Production of O$_{2}$(a$^{1}\Delta _{g})$ molecules in flowing Ar-O$_{2}$ surface-wave microwave discharges

The possibility of development of an electric discharge oxygen-iodine laser stimulates nowadays many studies on the production of O$_{2}$(a) in discharges. The laser would operate on the electronic transition of the iodine atom at 1315~nm, the population of the upper laser state occurring in the reaction of O$_{2}$(a) with I. In order to achieve population inversion between the iodine upper and lower states and thus positive gain, the yield of O$_{2}$(a), [O$_{2}$(a)]/[O$_{2}$(X)], should be at least equal to the threshold yield, which at 400 K is 24{\%}. In this work we develop a discharge model to investigate the O$_{2}$(a) yield in an Ar-O$_{2}$ flowing surface-wave microwave discharge created in a 1~cm diameter tube and follow its evolution in the afterglow downstream the discharge. Our calculations show that the O$_{2}$(a) threshold yield necessary for positive gain can be achieved at 10~mbar, the yield increasing with pressure and reaching 50{\%} at 50~mbar. Furthermore, the yield increases with Ar addition into O$_{2}$, as a result of the enhancement of O$_{2}$ dissociation with the Ar content. We also show that the density of O atoms in the afterglow, which can quench the upper laser state, can be tuned to the desired levels.