# X-ray Spectroscopies of High Energy Density Matter Created with X-ray Free Electron Lasers
## 1 Introduction  
The recent progress in development of short-wavelength free-electron lasers (FELs) has opened up a variety of opportunities in diverse fields such as atomic physics, plasma physics, ultrafast chemistry, and biomolecular imaging [1; 2; 3; 4]. The parameter that distinguishes FELs the most from other light sources is the peak brightness, which is about a billion times greater than that of synchrotrons. Handling light intensity in excess of \(10^{16}\) W/cm\({}^{2}\), which had been available only in infrared and optical regimes, has become feasible in EUV and X-ray regimes, and a nonlinear response of matter involving core electrons in femtosecond scales can be expected. Materials absorbing large numbers of X-ray photons are also anticipated to occur in extreme temperature and pressure conditions. Under such extreme environments, normal matter behaves abnormally and often regulates the physical processes in stars and large planets [5], inertial confinement fusion [6], as well as the applied processes of laser machining and ablation [7]. High energy density (HED) science is defined as the study of matter at extreme radiation, pressure, and temperature corresponding to energy densities in excess of about \(10^{11}\) J/m\({}^{3}\)[8; 9]. As illustrated in Figure 1, HED conditions are widespread in the universe and laboratories. Within the regime of HED states, warm dense matter (WDM) representing the state where the thermal energy is comparable to the Fermi energy, the ions are strongly coupled. \[\Gamma=\frac{Z^{2}e^{2}}{r_{0}k_{B}T}\ \geq 1 \tag{1}\]  
Here, \(\Gamma\) is the plasma coupling parameter. When \(\Gamma\) is an order of unity or greater, the plasma is considered as strongly coupled. \(Z\) is the ion charge, and \(r_{0}\) is the inter-particle distance. In general, WDM is partially ionized, and free electrons are also partially degenerated. Hot dense matter (HDM) represents the states with higher temperature with similar density. Owing to the sufficiently high temperatures, in HDM, a variety of charge states are assembled and free electrons are no longer degenerated [10; 11]. As intermediate states of matter between the well-defined disciplines of condensed matter and plasmas, the investigation of WDM and HDM provides key understanding of non-equilibrium phase transitions and energy relaxation processes in extreme conditions. However, the complicated interplay of the physical processes in HED matter is difficult to describe. Quantitative research on HED materials requires the ability to generate and diagnose well-defined high-temperature, high-density, and high-pressure conditions. Generally, they can be obtained by focusing a high-power laser or particle beam onto dense targets. However, such extreme matter is often non-uniform and quickly transforms to low-density plasma in a timescale of femtosecond to nanoseconds. The material properties are often measured for multi-stages instead of a single state. Optical diagnostics using femtosecond lasers have been the fastest means but could provide limited information about the surface of dense matter and outer electrons. The lack of experimental techniques to quantify single-state parameters at various temperature-density conditions has posed obstacles in the measurement of the fundamental properties and testing the theoretical description of simple materials such as hydrogen, carbon, and gold in the HED states. In this context, the development of XFEL was an important step for advancing HED science. XFEL can heat solid samples to a temperature of millions of degrees to produce WDM and HDM, unlike any previous device. The typical long penetration length of X-rays enables it to heat a larger volume (thickness) of the sample than the optical lasers. Owing to the femtosecond pulse duration, this heating  
Figure 1: Phase diagram of warm and hot dense matter. WDM and HDM lie at the confluence of plasma and condensed matter.