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Ultrafast Spectroscopy of Warm Dense Matter Print

Being neither solid, liquid, gas, nor plasma, warm dense matter (WDM) occupies a no man's land in the map of material phases. Its temperature can range between that of planetary cores (tens of thousands K) to that of stellar cores (hundreds of thousands K). Not only is it prevalent throughout the universe, it is relevant to inertial confinement fusion (ICF) and material performance under extreme conditions. However, because of its extreme temperatures and pressures, WDM tends to be drastically transient and thus difficult to study in the laboratory. Now, researchers have set up ultrafast x-ray absorption spectroscopy at the ALS to measure the electronic structure of WDMs, demonstrating that fast-changing electron temperatures of matter under extreme conditions can be determined with picosecond resolution.

A Freeze-Frame Shot
of Warm Dense Matter

What is the nature of the Earth's core? Why does Jupiter have a strong magnetic field? Can we bring stars into the laboratory for fusion energy? What chemistry emerges when core (inner orbital) electrons are forced to interact with valence (outer orbital) electrons? What phenomena appear when photons, electrons, and ions are at high density with high energies comparable to their binding energies? A common thread in these questions is warm dense matter: matter that lies at the confluence of solid, liquid, gas, and plasmas. It is none of them, but can have the properties of all. In disciplines such as condensed matter or plasma physics, one force often dominates over the others, allowing smaller forces to be neglected in physical theories.

In the warm dense matter regime, however, electrical Coulomb energy—dominant in condensed matter—is comparable to thermal energy—dominant in plasmas. Thus, although classical electric forces are in play, pure quantum mechanical phenomena can hardly be ignored. Clearly the theoretical modeling in this case is not straightforward. It is also a regime where good experimental data are in short supply. In this work, Cho et al. demonstrate a way to freeze and capture such data in the split second before a laser-heated copper sample is destroyed. Our full understanding of planet formation and structures as well as the evolution of an imploding inertial fusion capsule depends on our understanding of matter in the complex warm dense matter regime.

Phase diagram

Temperature versus density for various structures in the universe. Pressures corresponding to this temperature and density are between 100,000 and one billion atmospheres. Figure from "Basic Research Needs for High Energy Density Laboratory Physics," DOE Office of Science and NNSA (2010).

One common method to create WDM conditions is the isochoric (constant-volume) heating of a solid. A femtosecond laser system at Beamline 6.0.2 delivers an intense laser pulse to heat a thin copper foil rapidly (~150 fs), maintaining the initial volume of sample. Under strong excitation, electron temperature can increase up to ~10,000 K (1 eV) while the lattice remains cold (nonequilibrium condition). Before equilibrium is reached in a few tens of picoseconds, the superheated sample maintains its original density by inertia. The matter is "warm" (compared to a "hot" plasma) but still as dense as a solid—warm dense matter. On a longer time scale (>100 ps), it expands into a plasma. Therefore, to probe a warm dense state undergoing a nonreversible process, an ultrafast technique faster than the ALS pulse duration (70 ps) and a single-shot measurement capability are essential.

ALS Beamline 6.0.2 is equipped with a pink-beam sample chamber, upstream of the spectrograph (monochromator), for broadband x-ray absorption near-edge spectroscopy (XANES). In addition, researchers installed a grazing-incidence x-ray streak camera detector at the endstation. The detector has the ability to spread out x-ray pulses for a time resolution of ~1 ps. It also has a high quantum efficiency and 6-mm imaging length in the spectral direction; therefore, it can record a broad spectrum with a single camshaft x-ray pulse. This unique combination of beamline and detector allows recording of ultrafast XANES spectra of a sample of WDM that undergoes nonreversible change in a broad-band single-shot mode.

Beamline schematic and streak camera photo

Schematic of the x-ray absorption spectroscopy setup at Beamline 6.0.2. Warm dense copper is created by a femtosecond laser and probed at the pink-beam chamber upstream of the spectrograph. The broadband spectrum is swept across the CCD detector of an x-ray streak camera for picosecond temporal resolution. Inset: Photo of x-ray streak camera.

X-ray absorption spectra around the L-edge of warm dense copper, obtained ~2 to 20 ps after a femtosecond laser pulse heated the sample, show significant differences from the ambient-condition data. The edges are strongly shifted and broadened, and the above-edge absorption is smoother and lower, indicating that the electronic structure and electron distribution were significantly altered. A series of XANES calculations based on a first-principles density functional theory (DFT) molecular-dynamic simulation, when compared with the experimental data, showed that the shifting and broadening of the absorption edge can be used as a sensitive temperature sensor in the WDM regime.

Absoprtion spectra and electron temperature over time

Left: Comparison of XANES spectra for various conditions of copper: warm dense copper—experiment (black), warm dense copper—calculation (blue), and the ambient condition—calculated (red). Right: Evolution of the electron temperature of warm dense copper. Experimentally derived values are shown as squares. Solid lines represent temperatures calculated by the two-temperature model for two cases: an electron–phonon coupling constant of G0 (red) and temperature-dependent electron–phonon coupling (blue). The shaded curves include the experimental accuracies. Temperature-dependent coupling (blue) provides a better description of the observed dynamics.

The fast-changing XANES data indicate that the electron temperature peaks (~10,000 K) with optical excitation, then drops and reaches equilibrium with the lattice (~ 5,000 K) in 10 ps. This is faster than the time scale expected from the known electron­–phonon coupling constant of copper (>20 ps). The result suggests that in the WDM regime, the energy exchange rate between electron energy and atomic vibration is expected to be temperature dependent and is about 3 to 6 times faster than previously assumed.

The researchers here successfully demonstrated the ability of this technique to provide new data sets for WDM electronic structures and thermal properties that are quite different from what was previously assumed. The results will also serve as benchmarks for theoretical modeling in this regime and can be applied to further investigation of plasmas for fusion, astrophysics, planetary science, and extreme material science.



Research conducted by: B.I. Cho, K. Engelhorn, J. Feng, and P.A. Heimann (ALS); A.A. Correa, T. Ogitsu, Y. Ping, A.J. Nelson, and R.W. Lee (Lawrence Livermore National Laboratory); C.P. Weber (Santa Clara University); H.J. Lee (SLAC National Accelerator Laboratory); P.A. Ni and D. Prendergast (Lawrence Berkeley National Laboratory); and R.W. Falcone (ALS and University of California, Berkeley).

Research funding: U.S. Department of Energy (DOE) National Nuclear Security Administration - Stewardship Science Academic Alliances (NNSA - SSAA) and Office of Basic Energy Sciences (BES). Operation of the ALS is supported by DOE BES.

Publication about this research: B.I. Cho, K. Engelhorn, A.A. Correa, T. Ogitsu, C.P. Weber, H.J. Lee, J. Feng, P.A. Ni, Y. Ping, A.J. Nelson, D. Prendergast, R.W. Lee, R.W. Falcone, and P.A. Heimann, "Electronic structure ofwarm dense copper studied by ultrafast x-ray absorption spectroscopy," Phys. Rev. Lett. 106, 167601 (2011).

ALS Science Highlight #246


ALSNews Vol. 330