A Model for Barium Oxide Depletion From Hollow Cathode Inserts

In this paper, a chemical model to predict barium oxide depletion from hollow cathode insert will be developed. This model is based on the knowledge of the ternary diagram that describes the BaO-CaO-Al₂O₃ system and takes also into account the diffusive motion of barium oxide inside the insert. A comparison between numerical and experimental data is made to determine the diffusion coefficient inside the insert. The diffusion coefficient found presents an Arrhenius trend with activation energy similar to the one of barium oxide evaporation. A 2-D model is used to demonstrate how the temperature profile along the insert is a key parameter to calculate barium depletion. This is the first model the authors are aware of that includes both the complex chemistry of the BaO-CaO-Al₂O₃ system and the diffusion motion of BaO from the insert core to the surface.