X-ray lasers in cluster flows and in nanostructured targets

The paper presents a brief review of recent works concerning the modeling of X-ray lasers in cluster flows and in nanostructured targets. Calculations of the atomic characteristics are based on relativistic perturbation theory with a model potential of zero approximation. Two new results are discussed: (1) it is shown that a subpicosecond X-ray laser with $\lambda$ = 41.8 nm formed in a xenon cluster flow can serve as an alternative to a free-electron laser and (2) in heavy Ni-like ions ($Z\ge$ 60), the ionization of ions and recombination of electrons are balanced at electronic temperatures $\ge$ 1500 eV; thus, the state of a Ni-like ion is quasi-steady-state. The inversions of many transition levels of an X-ray laser are also quasi-steady-state. The possibility of experimental observation of X-ray lasers based on Gd$^{36+}$: $3p^{5}4d^{10}4p$ [$J$ = 0]–$3p^{6}3d^{9}4p$ [$J$ = 0] intrashell transitions in Gd$^{36+}$ with wavelengths in the water window region is discussed.