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A simple but appropriate analytical study has been made to investigate the dynamics of a capillary discharge-produced plasma, thus obtaining Z-scaling formulas for the experimental parameters for a collisional recombination pumped x-ray laser using H-like ions. The analysis has been found to be in an excellent agreement with the results from a series of magnetohydrodynamic (MHD) simulations both in the dynamics and in the prediction of the appearance of gain of the Hα line in the H-like ion for the elements with the atomic number z=4–13. The formulas are valuable because (1) they identify key physical processes and (2) serve as a guideline for the design of an experimental setup as well as the full MHD simulation and (3) provide an overview on the application of the capillary discharge to the recombination laser. The comparison of the experimental parameters for collisional recombination x-ray lasers with those for collisional excitation x-ray laser [Shlyaptsev et al. SPIE 2012, 99(1994)] has been made also.

Analytical study of the dynamics of capillary discharge plasmas for recombination x-ray lasers using H-like ions