# X-ray Spectroscopies of High Energy Density Matter Created with X-ray Free Electron Lasers
## 6 Conclusions  
Core-level transitions driven by the tightly focused X-ray and EUV FELs can compete with and possibly modulate intrinsic atomic transitions in plasmas, such as Auger processes, fluorescence, and collisions, thereby driving the nonlinear responses of matter. SA i.e., increased transmission at higher intensity, has been observed in a broad range of energies and materials such as EUV, soft X-ray in aluminum [30; 33], and hard X-ray in iron [17]. Irrespective of the photon energies and elements, photoionization by FELs at the above absorption edges are fast enough to deplete the ground states. An opposite trend of response (RSA) for soft X-ray was also reported in aluminum [35]. At the resonant core-level transition below the absorption edge, decreased X-ray transmission was observed in aluminum. These nonlinear responses in short-wavelength regime are of great importance in photonic applications such as improving the wave front of FEL beam [17] and the development of atomic X-ray lasers [36]. The isochoric heating of a solid target with an intense femtosecond FEL pulse is proved to be an experimental platform to create a large volume of high-energy-density matter with well-defined energy  
Figure 5: Comparison of IPD in solid-density aluminum plasmas. The classical models of SP [52] and EK [55] (green markers), and the modern calculations by [PERSON] et al. [58], [PERSON] et al. [59], [PERSON] [60], and [PERSON] et al. [61] (blue markers) are compared with the experimental results by [PERSON] et al. [53] (red markers). A reasonable agreement is found only for the ground state (Al 3+). Diverging results for higher charge states illustrate the difficulties in theoretical work even with modern computational tools. The data in the figure are taken from the [53; 58; 59; 60; 61] and replotted. densities in a wide range of parameters, which include hot-dense (e.g., aluminum at a temperature of 100 eV [16]) and warm-dense conditions (e.g., carbon at 6-10 eV [13] and silver at 10-15 eV [50] at their initial solid densities). In comparison to nanometer-thick targets heated with an optical laser for reasonable uniformity, the use of X-ray FEL allows to heat micron-thick targets with improved uniformity. It provides great advantage in the investigation of a bulk of HED matter in longer confinement periods. The measurement of X-ray emission and absorption spectra are complementary to probe both the occupied and unoccupied electronic states, which affect basic plasma parameters such as ionization potential and temperature, as well as the transport properties such as optical and thermal conductivities in HED conditions. The measurement of K-shell emission spectra for the XFEL-heated matter has yielded the first experimental measurement of IPD in aluminum with 100-200 eV temperature and solid density. The precise control of XFEL photon energy allows to determine the K-edges and the continuum lowering of various Al charge states in such plasma conditions within a few eV. The FEL experiments provide accurate benchmark data for re-evaluating existing IPD models and guiding the further theoretical and computational advances on this fundamental but challenging subject of HED matter. With further development of FEL technology, X-ray pulses with attosecond duration, narrow bandwidth, and temporal coherence are also available and open new opportunities to study material properties and light-matter interactions in extreme conditions. For example, nonlinear X-ray spectroscopic technique, such as resonant inelastic X-ray scattering (RIXS) using attosecond coherent XFEL pulses shed light on the direct observation of relocalization of electronic wave packets excited from core-levels in the HED plasma environment. New sets of experimental data in femtosecond and nanometer regimes with advanced computation and theories will afford to not only address long standing questions, but also find new outstanding ones in plasma physics, fusion science, as well as X-ray optics.