Nonlocal heat transport and improved target design for x-ray heating studies at x-ray free electron lasers

The extremely high-power densities and short durations of single pulses of x-ray free electron lasers (XFELs) have opened new opportunities in atomic physics, where complex excitation-relaxation chains allow for high ionization states in atomic and molecular systems, and in dense plasma physics, where XFEL heating of solid-density targets can create unique dense states of matter having temperatures on the order of the Fermi energy. We focus here on the latter phenomena, with special emphasis on the problem of optimum target design to achieve high x-ray heating into the warm dense matter (WDM) state. We report fully three-dimensional simulations of the incident x-ray pulse and the resulting multielectron relaxation cascade to model the spatial energy density deposition in multicomponent targets, with particular focus on the effects of nonlocal heat transport due to the motion of high energy photoelectrons and Auger electrons. We find that nanoscale high-$Z$/low-$Z$ multicomponent targets can give much improved energy density deposition in lower-$Z$ materials, with enhancements reaching a factor of 100. This has three important benefits. First, it greatly enlarges the thermodynamic parameter space in XFEL x-ray heating studies of lower-$Z$ materials. Second, it allows the use of higher probe photon energies, enabling higher-information content x-ray diffraction (XRD) measurements such as in two-color XFEL operations. Third, while this is merely one step toward optimization of x-ray heating target design, the demonstration of the importance of nonlocal heat transport establishes important common ground between XFEL-based x-ray heating studies and more traditional laser plasma methods.

Figure 1

Representations of three types of multicomponent targets composed of sample material (green) and heater cladding (yellow). (a) A porous subtrate filled with sample material; (b) a mixture of cladding and sample nanoparticles embedded in a solid matrix; (c) a multilayer film.

Figure 2

Visualization of a 3D Monte Carlo simulations of electron transport in (a) Au-diamond-Au and (b) Au-Fe-Au targets heated by 7 keV photons, incident normally from the top of the page. For readability, only $10\%$ of tracks originating in the Au layer are displayed in (a). Electron tracks are projected onto the plane of the page; showers resulting from photoexcitation of Au and C or Fe atoms are red (thin) and blue (bold), respectively. Most electron tracks in the interior layers are due to absorption events in the Au.

Figure 3

Linear energy deposition due to 7 keV photons incident on an Au-C-Au target displayed for several thicknesses of the central C layer and a fixed outer cladding thickness of 50 nm, compared to the linear energy deposition created by 7 and 2 keV photons incident on bulk C. The large, expected decrease in direct absorption of the higher-energy x rays by the unclad samples is more than compensated by the nonlocal heating from electron transport between the Au and the interior material for the Au-C-Au target.

Figure 4

(a) Linear energy deposition density generated by 7 keV photons incident on an Au-$\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$-Au target, displayed for several thicknesses of the central $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ layer and a fixed Au cladding thickness of 50 nm. (b) Histograms of energy deposition density in volume elements of the $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ inclusions in Au-$\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$-Au targets, displayed for several thicknesses of the Au cladding and a fixed $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ layer thickness of 50 nm.

Figure 5

Linear energy deposition in layered Au-Fe-Au and Au-$\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$-Au targets of 150 nm total thickness stimulated by 7 keV photons (solid curves). Dashed lines on the left indicate energy deposition in bulk $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ and Fe at photon energies of 7.12 keV (above the Fe K-edge) and 7 keV (below the edge). The multilayer configuration sufficiently enhances energy deposition so as to partially compensate for the difference between pre- and above-edge x-ray photoelectric cross sections. The benefit is particularly pronounced in $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ due to its much lower density and photoelectric cross-section.

Figure 6

Simulated powder diffraction of 50 nm Au-50 nm $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$-50 nm Au stimulated by x rays below the Fe K-edge (blue) compared to that resulting from photons above the edge incident on bare $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$, including fluorescence background(green). The diffraction signal is based on empirical models for the elastic scattering form factors of Au, Fe, and O, while the fluorescence background is calculated from the tabulated $K$-shell photoelectric cross section of Fe [50]. The detector may be substantially shielded from the Au M-shell emission, and its contribution to the background is therefore neglected.