Analysis of the temperature and stress distributions in ceramic window materials subjected to microwave heating

The temperature and stress and distributions generated in ceramic materials currently employed in microwave gyrotron tube windows were determined for a variety of operating conditions. Both edge- and face-cooled windows of either polycrystalline BeO or polycrystalline Al/sub 2/O/sub 3/ were considered. The actual analysis involved three steps. First, a computer program was used to determine the electric field distribution within the window at a given power level and frequency (TE/sub 02/ wave propagation assumed). This program was capable of describing both the radial and axial dependence of the electric field. The effects of multiple internal reflections at the various dielectric interfaces were also accounted for. Secondly, the field distribution was used to derive an expression for the heat generated per unit volume per unit time within the window due to dieletric losses. A generalized heat conduction computer code was then used to compute the temperature distribution based on the heat generation function. Third, the stresses were determined from the temperature profiles using analytical expression or a finite-element computer program. Steady-state temperature and stress profiles were computed for the face-cooled and edge-cooled windows.