Numerical simulation of Ni-like Xe plasma dynamics and laser gain in a low inductivity capillary discharge

X-ray lasers based on transitions in highly charged \textit{Ni}-like ions generating in the "water window" wavelength range can be pumped by compact laboratory discharge sources. This makes them promising candidates for use as compact coherent X-ray sources in laboratory applications including biological imaging and investigations of carbon containing materials. In this paper, the results of numerical simulations of the plasma dynamics and kinetics in an X-ray laser based on transitions in \textit{Ni}-like xenon ions are reported. The laser active medium is created by an extended low-inductive high current Z-discharge capable of producing two successive electrical pulses. The non-equilibrium multi-charged ion plasma dynamics is studied numerically using a non-stationary 1D two-temperature radiation-MHD model, which describes plasma hydrodynamics, non-stationary ionization, transfer of the continuum and line radiation as well as processes in the pumping electrical circuit. The ionic energy level populations are calculated in the quasi-stationary approximation. The simulation results allowed determination of the electrical and energy pumping parameters necessary to obtain a weak signal gain for the working transitions of the order of $g^+\sim1$ $\mbox{cm}^{-1}$. It was demonstrated that plasma with the electronic temperature of more than 400 eV and the density of more than $10^{19}$ $\mbox{cm}^{-3}$ can be created by a low inductive two step discharge with peak current exceeding 200 kA.