A scheme employing neonlike krypton ions is under intensive theoretical and experimental investigation to determine the feasibility of developing a pulsed-power driven laboratory x-ray laser. The scheme depends on discharging 100's of kilojoules of electrical energy through co-axial cylindrical krypton gas puffs generating a dense, hot, uniform, homogeneous, and highly ionized krypton plasma. The dynamics of energy absorption are such that self-generated magnetic fields compress and accelerate radially inward theiouter plasma with speeds approaching 5 x 10 cm/sec. When the outer plasma impinges and stagnates on the inner plasma, shock waves are sent through the system as the plasma reverberates and bounces outward. Near the interface between the two interacting plasmas, and along the axis, conditions appear to be conducive to the establishment of a population inversion with the subsequent emission of coherent soft x-rays with measurable gain. The theory, analysis, and numerical simulations are based on a fully coupled self-consistent one-dimensional non-LTE radiation hydrodynamics model including the effects of opacity and radiation transport. The multi-level ionization dynamics is evaluated in the collisional radiative equilibrium (CRE) approximation for the manifold of both ground and excited states distributed throughout the various stages of ionization. In addition, particular emphasis is placed on the atomic structure of the neonlike ionization stage which in our model consists of 48 excited levels in j-j coupling. The evolution of the level populations as functions of the various atomic processes provides information on the conditions necessary to establish population inversions and the emission of coherent radiation in the lasing transitions. The spectral line profiles are represented by Voigt functions. A complete history of the implosion and radiation dynamics will be provided for the cases under investigation.