Modeling of the radial heat flow and cooling processes in a deep ultraviolet Cu\(^+\)Ne-CuBr laser (Q1036396)

Summary: An improved theoretical model of the gas temperature profile in the cross-section of an ultraviolet copper ion excited copper bromide laser is developed. The model is based on the solution of the one-dimensional heat conduction equation subject to special nonlinear boundary conditions, describing the heat interaction between the laser tube and its surroundings. It takes into account the nonuniform distribution of the volume power density along with the radius of the laser tube. The problem is reduced to the boundary value problem of the first kind. An explicit solution of this model is obtained. The model is applied for the evaluation of the gas temperature profiles of the laser under the conditions of free and forced air-cooling. Comparisons with other simple models assuming a constant volume power density are made. In particular, a simple expression for calculating the average gas temperature is found.