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Parameter limits of thermal instabilities in high-frequency CO2 laser discharges

A simple formula giving parameter limits for stable operation with respect to thermal instabilities of high-frequency excitation of CO2 laser discharges is derived from a discharge model including the continuity equation for the electron density and the neutral gas density, the energy equation for the neutral gas and Ampere's law for the electric field. For stable discharge operation, a limiting value of the product of the neutral gas density and the discharge width must not be exceeded. This limit is also determined by the excitation frequency. The discharge is stabilized mainly by the frequency-dependent reduction in the electric field accompanying a corresponding increase in the electrical conductivity and by those processes that lead to a smoothing of particle densities and the temperature. These processes are diffusion and heat conduction and especially turbulence-induced transport processes. A quantitative description of the turbulent transport processes is beyond the scope of the present paper. The effect of the turbulent gas flow is roughly approximated by an effective heat conductivity.