Characterizing plasma conditions in radiatively heated solid-density samples with x-ray Thomson scattering

We have developed an experimental platform to generate radiatively heated solid density samples for warm dense matter studies at the OMEGA laser facility. Cylindrical samples of boron and beryllium are isochorically heated by K- and L-shell emission from x-ray converter foils wrapped around the cylinders' radii. X-ray Thomson scattering (XRTS) measures the temperature and the ionization state of the samples as function of time. Temperatures approach 10 eV, and the ionization states are found to be $Z_{\text{B}}=3$ and $Z_{\text{Be}}=2$. Radiation hydrodynamics simulations were performed to confirm a homogeneous plasma state exists in the center of the sample for the duration of the experiment. Results from the study can be extended to improve understanding of radiative heating processes in the warm dense matter regime.

Figure 1

(a) A schematic of the target geometry, laser configurations, and scattering $k$-vectors. (b) A photograph of the boron target. (c) Two images of raw data. The top image shows the spectrometer calibration spectrum from a brass foil with the $\mathrm{Zn}\mathrm{He}\text{−}\alpha$ doublet at 8.97 keV in the center of the strip, as well as Cu $\mathrm{He}\text{−}\alpha$ at 8.37 keV and Cu $\mathrm{He}\text{−}\beta$ at 9.87 keV. The bottom picture shows XRTS data from a B sample on the same energy scale as the calibration shot. The elastic scattering feature appears on the right side and the Compton (inelastic) scattering feature is on the left. In both spectra, the photon energy increases from left to right.

Figure 2

A plot of 1D hydrodynamics simulations of boron mass density versus radius and time. The white box indicates the implosion times and region of the cylinder probed by our XRTS measurements. The simulations indicate that XRTS measurements are made before the shock front reaches the region of the cylinder that is probed by x-rays.

Figure 3

1D radiation hydrodynamics simulations of boron electron temperature versus radius and time. The dashed black box indicates the probed volume and time range measured by XRTS. The simulations show that we expect temperatures to remain relatively constant after the laser drive turns off.

Figure 4

(a) The boron ion structure factor versus $k$ for solid density (2.36 g ${\mathrm{cm}}^{-3}$), 10 eV boron with $Z_B=3.0$, as calculated by several models available in the MCSS code [40, 41]: Debye-Hückel [42], effective-Coulomb, and finite-wavelength screening [34]. (b) A plot of the B screening cloud contribution versus $k$ as calculated by several models available for the electron-ion potential in the MCSS code [40, 41]: effective-Coulomb, the hard empty core, and the soft empty core. In both cases, the experimental $k$-value of the experiment (7.9 ${\AA }^{-1}$) is noted by the dashed vertical line. The ion structure factor converges to 1 and the screening cloud converges to 0 at the experimental $k$-value for all models considered. This increases confidence in the modeling of elastic scattering for this scattering geometry.

Figure 5

Left: a ${\chi }^2$ map versus electron temperature and B ionization state. $1\sigma$ confidence intervals are marked by the white dashed curve. The best fit is found at a temperature of $T_e=8.6_{-3.1}^{+2.7}$ eV with $Z_B<3.1$. Right: an illustration of ionization sensitivity (top right) and temperature sensitivity (bottom right) in the fitting. Both plots show the data and the best fit, as well as one or two other modeled spectra that vary ionization and electron temperature, respectively.

Figure 6

A comparison of the experimentally measured boron electron temperatures versus time with predictions from 1D rad-hydro simulations for several different incident laser intensities. The nominal laser intensity, indicated by $I_0$, was 1070 TW ${\mathrm{cm}}^{-2}$. The power of the laser drive in the simulations had to be tuned to $0.31I_0$ match the measured temperatures, highlighting the importance of measuring the plasma conditions in radiative heating experiments.

Figure 7

The best fit to the B data at 1.68 ns, along with the individual contributions to the scattering spectrum. The blue wing of the free-free feature overlaps with the elastic scattering feature. Increased electron temperature broadens the free-free feature, which then adds with the elastic scattering feature to give the appearance of increased elastic scattering in the final spectrum.

Figure 8

Left: a ${\chi }^2$ map versus electron temperature and Be ionization state. $1\sigma$ confidence intervals are marked by the white dashed curve. The best fit is found at a temperature of $T_e=6_{-5}^{+5}$ eV with $Z_{\text{Be}}<2.2$. Right: an illustration of ionization sensitivity (top right) and temperature sensitivity (bottom right) in the fitting. Both plots show the data and the best fit, as well as one or two other modeled spectra that vary ionization and electron temperature, respectively.