## 1 Introduction  
In some of the first studies of the effects of focussing the output of the X-ray Free Electron Laser (XFEL) pulse of the Linear Coherent Light Source (LCLS) at irradiances of order \(10^{17}\) Wcm\({}^{-2}\) onto foil targets, it was demonstrated that hot (up to 200 eV) plasmas could be created at exactly solid density [1, 2]. The materials studied to date have been low-\(Z\) elements, such as Mg, Al, and Si, with the incident photon energy of the XFEL being around and above the associated K-shell ionisation energies--i.e., in the 1-2 keV range. Diagnosis of the plasma conditions and associated physics was made by observing the K-shell emission of the various charge states produced, with L-shell electronsfilling the single or double core holes in the ions created by the XFEL, thus leading, in many cases, to emission all the way up to the hydrogenic species (i.e., Ly-\(\alpha\)). As the final temperatures produced are insufficient to thermally excite the K-shell of such ions, the observed emission spectrum is gated by the pulse length of the LCLS beam itself (typically sub-100 fs), and on such a timescale, the micron scale solid density plasma is effectively confined by its own inertia. Detailed studies of the X-ray spectra have led to an improved understanding of ionization potential depression (IPD) [3; 4; 5], as well as affording measurements of the femtosecond collisional ionization rates by means of the Auger-clock method [6; 7]. Given the relatively long penetration depth of the X-rays compared with optical light, a study of the emission from slabs of plasma of varying thickness (from a few tens to a few hundred nm) has allowed direct measurements of K-shell opacity [8]. In addition to the above experiments, saturable absorption of the incident X-ray pulse has also been demonstrated by tuning of the photon energy of the incident beam, such that when it creates and heats the solid-density sample, the K edges of the ions present in the hot collisional plasma--which have energies that increase as a function of ionization have energies exceeding the photon energy of the X-rays [9]. Saturable absorption is a potentially useful phenomenon, in that it increases the effective absorption length of the X-rays, leading to more uniform deposition of the incident X-ray energy, with a concomitant reduction in temperature and electron density gradients in the direction of the XFEL beam. Such an improvement in the uniformity of the plasma conditions is of importance in experiments designed to specifically measure plasma parameters as a function of temperature and electron density. The X-ray spectra collected in the experiments mentioned above have been simulated by use of the atomic-kinetics code SCFLY [10]. SCFLY is a thoroughly revised version of the widely available collisional-radiative FLYCHK suite [11; 12], and is specifically tailored for X-ray laser problems, using super-configurations to describe the atomic physics of the system [13]. In comparison with FLYCHK, rather than using a simple screened hydrogenic model, SCFLY uses calculated atomic quantities that are given as an input by the user generated, for example, by the DHS code [14]. However, despite its usefulness and evident successes, it should be borne in mind that SCLFY is a 0-D code, and as such, is not well-suited for modelling situations where the incident X-rays are rapidly absorbed, resulting in significant gradients along the direction of incidence of the FEL beam. Although such effects can, to a certain extent, be accounted for by use of multiple simulations of successive thin laminae of plasma-with the calculated exit spectrum of the FEL from one lamina being used as the incident beam for the next [9], such an approach is far from ideal. We return to this point below, when we outline the use of the multi-dimensional Cretin code for the work presented in this paper [15].