Amplification of light as a result of transitions in helium-like ions in a freely expanding plasma

It is shown that the 3¹D–2¹P transition in helium-like ions is of interest for the amplification of light of wavelengths λ < 50 nm. An analytic formula is derived for the gain due to this transition. An analysis is made of the time dependence of the gain in the model of consecutive recombination during vacuum expansion of an initially completely ionized plasma filament. An allowance is made for the recombination heating of electrons, reabsorption due to the 2¹P–1¹S₀ radiative transition, and changes in the ion composition of the plasma during its expansion. It is shown that the maximum value of the gain for the C v ion [λ (3¹D–2¹P) = 26.7 nm] is ~1 cm^–1.