Thermal instability in high−power laser discharges

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Abstract
The thermal and acoustic instabilities that could possibly cause arcing in high−power pulsed and cw gas lasers have been investigated. A cubic dispersion relation is obtained from linearization of the coupled hydrodynamic and Ohmic equations in which the electrical conductivity is dependent on the neutral density. We find that when the thermal wave is unstable the acoustic waves are damped, and vice versa. The growth rate of the instability is proportional to the power density for low input powers while it goes as the cube root of the power density for high input powers.