Numerical study of overpopulation density for laser oscillation in recombining hydrogen plasmas

The dependence of overpopulation density (OD) on ground-level population density (n1) and electron temperature (Te) in a recombining hydrogen plasma is evaluated for line pairs with the principal quantum numbers (2,3), (3,4), and (4,5). The approach is based on the simultaneouss solution of the quasi-steady-state rate equation (including interatomic-collision terms) and the optical-escape-factor equation for the Lyman series with Doppler profile. Calculations are performed for optically thin and thick plasmas at a fixed atomic temperature of 0.15 eV, over a Te range from 0.1 to 1 eV and an electron-density (ne) range from 10 to the 11th to 10 to the 17th per cu cm. It is shown that peak OD occurs at an ne slightly below that at which population inversion is destroyed, that peak OD is inversely sensitive to Te, and that peak OD(2,3) is the highest of the three peak OD. Laser oscillation is determined to be possible for (2,3) at Te higher than for (3,4) and (4,5), if self-absorption is negligible. The OD remains constant as n1 increases, up to the point at which significant self-absorption occurs. No laser oscillation is expected at level (4,5), nor in optically thick plasma at any level, for the realistic cavity parameters and temperatures used in the calculations.