Time-Resolved XUV Opacity Measurements of Warm Dense Aluminum

The free-free opacity in plasmas is fundamental to our understanding of energy transport in stellar interiors and for inertial confinement fusion research. However, theoretical predictions in the challenging dense plasma regime are conflicting and there is a dearth of accurate experimental data to allow for direct model validation. Here we present time-resolved transmission measurements in solid-density Al heated by an XUV free-electron laser. We use a novel functional optimization approach to extract the temperature-dependent absorption coefficient directly from an oversampled pool of single-shot measurements, and find a pronounced enhancement of the opacity as the plasma is heated to temperatures of order of the Fermi energy. Plasma heating and opacity enhancement are observed on ultrafast timescales, within the duration of the femtosecond XUV pulse. We attribute further rises in the opacity on ps timescales to melt and the formation of warm dense matter.

Figure 1

Experimental setup: the XUV pulse is split and delayed in time before both pulses are focused on the sample by a multilayer coated off-axis parabolic mirror. The transmitted signal is measured by a downstream CCD camera.

Figure 2

Schematic representation of the functional optimization approach used to extract the opacity as a function of electron temperature and density by constraining it to best match the dataset of integrated transmission measurements.

Figure 3

Total experimental and simulated transmission measured through 200 (a) and 300 nm (b) foils for a range of different total FEL energies on target, alongside the simulated transmissions within a $2\sigma$ band. (c) Absorption coefficient extracted by our functional optimization approach. The curve is constrained by the data up to the peak temperatures of 26 eV. Bands are determined by MCMC calculations. Also plotted are the theoretical predictions based on Ref. [10] assuming either cold ions or an equilibrated system, the IB-based theory of Iglesias [14], and the cold absorption from the CXRO database [33].

Figure 4

Pump-probe transmission measurements in Al samples 200 and 300 nm thick. Negative times correspond to the probe pulse arriving first and positive times to the pump arriving first. The simulated transmissions for a single (diamond) or two pulses (cross) are also shown, where the forward model was used with the absorption coefficient extracted from the single-short self-heating data.