Influence of the number of atomic levels on the modelling of collisional X-ray lasers

The number of atomic excited levels considered in codes modelling X-ray lasers is generally very limited. A few dozens or even two or three are considered while thousands times more do exist. We compute populations, gain and spectra with tens of thousands of levels out of equilibrium to model a Zinc Ne-like X-ray laser. The maximum gain, its thermodynamic conditions as well as the transverse spectrum compare well with the experiment. The gain is marginally reduced for stationary plasmas when the number of levels increases. But the radiative losses are strongly enhanced for thick plasmas. For transient schemes, some neighbouring levels are strongly coupled with the lasing levels and will modify the solution of the Maxwell Bloch equations in case of seeding with high harmonics.