## 3 Results  
### Simulation Results  
Figure 3 shows the results for the temperature and mean charge predicted across the target for the four XFEL photon energies of consideration. The vertical axis of the figures corresponds to the depth of the target, with the XFEL beam, irradiating at 0 nm (top of the figures). The pulse shape is plotted for comparison. It can be seen that, except for the case at 1400 eV, there is a significant temperature gradient across the target, with the surface that is irradiated by the laser (top) being about two times hotter than the back of the target. Surprisingly, in the 1400 eV case, this hot region at the front of the target is not present, and the target is uniformly heated to \(\sim\)100 \(\pm\) 20 eV. Similar gradients appear in the mean charge (\(\bar{Z}\)) of the targets. For a photon energy of 1400 eV, after the XFEL beam has left the target (around t = 250 fs), the ionisation is roughly constant across the depth of the plasma, and the mean charge equals 12-13. However, for the other photon energies under consideration, the hot region at the front of the target gets ionised further (\(\bar{Z}\sim 16\)), whereas the back of the target remains at lower ionisation levels. This is most noticeable for a XFEL photon energy of 1300 eV, where the front of the target is S-like (\(\bar{Z}\sim 16\)), while the back of the target is Sc-like (\(\bar{Z}\sim 11\)). The reason for this more uniform behaviour when the photon energy of the XFEL beam is 1400 eV is related to both the position of bound-bound (L-M) transitions and the L-edges of the various ion stages as the plasma heats up. This can be understood by studying Figure 4, where we show results of Cretin simulations of the opacity at the front (left) and back (right) of the targets for XFEL energies of 1300 (Figure 4a) and 1400 eV (Figure 4b) as a function of time and photon energy, for the peak intensity of the laser. In this case, the front refers to the laser-irradiated surface of the target, and the laser pulse is indicated in white in all cases. Additionally, the photon energy of the XFEL is indicated as a dashed orange line. Each of the inset plots below the figures shows a more detailed lineout of the time evolution of the plasma opacity at the photon energy of the XFEL. It can be seen that, initially, the bound-bound absorption lines lie around \(\sim\)1190-1220 eV, whereas the L (bound-free) absorption edge of the cold material sits at \(\sim\)1250 eV. That is to say in all cases the photon energy of the XFEL lies above the cold L-edge, and thus is initially efficiently absorbed, and thus the target starts to heat and be ionised. As higher charge states are generated, both the L-M bound-bound transitions and the bound-free L-edges of these higher charge states lie at higher energies. In both the 1300 and 1400 eV cases, the heating is such that rapidly the L-edges of the ions produced lie above the incident photon energy, and the L-shell bound-free absorption decreases (which leaves photoionisation of the M shell as the main laser absorption mechanism). In the case of an incident photon energy of 1300 eV, just after the middle of the XFEL pulse, the heating is such that the L-M bound-bound transitions of the ions come into resonance, and the absorbed energy increases rapidly as a consequence, and the associated shorter absorption depth leads to the large temperature gradients shown in Figure 3. In contrast, for an incident photon energy of 1400 eV,we have a situation where the L-M transitions never come into resonance, and the L-edges of the ions in the heated system lie above the photon energy, leaving only M-shell photoionisation as the dominant absorption mechanism throughout the laser pulse. This bound-free M-shell absorption is about an order of magnitude less than that of the L-shell, and thus the 1400 eV photons are poorly absorbed, but the plasma as a consequence has a more uniform temperature gradient.