Plasma conditions required for attainment of maximum gain in resonantly photo-pumped aluminum XII and neon IX

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Abstract
We present a detailed analysis of the plasma conditions required to optimize gain in two proposed x-ray lasing schemes using resonant photo-pumping. In one proposed configuration, the Si XIII line 1s2-1s2p1P at 6.650 Å pumps Al XII 1s2−1s3p1P at 6.635 Å, inverting the Al XII n = 3 and n = 2 levels which are separated by 44 Å. A similar approach which utilizes the Na X 1s2-1s2p1P line at 11.00 Å would invert the n = 4, 3, and 2 levels of Ne IX. Conditions in the pumped neon and aluminum plasmas, and in the pumping silicon plasma, are calculated using a multistage, multilevel atomic model with multifrequency radiation transport. For modeling the pumping sodium line we have inferred the intensity from a spectrum of a neon filled, laser-imploded glass microballoon containing sodium impurities obtained at Rochester. The pump line intensities calculated for Si and inferred for Na are equivalent to blackbodies of 252 and 227 eV, respectively. It is found that peak gain for the 3-2 lines of about 100 cm−1 occurs at ion densities of 1020 cm−3 and 4×1020 cm−3 in the pumped neon and aluminum plasmas, respectively. Temperatures required to maximize gain in the pumped plasmas are found to be 50 and 100 eV, for neon and aluminum, respectively. Finally, since the silicon and aluminum lines are slightly off resonance, we have investigated the effect of streaming the plasmas toward each other at various velocities to offset some or all of the wavelength difference. It is found that a streaming velocity of 6.8×107 cm sec−1—fully offsetting the wavelength difference—will approximately triple the achieved gain compared to the zero velocity case. Lesser increases in gain occur with partial velocity offsets.