Modelling of barium transport in dispenser cathodes

Abstract

A theoretical modelling of the barium transport in dispenser cathodes has been developed from the general considerations of diffusion as well as the fundamental nature of the barium surface migration. Realistic second-order kinetics for the barium desorption has been employed. The diffusion of barium from the generating to the emitting sites of the cathode has been considered to be comprised of two independent processes, viz., (i) the bulk diffusion to the pore ends on the surface, and (ii) the subsequent surface diffusion/migration. The solution of the first process has been obtained using an approximate analytical method (the integral method), whereas the second process leads to an analytical solution. Time-dependent profiles of barium concentration versus distance from the source (the edge of the pore) were obtained at the cathode operating temperature (≈1300 K) of type-B cathode. Consequent to the barium evolution on the surface, the increase in time-dependent pore depth has been considered in determining the barium surface source location. The variable source strength (content) of the barium has been incorporated into the problem by means of the boundary condition. The results are presented, and a method of estimation of the ideal life of the cathode is presented. © 1994.