Recombination and Photo-pumping Mechanisms for Producing Gain on Hydrogen-like Balmer Alpha Lines

Two of the most promising classes of schemes for X-ray laser action are the recombination approach, in which population inversions are produced by the decay cascade following electron recombination into high-lying quantum states of a recombining ion, and the photo-pumping approach, in which population inversions are produced by direct pumping of the upper quantum state by photo-excitation from the ground state. In this paper, the recombination and photo-pumping approaches for producing x-ray lasing on the hydrogen-like Balmer alpha line are compared and the effects of the hydrogen-like fine structure on the plasma and other conditions required to achieve Balmer alpha gain are examined. For electron densities Ne s; 10' Z 7 (where Z is the atomic number of the hydrogen-like ion), it is shown that Balmer alpha gain can be much more difficult to produce than is predicted by simple calculations assuming all sub-levels are populated statistically. It is shown, for example, that Balmer aipila gain produced by 1s-3p photo-pumping becomes impossible for electron densities We < loi0 Z 7 because the 2slI2 sub-level becomes metastable.