Dynamics of femtosecond heated warm dense copper with time-resolved L3-edge XANES

Abstract

Combining experimental set up and ab initio molecular dynamics simulations, we were able to follow the time evolution of the X-ray absorption near edge spectrum (XANES) of a dense copper plasma. This provides a deep insight into femtosecond laser interaction with a metallic copper target. This paper presents a review of the experimental developments we made to reduce the X-ray probe duration, from approximately 10 ps to fs duration with table-top laser systems. Moreover, we present microscopic scale simulations, performed with Density Functional Theory, as well as macroscopic simulations considering the Two-Temperature Model. These tools allow us to get a complete picture of the evolution of the target at a microscopic level, from the heating process to the melting and expansion stages, with a clear view of the physics involved during these processes. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Keywords: Density Functional Theory; X-ray absorption; X-ray sources; femtosecond dynamics; laser heating; warm dense matter.

Figure 1.

Numerical simulation of the ultrafast non-equilibrium transition of copper from solid to WDM. The energy of a femtosecond optical laser pulse is suddenly deposited in the electrons of the system (femtosecond scale), then progressively transferred to the lattice (picosecond scale). (a) Cold solid lattice before heating: the electron temperature $T_e$ equals the ion one $T_i$. (b) Just after heating, a strongly out-of-equilibrium situation is transiently produced where electrons are hot while the lattice is still cold and solid-like. (c) A few picoseconds later, the lattice disappears as electrons and ions progress up to their thermal equilibration. (d–f) Calculated absorption spectra in the XANES region, corresponding, respectively, to (a–c). The cold XANES signal shown in (d) is reported in dashed line in (e), (f). (Figure taken from [9].)

Figure 2.

Schematic view of the picosecond time-resolved XANES station developed at CELIA laboratory, based on the M-shell emission. (Figure taken from [13].)

Figure 3.

(a) Some copper L3-edge XANES spectra registered through a cold sample (black) and a laser heated sample (red). The X-ray source shows broadband spectra in the region of interest. (b) Evolution of the pre-edge with the pump-probe delay, when using the M-shell emission from the Xe cluster jet (red), and the CsI solid target (blue), as the X-ray probe. (Figure taken from [13].)

Figure 4.

Schematic view of the femtosecond time-resolved XANES experiment at LOA laboratory, using the Betatron X-ray source. (Figure taken from [9].)

Figure 5.

(a) Temporal X-ray profile of the Betatron source, resulting from particle-in-cell simulations (inset: corresponding two-dimensional map of the plasma density showing the electron bunch accelerated in the wake of the laser pulse). (b) Evolution of the electron temperature deduced from femtosecond time-resolved XANES measurement at the copper L3-edge. (Figure taken from [9].)

Figure 6.

(a) Copper XANES spectra calculated for various conditions with $T_e=T_i$, at solid density. (b) $s$- and $d$-states for the corresponding spectra. The shade part correspond to the unoccupied states. (c) Evolution of the pre-edge integral (shaded part in graph (a)) as a function of the electronic temperature $T_e$, calculated with different conditions for the ion temperature $T_i$ and density $\rho$. (Figures taken from [20].)

Figure 7.

Results of two-temperature hydrodynamic calculations performed when $0.4\hspace{0.17em}\mathrm{J}\hspace{0.17em}{\mathrm{cm}}^{-2}$ is uniformly deposited in an 80 nm copper foil. (a) $T_e$-dependent coefficients $G$ and $C_e$ used in the simulation, as derived from [25]. (b) Two-dimensional (longitudinal/temporal) evolution of the density. (c) Corresponding time evolution of the energy balance. (Figure taken from [27].)

Figure 8.

Schematic view of the laser pump/X-ray probe experiment. The laser, with an intensity of ${10}^{14}\hspace{0.17em}\mathrm{W}\hspace{0.17em}{\mathrm{cm}}^{-2}$, heats a copper sample of 100 nm thickness deposited on a PET substrate. (Figure taken from [31].)

Figure 9.

(a) Evolution of the electronic temperature as a function of the initial depth and time, for diffusive transport. The laser deposition happens in the first 20 nm. (b) Electronic temperature dynamics retrieved from XANES spectra, compared with three TTM simulations: ballistic transport (BT), diffusive transport (DT) and composite transport (CT). (Figure taken from [31].)

Figure 10.

(a) Some time-resolved XANES spectra measured at $F_{\text{abs}}=0.065\hspace{0.17em}\mathrm{J}\hspace{0.17em}{\mathrm{cm}}^{-2}$. (b) Some calculated XANES spectra. (c) Corresponding computed projected DOS on s-states. The van Hove singularities characteristic of the fcc crystalline phase are indicated with arrows. (Figure taken from [23].)

Figure 11.

(a) Time evolution of electron ($T_e$) and ion ($T_i$) temperatures estimated with the two-temperature code, compared with $T_e$ measurements at $F_{\text{abs}}=0.065$ $\mathrm{J}\hspace{0.17em}{\mathrm{cm}}^{-2}$ (circles). (b) Time delay $\mathrm{\Delta }{t}_{\text{obs}}$ measured for the electron structure transition from fcc to liquid, compared with calculated melting time $\mathrm{\Delta }{t}_m$, as a function of the absorbed laser fluence. (Figure taken from [23].)

Figure 12.

Time evolution of $T_e$ retrieved from time-resolved XANES measurements. (a) Data registered with an absorbed fluence of $0.4\hspace{0.17em}\mathrm{J}\hspace{0.17em}{\mathrm{cm}}^{-2}$, and compared with different calculations. (b) Data at different laser fluences compared with the hydrodynamic simulations performed with $T_e$-dependent coefficients. (Figure taken from [27].)