory

Time-domain Inelastic X-ray Scattering from Phonons

P. Olmer, Acta Cryst. 1, 57 (1948)

LA

TA

Aluminum

Inelastic X-ray Scattering:

M. Le Tacon et. al, Nat. Phys. 10,52 (2014)

Underdoped YBCO

ID28 ESRF

X-ray Diffuse Scattering:

2d

x-rays

M. Holt et al., PRL 83 (1999).

fit to Bose-Einsteindistribution.

Si

GaAs

Sudden Softening

GaAs

Inducing temporal coherences on the noise

independent modes (oscillation at twice frequency):

phonon-phonon interactions Electron-phonon interactions

Non-equillibrium populations Non-equillibrium frequency (forces)

Time and momentum-domain x-ray scattering:

X-ray

probe

pumpt

020

10

50 100 150 200 250 300 350 400 450 5000

0.5

1

1.5

2

2.5

3

3.5

4

-2.5

-2

-1.5

-1

-0.5

0

Ener

gy [m

eV]

Trigo et al. Nature Physics. 9, 790, 2013

BZ edge BZ edge

Trigo, Zhu, et al. in preparation

extracted TA phonon dispersion (Ge) H

alf f

requ

ency

[TH

z]

Liquids

G. Ruocco, F. Sette, J. Phys. Cond. Matter 11, R259 (1999)

G. Ruocco, F. Sette, J. Phys. Cond. Matter 11, R259 (1999)

Cross-section &

dynamic structure factor:

Free particle regime: impulse approximation

Microscopic regime relaxation processes invoked to account for the spectral shape and the broadening of the excitations

Macroscopic regime hydrodynamics

v=ħw/q

Si(4,4,4): ΔE/E=5•10-6

Working conditions: Bragg angle @ ϑPM=87o EPM=7919.1 eVΔEPM~100 meV

Sensitive to the seed crystal angle at the level of 0.001o

Si(4,4,4) analyzer

CSPAD detector

Be lens

focusing mirror

Si(4,4,4) mono

sample

Seeded beam

Optical laser

@ MEC: CSPAD (110 m pixel size) & diced Si(444) crystal with R=1 m & =87° ~100 meV @ 7919 eV

Huotari et al., J. Synchrotron Rad. 12, 425 (2006)

-~10.000 cubes of 0.7x0.7x2.3 mm3

- perfect crystal properties- collection of sufficient solid angle

-200 -100 0 100 2000.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ized

inte

nsity

Energy ( meV )

FWHM=98 meV !

-400 -300 -200 -100 0 100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed in

tensi

ty

Energy ( meV )

Al @ ρ=7.00.9 g/cm3

=152 13 meV

2θ=30o, Q=2.1 Ǻ

-1

Q0=3.70.1 Ǻ-1

; Q/Q0=0.57

Elastic scatterer (SiO2)

-300 -200 -100 0 100 200 300

0.2

0.4

0.6

0.8

1.0

1.2

Peak width gives viscosity

Norm

aliz

ed in

tensi

ty

Energy ( meV )

Peak position gives sound velocity

Fit results

viscosity:

σ ~ 5 mPa s

sound velocity:

v ~11 km s-1

Liquids (Water)

Ion Acoustic Waves (WD Aluminum)

Plasmons

Hill, J. P., et al. "Inelastic X-ray scattering study of solid and liquid Li and Na." Physical review letters 77, 3665 (1996)

The High Energy Density Science space

Density (g/cc)10-4 10-2 0

Tem

pera

ture

(K)

102

106

1010 Relativistic Plasma

Radiative Plasma

Non-ideal Plasma

102 104

Degenerate and strongly coupled

Plasma

HED spacePressure > 1 Mbar

G = 0.1

G = 1

T e = E Fermi

Long Pulse Laser 10 J

Warm Dense Matter

Single-shot plasmons determine compression

Plasmon dampingdetermines conductivity

• Density, Temperature• Characterize laser shock-

compressed Al- Compressed solid,- Co-existence phase- Warm Dense Matter

• First Conductivity measurements with independent Te, ne data

• Solid Al at T = 6 eV

Inelastic x-ray scattering measures physical properties of warm dense matter

L. Fletcher et al. Nature Photonics 9, 274 – 279 (2015) D. Chapman et al. Nature Communications DOI: 10.1038/ncomms7839 (2015)

Pressure, P = 5 Mbar

Coupling Parameter G

High resolution x-ray scattering observations ofplasmons in Al using the seeded beam at 8 keV

High resolution x-ray scattering observations ofplasmons in Al using the seeded beam at 8 keV

X-ray scattering from isochorically heated Al with seeded beam resolves plasmons

SASESeeded

Forward (plasmon) spectrometer

Backward (Compton) spectrometer

Plasmon

First measurements of the dynamic structure factor along the Al isentrope

• Scientific Achievement• Demonstrated novel in situ

measurements of the electron temperature, pressure, and density in the warm dense regime

• Significance and Impact• Precision measurements of the

isentrope of Al• This is a new tool to test the

microphysical models and to determine the physics properties of matter in extreme conditions

(bottom) pressure vs, density data for compressed aluminium(top ) DFT-MD simulations of the structural evolution from solid-state aluminum to WDM transition (left-right)

http://www.nature.com/nphoton/journal/vaop/ncurrent/full/nphoton.2015.41.html

Detailed balance

Is the dynamic structure factor of the free electrons

Summary

Inelastic x-ray scattering using FELs provides unique information that is crucial to understanding important properties of condensed matter

additional information and examples