Exploring and understanding ultrafast processes at the atomic level is a scientific challenge. Femtosecond X-ray Absorption Near-Edge Spectroscopy (XANES) arises as an essential experimental probing method, as it can simultaneously reveal both electronic and atomic structures, and thus potentially unravel their non-equilibrium dynamic interplay which is at the origin of most of the ultrafast mechanisms. The key point of this investigation is the achievement of a femtosecond X-ray source suitable for routine experiments. This paper will show the progressive development and improvement of such laser-plasma-based X-ray sources, starting from the picosecond down to the femtosecond scale. Time-resolved XANES measurements have been achieved and interpreted using ab initio quantum molecular dynamics simulations. This diagnostic was used to shed new light on the non-equilibrium physics involved in various materials. This paper will focus on results devoted to the non-equilibrium dynamics of a copper foil brought from solid to warm dense matter regime, by the use of a femtosecond laser pulse. Particular emphasis will be given to the recent study of the ultrafast electronic transport, which was revealed by the femtosecond time resolution.
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