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We develop a set of analytical approximations for the estimation of the combined effect of various photoionization processes involved in the resonant four-wave mixing generation of ns pulsed Lyman-α (L-α) radiation by using 212.556 nm and 820-845 nm laser radiation pulses in Kr-Ar mixture: (i) multi-photon ionization, (ii) step-wise (2+1)-photon ionization via the resonant 2-photon excitation of Kr followed by 1-photon ionization and (iii) laser-induced avalanche ionization produced by generated free electrons. Developed expressions validated by order of magnitude estimations and available experimental data allow us to identify the area for the operation under high input laser intensities avoiding the onset of full-scale discharge, loss of efficiency and inhibition of generated L-α radiation. Calculations made reveal an opportunity for scaling up the output energy of the experimentally generated pulsed L-α radiation without significant enhancement of photoionization

Photoionization pathways and thresholds in generation of Lyman-α radiation by resonant four-wave mixing in Kr-Ar mixture