Residual energy and its effect on gain in a Lyman-α laser

To examine prospects for gain in a Lyman-α recombination laser driven by a high-intensity, short-pulse laser, we calculate the residual energy in both hydrogen and helium during recombination after the ionizing pulse. The expected gain as a function of residual energy and density is then separately evaluated. The residual energy calculation includes above-threshold ionization (ATI) in the presence of a background plasma, as well as inverse-bremsstrahlung heating. At electron densities over ${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$ but below critical density, the plasma reduces the ATI energy by approximately a factor of 2, but without a previously reported dependence on the pulse width. Inverse-bremsstrahlung heating can be significant, but is not dominant for the parameters considered. Detailed recombination-laser gain calculations were performed for the Ly-α transitions of both H and He, using Stark profiles to represent the laser line cross section. To obtain gain of near 2 ${\mathrm{cm}}^{\mathrm{-}1}$ lasting at least a few ps, the H plasma temperature must be less than 3.5 eV and electron density between 4×${10}^{17}$ and 4×${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$; for He, the temperature must be less than 15 eV and the electron density between 2×${10}^{18}$ and 2×${10}^{19}$ ${\mathrm{cm}}^{\mathrm{-}3}$. Our calculations indicate that these conditions can be satisfied for H, if the driving laser intensity is above 4×${10}^{14}$ W ${\mathrm{cm}}^{\mathrm{-}2}$, and for He, if the laser intensity is above 1.7×${10}^{16}$ W ${\mathrm{cm}}^{\mathrm{-}2}$ and the wavelength is below 0.6 μm.