Self-consistent analytical model of the radial temperature profile of a high-powered He-SrBr_2 laser

摘要

There is significant practical interest in the determining of the thermal parameters of metal vapor and metal vapor halide lasers. This study develops a self-consistent analytical model determining the radial temperature profile of a high-powered strontium bromide (SrBr_2) vapor laser, emitting in the infrared spectrum. The model is built under the assumption of arbitrary distribution of power density for the internal heat source without any given specific experiment measurements. It makes it possible to evaluate the nature of the main physical processes of the transfer of heat from the center of the tube to its interaction with the ambient environment. An exact solution of a heat conduction equation with first- and second-order boundary conditions is applied for the active laser medium. New boundary conditions are proposed, including third and fourth order ones, taking into account the various heat transfer processes through the layers of the gas discharge tube. Structural materials, the thermal conductivity of the helium layer between the ceramic and quartz tubes, the transmittance of heat in the outer quartz tube and suitable boundary conditions for the thermal insulation and the ambient environment are taken into consideration. The model is applied to calculate the temperature distribution within the laser tube of an existing high-powered SrBr_2 laser in the case of natural convection. Very good fit is achieved with the experiment. The model is applicable for preliminary evaluation of the temperature profile of both existing and new metal vapor and other similar laser devices.