Spatial distributions of the intensities and inversion factor of the F IX ion lines of the Lyman series are studied as functions of the irradiation conditions. Laser plasma was produced by the first-harmonic radiation from a Nd laser (10-35 J, 0.6 ns) focused on a flat solid target. It is shown that, for moderate intensities (≈10¹⁴ W/cm²), the use of phase plates, which smooth spatial beam inhomogeneities on the target, results in an appreciable increase in size of the emission region of recombining F IX ions. The experimental data are compared with calculations by the "Ion" computer code. Experiments on forming an extended active medium for lasing at the 4-3 transition of the hydrogen-like lithium ion are numerically simulated. This transition, having a wavelength of 208 nm in the UV spectral region, affords the inversion pickup using a resonator with available highly reflecting Al+MgF₂ mirrors.