# X-ray Spectroscopies of High Energy Density Matter Created with X-ray Free Electron Lasers
## 4 Isochoric Heating of Solid with X-ray  
Since the development of high-energy short-pulse lasers using the chirped pulse amplification (CPA) technique [37; 38], there have been many studies regarding the isochoric heating of solid density targets using femtosecond optical laser pulses [39; 40; 41; 42]. However, these types of experiments have many difficulties that hamper the well-defined states of sample conditions. The optical laser deposits the energy in the skin depth (typically a few tens of nanometers) of material, and the heated sample with nanometer thickness releases very rapidly, often on the timescale of the laser pulse (~100 fs). The interpretation of these experiments is further hindered because the time scale of the hydrodynamic expansion of the heated material is comparable with that of the electron-ion equilibration [43; 44; 45]. Therefore, it is highly desirable to explore the heating mechanisms of thicker layers of material using short bursts of energetic beams. If intense short pulses of X-ray at appropriate wavelengths are produced, a well-defined material with thickness in terms of micrometer can be heated to HED conditions in a controlled manner [10; 46; 47]. With the advent of XFELs, this concept has become feasible and provides attractive experimental platforms to study material properties and light-matter interactions in HED conditions. The first experiment of its kind was conducted at the LCLS to heat aluminum with a focused XFEL pulse [16]. An aluminum foil with 1-mm thickness was irradiated with 80 fs pulses at photon energies in the range of 1470-1830 eV (below and above the Al K-edge). The peak intensity was \(1.1\times 10^{17}\) W/cm\({}^{2}\). Figure 4 shows the spectrally resolved K\(\alpha\) emission from various charge states as a function of the XFEL excitation photon energy. When the XFEL photon energy is above the K-edge (1560 eV), the initially dominant process is K-shell photoionization. Once created, a K-shell vacancy decays either radiatively or non-radiatively. In the radiative process, a core-hole is mainly filled by an L-electron (2p-1s transition) and a K\(\alpha\) photon is emitted. Though this fluorescent rate is small (4%) in Al, owing to the large number of incident photons in an FEL pulse, a single-shot XES measurement is feasible. K\(\alpha\) emission lines from charge states 4+ to 11+ are observed, indicating the formation of highly-ionized plasmas. The dominant (96%) recombination process of a core-hole is non-radiative KLL Auger decay. A K-hole is filled with an L-electron while another L-electron is emitted, and the level of ionization is increased. Energetic Auger electrons have large collisional rates and quickly thermalize with free electrons. The collision of free electrons at a high temperature dominates the ionisation dynamics and determines the charge state distribution in the system [49]. The processes happen in a duration of pulse to ensure that the electronic system is effectively heated by an XFEL. However, the electron-ion relaxation and hydrodynamic expansion of the sample do not take place yet, and an isochoric condition  
Figure 4: Spectrally resolved Al K\(\alpha\) emission (1460–1680 eV) as a function of XFEL excitation photon energy (1470–1825 eV). K-shell emission lines from Al charge states from 4+ to 11+ are marked. Emissions in the upper-left side of the graph are driven by the photoionization of a K electron to continuum by XFEL pulses. The onsets of emission lines correspondto the K-edge of charge states [16]. Bound–bound transitions can be observed as islands in the emission spectrum. Here, these correspond to the resonantly-driven 1s–2p transitions [48]. Photoionization corresponds to driving the 1s electrons into some state in the continuum. Such transitions yield broadly flat emission intensities over an extended range of FEL wavelengths, observed experimentally at higher FEL photon energies. The data in the figure are taken from the [16; 48] and replotted. can be achieved.