Abstract
Soft x-ray lasers operating in the super- $100\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ regime and using grazing incidence pumping methods are now established as efficient sources of radiation in this waveband. The concepts underlying this approach are to separate the ionization and excitation phases of the laser, and to match the pumping density of the latter to the optimal for gain generation. It is therefore of considerable interest to examine whether these ideas can be successfully applied to sub-$100\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ lasers. Three problems arise: first the adverse scaling of ionization with temperature for high atomic number ions, second the strong thermal conduction at these temperatures leads to a large hot zone upstream of the absorption, and third the optimum pumping density is greater than the critical density of $1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ wavelength, solid state pump lasers. Using analytic models and simulation we identify a strategy to overcome these problems using a pre-pulse of a mixed harmonic and fundamental radiation of Nd-glass laser radiation followed by the main pumping pulse of the fundamental normally incident. Due to the large upstream thermal zone and the high ionization temperature, we find that the energy required in the pre-pulse is much ($\ensuremath{\sim}3$ times) larger than that in the main, and that the energy needed consequently scales rapidly with the atomic number and therefore decreasing x-ray wavelength. Systems generating output energies of a few tens of $\ensuremath{\mu}\mathrm{J}$ are examined at wavelengths between 50 and $70\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$.
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