Probing warm dense matter using femtosecond X-ray absorption spectroscopy with a laser-produced betatron source

Abstract

Exploring and understanding ultrafast processes at the atomic level is a scientific challenge. Femtosecond X-ray absorption spectroscopy (XAS) arises as an essential experimental probing method, as it can simultaneously reveal both electronic and atomic structures, and thus potentially unravel their nonequilibrium dynamic interplay which is at the origin of most of the ultrafast mechanisms. However, despite considerable efforts, there is still no femtosecond X-ray source suitable for routine experiments. Here we show that betatron radiation from relativistic laser-plasma interaction combines ideal features for femtosecond XAS. It has been used to investigate the nonequilibrium dynamics of a copper sample brought at extreme conditions of temperature and pressure by a femtosecond laser pulse. We measured a rise-time of the electron temperature below 100 fs. This experiment demonstrates the great potential of the table-top betatron source which makes possible the investigation of unexplored ultrafast processes in manifold fields of research.

Fig. 1

Numerical simulation of the ultrafast nonequilibrium 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 after, 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. See the Methods section for simulation details

Fig. 2

Setup of the experiment. A 50 TW, 30 fs laser pulse is focused onto a supersonic jet of 99% helium/1% nitrogen gas mixture. The interaction of the laser with the underdense created plasma yields the generation of a betatron X-ray pulse (see Methods for details). The latter is focused by a toroidal mirror on the Cu sample placed at normal incidence. A spectrometer composed of a toroidal crystal and an X-ray charge-coupled device (CCD) camera then record the transmitted spectrum. In parallel, a synchronized laser pulse (pump), with adjustable delay with respect to the X-ray pulse and with adjustable fluence, is used to heat the Cu sample up to the WDM regime. The absence of jitter is ensured by the fact that the pump laser and the laser-generated X-ray pulse originate from the same laser source

Fig. 3

Time-resolved XAS data. Selection of some measurements near the Cu L-edges (L₃ and L₂), without and with the pump pulse (incident fluence of 1 J cm⁻²), for three different X-ray probe delays. a Normalized X-ray absorbance. The shadowed area indicates the standard deviation of the measurements over a series of 50 consecutive shots. b Differential absorbance with respect to the curve without pump. Clear pre-edges appear a few eV below the L-edges just after the sample heating

Fig. 4

Time evolution of the electron temperature. The data deduced from time-resolved XAS measurements (full circles) are compared with the two-temperature hydrodynamic calculation (plain line). The calculated ion temperature is also plotted (dashed line). The incident fluence is 1 J cm⁻². The experimental data indicate a rise-time of 75 ± 25 fs (line and shadowed area in the inset). The gradual decrease observed at longer time is well reproduced by the model and is understood as the electron−ion thermal equilibration. Error bars are calculated from the integrated standard deviation within the pre-edge in the XAS data series

Fig. 5

Result of particle-in-cell simulations. Main curve: temporal X-ray profile calculated on-axis for 930-eV photons. Inset: Two-dimensional map of the plasma density n_e, showing the electron bunch accelerated in the wake of the laser pulse