Two-dimensional calculation of the temperature field of a continuous optical discharge in air

A calculation is made of the temperature field of a continuous optical discharge in air, sustained by CO₂ laser radiation. The refraction of a laser beam in the discharge plasma and the radiative heat transfer are taken into account. Good agreement with experiment is obtained. It is established that the refraction leads to a strong broadening of the caustic and to a shift of the beam constriction toward the laser so that the discharge becomes localized in the region of the highest radiation intensity. This explains why a high-power optical discharge is never localized at the geometric focus, even when there is sufficient radiation power in that region. The threshold and upper limits for a discharge to occur are derived as a function of the power and the focal length of the lens.