An improved model of gas temperature in a copper bromide vapour laser

A new analytic model is proposed for calculating the temperature profile of gas in the transverse section of the discharge tube of copper bromide lasers emitting at 510.6 and 578.2 nm. The model is described by the quasi-stationary heat conduction equation with the boundary conditions of the third and fourth kinds taking into account the alternating volume electric power along the tube radius. The exact solution of the problem is obtained. The model was used to calculate the temperature profiles of the discharge in the case of natural and forced convection cooling. The obtained results are compared with previously known temperature distributions. The improved model proposed in the paper can be used to analyse existing lasers and develop new lasers.