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) Temperature (K) Relativistic Plasma Radiative Plasma Non-ideal Plasma Degenerate and strongly coupled Plasma HED space Pressure > 1 Mbar  = 0.1  = 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: n = 2d sin  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

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 2d x-rays M. Holt et al., PRL 83 (1999). fit to Bose-Einstein distribution. 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 populationsNon-equillibrium frequency (forces) Time and momentum-domain x-ray scattering: X-ray probe pump  Energy [meV] Trigo et al. Nature Physics. 9, 790, 2013

BZ edge Trigo, Zhu, et al. in preparation extracted TA phonon dispersion (Ge) Half frequency [THz]

Liquids

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=ħ  /q

Si(4,4,4): ΔE/E= Working conditions: Bragg ϑPM=87 o EPM= eV ΔEPM~100 meV Sensitive to the seed crystal angle at the level of o 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°  ~ eV Huotari et al., J. Synchrotron Rad. 12, 425 (2006) -~ cubes of 0.7x0.7x2.3 mm 3 - perfect crystal properties - collection of sufficient solid angle

FWHM=98 meV ! ρ=7.0  0.9 g/cm 3  =152  13 meV 2θ=30 o, Q=2.1 Ǻ -1 Q 0 =3.7  0.1 Ǻ -1 ; Q/Q 0 =0.57 Elastic scatterer (SiO2)

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) Temperature (K) Relativistic Plasma Radiative Plasma Non-ideal Plasma Degenerate and strongly coupled Plasma HED space Pressure > 1 Mbar  = 0.1  = 1 T e = E Fermi Long Pulse Laser 10 J Warm Dense Matter

Single-shot plasmons determine compression Plasmon damping determines conductivity Density, Temperature Characterize laser shock- compressed Al -Compressed solid, -Co-existence phase -Warm Dense Matter First Conductivity measurements with independent T e, n e 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: /ncomms7839 (2015) Pressure, P = 5 Mbar Coupling Parameter 

High resolution x-ray scattering observations of plasmons in Al using the seeded beam at 8 keV X-ray scattering from isochorically heated Al with seeded beam resolves plasmons SASE Seeded 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)

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